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.

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

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!

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

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

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:

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.

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:

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:

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

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?

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.

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:

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:

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:

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:

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:

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:

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:

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:

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, 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/