Iowa Council of Teachers of Mathematics Featured Articles

Connecting Algebra with Finance by Kellie Pryor

Wendy Weber — Sat, 28 Mar 2026 23:26:15 GMT

“Why didn’t they teach us this in math class?” How many times have we seen a social media post from a friend, family member, or even former students with this general sentiment? These posts can be frustrating to hear as a math teacher, and my first instinct is often, “We do teach it! You probably just didn’t pay attention!” However, the frequency of these posts eventually led me to wonder, can we do a better job making connections between the classroom math skills and real world scenarios? Of course I’ve taught the basic: write an equation for Annie buying $0.50 apples and $2 candy bars, but that’s not why former students are complaining. They want real financial math!. They want to know what is being deducted from their paychecks, how to pay their taxes, and what does 100/300 BI mean when they are researching auto insurance.

Thanks to a generous grant from ICTM, Bettendorf High School was able to purchase textbooks and offer a new math course this year focused on financial literacy- with a mathematical approach rather than economics or social studies. In this course, we practiced Algebra II standards as we explored price comparisons and finding good deals through frequency tables and normal curves. We practiced budgeting using a 50-30-20 model and classified daily purchases into essentials, lifestyle and savings categories. One student appreciated the early education, stating that our units on “budgeting and saving will help you a lot in the real world without having to learn these things after you messed up already.” Students learned some background on FICA taxes and how to calculate what should be withheld from their paychecks. Another student shared, “Financial math helped me so much with my job. I can better understand why money is taken out of my paycheck and exactly where it’s going. The budgeting activities were also a huge help and I was able to translate them to my own money.” Other units explored health insurance premiums, auto insurance coverage, and credit scores. We wrote algebraic expressions and performed calculations, but we also listened to guest speakers from the financial industry and learned a great deal of vocabulary.

One of the biggest successes that I took away from teaching this course was the huge increase in student buy-in. I made the ambitious claim during the first week that we would learn math that they would want to know and would use outside the classroom, and I think we were able to meet that goal. One student commented “Before taking this class I had no idea about how to build my credit at all, let alone buying a house. I have learned so much through taking this class and compared to other classes, the things I've learned have stuck with me.” As educators, our goal is to prepare our students to be successful outside of the classroom. I believe that Financial Algebra is a great step toward meeting that goal.

The Power of Student-Centered Curriculums in Mathematics

April Pforts — Sat, 04 Jan 2025 02:05:37 GMT

Creating meaningful and engaging learning experiences is a top priority in today's ever-evolving educational landscape. One of the most effective ways to achieve this goal is by implementing student-centered curricula. These curricula place the learner at the heart of the educational process, fostering engagement, critical thinking, and deeper understanding—especially in mathematics.

Student-centered approaches can transform classrooms, empower learners, and create environments where all students can thrive. Here's a closer look at what student-centered curriculums entail and their benefits to math education.

What Is a Student-Centered Curriculum?

A student-centered curriculum is designed to:

Prioritize student interests, experiences, and goals.
Focus on active learning through problem-solving, inquiry, and exploration.
Allow students to take ownership of their learning by making choices and engaging in self-directed tasks.
Use collaborative learning strategies to encourage teamwork and communication.
Adapt to diverse needs, leveraging differentiation to meet every student where they are.

Unlike traditional, teacher-centered curriculums, which are primarily lecture-based and content-driven, student-centered curriculums shift the focus to the learner's needs, abilities, and interests. This approach empowers students to participate in their education, actively developing autonomy and confidence.

The Benefits of Student-Centered Curriculums in Mathematics

1. Enhanced Engagement and Motivation

Student-centered curriculums foster intrinsic motivation by tapping into students' natural curiosity and involving them in relevant, real-world problems. In mathematics, this could mean exploring financial literacy, data analysis on community issues, or designing solutions for environmental challenges. When students see the relevance of math in their lives, their engagement soars.

2. Deeper Understanding of Mathematical Concepts

Active learning strategies, such as inquiry-based tasks or collaborative problem-solving, encourage students to dive deeply into concepts rather than passively memorizing procedures. This results in a stronger conceptual foundation and better retention of skills.

3. Development of Critical Thinking and Problem-Solving Skills

Student-centered approaches challenge learners to think critically, reason logically, and solve complex problems. Whether tackling open-ended questions or working through multi-step problems, students learn to approach challenges confidently and creatively.

4. Supports Differentiation and Equity

A student-centered curriculum recognizes that each learner is unique. By offering multiple entry points, flexible pathways, and opportunities for choice, teachers can meet the diverse needs of students. This approach is particularly impactful in addressing achievement gaps and promoting equity in math education.

5. Fosters Collaboration and Communication

Collaborative tasks and group projects help students develop interpersonal skills while deepening their understanding of mathematical concepts. Explaining reasoning, debating strategies, and working toward a shared solution build academic and social skills.

6. Encourages Ownership of Learning

When students are involved in setting goals, choosing tasks, and reflecting on their progress, they develop a sense of ownership. This leads to greater accountability, perseverance, and a growth mindset.

What Does a Student-Centered Math Classroom Look Like?

Real-World Applications

Tasks are designed around authentic problems that resonate with students' interests and experiences. For example, middle schoolers might calculate the costs of building a playground, and high school students might analyze statistical trends in sports.

Choice and Voice

Students can choose tasks, strategies, or formats to demonstrate their understanding. For instance, they might solve problems using visual models, equations, or written explanations.

Collaborative Learning

Group discussions, peer teaching, and cooperative problem-solving are integral to learning. A student-centered classroom is bustling with conversation and idea-sharing.

Teacher as a Facilitator

Instead of delivering content, the teacher acts as a guide, asking probing questions, providing feedback, and supporting students as they explore and construct knowledge.

Implementing Student-Centered Curriculums: Key Considerations

1. Start Small

Transitioning to a student-centered approach doesn't have to happen overnight. Begin with a single lesson or unit incorporating choice, collaboration, and real-world connections.

2. Leverage High-Quality Instructional Materials

Use resources that align with research-based practices and offer rich, active learning and inquiry tasks.

3. Provide Professional Development

Equip teachers with strategies to design and implement student-centered instruction effectively. Coaching and collaborative planning time can support this shift.

4. Embrace Formative Assessment

Frequent check-ins, student reflections, and informal assessments help teachers tailor instruction to meet the needs of their learners.

5. Foster a Growth Mindset Culture

Create a classroom environment where mistakes are viewed as opportunities for learning and persistence is celebrated.

The Impact of Student-Centered Curriculums

When implemented thoughtfully, student-centered curriculums can transform math classrooms into dynamic spaces of exploration and discovery. Students become better mathematicians and develop critical life skills such as communication, collaboration, and adaptability.

As educators, we can create learning environments where students feel empowered to ask questions, take risks, and explore the beauty and utility of mathematics. By embracing student-centered curriculums, we can ensure that all learners see themselves as capable mathematicians ready to tackle future challenges.

How can you take the first step toward student-centered instruction in you classroom or district? Let's start the conversation-share your ideas, successes, and questions below!

image 1 attribution: https://im.kendallhunt.com/MS/teachers/what_is_pbc.html

Steps to Adopting High-Quality Instructional Materials

April Pforts — Sun, 08 Dec 2024 22:24:11 GMT

Finding High-Quality Math Instructional Materials with EdReports

Choosing the right instructional materials is one of the most impactful decisions schools and districts can make to ensure students receive a high-quality education. But with so many options available, how can educators identify rigorous resources that are aligned to grade-level standards and effective for their students? That’s where EdReports comes in.

What is EdReports?

EdReports is a nonprofit organization that provides free, comprehensive reviews of instructional materials for K-12 education. Its mission is to ensure all students can access materials that meet high academic standards, foster engagement, and promote equity.

For mathematics, EdReports evaluates materials based on three key criteria:

Alignment to Standards: Are the materials aligned with college—and career-ready standards, such as the Common Core?
Rigor and Mathematical Practices: Do the materials strike a balance between procedural skills, conceptual understanding, and application?
Usability: Are the materials teacher-friendly and adaptable for diverse classroom needs?

By focusing on these areas, EdReports empowers educators to make informed decisions about instructional resources that truly support student learning.

The EdReports Process

EdReports uses a rigorous, transparent review process carried out by expert educators. Reviewers assess materials for alignment with grade-level standards and provide detailed feedback, including strengths and weaknesses. The results are then published on the EdReports website, making it easy for schools and districts to compare resources.

The reviews are clear and actionable, offering insights into how well materials:

Address grade-level content standards.
Promote coherence across lessons and grade levels.
Support diverse learners, including English learners and students with disabilities.

Steps to Adopting High-Quality Instructional Materials

EdReports also guides how schools and districts can effectively adopt new instructional materials. Their Adoption Steps framework ensures a thoughtful, inclusive, and data-driven process. Here’s an overview:

Step 1: Plan and Prepare

Assemble a diverse adoption team that includes teachers, administrators, and other stakeholders.
Define the district’s goals and priorities, such as alignment to standards, equity, or support for differentiation.

Step 2: Investigate the Options

Use EdReports reviews to identify materials that meet grade-level standards and instructional goals.
Narrow down options based on the needs of your students and educators.

Step 3: Gather Evidence

Pilot the materials in classrooms and gather feedback from teachers and students.
Evaluate how well the materials meet the criteria established during the planning phase.

Step 4: Make a Decision

Use a collaborative decision-making process to select the best-fit materials.
Ensure alignment with district priorities and include a plan for professional learning.

Step 5: Implement and Support

Provide robust training for teachers to help them use the materials effectively.
Continuously gather feedback to refine and improve implementation.

Why High-Quality Materials Matter

Research shows that using high-quality instructional materials can significantly impact student achievement. Materials aligned to grade-level standards help ensure that all students have access to rigorous content, setting them up for long-term success.

EdReports simplifies finding these materials, giving educators the tools to make data-driven decisions. By following the Adoption Steps framework, schools and districts can confidently select resources that meet the unique needs of their students and teachers.

Start Your Journey with EdReports Today

Whether you’re starting a new adoption cycle or looking to evaluate your current resources, EdReports is your trusted partner in identifying high-quality instructional materials. Explore their reviews and adoption tools at EdReports.org to ensure your students receive the education they deserve.

Empower your classrooms. Choose the best for your students.

Lauren Anders' ICTM Conference Highlights

Wendy Weber — Sat, 23 Nov 2024 16:52:58 GMT

This past month, I had the opportunity to attend the ICTM conference that left me energized, inspired, and ready to implement new strategies in my classroom. The sessions I attended were a perfect mix of theory, practical tools, and innovative approaches to teaching math, including discussions on standards-based grading, closing achievement gaps, and the use of manipulatives across all grade levels. Here are some key takeaways from the conference that I believe will shape my teaching moving forward.

Embracing Standards-Based Grading
One of the most compelling sessions I attended focused on standards-based grading (SBG). This approach, which evaluates students based on their mastery of specific learning standards rather than cumulative point accumulation, has always intrigued me. The session gave me a clearer understanding of how to implement SBG in a way that promotes mastery learning and provides more accurate feedback to students. My district will be moving away from our traditional grading system sometime in the next few years and we have started building our proficiency scales that we will use to grade. It was awesome to see and hear from teachers around Iowa what their experiences with standards based grading have been and how much better students understand where they are in their mathematical understanding of a concept and what they can do to increase their competency.

I particularly appreciated the emphasis on using formative assessments to guide instruction and how to adjust grading to reflect true understanding. Moving away from traditional grading, where an incomplete understanding can still result in a passing grade, helps to clarify learning goals and ensures that students are held accountable for mastering essential concepts. This idea of continuous, flexible assessment aligns more closely with my teaching philosophy, where growth is celebrated and every student’s individual learning path is honored.

Addressing Achievement Gaps
Another major focus of the conference was closing achievement gaps, a topic that resonated deeply with me. Dr. India White highlighted strategies to support underperforming students, such as targeted interventions, differentiated instruction, and creating a more inclusive classroom environment. I learned the importance of fostering strong teacher-student relationships and how these connections can help students feel empowered to overcome obstacles.

What stood out to me was the role of culturally responsive teaching in bridging achievement gaps. Integrating students' cultural backgrounds into the learning process not only helps them feel seen but also makes math feel more relevant and engaging. I am very thankful to have a curriculum that already implements so many 21st century topics and leaves room for me to be flexible and make changes where I see fit. I left the session with a renewed commitment to make my classroom a place where every student can thrive, regardless of their starting point.

Math-ish: A New Way to Conceptualize Real-World Problems
One of the most engaging sessions of the conference was the keynote presentation by Jo Boaler in which we explored the idea of “ish”. “Ish”-ing, in a sense, is using what you already know about a problem or situation and making an educated estimation of what a solution could, or could not, be. Having conversations with students, especially about those lengthy word problems before they tackle solving them algebraically or calculating the actual solution not only helps them build their mathematical understanding, but allows them to make connections to the real world, understand realistic and unrealistic outcomes, and build their confidence in actually solving the problem because they can now recognize what the answer should be and what it represents.

“Ish”-ing is a very powerful tool for building number sense, and even with my 9th graders I have seen a great change in their ability to reason about a problem. We have been exploring systems of equations this month and I love having conversations about whether or not solutions can be negative, decimals, fractions, even numbers, odd numbers, etc. and how we know before we even graph or solve using substitution or elimination! They are much more confident and excited about their answers when they have an understanding of the outcome beforehand and I am thankful to have a tool that makes my students better problem solvers and more self-assured in their math abilities!

Moving Forward
In the coming weeks, I plan to integrate the ideas from the conference into my teaching practice. From incorporating my own proficiency scales to introducing my students to standards-based grading to addressing achievement gaps through targeted interventions and bringing the power of “ish” into all levels of instruction, I feel more equipped to support my students' growth.

Attending this conference was a reminder that teaching is a dynamic, evolving field, and there is always more to learn and ways to improve. I’m excited to continue my journey as a math educator, armed with fresh insights and strategies that will not only improve my own practice but, most importantly, help my students succeed.

Lauren Anders
9th grade math teacher
Ottumwa CSD

SCED Codes for Iowa's Academic Standards for High School Mathematics Course Pathways

April Pforts — Tue, 05 Nov 2024 15:52:03 GMT

The updated Iowa Academic Standards for Mathematics Model High School Course Pathways, adopted on April 26, 2024, provides a structured roadmap for high school mathematics courses. This document outlines the different paths students can take depending on their interests, career goals, and post-secondary ambitions. Here's a closer look at the pathways and what each component of this document means for students, educators, and schools.

Key Highlights of the Pathways

The standards introduce multiple course sequences tailored to support students' diverse career interests. They particularly emphasize pathways aligned with college readiness and career technical education. Each pathway offers flexibility while ensuring students cover essential mathematical concepts.

Core Course Pathways: Algebra 1, Geometry, and Algebra 2

These courses build a foundational understanding of mathematics principles and are essential for all high school students. The required standards have been bundled into these three courses.
Algebra 1 (SCED Code 02052): This course covers the basics of the real number system, operations with polynomials, and solving equations. It lays the groundwork for future algebraic and problem-solving skills.
Geometry (SCED Code 02072): A formal study of plane and solid geometry, covering properties, deductive reasoning, and postulates and theorems. The standards for geometry include algebraic components to reinforce continuity in students' learning.
Algebra 2 (SCED Code 02056): Delves into functions and equations in greater depth, emphasizing symbolic, graphic, tabular, and verbal representations. Students explore linear, quadratic, and higher-degree functions, setting the stage for advanced studies.

Advanced Course Options: Trigonometry/Algebra

Students aiming for STEM fields may require courses such as Trigonometry/Algebra (SCED Code 02106). This course includes trigonometric functions, complex numbers, and more advanced algebra, preparing students for calculus.
Precalculus or Trigonometry is recommended to bridge students into calculus, particularly for those pursuing fields like engineering, physical sciences, or certain social sciences. These courses are necessary for students in specific pathways to ensure they're ready for Calculus.

