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  • 9 Jan 2022 3:56 PM | Wendy Weber (Administrator)

    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

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


    Angie Shindelar
    ICTM President

  • 30 Nov 2021 9:09 AM | Wendy Weber (Administrator)

    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. 

  • 23 Nov 2021 2:49 PM | Wendy Weber (Administrator)

    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!

  • 9 Aug 2021 2:00 PM | Wendy Weber (Administrator)

    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!

  • 7 Aug 2021 7:15 PM | Wendy Weber (Administrator)

    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

    1. Build an informed society;
    2. Connect mathematics with students’ cultural and community histories as valuable resources;
    3. Empower students to confront and solve real-world mathematics as a tool to confront unjust contexts, and
    4. 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

  • 6 Aug 2021 2:31 PM | Wendy Weber (Administrator)

    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.

  • 4 Mar 2021 2:17 PM | Wendy Weber (Administrator)

    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.

  • 7 Jan 2021 11:07 AM | Wendy Weber (Administrator)

    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.

    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 ( 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.  

  • 18 Oct 2020 6:26 PM | Wendy Weber (Administrator)

    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

  • 3 Jul 2020 10:57 AM | Wendy Weber (Administrator)

    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:

    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. 

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