Integrated Course Options: Integrated I, II, and III

Integrated Math courses offer an alternative approach by blending Algebra, Geometry, and Algebra 2 content across three consecutive courses (Integrated I, II, and III). This pathway can replace the traditional sequence and might appeal to students who benefit from a less segmented approach to learning math.

Career Pathways and Flexibility in Course Choices

The pathways allow students to customize their high school math journey based on their career aspirations:

All Career Pathways: Students who initially choose non-STEM fields but later wish to shift into a math-intensive path, such as calculus, may need to complete a summer or semester bridge course to be prepared.
Life Science, Social Science, Healthcare, Business, and Technical Careers: Students on these pathways can pivot into calculus during their senior year if desired, though this might require additional preparation.
Engineering and Physical Science Careers: Students with a strong interest in math may opt for advanced applications of math or statistics in their senior year instead of taking calculus. This choice allows for an in-depth focus on mathematical applications related to their fields of interest.

SCED Codes: A Consistent Framework for Course Data

Each course in the pathway is linked to a School Courses for the Exchange of Data (SCED) code, a standardized system that helps schools and states manage course information. For example:

Algebra 1 (SCED Code 02052) provides basic math literacy.
Geometry (SCED Code 02072) provides basic math literacy.
Algebra 2 (SCED Code 02056) advances students' understanding of algebraic functions.
Trigonometry/Algebra (SCED Code 02106) extends Algebra 2 by incorporating trigonometry for students heading into advanced studies.

Final Thoughts

The Iowa Academic Standards for Mathematics Course Pathways ensures that high school students in Iowa receive a comprehensive, flexible mathematics education. By allowing students to switch pathways with the aid of bridge courses, the standards reflect an understanding of students' evolving academic and career interests. This structure supports Iowa's commitment to preparing all students, whether college-bound or pursuing technical careers, with the mathematical foundation needed for future success.

Brooke Fischel's Aha! Moments

Wendy Weber — Mon, 07 Oct 2024 02:32:23 GMT

I was privileged to attend the NCTM Annual Meeting & Exposition in Chicago this month. Nothing energizes a teacher with new ideas more than a conference and a chance to network with other math education professionals. I will impart on you my three favorite strategies from NCTM sessions.

It is apparent that engagement with students remains the paramount focus of sessions. This type of engagement has evolved during my career, and I was pleased to see several sessions given by Peter Liljedahl in his efforts to pair Building Thinking Classrooms with other platforms to broaden the base of its use in math classrooms of all levels. I spent some time in sessions learning how other educators use “thin-slicing” to use vertical boards to teach mathematics day-to-day. Thin-slicing refers to a method where each problem is a bit harder than the prior question, moving students to higher levels along the way. There was a strong use of learning progressions, which I assume many of you already use in your current curriculum to move student thinking from entry-level to high-level throughout the lesson. My favorite session was given by Emily Kerwin, where she asked calculus students to look at a function and its derivative before learning the Power Rule and asking them to write what they felt the rule might be. Each new problem invited a new wrinkle and modification of the rule to include new issues they were encountering. This seems like it could be extended to many math topics in a variety of courses.

On a whim that there was a useful session to renew the way I teach logarithms, I happened upon Philip Dituri’s session, and it was magical. He introduced me and others to manipulatives that allowed students to physically play with logarithms to facilitate content knowledge development in logarithms and their laws. FiCycle, a non-profit organization, makes 3D log manipulatives for sale, but they also provide free paper 2D manipulatives that could be laminated. Meaning, every teacher’s budget can allow for this type of student experimentation. I was impressed by the ease of use and blissfully simple approach to help student discover laws of logarithms before we generalize the learning with symbolic representations. If this is a topic you teach that could use an increase in student interest, check it out!

But, perhaps the biggest Aha! Moments were experienced in Chris Shore’s Clothesline Math session. This is the number sense I have always wanted to develop with high school students and didn’t know it existed. With so many session choices, it was only Shore’s promise to “blow your mind” that convinced me to check it out. He delivered. Again, blissfully simple approaches make for the best learning opportunities. Who would have thought a piece of string and some cardstock would allow teachers to facilitate algebraic line segment addition, solve for x, and never need to write the equations down or do symbolic manipulation. It was a prime example of the way our lessons should start with conceptual knowledge and later move to procedural fluency when our understanding is solid and the focus moves to efficiency. I was so mesmerized, I purchased his book the moment I left the session. Shore provides many videos online and free resources as people help develop this approach for all mathematics subjects and topics.

My parting advice is to attend conferences! Be a life-long learner! I hope you experience the renewed spirit of teaching when you discover strategies and sessions that speak to you!

Brooke Fischels

High School Mathematics Teacher

Ottumwa High School

Unlocking Potential: The Cognitive Benefits of All Students Taking Algebra 2

April Pforts — Wed, 02 Oct 2024 02:19:20 GMT

Unlocking Potential: The Cognitive Benefits of All Students Taking Algebra 2

Mathematical literacy is more crucial than ever in today's rapidly evolving world. Among the various math courses available to high school students, Algebra 2 is a pivotal class offering profound cognitive benefits. While some may question the necessity of Algebra 2 for all students, its advantages extend far beyond basic arithmetic. Here, we'll explore the cognitive benefits of taking Algebra 2 and why it is essential to every student's educational journey.

1. Enhanced Problem-Solving Skills

One of the most significant benefits of Algebra 2 is the development of problem-solving skills. The course introduces students to complex, multi-step problems that require critical thinking and logical reasoning. By tackling these challenges, students learn to analyze problems from different angles, identify relevant information, and devise strategies to arrive at solutions. These skills are vital in math and applicable in everyday life, from making informed decisions to resolving conflicts.

2. Improved Logical Reasoning

Algebra 2 emphasizes logical reasoning by studying functions, equations, and inequalities. Students learn to construct rational arguments and draw conclusions based on given premises. This ability to reason logically is essential in mathematics and various disciplines, including science, law, and ethics. By honing their logical reasoning skills, students become more adept at evaluating arguments, making sound decisions, and understanding complex issues.

3. Advanced Analytical Skills

As students explore concepts such as quadratic functions, exponential growth, and data analysis, they develop advanced analytical skills. Algebra 2 encourages students to interpret and manipulate data, making it easier to identify patterns and trends. These analytical skills are invaluable in today's data-driven society, where the ability to sift through information and make informed conclusions is paramount.

4. Cognitive Flexibility

Algebra 2 promotes cognitive flexibility—the ability to adapt thinking in response to new information or changing circumstances. Students are often encouraged to approach problems from multiple perspectives and explore various methods for finding solutions. This flexibility fosters creative thinking and adaptability, which are increasingly essential skills in a world characterized by rapid change and uncertainty.

5. Resilience and Perseverance

Studying Algebra 2 has its challenges. Students will encounter difficult concepts and complex problems that may initially seem insurmountable. However, by working through these challenges, they learn the value of perseverance. Grappling with complex material builds resilience, teaching students that persistence can lead to success. This growth mindset is essential in academics and all areas of life.

6. Preparation for Future Learning

Algebra 2 is a critical stepping stone for higher-level math courses like calculus and statistics. The concepts learned in Algebra 2 are foundational for understanding more advanced topics in mathematics and related fields. By taking Algebra 2, students are better prepared for college-level coursework and future careers in STEM fields, which often require strong mathematical skills.

7. Real-World Applications

Beyond academics, the skills developed in Algebra 2 have practical applications in everyday life. From managing personal finances to making data-driven decisions in various professions, algebraic thinking is a valuable tool. Students learn to model real-world situations mathematically, equipping them with the skills to tackle challenges in their future careers and personal lives.

The cognitive benefits of all students taking Algebra 2 are profound and far-reaching. From enhanced problem-solving and logical reasoning to improved resilience and real-world application, the skills gained in this course lay the groundwork for academic and personal success. In a world that increasingly relies on data and analytical thinking, equipping every student with a solid foundation in Algebra 2 is beneficial and essential.

By advocating for all students to take Algebra 2, we are investing in a future where they are not only mathematically literate but also critical thinkers capable of navigating the complexities of the modern world. Let's unlock the potential of our students by ensuring they all experience the transformative power of Algebra 2!

Cracking the Code: Unpacking Fluency in Iowa Academic Standards for Mathematics?

April Pforts — Sat, 31 Aug 2024 18:46:54 GMT

Math fluency can be defined as the ability to work with numbers, operations, and procedures with ease. It is the ability to apply procedures efficiently, flexibly, and accurately, including fact, computational, and procedural fluency. Critical end-of-grade-level standards are identified in grades K-8, where fluency should be expected by the end of the grade.

There are three types of fluency in the Iowa Academic Standards for Mathematics. They are:

Fact Fluency - The ability to apply single-digit calculation skills efficiently, appropriately, and flexibly.

Computational Fluency - The ability to perform four operations across different number types, such as whole numbers and fractions, regardless of the number's magnitude.

Procedural Fluency - The ability to carry out procedures accurately, efficiently, flexibly, and appropriately. This includes basic fact fluency, computational fluency, and other procedures, such as finding equivalent fractions. Procedural fluency also applies to multi-digit whole numbers, rational numbers, comparing fractions, solving proportions or equations, and analyzing geometric transformations.

Fact Fluency

Fact fluency is the ability to recall basic math facts, such as addition, subtraction, multiplication, and division, without conscious effort.

It is NOT MEMORIZATION

It is NOT SPEED (TIMED DRILLS)

Computational Fluency

Computational fluency is the ability to perform math calculations using strategies. It's more than just being able to produce correct answers quickly, and it involves conceptual understanding, flexibility, and efficiency. Students who are computationally fluent can use strategies and their existing knowledge to solve more challenging problems.

Flexibility

Comfortable with more than one approach.
Choose strategy appropriate for the numbers.

Efficiency

Easily carries out the strategy, uses intermediate results.
Doesn't get bogged down in too many steps or lose track of the logic of the strategy.

Accuracy

Can judge the reasonableness of results.
Has a clear way to record and keep track.
Concerned about double-checking results.

Procedural Fluency

Procedural fluency is a mathematical skill that involves knowing procedures, understanding when and how to use them correctly, and being able to perform them accurately, efficiently, and flexibly. It also includes the ability to apply procedures to different problems and contexts, modify procedures based on others, and recognize when one strategy is more appropriate than another.

Procedural fluency, including fact and computational, also attends to the three components of efficiency, flexibility and we can say that it is made up of three components and six related actions that allow us to better understand what we are talking about:

In summary, fluency in the Iowa Academic Standards for Mathematics is a multifaceted skill that extends beyond simple rote memorization. It encompasses fact fluency, computational fluency, and procedural fluency, each playing a critical role in a student's mathematical development. By mastering these elements, students build a solid foundation for solving complex problems and developing a deep understanding of mathematics. As they progress through the grades, these fluency skills prepare them to tackle increasingly sophisticated mathematical challenges with confidence and competence.

Image 1 attribution: https://blog.innovamat.com/en/routine-octahedron-fluency-in-the-classroom

Image 2 attribution: https://positivelylearningblog.com/fact-fluency-for-math/

Image 3 attribution: attribution: https://blog.innovamat.com/en/routine-octahedron-fluency-in-the-classroom

Streamlining Success: Key Updates to Iowa's High School Mathematics Standards

April Pforts — Mon, 29 Jul 2024 19:38:25 GMT

Some of the most significant updates to the Iowa Academic Standards for Mathematics are the substantial high school-level changes. To fully understand and appreciate these changes, it is essential to first recognize what has been removed from the standards.

In the previous standards, "Iowa" standards were added to high schools, which have now been removed. This decision was not made lightly, and it's essential to understand that those standards are indeed valuable. However, the truth remains that algebra content remains the biggest gatekeeper concerning post-secondary opportunities. Therefore, the team removed those standards to allow more "Focus" (spending the instructional time on content that will impact the post-secondary gatekeeper most, page 3).

Another removal was the standards, indicated by (+), that were beyond post-secondary success and not meant for all students, which increased the "Focus" of the high school standards. If the team deemed a (+) standard necessary for all students, they changed it to a required standard. This change increases the depth over the breadth of the critical content.

The revision team also had the authority to remove any standard deemed not essential for all students, resulting in a streamlined list of standards necessary for all learners. Having a list needed for all students allowed a division of standards into accessible courses for all students and for the clusters to receive the appropriate Focus within and across the course. The remaining standards formed the required standards for all students.

On page 108 of the Iowa Academic Standards for Mathematics, a table showing this distribution across courses can be found. Bold text indicates standards that fall within Major Clusters; see page 3 for an explanation. Additionally, thishigh school course progression can further illustrate the Major Clusters in high school. These are all the clusters marked as Major Clusters which means that they will be where instruction should be focused for most of the instructional time.

From there, the remaining list of standards, which are required for all students, have been divided into three distinct yearlong courses: Algebra 1, Geometry, and Algebra 2. A comprehensive table showcasing the High School Required Standards by Course emphasizes the collective standards across the three-year sequence. While most schools in Iowa follow the Algebra 1, Geometry, and Algebra 2 sequence, variations in specific standards alignment may exist due to local curriculum choices.

The Conceptual Categories, which begin on page 98, have been retained with the notable inclusion of modeling as the first category. This change highlights the significance of modeling and its relationship to other conceptual categories. It is worth noting that this modeling aligns with the Standards of Mathematical Practices #5 and is indeed the same. Modeling becomes more sophisticated and significant when attending to the "Rigor" aspect of the standards.

Lastly, the (★) was retained, to denote standards with full mathematical process listed on pages 100 - 101 is indicated.

In conclusion, the revisions to the high school standards in mathematics aim to streamline the content for enhanced clarity and alignment with national best practices. It is the responsibility of educators and stakeholders to familiarize themselves with these changes, as this is crucial for ensuring effective implementation in classroom instruction.

August 2024 Summer Mathematics Professional Learning Sessions

2024 Iowa Academic Standards for Mathematics Implementation Resources Guidebook

Breaking Down the Iowa Academic Standards for Mathematics Revision

April Pforts — Sun, 02 Jun 2024 17:16:31 GMT

The New Iowa Academic Standards for Mathematics have been significantly revised to enhance clarity and understanding for educators and students alike. Here’s a brief overview of the key highlights:

Document Format: The revision introduces a user-friendly table format, making it easier to navigate and understand.

Level of Focus and Rigor: Each standard is now categorized based on its level of focus (Major, Supporting, or Additional Work) and rigor (Conceptual, Procedural, Application), providing a clear roadmap for educators.

Standards of Mathematical Practices (SMP): The standards now include three bundles of SMP—Communicating Reasoning, Problem Solving, and Modeling and Data Analysis—fostering a holistic approach to mathematical learning.

K-5 Revisions: The revisions in the K-5 standards primarily focus on language adjustments to enhance clarity. Notable changes include the addition of counting backward in Kindergarten and the inclusion of time and money standards in Kindergarten and 1st grade.

6-8 Revisions: The 6th grade standards emphasize the use of technology to handle complicated cases. Cube roots are also identified for bases 1-5 and 10 in the 8th grade standards.

High School Revisions: The high school standards have been divided into courses—Algebra 1, Geometry, and Algebra 2—making it easier for educators to align the curriculum. Noteworthy additions include standards beyond college and career readiness and the inclusion of course indicators in both Algebra 1 and Algebra 2.

Overall, the revisions aim to provide a comprehensive and coherent framework for mathematics education in Iowa, ensuring that students are equipped with the necessary skills for success in both higher education and the workforce.”

2024 Iowa Academic Standards for Mathematics Implementation Resources Guidebook (Session 1 Training)

Session 2 Training July/August

In Memory of Teresa Finken, by April Pforts

Wendy Weber — Sun, 05 May 2024 13:40:52 GMT

On Friday, April 12, 2024, Dr. Teresa Finken passed away peacefully at her home in Iowa City, IA. A Celebration of Life open house will be held at The Heights Rooftop in Iowa City on June 8, 2024, from 2-5pm. Instead of flowers, please send a donation to Tapestry Farms, a local nonprofit Teresa donated her time and resources to.

Teresa made a significant impact by serving as ICTM’s Post-Secondary Vice President and overseeing the management of the journal for ICTM. She dedicated numerous hours to reviewing, editing, and writing articles for the journal. ICTM honored her at the 2023 Fall Conference with the Lifetime Achievement Award. It is with this same dedication in mind that ICTM is reintroducing the journal in a revised format, known as ICTM Journal 2.0.

Please take some time to share a memory on the Tribute wall.

Here is a list of the journals she authored:

ICTM Journal 2019-20. Late Development of Place Value in Base 10

ICTM Journal 2017-18 Introducing Angle Measure

ICTM Journal 2018-19. What is a Moebius Strip? Written with Deidra Baker

ICTM Journal 2017-18. Mathematics Is All Around Us. T. Finken & D. Baker

ICTM Journal 2016-17. Book Review: Hidden Figures; A Timeline for the History of Mathematics.

ICTM Journal 2016-17. Book Review Moebius Noodles: Adventurous Math for the Playground Crowd.

ICTM Journal 2015-16. Why are some numbers even and others odd? Rule versus reason.

ICTM Journal 2014-15. Where Does Pi Come From?

ICTM Journal 2013-14. What Is So Cool About Snow?

ICTM Journal 2013-14. Briefing on ACT’s Report: The Condition of STEM 2013 Iowa

ICTM Journal 2012-13. Fractal Cauliflower.

Wildcat Warriors Game Club

Wendy Weber — Wed, 13 Mar 2024 14:34:38 GMT

In 2023, Humboldt High School received funds from the ICTM Extra Curricular Grant to purchase board games for their game club. Read about the impact of the grant on their students...

The Wildcat Warriors Game Club and Teacher Sponsors

The grant allowed for the purchase of 8 different board / card games for classroom and board game club usage. We chose a variety of games to allow for students to participate in different manners. The games consisted of a cooperative (Magic Maze, up to 8 players), head to head (Battleline, 2 player) other games with 2 to at least 4 players (Arboretum, Stone Age and Kingdomino). Enter the Spudnet and Battle Chips with 2-6 players. No thanks! is a card game for 3-7 players. All of the games are relatively easy to learn and have varying degrees of strategic thinking. By participating in these games, students have an opportunity to be involved in a cognitively demanding and interesting game. There is also mathematical computation and geometrical thinking in many of the games listed. Problem solving skills are developed throughout the gaming process. A social component is gained by interacting with other participants.

The purpose of the club and using board games in the classroom are as follows:

The board and / or card games allow players to create strategies and become competent and confident in choosing those strategies.
The club fills a unique niche for our student body. The board game club provides an opportunity for its members to be involved in a school sanctioned activity that fits well with their own personal identities and passions
All grade levels are able to participate in the games.
This practice of playing games is cognitively demanding and interesting to many students. There is also mathematical computation and geometrical thinking in many of the games listed. Problem solving skills are developed throughout the gaming process. There is also a social component that is gained by interacting with other people playing games.

Since purchasing the games, we have played one of them in the Introduction to Computer Science class. It is called Battle Chips by Codomo, a 2 to 6 player game. It integrates the idea and / or language of computer science. Functions, Algorithms, Failure Conditions, Programming Bugs, For Loops, While Loops, Nested Loops, Variables, Boolean Statements and 10 other Computer Science related commands are included in game play. As students played the game, they would recognize the terms learned from their programming and applied them to the game play.

Board Games Purchased with Grant Funds

After playing the game, we asked the players what they thought about the game:

Liked: “The intensity of the point system.” “Great game, thinking about buying it myself.” “A lot of elements to think about.” “Made teams to attack other players that were in the lead.” “Applied strategies and attacks against others.” “I liked the complexity and the several outcomes to the cards.”

Disliked: “Setup took some time.” “It was slow.” “Easily ganged up on.” “Initially it was hard to understand instructions.”

Interaction with other players: “Could make teams against other players.” “We zapped each other.” “Attacked and made strategies against each other.” “I teamed up with two other players and I really enjoyed stealing other players' cards.”

We will continue to use the Battle Chips game in the Introduction to Computer Science class.

We also teach a Math Topics class that encourages problem solving skills. We have incorporated games into the curriculum. They have been used to encourage logic, geometrical and strategic thinking. We have played No Thanks! multiple times. It is a card game designed to be as simple and engaging.

The rules are simple. Each turn, players have two options:

play one of their chips to avoid picking up the current face-up card
pick up the face-up card (along with any chips that have already been played on that card) and turn over the next card

However, the choices aren't so easy as players compete to have the lowest score at the end of the game. The deck of cards is numbered from 3 to 35, with each card counting for a number of points equal to its face value. Runs of two or more cards only count as the lowest value in the run - but nine cards are removed from the deck before starting, so be careful looking for connectors. Each chip is worth -1 point, but they can be even more valuable by allowing you to avoid drawing that unwanted card.

We have also played Ticket to Ride, Settlers of Catan and Coup in the Math Topics class.

There are currently two teacher sponsors and five to ten students that attend the club twice a week after school from 3:30 to 5:30. This is our fourth year meeting as a club. We were also able to join a board game organization called TableTop Alliance. They are a nationwide organization that provides games for nonprofit game clubs. After becoming part of the organization, they donated $500 worth of boardgames. If there is interest in forming a game club or using games in the classroom feel free to contact me at plauger@humboldt.k12.ia.us If other school districts have a game club, maybe we could join together for a tournament or game day.

Submitted by Chandra McMahon on behalf of Humboldt High School Mathematics Instructors

How an Algebra/Finance Course Can Compound Interest, Robert Gerver & Richard Sgroi

Wendy Weber — Thu, 30 Nov 2023 00:18:25 GMT

How an Algebra/Finance Course

Can Compound Interest

The circumstances of peoples’ economic struggles are complex and systemic, as are the potential solutions. But there is one simple solution to prepare the next generation for economic adulthood: Teach financial literacy in high schools. (Hertenstein, 2023).

A recent survey conducted by The TIAA Institute-GFLEC Personal Finance Index reports that there is a tendency for financial literacy knowledge to be low among all of the US adult generations but the level of financial knowledge is at its worse in young adults. (Yakoboski et al., 2023). State education departments across the nation have been grappling with this problem over the last decade and recently many, including Iowa, have instituted new financial literacy curriculum standards and graduation course requirements. As of the 2022-23 school year, Iowa students need a personal finance course to graduate from high school. While some schools offer these courses under the business or social studies departmental umbrellas, the mathematics department is really the best fit.

How can math departments take the lead in helping students meet this new finance requirement?

This was a question that we faced years ago in our home school districts, and to answer it, we created, field-tested, and revised a curriculum, Advanced Algebra with Financial Applications, that is currently used in all 50 states. Advanced Algebra with Financial Applications is a mathematical modeling course with an Algebra 1 prerequisite. It is algebra-based, applications-oriented, and technology-dependent. The course addresses college preparatory mathematics topics from Algebra 2, Statistics, Probability, and Precalculus, under eight financial umbrellas: Discretionary Expenses, Banking, Investing, Employment and Income Taxes, Automobile Ownership, Consumer Credit, Independent Living, and Retirement Planning and Budgeting.

It is our contention that students should take a quantitative financial literacy course as a mathematics requirement before graduating because finance and mathematics are inextricably tied together.

Which students can benefit from taking a financial algebra course?

Students who might not be ready to take Algebra 2
Students interested in a financial algebra course after taking Algebra 2
Students who must pass a financial literacy course graduation requirement
Students looking to take a core course alternative to Algebra 2
Students in need of a 3rd or 4th year math credit
Students looking to take a mathematics elective concurrently with another mathematics course

How does the course meet both the mathematical and financial needs of these student populations?

The mathematics topics contained in this course are introduced, developed, and applied in an as-needed format in the financial settings covered. Students are encouraged to use a variety of problem-solving skills and strategies in real-world contexts, and to question outcomes using mathematical analysis and data to support their findings. The course offers students multiple opportunities to use, construct, question, model, and interpret financial situations through symbolic algebraic representations, graphical representations, geometric representations, and verbal representations. It provides students a motivating, young-adult centered financial context for understanding and applying the mathematics they are guaranteed to use in the future.

What resources are available for creating your Advanced Algebra with Financial Applications course?

In all likelihood, your college math education courses did not equip you with specific financial algebra teaching methods in the manner that they addressed the algebra and geometry teaching methodologies. Consequently, you will need access to resources that help you design and teach your course. Let's take a look at some key resources.

Next Generation Personal Finance (www.ngpf.org) NGPF has a financial algebra curriculum, worksheets, lesson plans, videos, and professional development materials, all available for no charge.
Jump Start Coalition (www.jumpstart.org) JumpStart is a coalition of corporations that offer finance-related PDF print materials, videos, professional development and other resources for educational purposes. Some are available for free and others have a cost.
www.financialalgebra.com This website is a gold mine of videos and teaching resources created by the authors of the article you are reading. There are ten links that teachers all across the country have found to be very helpful for curriculum writing and teaching strategies.
Google Searches The Internal Revenue Service, NY Stock Exchange, Federal Reserve Bank, Insurance Information Institute, Federal Deposit Insurance Corporation have websites that offer free materials for teachers. The FDIC website has a financial education program called "How Money Smart Are You?"
Money Experience (www.moneyexperience.com) Money Experience software is an online simulation that helps students make financial decisions. A short video on their website explains how the simulation works.
Foundations of Money (www.theIMfoundation.org) Their Foundations of Money initiative offers free written and video material to teachers.
Financial Life Cycle Math (www.ficycle.org) FICYCLE provides lessons, for-sale workbooks, and teacher training.
Financial Algebra: Advanced Algebra with Financial Applications This is a comprehensive textbook that contains material for a full-year financial algebra course. The package has many teacher resources.
Institute for Educational Development (www.IEDseminars.org) The Institute offers 5-hour virtual professional development seminars on teaching a financial algebra course, PD hours and college credit is available.
The Truth About Your Future (www.thetayf.com) Finance guru Ric Edelman offers videos, a newsletter, master class articles and more about financial issues.
The Stock Market Game (www.stockmarketgame.org) The SIFMA Foundation's Stock Market Game is an online simulation about investing. Since its inception in 1977, over 20 million students worldwide have participated.
Data is Beautiful (www.reddit.com/r/dataisbeautiful) This site has many fascinating non-routine graphs on real-life data. It is a great source for problems that can help keep your course current.

Undoubtedly your own personal Internet search could produce even more resources. Once you get a skeleton for your curriculum, you can use any or all of the resources to supplement your program. This vast collection of material assures the financial algebra teacher that there are plenty of places to turn to for lessons, ideas, projects, videos, and activities.

What is the suggested course content?

Here is a brief overview of the 8 units in the course. A more detailed explanation of the units can be a www.financialalgebra.com on the “Course Proposal” page.

Unit 1: Discretionary Expenses

In this unit, students will learn about essential and discretionary expenses, with a focus on the latter. Statistics will be used as a means of modeling, analyzing and describing trends in non-essential spending. Students will:

compute measures of central tendency, measures of dispersion, and compare the advantages and disadvantage of each.
study the normal curve and calculate z-scores.
plot and interpret bivariate spending data through the use of scatterplots and linear regression equations as well as interpret the Pearson Product-Moment Coefficient of Correlation.

This accessible introduction to statistical analysis in the context of spending will be broadened and made transferable to other financial topics throughout the course.

Unit 2: Banking Services

This unit answers the question “Where can people keep the money that they earn?” as students explore:

checking and savings accounts, bank statements, debit cards, and certificates of deposit
simple interest, compound interest, continuous compounding, and how to use logarithms as a tool to determine the term of any type of savings account
present and future value of a savings account

This allows students to evaluate the relative risk of bank accounts as compared to other types of investments they will be studying in the course.

Unit 3: Investing

Students are introduced to basic business organization terminology in order to read, interpret, chart, algebraically model stock ownership and transaction data, and identify trends. In this unit, students will:

use algebraic ratios and proportions to model percent increases, decreases, moving averages, stock splits, and dividend yields
learn how entrepreneurs use randomized designs, matched-pair designs, observational studies, hypothesis testing, and inferential statistics to make decisions in the development of new businesses and products
determine the efficacy of producing a product, by creating and interpreting supply and demand curves, expense equations, revenue equations, and profit equations
find optimal outcomes through the use of linear programming techniques

Throughout this unit, students identify investment trends using mathematics.

Unit 4: Employment and Income Taxes

High school students are at the age where they are beginning to work, and have lots of questions about our tax system. In this unit, students will:

learn about employment, salaries, paychecks, deductions, benefits, and Social Security payments.
use piecewise functions to model commissions, royalties, and piecework pay.
model the FICA tax function using the graph of a piecewise function with cusps.
explore, model, graph and interpret the Internal Revenue Service’s tax tables, schedules, and worksheets

Students learn how these piecewise functions and polygonal graphs can be used when filing the IRS tax form 1040 package.

Unit 5: Automobile Ownership

Most high school students anticipate getting a driver's licenses in the near future. In this unit, students will:

use various functions, their graphs, and data analysis as a tool in the responsible purchase and operation of an automobile
model auto sales and purchases using logarithms, frequency distributions, modified box and whisker plots, stem and leaf plots, and linear and curvilinear regression
model auto deprecation using arithmetic and geometric sequences
examine the probability inherent in auto insurance by using conditional probability, two-way tables, independent events and Venn diagrams
explore projectile motion, irrational functions and parabolas in the context of accident deconstruction

This unit helps students answer the many questions they have about becoming a responsible driver.

Unit 6: Consumer Credit

Credit raises a person's standard of living, but it comes at a price. In this unit, students will:

learn how to use mathematics to make wise credit choices that fit their needs, current financial situation, and future goals.
explore loan information and model that data using regression analysis to find the linear, quadratic, cubic, and exponential equation of best fit
use exponential and rational functions in the forms of the simple interest formula and the monthly payment formula to determine the total cost of borrowing for an education and large purchases

This unit helps students make sound choices when they borrow money.

Unit 7: Independent Living

"Leaving the nest" is in the not-to-distant future of all high school students. In this unit, students will:

explore moving, renting, and purchasing a place to live
analyze the geometric demands of floor plans, areas of shaded and irregular figures, apothem, and discover the relationship between area and probability
employ trigonometric functions, the Pythagorean theorem, slope, and similar triangles to model ladder safety, deck building, and proximity to falling trees
use rational functions with multiple independent variables to model air conditioning BTU requirements

Students come to the realization that housing is extremely expensive, and requires planning and a knowledge of mathematics.

Unit 8: Retirement Planning and Budgeting

The focus of this unit is on the mathematics of fiscal plans that workers can make years ahead of their retirement. Here, students will:

explore retirement savings plans, both personal and Federal, employee pension programs, and life insurance
use rational functions to model present value, future value, and periodic investments
compute Social Security benefits
use graphs to model investment diversification
employ probability and expected value to compute how life insurance companies can earn a profit
explore how rational functions can be used to model average costs over time
use the greatest integer function as part of a piecewise function that is used to model household expenses over time
use matrices to model budget situations, and organize budget information

The unit culminates with the creation of a budget, incorporating categories that reflect all of the units in the course.

Why will you be excited to teach Advanced Algebra with Financial Applications?

The relationship between fiscal responsibility and financial education is undeniable. Offering financial education in a mathematics course builds fiscal confidence and responsibility. It is rewarding to students see, enjoy, and implement mathematics they will use in their everyday lives. And as for their perpetual question of “when are we ever going to use this?”, the real-world answer is “the rest of your lives!”

BIBLIOGRAPHY

Hertenstein, Isaac. “ ‘Young People Know More About TikTok and Minecraft Than Money.’ Teenagers Want To Be Smarter About Finances – Teach Them.”, MarketWatch, 21 January 2023, marketwatch.com/story/young-people-know-more-about-tiktok-and-minecraft-than-money-teenagers-want-to-be-smarter-about-finances-teach-them-11674198585. Accessed 17 April 2023.

Yakoboski, P., Lusardi, A., Hasler, A. “Financial Literacy, Longevity Literacy and Retirement Readiness”, TIAA Institute, 12 January 2023, tiaa.org/public/institute/publication /2023/financial_literacy_longevity_literacy_and_retirement_readiness. Accessed 17 April 2023.

Artificial Intelligence, Data Literacy, and Preservice Mathematics Teacher Training, Heather Gallivan & Eric Weber

Wendy Weber — Wed, 29 Nov 2023 21:47:38 GMT

Artificial Intelligence, Data Literacy, and Preservice Mathematics Teacher Training

Heather Gallivan, University of Northern Iowa

Eric Weber, Iowa State University

The rise of Artificial Intelligence. The advent of ChatGPT – an interactive artificial intelligence (AI) platform – has started a national and global conversation of what AI does for us and what it can (and cannot yet) do. These and other AI entities have the potential to touch upon every aspect of the human experience. Since AIs are built upon data science and machine learning methodologies, data literacy among the populace at large is as crucial to society as ever. While all disciplines will play a role in developing the data literacy of K-12 students–hence, all disciplines will have contributions to deliver–we believe that mathematics teachers at the primary and secondary levels are best positioned to implement the charge of informing our students of the issues, challenges, and possibilities presented by data literacy, data science methodologies, and AI in general. In particular, the potential for fundamental transformation of society that AI poses calls for mathematics teacher educators to train mathematics teachers in the relevant data literacy and data science content. This position paper will accomplish the following intertwining objectives: 1) define data science and data literacy; 2) review the current state of data science and literacy education and mathematics teacher training within the State of Iowa and at the national level; 3) our own contributions to mathematics teacher preparation for data science; 4) support our claim that in-service and pre-service mathematics teachers will be at the forefront of nationwide efforts to increase data literacy across all sectors of society as full scale deployment of AI becomes actualized.

What is Data Science? As the evolution of data-driven methodologies accelerates, the scope of our efforts to further data science education in Iowa remains in flux–even the terminology itself evolves rapidly. Despite this constant churning, let us start with the terminology. Within academia–higher education especially–the dominant term in recent years has been “data science”. Broadly, data science is “the science of learning from data” (Engel, 2017, p. 44). However, there is no consensus on how to define data science or how it overlaps and/or differs from other terms like artificial intelligence (NASEM, 2018, 2023; Rosenburg & Jones, 2023). For our purposes here, we shall refer to data science and artificial intelligence interchangeably–not because they are, but rather because we believe that ChatGPT and similar AI platforms will ultimately render the “data science” phrase obsolete. Data literacy on the other hand, is more well-defined in the field of mathematics and statistics education. Data literacy involves not only being able to analyze, interpret, and evaluate data and statistics (i.e. statistical literacy), but to also be a critical consumer of data (Gould, 2017); recognizing “what we and others can do with data, what data can do to us, and what kind of world we can create with data” (Louie, 2023, p. 1).

We emphasize that regardless of how we refer to the content or the discipline, the content itself is a re-coupling of the academic disciplines of mathematics, statistics, and computer science. This places mathematics teachers at the forefront of delivering data science/literacy content in the nation’s K-12 schools. Let’s now consider where data science education currently stands at the K-12 level.

Data Science at the K-12 Levels. Just as the terms we use for data science are ever changing, the field of data science in K-12 education is “still developing and open to being shaped” (Rosenburg & Jones, 2022, p. 1). However, policy documents and reports from national organizations have made statements regarding what data science and data literacy concepts K-12 students need to know. The Pre-K–12 Guidelines for Assessment and Instruction in Statistics Education II: A Framework for Statistics and Data Science Education (GAISE II) report (2020) acknowledges that “the demands for statistical literacy have never been greater” (p. 1). This report provides a framework for how statistical and data literacy should be developed from the early grades through high school. The report highlights new skills for students, including a focus on the entire statistical investigative process, multivariate thinking across all grade levels, and incorporating technological tools to aid in data analysis. The Iowa Core Standards for Mathematics also have standards that reference data analysis and statistics from Kindergarten (Classify objects into given categories; count the numbers of objects in each category and sort the categories by count; K.MD.B.3.) through high school (e.g. summarize, represent, and interpret data; S-ID.A, S-ID.B, S-ID.C).

Given this emphasis on developing data and statistical literacy and analysis skills for K-12 students, many states nationally have begun to offer programs and coursework in data science. Currently, there are 14 states which have data science programs of varying depth and size; the majority of which are being taught by mathematics teachers (Drozda, Johnstone, & Van Horne, 2022). All 50 states have standards that reference data, but only 5 states have standards that are data science specific. For example, California released a Mathematics Framework in July 2023 that has an entire chapter devoted to data science across all grade bands from pre-kindergarten to high school (California Department of Education, 2023). There are several data science and statistics curricula that have been developed for high school students in recent years. These include CourseKata, YouCubed, Introduction to Data Science, and Bootstrap: Data Science (web addresses available in the resources below). All of these web-based resources are freely available for use by teachers. In Iowa, data science has also gained in popularity. Many high schools in Iowa teach coursework in statistics, which has overlapping concepts with data science (e.g. analyzing multivariate data in high school); and at least one high school in Iowa is currently offering coursework in data science utilizing the Skew the Script curriculum materials. Further, the state of Iowa has officially adopted course descriptions for data literacy and data science (you can search for data science and data literacy course descriptions at the link under Resources below), anticipating the desire for high schools to start officially offering such coursework for credit.

With this increased national and state-wide interest in and need to offer K-12 coursework in data science, there will be a need for teachers to teach these courses. But where do we start? For example, do we need to define state-level standards for data science? Offer professional development for in-service teachers to learn to teach data science? We contend that a good place to start is in teacher preparation, especially at the preservice mathematics teacher level.

Mathematics Teacher Preparation in Data Science. Since the goal of K-12 education in data science is to develop students’ ability to develop data literacy and data analysis skills (GAISE II, 2020), teacher preparation needs to focus on current and future teachers developing these skills as well. Teachers need to have experiences where they work with multivariate data sets, ask statistical questions, etc. with data sets that are meaningful in order to be able to give those experiences to their students. In other words, teachers need experience engaging with data themselves before creating these opportunities for students. The vast majority of K-12 data science courses offered in the United States are taught by mathematics teachers (Drozda, Johnstone, & Van Horne, 2023) and thus, are in the best position to continue to move data science education forward. We feel that future mathematics teachers are an important group to target for teacher preparation.

Our long-term vision is for all future teachers, regardless of discipline, to experience substantial data literacy and data science content in teacher preparation courses. In STEM fields at the secondary level, “substantial” may involve several courses dedicated to data science. For example, the AMTE Standards document (2017) recommends middle school mathematics teachers having two courses in statistics and data science and high school mathematics teachers to have three to be sufficiently prepared to teach statistics and data science content. However, the current challenge is two-fold: 1) fully developed data science curricula for preservice mathematics teachers do not exist; 2) we do not have space in current teacher preparation programs to introduce new courses to deliver data science content. Both of these challenges are exacerbated by the shifting specifications of the data science discipline and the associated licensing requirements for teachers.

Despite these challenges, we feel it is necessary to start, even if in small increments. We argue that the mathematics community has a significant advantage in the form of a fully developed infrastructure–curriculum, educational standards, pipelines from preservice to in-service teaching opportunities–over statistics and computer science (where mathematics teachers often teach coursework in these areas as well). Thus, we believe that future mathematics teachers are in the best position currently to be trained in teaching data science. In response to challenge 1), we have created a 6-week data science module to develop preservice secondary mathematics teachers’ data science content knowledge and mathematical knowledge for teaching data science. We have implemented this module with preservice teachers in the state of Iowa during one of their required content courses for the teaching major and licensure. Thus far, we have shown positive results in developing preservice secondary mathematics teachers’ knowledge of a few data science concepts (e.g. data classification and model fitting). The purpose of this module is to begin the conversation on what content knowledge the field believes is important for preservice mathematics teachers to know and how we can best prepare them to teach data science concepts in the future.

In response to challenge 2), we are beginning to explore how we can deliver content within the existing teacher preparation programs. First, our intent is to design and develop short 4-8 week drop-in data science modules that could be embedded within other teacher education coursework. Further, every course at the post-secondary level has a list of learning objectives that are meant to advance the students’ understanding of the overall program’s objectives. We contend that within mathematics teaching programs, we can design and deliver data science content that still meets the course learning objectives while also conveying relevant data literacy concepts. For example, within a teaching methods course, our learning objectives are often pedagogical in nature (i.e. how to teach mathematics content). To engage students in meeting those pedagogical goals, data science concepts can be the content in which preservice teachers engage in those pedagogical goals (i.e. writing a lesson plan over a data science concept). Additionally, mathematics teacher education programs often contain content courses that have learning objectives to develop preservice teachers’ mathematical knowledge for teaching (Ball, Thames, Phelps, 2008); namely, the specialized content knowledge required to teach mathematics. Data science could also be a topic covered to support preservice teachers in developing this knowledge. Based on our pilot project, course content can be changed moderately to meet both objectives in single courses, and we believe that this approach can be successful in multiple courses.

To advance our mission of preparing teachers to teach data science in K-12, we intend to further develop our modules as the field of data science and AI evolves to meet the needs of current and future teacher learning. We also intend to expand our modules to a full-length course in data science and create smaller modules that can be used to introduce and develop data science content in other relevant mathematics teacher education coursework. To bring our vision to fruition, we will eventually expand our modules to meet the needs of teachers other than those of mathematics–computer science, general science, elementary, and other content area teachers also will likely have opportunities to teach coursework in data science at the K-12 level and it is important to prepare them as well. Finally, we would like to expand our efforts in the future by providing professional development opportunities or graduate level coursework for in-service mathematics teachers. To reiterate, the conversation needs to start somewhere, and we feel we are in a position as mathematics teacher educators to begin that conversation through the development of curriculum materials for preservice teachers.

“All-Hands” Approach to Data Literacy. Because AI has such great potential to transform every aspect of society, data science and data literacy instruction at the primary and secondary levels will require a similar transformation. We don’t know what the future holds for data scientists in terms of the problems and goals they will have, which means the goals for data science education will have to adapt and change as the field progresses (Rosenburg & Jones, 2023). This will necessitate an “All Hands” approach to accomplish such a sizable task–all disciplines will be affected eventually, and thus teachers across all disciplines will need to be prepared for those changes. We are beginning the task of adapting preservice mathematics teacher curriculum as the “tip of the spear” effort to accommodate the coming changes due to AI, whatever the scale of those changes may be. We conclude with a call for partners: we would be delighted to partner with in-service mathematics teachers who desire to join the effort to better prepare our students for the future in which AI is a prevalent reality.

This article is based upon work supported by the Iowa Space Grant Consortium under NASA Award No. 80NSSC20M0107.

References

Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. Association of Mathematics Teacher Educators. amte.net/standards

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554

Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Perez, L., & Spangler, D. A. (2020). Pre-K–12 guidelines for assessment and instruction in statistics education II (GAISE II): A guideline for precollege statistics and data science education. National Council of Teachers of Mathematics. https://www.amstat.org/asa/files/pdfs/GAISE/GAISEIIPreK-12_Full.pdf

California Department of Education. (2023). Mathematics framework for California Public Schools: Kindergarten through grade twelve (Mathematics Framework)

Drozda, Z., Johnstone, D., Van Horne, B. (2023). Previewing the national landscape of K-12 data science implementation (National Academy of Sciences, Engineering, and MedicineFoundations of Data Science for Students in Grades K-12: A Workshop). https://www.nationalacademies.org/event/09-13-2022/docs/D16254F310D01BBDA873920E4EFB8151F2D8334181AA

Engel, J. (2017). Statistical literacy for active citizenship: A call for data science education. Statistics Education Research Journal, 16(1), 44-49.

Gould, R. (2017). Data literacy is statistical literacy. Statistics Education Research Journal, 16(1), 22-25.

Louie, J. (2023).Critical data literacy: Creating a more just world with data (National Academy of Sciences, Engineering, and Medicine Foundations of Data Science for Students in Grades K-12: A Workshop). 3https://www.nationalacademies.org/event/09-13-2022/docs/D16254F310D01BBDA873920E4EFB8151F2D8334181AA

National Academies of Sciences, Engineering, and Medicine [NASEM]. (2018), Data science for undergraduates: Opportunities and options. National Academies Press.

National Academies of Sciences, Engineering, and Medicine [NASEM]. (2013), Foundations of data science for students in grades K-12. National Academies Press.

Rosenburg, J. M. & Jones, R. S. (2023). A secret agent? K-12 data science learning through the lens of agency (National Academy of Sciences, Engineering, and Medicine Foundations of Data Science for Students in Grades K-12: A Workshop). https://www.nationalacademies.org/event/09-13-2022/docs/DD667E469D0EC5DD91A7D85BC839A9852491A3CF9F15

Resources

Bootstrap: Data Science: https://www.bootstrapworld.org/materials/data-science/

CourseKata: https://coursekata.org/

Introduction to Data Science: https://centerx.gseis.ucla.edu/idsucla/

Iowa Course Descriptions Search: https://nces.ed.gov/scedfinder/Home/Search

Skew the Script: https://skewthescript.org/ap-stats-curriculum

YouCubed: https://www.youcubed.org/

How to Consistently Garner Students’ Attention, by Brooke Fischels

Wendy Weber — Thu, 06 Oct 2022 20:13:39 GMT

Despite our best efforts to actively engage our students in mathematical thinking, there are times when all you see is a sea of blank stares and the sound of crickets. In Fall 2022, I used an ICTM Travel Grant to attend the NCTM Annual Meeting & Exposition in Los Angeles, California in search for some guidance to increase student engagement. Throughout the conference, I listened to speakers share ideas on how to consistently garner students’ attention - every period. What I learned is not new, but perhaps assembled in a new way for me. I will share some of the highlights.

Iowa State University Professor Ji-Yeong I adeptly points out that students work best when they are competing and content is delivered hands-on. Their engagement is more natural and curious when the setting doesn’t seem to be a math task. For instance, the launch to one of her Algebra 2 geometric sequence lessons was asking groups of students to fold chart paper as many times as possible. They made predictions about how many times they could fold it and how small they could get the paper. I can visualize just how excited my own students would be to engage in this activity and have tangible results to build mathematical ideas on. Their enthusiasm would get them invested in the task and they would be able to connect the things they were doing in class with mathematical concepts.

Robert Kaplinsky shared the hallmarks of unforgettable lessons. One such characteristic was problems with unexpected results cause us to shift our thinking, and hence, making the lesson more memorable. Making mathematical ideas “stick” came from Chip Heath and Dan Heath’s book, Made to Stick: Why Some Ideas Survive and Others Die… I imagine that in the lesson described above about folding chart paper in half, students are surprised by their limitations and it assists in the memory of the experience.

As a teacher of many emerging English learners, I appreciated Iowa State University Professor Ji-Yeong I’s guidance on providing 5-Act Tasks. This is a take on Dan Meyer’s 3-Act Tasks, but in addition to Acts 1, 2, and 3, there was a new Act 0 where vocabulary is intentionally discussed or missing prerequisite skills are demonstrated just-in-time for the learning. There is also an Act 4 where students debrief what was learned and spend more time formalizing notes on vocabulary or the mathematics used. I wholeheartedly believe that all students would benefit from this practice and will make plans to incorporate the additional acts into my lessons in the future.

Finally, Dan Meyer enlightened teachers on his critique of calling errors “mistakes,” when in many cases they were unlearned knowledge about a subject. Especially when students are new to a concept, many of their errors were not mistakes. (Mistakes were defined as not answering the questions in which students were asked to solve.) In many cases, they had oversimplified the problem and weren’t even aware of characteristics or conventions that make some problems unique. He illustrated many examples and used them to explain why students think they are “so bad at math,” when in fact, math education has created a culture where natural inquiry, curiosity, and trials are not prioritized. Students feel a need to be perfectionists because that’s what we have lead them to believe, even though that is not the way we approach science, language arts, or social sciences where questioning, drafts, and experimentation are regularly used and valued. The lesson here is that we don’t want to undo all of the good work we are doing by labeling undeveloped thinking as mistakes.

Finally, I appreciate the efforts of ICTM for getting math teachers to conferences to be life-long learners to hone a craft that is never going to be perfect, but can be perfected every year and every lesson along the way.

Brooke Fischels

Mathematics Department Chair and Mathematics Teacher

Ottumwa High School

Ottumwa, Iowa

Welcome back to school for 2022-2023 from the IDE Mathematics Consultant

April Pforts — Sat, 03 Sep 2022 16:42:25 GMT

Welcome back to school for the 2022-2023 Iowa school year!

It is my honor and privilege to serve the state as the mathematics consultant at the Iowa Department of Education. One of the unique privileges this role has, is to belong to the professional organization, the “Association of State Supervisors of Mathematics,” which is also known as ASSM. ASSM is similar to the National Council of Teachers of Mathematics or NCTM and National Council of Supervisor of Mathematics or NCSM. Each of these professional organizations provides the collective efficacy for mathematics educators across this nation to improve student outcomes, or as I like to call them, students’ hopes and dreams for their futures.

Did you know that Iowa has an affiliate of each of these organizations, well not for ASSM because that would be a group of just myself, but they do for NCTM and NCSM, which are known as the Iowa Council of Teachers of Mathematics (ICTM) and the Iowa Affiliate of the National Council of Supervisors of Mathematics (IA-NCSM). These organizations work in tandem to provide professional learning communities and opportunities for mathematics educators across the state. This means that ICTM and IA-NCSM are the collective efficacy for Iowa mathematics educators to improve student outcomes in mathematics so students can fulfill their hopes and dreams without mathematics being a barrier.

The collective efficacy of ICTM and IA-NCSM, make these two organizations two of the most important organizations in Iowa mathematics education. This fact is why I serve as the secretary for both ICTM and IA-NCSM and these organizations are so very near and dear to my heart. Another very significant reason that these professional organizations are extremely important is because they help to recognize the state finalists for the Presidential Award of Excellence in Mathematics and Science Teacher or PAEMST. This is the highest honor and recognition that a mathematics teacher can receive! Did you know that the state awardees, funded from the national level, also get a trip to Washington, D.C., and $10,000 to use any way they choose?

See the 2022 ICTM Conference information below and my “Call to Action,” and I will look for YOU on October 15 for the best ICTM Conference ever! Lastly, I want to say “THANK YOU!,” for continuing to teach so students can fulfill their hopes and dreams without mathematics being a barrier. “I appreciate YOU!,” and all you do to be part of the collective efficacy! Humbly at your service~April Pforts, IA’s State Supervisor of Mathematics, april.pforts@iowa.gov

1.ICTM Conference – October 15

a.Join ICTM

b.Register for the Conference – 4-nationally recognized speakers

c.Spread the Word: Flyer, Facebook, Instagram, Twitter

2.IA-NCSM – October 15

a.Join IA-NCSM

b.Conference Sessions

c.Save the Date – Relicensure Credit

3.PAEMST – Open now

a.Nominate an educator

b.Apply yourself

c.Find Iowa Awardees

Call to Action:

1.Join one or both ICTM and IA-NCSM today!

2.Plan to attend the conference on October 15!

3.Spread the word on social media!

K-3 Number Sense PD by Brenda Kelly, AHSTW CSD

Wendy Weber — Tue, 14 Jun 2022 15:35:15 GMT

Our students at AHSTW were struggling with learning Number Sense in the Primary (K-3) grades. We were also looking to purchase a new math curriculum. In order to educate our staff and make sound decisions for our students, it was decided that we needed to learn more about the eight mathematical practices. The Primary Building Principal and the three building-level instructional coaches began to build professional development around the book Principles to Actions, Ensuring Mathematical Success for All, by the National Council of Teachers of Mathematics.

The learning for the leaders of the professional development began by reading the book. Then, we had conversations about what we wanted the goal of the learning for our teaching staff to be. We determined that the target audience would be all primary teachers, those intermediate teachers (grades 4-8) who teach mathematics, plus any high school mathematics instructors. The goal would be to inform teachers about the eight effective mathematical practices as defined by the National Council of Teachers of Mathematics, and help them learn ways to implement the practices into their daily math lessons. It was determined that this learning would take place during the monthly professional development held on-sight at the district level.

We began in October by sharing the Eight Mathematical Teaching Practices with our group of math teachers. We asked them which, if any, they were using in their classrooms currently, and which they felt would be valuable in a new curriculum. As part of this conversation, we asked teachers to think about their experiences as a learner in mathematics as a child.

In November, we did a brief review of the 3 Key Shifts in Mathematics. The team determined that we needed to review the Key Shifts in order to assure that all math teachers were keeping those ideas at the forefront of their learning as we integrated the concepts of the effective teaching practices. We wanted to make sure that our teachers were aware of best practices when it came to how students learn mathematics and were able to apply that learning.

Once we finished that review, we moved into learning about building procedural fluency from conceptual understanding. With the Common Core Standards came a new understanding of the term “fluent”. Several of our teachers were still struggling with this new definition. We determined that this concept needed more exploration to understand. During this month’s professional development, we spent a lot of time using different models and explanations of fluency to help teachers grasp that “fluent” does not simply mean “fast”. About half of the November professional development time was spent focused on the concept of fluency. This is an area that we are still working to develop, district-wide.

During our January meeting, we determined that we needed to refocus on the “why” behind our professional development for this year. Teachers were hitting that mid-year slump and needed a refresher to motivate them as to why we were pursuing this learning opportunity. After we reviewed that, we touched briefly on the importance of making sure that students were given the opportunity to learn math in a sequential manner. The idea of concrete to pictorial to abstract made a lot of sense to our primary teachers, but was a real stretch, and even met with resistance from our middle school and high school staff. They were not ready to hear that eighth and ninth graders, much less students beyond that, needed to use manipulatives to understand abstract concepts in math class.

This month we also focused on two more of the instructional strategies. We choose to cover implementing tasks that promote reasoning and problem solving and supporting productive struggle in learning math. We knew these were going to be two difficult ones to grasp, but felt they went well together. We tied in a couple of different ideas to the discussion around productive struggle to help them understand that students NEED to struggle to learn! This is where many teachers want to help students too much, yet it’s where students need to spend some time as that’s where the learning actually happens.

February professional development was amazing! For whatever reason, maybe it was the one where teachers felt like they had something they could take right back to their classrooms and use, or maybe we, as presenters, were more comfortable with this content, but this was when teachers started making connections and starting giving terrific feedback to us as presenters. The strategies of using and connecting math representations, facilitating meaningful math discourse, and posing purposeful questions, allowed us to pull in a variety of different strategies that our area education association (AEA) professionals had shared with us that we thought were very useful.

We used a variety of examples of the Lesh Model for teachers to have students share their answers. Our transitional kindergarten and first grade teachers did an outstanding job of using this in their classrooms! We also used the website “Which One Doesn’t Belong?” to model how to facilitate math discourse and pose purposeful questions. At the end of this presentation, we included a resources page that allowed teachers to go back to their classrooms and use some of the tools that we had used throughout the day. Even though it was a dreary day in February, the feedback was terrific, and teachers were getting excited about what they were learning!

The team felt like we had great momentum going into the professional development day for March, however, we also knew that it was going to be the last day of learning about the effective practices for math for the year. We only had one practice, elicit and use evidence of student thinking, left to cover, but we wanted to make sure that we left on as high a note as last month, and that people were motivated to continue to implement these strategies in their classrooms.

We spent some time at the beginning of the day discussing and writing learning goals and success criteria. As a district, we follow the CRISS Framework for Teaching and Learning, so throughout the professional development, we wanted to make sure that was also part of the focus as we thought about lessons and how they are laid out. We also wanted to encourage teachers of math to focus not so much on the right answer, but rather on how students arrived at their answer. Did you add first, or multiply? Were you wanting to put things into groups, or separate the groups? Tell me more about what you are thinking … Encouraging students to explain their thinking instead of focusing on the answer is a huge part of the last effective practice. If we can get them to explain their thinking, then we can build on what they already know to help them learn from there. Also, it helps other students to know how they got to their answer, whether the answer is right or wrong.

The time ended with a review of the eight effective teaching practices. We provided some time to think and discuss about what they had learned and what they were going to do with their new learning, and how they were going to transfer their knowledge to their classroom. Again, we provided a slide of resources, as that seemed to receive a lot of positive responses from the last session.

I mentioned that teachers did implement some of the strategies that were suggested in our presentations. Several of them have read various parts of the book as we were presenting the strategies throughout the year. Our FAST math results do not reflect whether or not our students are impacted by our professional development this year.

In the school year 2020-2021, our kindergarten students fell by 10% proficiency from fall to spring on the FAST earlyMath composite. However, the kindergarten only fell by 4% on the same test in the same time period in the 2021-2022 school year. The AHSTW first grade students gained 4% proficiency from fall to spring on the FAST earlyMath composite in the 2020-2021 school year but gained 6% proficiency in the 2021-2022 school year. Similarly, the second grade was 20% more proficient in the spring of 2021 than in the fall of 2020 on the FAST Math automaticity assessment but was 25% more proficient in the spring of 2022 than in the fall of 2021. Third grade however, showed the most loss. They fell by 1% proficiency from fall 2020 to spring of 2021 on the FAST Math automaticity assessment. The scores on the fall of 2021 fell significantly, by 10%, to the spring of 2022 for the third grade.

Overall, we made growth, however, it is not consistent, and it is not all above 80%. There is also not enough information to tie the results we received to the professional development that we presented. It could have been the changes in something a teacher did or did not do in a classroom. We would need more information to be able to draw a conclusion like that. We have now adopted a new curriculum, and we are eager to see if we see scores above 80% to show that our universal tier is working.

Happy New Year! by Angie Shindelar

Wendy Weber — Sun, 09 Jan 2022 21:56:23 GMT

Happy New Year ICTM Members!

As the new ICTM President, I want to wish everyone well as we welcome 2022! I thought you would also enjoy a fun fact for ICTM… 2022 marks our 55th anniversary! The organization officially began in October 1967.

While our professional and personal lives continue to be disrupted with concerns over the pandemic, the ICTM Board has used the disruption as a space for reflection and envisioning ICTM for the future. We are excited about the future of ICTM and increasing the member benefits through new opportunities for professional growth and collaboration. We would also welcome your suggestions of how to improve our organization! Send your suggestions to ICTMPres@gmail.com.

Thank you for sharing your passion for math learning with students and for being an important part of their education journey.

Warmly,

Angie Shindelar
ICTM President

NCTM Virtual Conference Highlight by Lynn Selking

Wendy Weber — Tue, 30 Nov 2021 15:09:38 GMT

NCTM Virtual Conference Highlight

NCTM held their Virtual Conference Nov 17-20, 2021. The conference is structured with evening live keynote sessions, live daytime and early evening sessions and video-on-demand sessions. There are also Roundtable events where a person can meet in a Zoom meeting to talk to presenters or vendors. Vendors have exhibits. There are usually some social events or games. This year, you could sign up for a murder mystery event. Live sessions are recorded and those recordings become available within 10 days. The video-on-demand sessions are available immediately and all of the recordings are available until January 4 this year.

One of my favorite sessions this year was the video-on-demand “Build a Math Community through Social Emotional Learning.” The presenters were Rachel Mane and Ashley Taplin. You can follow them on Twitter at @ManelyMath and @AshleyPTaplin. Follow on Instagram at @ManelyMath and @TaplinsTeaching. They are both math specialists in San Antonio, TX.

The content focused on the 3 CASEL signature practices: Welcoming Routines, Engaging Practice, Optimistic Closure. They had designed a very effective recording for the conference participant. They shared some valuable resources for Welcoming Routines that you might take a peek at, such as Check-ins Compilatio and Weekly/Daily Check ins.

For Engaging Practice, they shared tools to support student discourse, such as, Try it-Talk it-Color it-Check it, Stand Talk Sit paired with Quick Write, Think-Ink-Combine & Refine, Jigsaw, Numbered Heads and Chat Stations.

They also shared some strategies for Optimistic Closure. These were Small Group One-Minute Accolade, 3-2-1 Summary, Reflective Questions, Roll your Roll, and One Word Whip Around.

Personally, I find some compelling advantages for hosting conferences virtually. Obviously, there are a number of advantages in terms of eliminating travel expenses for everyone and venue expenses for the organization.

A virtual conference sort of levels the playing field in terms of who can present in terms of available travel funds and release from work. Additionally, I do know some popular presenters who are committed to reducing greenhouse gases caused by aircraft. They have decided to decline speaking at conferences if they would need to travel by air. Another benefit is having the video recordings available for viewing during the weeks following the conference. A person does have to commit time to watching the recordings. (Pro tip: You can turn the speed up on the video to decrease the amount of time each recording takes to view.) I hope you consider attending future virtual conferences by NCTM.

Resources from the Kentucky Center for Mathematics by Lori Mueller

Wendy Weber — Tue, 23 Nov 2021 20:49:54 GMT

Are you looking for a good place to go for resources for your classroom? Kentucky Center for Mathematics has several resources available to you on their website. There are resources for Algebra including rich mathematical tasks and suggestions for implementing them. As well as instructional routines and lesson exemplars.

There are three curricular units on learning mathematics through representations. The units cover fractions, positive integers, and negative integers.

One section is printable items such as dot cards, arrow cards, number lines, and even fun math signs to hang in your room or use as a slide in a slide deck. The list of printable items is way to long to include in this message.

Those of you that teach online will find their section on virtual math resources to be very helpful, but any teacher would be able to make use of these online resources.

Also included on this site are resources for Family Math. These are things that can be sent home for families to use, or they can be used for a Family Math Night at the school.

Coaches will find a section just for them with helpful resources for your instructional coach toolbox.

This is the link to these resources. Have fun exploring!

"Seven Doors In" Summer Book Study, by Vicki Hamdorf

Wendy Weber — Mon, 09 Aug 2021 19:00:38 GMT

ICTM hosted their first book study this summer. We read the book “Seven Doors In” by Beth Rondeau Deacon. Beth is a mathematics teacher in the Keokuk High School. She spent 3 years teaching in prison and the book is about her experiences there. Teachers from all over Iowa joined the book study. The book promoted great discussions about education, diversity and prison reform. Several guest speakers appeared throughout the 6 weeks, including the director for the upcoming movie. This book study will be held again this fall. Watch for more information in future newsletters. Plans are being made for other book studies in the future!

Reflections on NCTM's Affiliate Leadership Conference by Lori Mueller

Wendy Weber — Sun, 08 Aug 2021 00:15:35 GMT

NCTM’s Affiliate Leadership Conference was held in July. There were many great sessions and like all the conferences I have ever attended with NCTM it was high quality and very interesting. The theme this year was, Courageous Actions in Leadership: Turning Talk into Meaning.

There were several presentations on a wide variety of topics around leadership, but I want to focus on two sessions.

Social Justice in Mathematics Teaching and Learning

The first session that was very thought provoking for me was the session by Dr. Robert Berry, Past President of NCTM and the Samuel Braley Gray Professor of Mathematics Education, and Associate Dean of Diversity, Equity, & Inclusion at the University of Virginia. He started out his session titled ‘Social Justice in Mathematics Teaching and Learning’ with a discussion on the difference between social justice and equity. This was a great discussion for me as I wasn’t sure that I knew the difference. This is the definition that Robert shared with us.

Access: Ensure access to and the fair distribution of human and material resources.

Participation: Creating equitable opportunities for people to access information to be fully participatory in decisions that affect their and others’ lives.

Empowerment: Supporting people’s sense of urgency in taking advantage of opportunities society affords as well as working toward eliminating all forms of oppression.

Human Rights: Acknowledging the rights inherent to each human being. Human rights include: the right to life and liberty, freedom from slavery and torture, freedom of opinion, and the right to work and education (United Nations, 2006).

So, it seems that Social Justice is much broader than just equity and that equity comes under the umbrella of social justice. What does this have to do with education? This quote from his book Mathematics Lessons to Explore, Understand, and Respond to Social Injustices gives us an idea of why this is so important.

“Teaching Math for Social Justice (TMSJ) is much more than the lessons teachers might implement in their classrooms. It is about the relationships they build with and among students; the teaching practices that help them do that; and the goals to develop positive social, cultural, and mathematics identities—as authors, actors and doers.” (p.23)

Robert tells us that by using mathematics to respond to social injustice we can

Build an informed society;
Connect mathematics with students’ cultural and community histories as valuable resources;
Empower students to confront and solve real-world mathematics as a tool to confront unjust contexts, and
Help students learn to use mathematics as a tool for democracy and creating a more just society. These points really hit home for me. If we teach with these goals in mind, we will be creating a better world for everyone.

Facilitating Transformative Conversations about Race in Education

The next session was by Jessica Stovall. Jessica Stovall is a doctoral candidate in the Race, Inequality, and Language in Education (RILE) program at Stanford University. She has received the Fulbright Distinguished Award in Teaching grant, the Stanford Enhancing Diversity in Graduate Education (EDGE) Fellowship, and the Ford Foundation Predoctoral Fellowship. Before Stanford, she taught English for 11 years in the Chicagoland area, and her racial equity work is featured on the Starz 10-part documentary series America to Me.

Jessica’s session used video clips from the America to Me series to spark conversation around racial inequities. She would show us a clip from the series and then put us into small groups to discuss the racial inequities shown in the clip. Each clip had its own questions. This sparked some very interesting discussions. People in the group noticed things that I didn’t notice, and I noticed things they didn’t. It really helped to bring awareness to issues that I didn’t realize were there. Sometimes we are so busy living life that we don’t stop to reflect on what is happening around us and we miss a lot of things. Jessica’s goal with this presentation was to give us the tools to start a conversation in our own schools and communities. This website, Participant, has the tools to start these discussions. I would encourage you to peruse this site and find all the tools that are available to you. The video clips and well as discussion guides are there for you to use.

Lori Mueller
President, Iowa Council of Teachers of Mathematics

"Asked and Answered: Dialogues on Advocating for Students of Color in Mathematics" Book Review by Kate Degner

Wendy Weber — Fri, 06 Aug 2021 19:31:36 GMT

I have recently read Asked and Answered: Dialogues on Advocating for Students of Color in Mathematics, by Drs. Pamela E. Harris and Aris Winger. I stumbled onto this resource through Harris and Winger’s podcast called Mathematically Uncensored. The book is a collection of 5 conversations around the topic of advocating for students of color in mathematics. The conversations (called dialogues) are:

Dialogue 1: An Introduction

Dialogue 2: Why Do You Want to Do This Work?

Dialogue 3: How Do I Even Start?

Dialogue 4: What Do I Do When....?

Dialogue 5: Who Do You Want to Be?

Harris and Winger (2020) wrote the book as the result of being asked the same questions over and over again during professional development workshops they lead on supporting students of color in the mathematical sciences.

Each dialogue begins with a handful (3 - 5) of pre-dialogue reflection questions. Readers are encouraged to use the space provided to physically write answers to the questions before moving on to read the dialogue. Similarly, at the end of each dialogue Harris and Winger ask post-dialogue reflection questions. In this way, this book is a resource not only of the expertise of Harris and Winger in mathematical spaces, but also a record of my own thoughts and reflections while working through this book. I hope to go back and read the book again (perhaps each summer?) and to use the pre- and post-reflection questions as a way to see my own evolution as a mathematics educator and advocate as well.

Many times throughout the book, the authors encourage you to stop reading and complete a task (google something, make a list, reflect on a particular experience), making this not just a resource to skim through and check off of your summer reading list, but a way to really reflect and grow as a human being and an educator.

Two things have stuck with me since I began reading the book. The first is a pre-dialogue question from Dialogue 2: “ Take account of your comfort. What mathematical spaces are you comfortable and uncomfortable in? How is this tied to your privileges and/or to the power you hold within those spaces?” (pg. 22) and the second is the central question for all teachers: “Who do you want to be?” (Dialogue 5).

The book is great reading for an individual, but I believe it would have a greater impact being read as part of a department or group of interested teachers. Many times I found myself wanting to ask questions relating my own experiences to the ideas addressed in the book. If anyone is interested in reading the book together please reach out via Twitter (@drkkdegner) or Instagram (@drdegnermath).

The book can be purchased on Amazon.

Let's Factor! by Suzanne Riehl

Wendy Weber — Thu, 04 Mar 2021 20:17:08 GMT

Divisibility, factoring, composing, decomposing -- these are important themes in mathematics. This article discusses those topics, but the reason I am writing about methods to factor is simply for the fun of it. I mentally factor numbers into primes as a pastime while waiting in line or confined in car. (Yes, I am a math nerd.) As a bonus, I learn as I play. I'll start with basic techniques and then share the 150 Method.

The Case to Axe State Testing by Dr. Clayton Edwards

Wendy Weber — Thu, 07 Jan 2021 17:07:37 GMT

Like most everyone else, my school year last year “ended” due to COVID-19, and I was very sad that I wasn't able to see my students again and properly celebrate how successful they were. I still provided optional assignments during that time. I got a hundred emails a day asking for feedback or to answer questions. That was great and I was happy for the communication, whether it was school related or not (I had a student email me at midnight one night with a screenshot of a movie she was watching just to let me know the main character looked like me...I love middle school), but I never realized how much I missed the student to student and teacher to student communication in the classroom until the pandemic. It was very difficult to simulate that form of communication online.

While there was a lot I missed about being at school, the one thing that I didn’t miss was having my students take our state assessment, ISASP (or Iowa Assessments previously). Not taking the test may have actually been one of the greatest successes to come out of last year. This is what I generally think about once our testing is finished…except replace “today” with “this week.”

If you don’t know me very well, you may be saying to yourself that I don’t like my students taking the test because we do poorly, which may reflect negatively on me. Maybe some sour grapes towards the test? If that was your initial reaction, you would be wrong. My students always do well on state assessments, and it isn’t because we prep or prepare for the test, but because we do things in class like collaborate, revise, justify, and struggle in a productive manner. In fact, if you look at my previous article on our initial ISASP experience, my 7th and 8th grade students scored the highest in the state of Iowa.

https://www.iowamath.org/Articles/8985018

So why would I prefer not to take the test if we do so well?

I design my class to be one big formative assessment. All of the work my students do in class helps me to make informed decisions about where each individual student should move next in his or her mathematical journey. It’s a process. I provide a task. The students experience the task. I give the students feedback along the way. Students use that feedback to improve and have a better understanding of the mathematics.

I benefit because I know exactly what my students know. I can hear their conversations. I can see their justifications. I can identify any misconceptions and intervene appropriately.

The students benefit because they have an opportunity to gather feedback and learn from the experience.

The problem with our current state test, any state tests that we have ever taken, and I assume any type of high stakes test that other states take, is that it is lacking any of these beneficial qualities.

I gain nothing from the results of these tests. I gain nothing from the experience of proctoring these tests. My students gain nothing from the results of these tests. My students gain nothing from experiencing these tests. It’s great to know that my students are “doing well.” I know I get many emails from parents congratulating us for “doing well.” I would rather be “doing well” than not, but what does “doing well” really mean? I have no idea because I don’t have the questions the students did on the test and I don't have their work and justifications from the test. Without these two items, I get the vaguest of vague feedback which is not helpful in the slightest to anyone.

I’ve heard of districts trying to analyze the data returned to them. What are they looking at? At best I can see a very general mathematical category and the number of questions my students got right or a percentile in that category. Not helpful. These categories reported are far too broad to pin down any real misconceptions. About the best I can do is peak my students’ interest and go to the Iowa School Performance Profile (https://www.iaschoolperformance.gov/ECP/Home/Index) and show them individually all the schools they “beat.” It’s awesome to be able to say that you did better than other schools, but is that really the goal? Doing this does nothing to inform my practice or help students improve.

Many districts then turn around and make arbitrary decisions based on these vague scores because using a score is simple, even if it doesn’t have a lot of meaning behind it. The MTSS process can suffer when students are placed in remedial time because of a score. Many of these students end up working on random skills and don’t make progress because you are using scores that have no substance other than a student is “good or bad” at math. What are the students to be working on? Fractions for example...that is too vague to effectively help a student improve.

This selection process based on scores goes much deeper than MTSS. For example, many years ago, we placed students into high school Algebra as 7th and 8th graders based on a single number (as I know many schools currently do). A single score. To this day I feel horrible for being a part of that decision. Sure, most of the students who were advanced did fine in high school Algebra, but I can only imagine the learning gaps that haunt them to this day that resulted from bypassing one or two full grades. If you haven’t checked the Iowa Core recently, there is a lot to process, and in hindsight, skipping that much material was an awful idea. I feel much better about the process today, as we do not look at test scores at all, but use a more standards based approach to make sure students that are advanced have shown a high level of proficiency in all mathematical standards that would be skipped.

High stakes testing has been around forever, but why does it continue? Just because we have always done it? As a method of accountability? As a way to compare schools? Maybe, although in my mind, none of those reasons has anything to do with helping students grow and prosper mathematically, which is what it should be about.

I am sure these tests aren’t going anywhere. I am not that naïve to think that something that runs so deep throughout education will go away just like that. If our students have to take the tests, could they be created to be useful and not just a time waster; something that is taken and never looked at again? Here are my recommendations:

1. Use the bare number of questions possible to feel like the standards were “covered.” The ISASP assessment had 50+ questions for math alone, and by the time my students justified everything to the best of their abilities, it took them almost three hours to complete.

2. Release the questions immediately after the test and let teachers hang on to student work. Teachers can go through the student work matched with each question to help make informed decisions, much like they would anyway in their own classrooms. Make new questions for the next year if you are worried about the questions floating around.

3. If the data that is typically collected on high stakes assessments to compare and judge is still necessary, you can still collect it regardless of the changes from items 1 and 2, although I still think this is counterproductive. Instead of pushing educators apart, work on teachers collaborating together on these assessment questions once the test is finished to better help their students improve. You can have a lot of great discussion when you have a math question and varying student work to accompany it.

If the powers that be keep mandating high stakes assessments as is, we will keep doing well. I am always proud of my students and what they are able to accomplish. Each of my students has enough personal pride and school pride to do well, even though they may not see the purpose of taking state assessments (I don’t either). Even though they will fight and claw to do the best they can, the point is they shouldn’t have to unless it will help them understand mathematics better in the long run.

Have you Heard of MTBoS and the Global Math Department? by Sarah Martin

Wendy Weber — Sun, 18 Oct 2020 23:26:08 GMT

Have you ever heard of MTBoS?

MTBoS stands for “Math Twitter Blog-o-Sphere'' and is a community of math teachers who blog and tweet. However, it’s way more than that! The MTBoS website has a directory of community members you can follow via Twitter. There is a search engine to search blogs on specific topics written by members of the community. There is also a Desmos bank to search for Desmos activities that have been made by members of the community. Another great thing about MTBoS is if you need help you can tweet with the hashtag #MTBoS. You will likely have an answer or suggestion in a matter of minutes, and if not then, at least by the end of the day.

The Global Math Department is another helpful resource. This group began with teachers who knew each other through Twitter, blogs, and Twitter Math Camp. It has since grown into a wide range of math educators who love to share their ideas with others. They have a weekly newsletter with bits of information that mainly come from Twitter. They also have a free weekly math webinar. I encourage you to explore their site and subscribe to their weekly newsletter.

Both the MTBoS and the Global Math Department have been great providers of information for me as a math teacher. They have also helped shape me into the math teacher I am today.

Sarah Martin
7th Grade Math Teacher
Shenandoah Middle School

Oh, Subtraction Hurts me! by Ed Rathmell

Wendy Weber — Fri, 03 Jul 2020 15:57:34 GMT

After a teacher asked me to talk with a second grade boy about subtraction facts, my goal was to determine how he was thinking to solve the problems. I soon found out that his strategy was to guess. He felt that he was off the hook as soon as he said an “answer.” The answer might be incorrect, but so what, …he didn’t really try. He had just guessed. Sometimes you guess right, sometimes you guess wrong.

But, his feelings became evident even before that. When I informed him that his teacher had asked me to talk with him about subtraction, he had a pained expression as he said, “Oh, subtraction hurts me!” That was one of the most uncomfortable interviews I have ever conducted. Subtraction really did hurt him, …and it was obvious during each problem I presented. He knew that he didn’t understand, and guessing was the only strategy that he had figured out yet.

Primary grade teachers have students like this every year. Unfortunately, the materials they have do not provide the kind of help that is needed for these students. Textbooks simply don’t provide enough time for most students to make sense and develop flexibility and fluency, that is, to deeply understand. The pandemic has exacerbated this problem, especially for those students.

Teachers have had an impossible job to recreate ways to teach math this past spring. It is not their fault. How do we help students make sense when we can’t be in the same room? How do we keep them actively involved? How do we know what they are thinking? How do we help them make connections? How do we know what they have learned? How do we know if some students are being left behind? How do we prepare them for success in school math next fall? …

It doesn’t make any difference if students are in our classroom, on-line, homeschooling, or on vacation. There are no shortcuts. They will not understand unless they make sense of the concepts and the reasoning strategies they can use in everyday life. Drill and practice seem like the best solution to many people, but over 75 years of research has clearly demonstrated that there are no long-term effects for most students. The focus is on the answer, not on how you can get the answer. In the 1940s, Brownell found that about 40% of all students did not even get any immediate effect. And drill and practice did nothing, for any student, to promote what we now call number sense.

Helping Students Understand Math

To make sense of math and be able to use it effectively, students need repeated experiences:

to make sense of a variety of ways to represent each concept so they have a better opportunity to recognize when that concept can be used in everyday life,
to make sense of a variety of reasoning strategies that can be used with each concept so they can efficiently use that concept with different numbers and in different contexts,
with those representations and reasoning strategies so they can be used flexibly and fluently, and
using those concepts and reasoning strategies to solve problems they will encounter in a variety of everyday situations.

These recommendations are all consistent with national and state standards. The one thing that differs slightly is the additional suggestion for repeated experiences. That comes from well-documented research on memory and learning. The reality is that students do need repeated experiences to develop flexibility and fluency in their thinking. It takes time for students to internalize new thinking so they spontaneously use it in appropriate situations.

For example, after two weeks of brief daily lessons on using ten to add and subtract in the spring of grade 2, less than half of them spontaneously used that thinking when provided the opportunity. Even though they could explain that thinking when specifically asked, they resorted to much less efficient counting in other situations. Students can receive huge benefits from extended opportunities to make sense of new concepts and new thinking. Practice in the use of new thinking is essential, if we expect students to actually use that thinking. Just because symbolic drill is not effective doesn’t mean that repeated experiences with the use of concepts and reasoning strategies is not needed.

Meaningful Distributed Instruction

Thirty-three years ago I had the pleasure of observing Marsha Bachman’s second grade math class in Grinnell. She used brief daily conceptual previews to help prepare her students for success with subtraction. These were not drill and not symbolic practice. They involved helping students make connections among concepts, manipulatives, and symbols. When I asked why she did that, she simply said, “I’ve found that it’s much easier for the kids when we get to subtraction.” Two weeks later after observing her students during the first day of instruction on subtraction, their understanding impressed me. By coincidence, I had just recently taught the same lesson using the same textbook, but with considerably more student confusion. That really got my attention!

Over the next few years, some of my undergraduate pre-service teachers and I tried similar approaches in action research studies. Altogether we covered about 20 different topics at grade levels ranging from K through grade 8. These conceptual previews led to overwhelming success. In every instance students had at least a 20% achievement advantage over students without the previews. Several of my graduate students also did action research projects for their MA papers. In each case using conceptual previews enhanced achievement with similar results.

I want to highlight one of these studies. Tammy Boeckman, a sixth grade teacher in Ft. Dodge at the time, got amazing results. After using daily conceptual previews for fractions and decimals for the entire year (no symbolic practice), her students, including more than her share with learning problems, earned a class average score of over 90% on a very comprehensive fraction and decimal assessment—two years in a row. Nationwide, eighth grade students averaged about 20% lower on very similar National Assessment of Educational Progress (NAEP) items. Despite not practicing computation with fractions or decimals, her students performed over 10% higher on computation than eighth graders typically did on similar NAEP items.

Since the late 1980s, everything I have written, both articles and curriculum, has been based on using brief daily conceptual experiences to help students make sense and enhance their math achievement. And I stressed the importance of using similar approaches in each of my teacher education classes. Since no instructional materials are organized like that, I decided to retire from teaching so I could create what I had been promoting for years. For a thorough discussion of meaningful distributed instruction, see Chapter 5, Number and Operations: Organizing Your Curriculum to Develop Computational Fluency in Achieving Fluency: Special Education and Mathematics (NCTM, 2011).

Now I have nearly completed an integrated and comprehensive collection of on-line lessons for addition and subtraction for students in grades K-3. They are currently over 1500 lessons that are:

daily,
supplementary,
brief (about 5-minutes),
conceptual,
animated,
planned with pauses after each question, and
accompanied by brief formative assessments for each expected outcome.

The pauses are designed to provide students the opportunity to think, solve, explain, and discuss their solutions, …before one animated illustration of a reasoning strategy that could be used to solve the problem is presented. The lessons are designed for teachers to use a problem solving approach to instruction. And there are enough repeated experiences for students to have time to make sense and to develop flexibility and fluency.

Brief 5-item paper-and-pencil assessments will quickly inform teachers about student progress towards expected content outcomes. A complete list of outcomes is listed at the bottom of our web site home page. Additionally, there are on-line assessments for each reasoning strategy designed to inform teachers about progress with basic facts, but more importantly, about progress on actually using the reasoning strategy being assessed. Immediately after a class has used the on-line assessment, teachers will have access to a list of students who are not yet using that strategy.

The topics include:

Counting and Comparing,
Numbers and Partitions,
Exploring With Word Problems, and
Reasoning Strategies.

The lessons are designed to help students make sense of different representations for the understandings and skills needed to use addition and subtraction. These representations include animated objects with five frames, ten frames, number lines, open number lines, tree diagrams, and part-part-whole diagrams. The animations also illustrate the step-by-step thinking that can be used with each of the reasoning strategies.

The counting and comparing lessons, not only help students learn these skills, they also address all of the common students errors. This is the underlying knowledge needed to be successful with addition and subtraction. Most of this has been created for pre-K children.

The numbers and partitions lessons help students learn to use the structure of the five frame or ten frame to solve partition problems without counting. Students will understand part + part = whole and whole – part = other part in ways that connect their knowledge about addition and subtraction, something that students often lack. This lack is partially the result of subtraction language that does not connect to addition knowledge. Also thinking of subtraction only as “take away” does not help students make those connections.

There is a section on each of the Cognitively Guided Instruction problem structures. Most of these lessons have students solve or create a word problem. The others are animated illustrations of each problem structure.

They also provide enough lessons to help students make sense of different reasoning strategies while using addition and subtraction. Each of seven different strategies has at least four weeks of lessons followed by six weeks of practice for that thinking—far more than most students will need. These strategies include counting on, counting back, counting up to subtract, using tens to add and subtract, using known facts (including doubles) to add and subtract, using nice numbers, and changing the problem to one that is easier. Additionally, estimation strategies include using front-end numbers, using nice numbers, using bounds, and using rounding.

These often overlooked reasoning strategies are crucial in helping students make progress in achievement. In Australia, bumps in achievement have been attributed to students developing new ways of thinking. For example, shortly after students learned to use ten to add and subtract, that group of students made a big jump in their achievement, as evidenced on tests. Those same reasoning strategies help with retention of basic facts. In three schools, all first and second grade students were interviewed to identify which reasoning strategies they could explain. Students who could explain a strategy beyond counting dropped about 10% in performance over summer vacation. Other students dropped over 50% in each school.

These on-line lessons are currently being provided free to anyone who registers so they can log in. You can examine the lessons and try them with your students by registering at: www.thinkingwithnumbers.com

Please encourage primary grade classroom teachers, special education and resource teachers, and perhaps most important now, parents of young children in the primary grades to try our web site with their children. It is free; it just takes a commitment to spend 5 minutes a day with your child. More importantly, it will make a difference in success with school math next fall.

Enjoy listening to your child. You can’t believe how much fun it is to hear new, but confident, and unexpected explanations.

Ed is an Emeritus Professor of Mathematics Education at the University of Northern Iowa. He is a former Iowa Council of Teachers of Mathematics President and long time member of the ICTM Executive Board.

PAEMST: What’s that? by Deb Little

Wendy Weber — Mon, 01 Jun 2020 19:48:40 GMT

Reflections from Deb Little, the 2018 PAEMST elementary math awardee

It sure is a strange sounding acronym. And this acronym is necessary, it stands for a mouthful of words! PAEMST, pronounced pam-st, stands for Presidential Award for Excellence in Mathematics and Science Teaching. Read on to learn more about PAEMST, my journey as the 2018 PAEMST elementary mathematics awardee, and why you should consider nominating yourself or someone else for this award.

What is PAEMST?

The PAEMST is the highest recognition that a kindergarten through 12th grade science, technology, engineering, mathematics, and/or computer science teacher may receive for outstanding teaching in the United States. I had never heard of it before I got nominated for it. Teachers do not go into teaching to get awards. When we read about someone getting an award we think something like, “Oh! Good for them! They must be a really gifted educator.” And then we continue about our work with children trying to do our best.

How did I become nominated for the PAEMST?

In November of 2017, Sandra (Sandy) Ubben had written and asked me if it would be okay to nominate me. Sandy is currently an Illustrative Mathematics Certified Facilitator. When I worked with her, she was a math consultant for Central Rivers AEA. To say that I was flattered to be nominated by my mentor and someone whom I consider a math educational genius is an understatement. I said, “Yes,” and didn’t think anything more about it. Then the emails from the PAEMST organization started to flood my inbox.

What happened next?

As I read over the emails from the PAEMST organization, I became a bit overwhelmed. I quickly realized that applying for this award would not be as simple as filling out a one-page application form and attaching my resume. It includes a written narrative and video recording of one’s class in action. The narrative would be a reflection of my lesson and a description of my contributions to education focusing on Five Dimensions of Outstanding Teaching:

Mastery of the content being taught in the lesson.
Use of instructional strategies that support student learning.
Effective use of assessment to support student learning.
Reflective practice and lifelong learning to improve teaching and student learning.
Leadership in education outside of the classroom.

I also learned that the PAEMST program is organized and run by the National Science Foundation (NSF) on behalf of the White House Office of Science and Technology Policy (OSTP). If chosen as an awardee, I would receive a certificate signed by the President of the United States, a trip to Washington D.C. to attend a series of recognition events and professional development opportunities, and a $10,000 award from the National Science Foundation. To be honest, I was not sure if I was worthy of such an award and decided at that point not to apply.

Why didn’t I think I was worthy?

Let’s face it. The words “excellence” and “highest honor” are a bit daunting. As a teacher, I’ve strived for excellence in my practice, but there are many lessons that I’ve reflected on that I would not describe as “excellent.” My journey as a teacher is constantly evolving. I could be described as Christina Tondevold says, “a recovering traditionalist.” In my practice of 27 years, I’ve moved from an “I do, we do, you do” approach to one that’s inverted. Now, my students grapple with a problem first and reason to find solutions in their own way. Next, class time is spent with students sharing their reasoning and sense making, asking questions of their classmates’ solutions, comparing what’s similar and different and most efficient. Conjectures are made and recorded and reflected upon in subsequent lessons. It is a flip of what went on for many years in my mathematics classroom. In January of 2015, I had taken a course offered by my AEA that gave me my first taste of the meaning of cognitively guided instruction. During the 2015 -2016 school year, Sandy Ubben worked closely with me to help me get better at facilitating this flipped version. At her request, I opened my classroom so that other educators could see these sense making learning sessions. I really felt like I was at an infant stage with facilitating this kind of mathematical learning.

What changed my mind about applying?

Right before my school’s winter break in December, I had a discussion with UNI professor, Amy Lockhart at a school event. I had taught both of Amy’s sons when they were in fourth grade. She encouraged me to apply for the PAEMST if for no other reason than to “honor the person who had nominated me.” I decided to apply and give the application process my best effort. I wanted to honor my nominator, Sandy Ubben.

What happened next?

I’m not going to lie. The application takes a considerable amount of time to complete. From January to the May 1 deadline, I spent many hours choosing a lesson video and then reflecting, writing, and revising my written narrative. I consulted with former PAEMST Awardee Annette Louk for advice on my application. I attended the online question and answer informational sessions held by the PAEMST organization. I spent hours reading research from math education leaders from sources like the National Council of Teachers of Mathematics (NCTM). Through this whole process, I learned so much about myself as a teacher because I was constantly asking myself why I do what I do in my mathematics work with students. It inspired me to dig deeper into my understanding of the practices that I had implemented in my classroom. By the time I submitted my application, I had grown as an educator.

After submitting my application, I learned that the applications are reviewed first at the state level. The Iowa State Selection Committee spends countless hours to choose 2 to 3 applicants to move on to the national level. The NSF convenes a national-level selection committee composed of scientists, mathematicians, education researchers, school and district administrators, and classroom teachers. Recommendations are sent to the White House Office of Science and Technology Policy (OSTP) for final selection.

In August of 2018, I found out that I was a state finalist along with Natalie Franke and Chris Mathews. In October, the three of us were formally recognized at the Iowa Council of Teachers of Mathematics Conference for being state finalists. In March of 2019, we were honored by Governor Kim Reynolds at a reception and luncheon in Des Moines. When I learned of the exceptional math leadership of my fellow finalists, I thought that there would be no way I would be chosen for the national award. I felt so honored to be standing alongside educators of their caliber.

When did you find out you had been selected as the national PAEMST awardee?

I had an inkling in late June of 2019. I was contacted by the PAEMST organization that they needed the FBI to do a background check. They were clear that this did not mean that I was the finalist and that saying anything about it to anyone could disqualify my application.

Then on September 27, 2019, I received an email from the PAEMST organization that I had been selected as the 2018 PAEMST Awardee and was given the steps to make flight and hotel arrangements for the recognition ceremonies and professional development events to be held from October 14 - 18. I was stunned, humbled, and so honored!

Why do I encourage others to apply for the PAEMST?

It is an excellent opportunity to reflect on the work you're doing in your classroom, to network, build relationships, learn with outstanding educators and other professionals across the country, and to be recognized for the skill and leadership with which you approach mathematics and/or technology, and science learning. You also will receive feedback from both the state selection committee and the national committee about your work. Rarely do we receive feedback from STEM leaders outside of our own districts. In addition, there is the $10,000 reward money. Unlikemost monetary awards that are earmarked for school-related use, this money can be used at your discretion. I am using it to help cover the costs to attend mathematical conferences and to take additional mathematics courses.

So how do you nominate yourself or someone else?

If you're interested in applying or nominating someone, you can find more information by visiting the PAEMST site. Every other year the award is open to either a K-6 or 7-12 teacher. The current 2020 nomination cycle is for K-6. Because of COVID-19, the application dates were adjusted. Part of the K-6 cycle application was due on May 1, and then those applicants have until October 26, 2020 to submit final applications. That would mean that the next cycle for applications will be for 7-12 STEM teachers.

What should I do while I wait for the next nomination cycle?

In the meantime, keep growing as a professional in the area of mathematics. If you haven’t already, sign up and become an active member of Iowa Council of Teachers of Mathematics (ICTM). The membership is very affordable and offers excellent resources. Become a member of NCTM so that you have cutting-edge research articles at your fingertips. Attend ICTM and NCTM conferences to learn in person from leading educators. Consider presenting at the next ICTM conference or writing a journal article for ICTM or NCTM. Invite other educators into your classroom. Learn and grow by honing your practice by working with a district math coach, a math consultant from your AEA, or a mathematics education professor from a local college. Get on Twitter (I call it my nightly P.D.) and connect with math educators across our state, nation, and world. I believe that we grow the most when we share our classroom practice and reflections with others.

Deb Little is a fourth grade teacher at Denver Community School District. She can be reached at dlittle@denver.k12.ia.us and on Twitter: @Mrs_Little_17.

Success on ISASP by Dr. Clayton Edwards

Wendy Weber — Mon, 06 Jan 2020 20:51:54 GMT

With all the fanfare leading up to ISASP, taking ISASP in April and May, and then waiting for the ISASP results, the process was draining on myself and the students. We didn’t do anything different to prepare for the assessment, but there were a lot of small events that brought on some unneeded anxiety. For example, I could tell my students were feeling the heat, as many teachers, including myself had mentioned a new and more expansive assessment throughout the school year to the students. When we took the test, students even had to deal with the Pearson person coming in and observing them testing. I have visitors from other districts come into my room regularly to check out what we are doing, so the students are used to it, but I can imagine as a student, that there is nothing like having a random stranger sit in during one of the more nerve wracking days of the year watching you like a hawk. I’ve got no problem with anyone having tattoos, but this guy had 100 of them, and my students commented that the tats were a little distracting! Students have plenty to worry about in their lives, and it was unfortunate that anything associated with ISASP stressed any of them out. The stress for myself and my students certainly wasn’t worth it, especially with the relative letdown that came when we took the test and realized that it really wasn’t a lot different than the old Iowa Assessments, and finally getting the results that didn’t help me to inform my teaching at all. All I learned is that my students did “well.”

Current 8th Grade (As 7th Graders With Me)
Proficient 66%
Advanced 22%
Not Yet Proficient 12%
State Average 60/10/30

Current 9th Grade (As 8th Graders With Me)
Proficient 42%
Advanced 49%
Not Yet Proficient 9%
State Average 61/11/28

Before you say that I have the best students already (I do love my students), both of these classes had been right at or below the state average as far back as the 6th grade. My students are improving because of what we do in class on a regular basis, and my high expectations for their learning. In this post, I will outline what I believe we do in class that makes us successful on ISASP and otherwise, and my strong recommendation for an appropriate amount of time to take the ISASP assessment, as I think this is one of the biggest misconceptions about ISASP that needs to be explained, especially to those who don’t have a mathematics education background.

I had a lot of curious people come up to me at a recent State Mathematics Leadership Team meeting and asked how my students did on the test. I let them know how well we did, and I got a lot of questions that made it sound like I had some sort of secret formula for success. Here was my “secret formula.” Avoid test prep. Avoid trying to dumb down material to work on “basics.” Avoid cramming before the test. None of these things work. Everything in this category promotes surface level learning. Students also sense when they are doing something that isn’t as rigorous as it probably should be, and worse, students know if you are giving them different material because they haven’t been successful with whatever everyone else is working on. If you think that is building confidence, it does the opposite and makes students feel worse about themselves. Special education students are no different, and I feel our special education population was successful on ISASP because I have similar expectations with them as I would any other student.

Here are some of my “secrets” I do that I would contribute to our success on this test. I am not into telling anyone how to do things in their own classrooms. Teachers are unique and should be allowed to let their uniqueness shine through. This may look different to you in your classroom than it does for me, but if you would like to talk about how this looks in my classroom, I would be happy to discuss.

Assess EVERYTHING, giving feedback to help make revisions

Anything my students do is assessed by me personally. I leave personal feedback on every assignment no matter how small or how large. I use class time to give verbal feedback as well. I want my students to have a good understanding of where they are, and I want to have a solid understanding myself of what my students know. A lot of the more informal ways of assessing don’t give me the information I need as a teacher to make informed decisions about my students’ mathematical understanding. Things like thumbs up/down, fist to five, completion points, and going over the homework as a whole class doesn't give me enough information about what a student really knows. Sure, assessing everything is time consuming, but it is worth it. Have you ever gotten to a final assessment and were surprised that your students did poorly? You may have been using one of those methods above. You should always know how your students will do on an assessment prior to the assessment because you have been giving feedback and assessing along the way. By the way, this has nothing to do with grades, just feedback.

Revisions

After I assess an assignment/assessment/task, it is always given back to a student to revise. The expectation is that revisions are made. I even work in time during class to allow for these revisions. It doesn’t make any sense to let a student move on who has only mastered 80% of an assignment. I can go over the answers with the class and pretend that the students thought through their mistakes in the 2 seconds I would give them, but I would be kidding myself. I allow for ample time for students to revise, and I will reassess after the revisions for full credit. Almost all of my students get 100% in my class because of this, and I absolutely think this is fine. I am only concerned that the content is understood and mastered. This is one reason we do so well on the ISASP assessment, or the NWEA MAP. We tie up any misconceptions right away.

Tasks to promote productive struggle

Some people shy away from 3-Act type tasks because they may take up large chunks of time, and most of the ISASP questions are more general multiple choice, which wouldn’t fit the format of a 3-Act task. I will give you an opposite viewpoint. My students excel on long and grueling tests because they have multiple chances throughout the year to develop productive struggle. They are willing to stick with something and not give up. They know how to make adjustments and persevere through tough situations. Part of fostering productive struggle is through the teacher’s questioning techniques, which obviously isn’t happening during ISASP, but another part is students utilizing strategies that they have learned to help themselves move forward when stuck. How many students have you had who have started out on fire on one of these large tests working hard and reading each question, only to revert and finish the last 30 questions in four minutes? Working on tasks that require some productive struggle can help students stick with the test for the long haul, because they are used to doing this daily in class.

Requiring justification for EVERYTHING

For anything my students do, they turn in accompanying work that gives me an idea of their level of understanding. For me, the point of assigning something is to see what they know, and if my students turn in pages of answers, I really don’t learn anything from that. I am looking for things like charts, tables, numbers with context, paragraphs, pictures, etc. I can diagnose misunderstandings much easier when students justify everything, and students feel better with their levels of understanding because they can explain it as well.

We are a 1:1 school, and while we use a lot of computer programs, we also probably use more paper than any school in Iowa. We use common programs like IXL, Buzzmath, and Desmos, and while answer are often typed onto a screen, I always check the justification to go with these question and answer screens. If you don’t require justification, 1:1 mathematics can quickly turn into a button mashing event. And you wouldn’t believe how easily students can hit buttons on computer programs and eventually get something correct….

This helps with ISASP as my students are used to showing this level of understanding for everything, including a standardized test. My students each averaged 5 pieces of scratch paper each during ISASP. Having students justify answers slows down the thought process causing students to think deeper about whether an answer is correct instead of just picking what first pops into their heads.

Longer time limits for assignments

Anyway you can build this into your classroom would be ideal. I have students that understand the mathematics at much different rates, and I have learned that it is silly to go with the one section of a book, and then move onto the next section the next day format. Some students will figure things out in a day, some will take three. When I bring this up, people always say that maybe the universal instruction needs to improve, and I wholeheartedly disagree with that opinion. When more time isn’t built in, oftentimes students move on without understanding. This happens multiple times over a student’s career putting them further behind each time until they are years behind. This takes the teacher being flexible and having multiple activities going on at once, but since I have changed to being more of a facilitator/questioner anyway, this works well. My students do well on ISASP because we have actually taken the time to make sure everyone understands each standard at a high level without moving on and leaving gaps in learning.

On the surface, ISASP appears to be untimed and very supportive of my students' everyday experience in class where they have time to think through and process problems and tasks. However, once I figured out how many questions were on the assessment, I knew I had to lobby for more time. The untimed moniker of ISASP was frustrating because it really wasn’t untimed. We had to finish the mathematics test in a day. While our district is very supportive of our needs as educators, it was probably hard for an administrator to understand that a middle school test could take an average of three hours to complete. Believe me, it sounds crazy just typing it. Couple that with administrators from our district hearing other districts say it took an average of 40 minutes for their students to take the mathematics portion on ISASP, and I could see how people could be skeptical about my three-hour time frame.

Here is my thought process. In my classroom, my students are used to analyzing a problem, thinking about their next steps to solve the problem, solving the problem, and providing justification for each problem showing their understanding. To do this for a standard mathematics problem, it may take 2 to 4 minutes. That doesn’t sound at all far fetched to me since I live it everyday in my classroom. My students have a deep understanding of mathematics because that is what I encourage. That is what the expectation is. Rewind back to ISASP. 52 questions. Each question different than the next. 2 to 4 minutes per question mimicking what we would do in class. About 500 sheets of scratch paper later. There is my average estimate of three hours to complete the test. If we averaged 40 minutes for the test, that would be less than a minute per question. I can only imagine the effort and thought going into each question would be low in that circumstance. 40 minutes seems like the more far-fetched option to me. Needless to say my middle school students were extremely successful. I am so proud of their efforts. The level of buy-in from my students was incredible.

Reading this post you may think I love standardized assessments and think about them often. I actually despise them if we are being honest. They take a long time to finish, and the results that I get don’t help me make better decisions in my classroom. Unless I can have the test questions after the test is over, and I can keep the scratch paper to match up with each question so I can examine my students’ thinking, the results don’t help me.

After participating with my role within ISASP the first year, I know I won’t be as stressed out the next time around. I plan on keeping things simple. I will continue to do the things that have worked in my classroom, that consequently translate to a deeper level of mathematical understanding, which will yield better results on these types of assessments. If I were to make a recommendation for ISASP, cut the number of questions in half. I think the state could still get the measurements they are looking for with far fewer questions, especially since the results received don’t help teachers make meaningful decisions anyway. Until the next iteration of ISASP, I will be saving my money to make an even bigger Cheez-It pyramid so the students’ will have plenty of testing fuel, for our ultra-fancy scratch paper pencils, and for the massive roll of paper it will take to cover all the walls in my room! I certainly will not be living for the next test, but rather the genuine excitement my students feel on a daily basis when a level of understanding is achieved!

UPDATE
The Iowa School Performance Profiles were recently released to the public, and our students got some outstanding news. The mathematics growth category is measured by matching students across the state by percentile on the old Iowa Assessment and comparing what they got on ISASP. For instance, all students in the state scoring at the 74th percentile on the old Iowa Assessments were compared using ISASP. We were very successful in those comparisons. We received the highest mathematics growth score in the state for both 7th grade (current 8th graders) and 8th grade (current freshman).

My students were extremely excited and proud to hear the news. There are a lot of middle schools in the state, and it is an honor to be considered the best of the best.

Before Basic Fact Instruction... by Angie Shindelar

Wendy Weber — Tue, 14 May 2019 05:00:00 GMT

Hello ICTM members! My name is Angie Shindelar and I serve on the ICTM Board as the Vice-President for Elementary. I previously taught elementary and middle school math at Nodaway Valley CSD. I am currently a Math Consultant for Green Hills AEA.

My recent articles have discussed effective instruction for addition and subtraction basic facts. You can find the articles on the ICTM website in the three previous newsletters if you are interested and missed them. In this article I continue with the basic fact theme but turn the focus to thinking about the learning progression prior to basic fact instruction. Understanding this progression and being intentional about building a foundation for basic fact instruction can ensure our students’ success in achieving fluency for addition and subtraction basic facts in a timely way. These critical understandings are important for K-2 teachers but also for teachers working with older students that are struggling to make sense of basic fact strategies fluency.

Prior to instruction in basic facts students should develop understanding of parts and wholes. There are three critical components to this work:

1) subitizing

2) knowing plus 1 and minus 1

3) composing and decomposing numbers

Below is a description of each component and a list of Iowa Core Math Standards that encompass the learning for each component.

The first critical component of developing understanding of parts and wholes is subitizing. Subitizing can be described as instantly seeing how many without the need to count. The human brain can instantly tell “how many” of up to 5 objects without having to count. Beyond 5, our brains have to break a quantity into smaller chunks. Subitizing experiences provide students opportunities to think about quantities in different arrangements and using different models. A typical subitizing experience is when a teacher quickly flashes a quantity for students to see and ask students, “How many do you see?” The teacher asks several students to tell how many they saw and how they knew how many there were. Students will describe everything from attempts to count the items individually, relating to arrangements they are familiar with, and describing smaller parts within the whole.

The quantity might be represented with a dot arrangement, a five/ten frame, or a rekenrek (number rack). Below are examples of different arrangements of a quantity. To build understanding of parts and wholes, students should experience visualizing quantities in various arrangements and with the different models.

When subitizing is a regular routine, students first become familiar with arrangements up to 5. Once the arrangements move beyond 5 the goal shifts to looking for the parts within the whole. Students learn to resist the temptation to count and instead focus on the arrangement looking for the smaller parts. For example, when shown the quantity of 6 in the arrangement below, students may agree there is 6 but describe how they knew differently. Some may see 3 and 3, while others noticed 4 and 2. By working on subitizing as a regular routine, students learn to look for parts they recognize in quantities typically up to 10.

One of the best resources for subitizing is Number Talks by Sherry Parrish. There is an entire section on subitizing with many examples of arrangements and models for quantities up to 10. This book really helped me understand the importance of providing different arrangements for each number and varying the model.

While subitizing is not specifically referred to in the Iowa Core Math Standards, it lives within the Counting and Cardinality standards. You can find references to subitizing when you read further about the standards and unpack the specific learning within them. This standard relates most closely to the subitizing work:

Understand the relationship between numbers and quantities; connect counting to cardinality. (K.CC.4.)

The second critical component of developing understanding of parts and wholes is plus 1 and minus 1. This can be tricky, because we often think of it as facts like 5 + 1 or 4 -1. However, prior to working on basic facts in this format, it is critical to build understanding of what plus 1 and minus 1 actually mean. Students in early grades spend a considerable amount of time counting and thinking about what number comes next, what is one more than, what number comes before, and what is one less than. They develop this understanding by connecting it to the count sequence and are typically successful and confident. However, when given problems like 5 + 1 or 4 - 1, too often we see students not make the connection of what is one more than, what number comes before, and what is one less than to addition and subtraction. It is often baffling to teachers as they see students counting fingers to solve.

As students are learning about these important understandings, it is critical to make explicit the connections to the language of addition and subtraction and representing with equations.

Explicitly discussing and modeling that one more than and what number comes next is written as +1 is critical to students making connections. They have to see visual models, hear the language relationship to addition and subtraction, and have opportunities to use mathematical symbols by writing equations to represent the plus 1 and minus 1 concepts.

Word problems also help students make connections to addition and subtraction. Posing addition and subtraction word problems as a regular part of students’ learning provides opportunities to use the language of one more or one less and make connections to addition and subtraction. Including connections to equations is key to this work. Here are examples of intentionally connecting the concept of plus 1 and minus 1 in word problems:

Sam has 6 toy cars. His brother gave him 1 more. How many toy cars does Sam have now?

Mei has 7 cookies. Rob has 1 less cookie than Mei. How many cookies does Rob have?

Students work on finding ways to represent the problem and solve. While sharing ways to represent, the teacher brings forward the discussion of what 1 more or 1 less means and how to record mathematically with an equation.

While plus 1 and minus 1 is not specifically referred to in the Iowa Core Math Standards, it lives within both the Counting and Cardinality and the Operations and Algebraic standards. You can find references when you read further about the standards and unpack the specific learning within them. The standards that encompass plus 1 and minus 1 are listed here:

Count forward beginning from a given number within the known sequence instead of having to begin at 1. (K.CC.2.)
Understand the relationship between numbers and quantities; connect counting to cardinality. (K.CC.4.)
Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (K.OA.1.)
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (K.OA.2.)
Fluently add and subtract within 5. (K.OA.5.)

The third critical component of developing understanding of parts and wholes is composing and decomposing numbers. Understanding that any number can be composed and decomposed in different ways is essential to later fact fluency work. For example, think about all the ways to make 6. Through exploring ways to make 6, for example, students build understanding of the quantity 6 as well as patterns and properties. Discussions of the combinations can highlight patterns like when we have 3 and 3, we can take away 1 from one group of 3 and give it to the other group of 3. So now have 2 and 4. If we again take away 1 from the group of 2 and give it to the group of 4, we now have 1 and 5, etc. Or we might highlight that 4 and 2 is a way to make 6, and we also see that 2 and 4 are shown. Exploring this brings forward discussion of the commutative property for addition.

Providing regular opportunities for students to engage with composing and decomposing numbers is essential. Discussion of students’ findings and connections to patterns and properties will deepen understanding of parts and wholes. Resources that highlight activities for parts and wholes understanding are Student-Centered Mathematics by John Van de Walle and Developing Number Concepts, Book 2 by Kathy Richardson. Here are a few activities I have assembled in this document based upon activities I have used from these resources.

In addition, the Put Together Take Apart problem type that requires finding both addends is a perfect opportunity for students to work on composing and decomposing. Below are examples:

There are 6 animals in the zoo. Some are tigers and some are bears. How many are tigers? How many are bears?

There are 7 chairs. Some are red and some are blue. How many are red? How many are blue?

Composing and decomposing numbers is specifically referred to in the Iowa Core Math Standards in the Operations and Algebraic standards. You can find more specific references when you read further about the standards and unpack the specific learning within them. The standards that encompass composing and decomposing numbers are listed here:

Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (K.OA.1.)
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (K.OA.2.)
Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). (K.OA.3.)
For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. (K.OA.4.)
Fluently add and subtract within 5. (K.OA.5.)

Note: There are first grade standards that also could be included, however I chose not to include them because the intent is to describe essential learning prior to working on basic fact strategies.

These three critical components for developing understanding of parts and wholes set students up for success as they begin formal work in fact strategies. Students that are learning fact strategies with ease and steadily working toward achieving fluency have a solid understanding of parts and wholes. Contrastly, when students are struggling with learning fact strategies and are not progressing as expected toward achieving fluency, you can almost guarantee the gap in their learning centers around unfinished learning around parts and wholes.

I am always interested in your thoughts and feedback for any of the topics I discuss in the ICTM newsletter. You can reach me at ashindelar@ghaea.org.