• Helping Students See Productive Struggle in Math as a Good Thing

    Posted by Thad Wilhelm on 4/28/2020 2:00:00 PM


    “For a math problem to truly be a problem, it must expose a lack of knowledge and promote productive struggle,” say Joel Amidon, Ann Monroe, and David Rock (University of Mississippi) and Candies Cook (Oxford Intermediate School) in this article in Kappa Delta Pi Record. But too many students think that if they struggle with a math problem, they’re deficient, even incompetent, and that can produce shame and result in them hating math. Interestingly, few adults feel shame for not being good at math (I’m just not a math person), while they’d be ashamed if they weren’t good readers. That’s because the assumption in the adult world is that math ability is innate, and math is something that’s done by people who are “smart” at it – scientists, engineers, mathematicians. 

    But in school, struggling in math classes does produce shame, and students cope in four ways: withdrawal, avoidance, attacking themselves, or attacking others. How can math teachers make productive struggle into a positive experience, minimize the possibility of shame, and help students see themselves as “doers of mathematics”? Amidon, Monroe, Rock, and Cook suggest the following:

    • Expand what it means to be a doer of math. One study described students using high-level, accurate math selling fruit outside a school, but struggling with the same math operations in class. Teachers need to bridge the gap by helping students see how math is used in everyday life and building their confidence as practical mathematicians. 
    • Use authentic, developmentally appropriate tasks. The authors mention two websites that have good problems: Illustrative Mathematics and NCTM’s Illuminations.
    • Use cooperative learning. This can foster positive interdependence, with success and failure as things that groups experience together. It’s important, say the authors, that teachers give cooperative groups “specific, public, and academic praise for students’ work with mathematics, specifically when a student productively struggles in making sense of a problem and perseveres in solving it.” 
    • See where students are on learning trajectories. Struggle is a factor of the appropriateness of the problems students are asked to solve and where students are on a learning continuum. The authors suggest the Common Core’s Coherence Map at Achieve the Core and the progressions outlined at the University of Arizona’s Institute for Mathematics and Education.
    • Redefine homework. The authors suggest two approaches: (a) framing homework as practice time (analogous to practice in sports, music, and theater), with the emphasis on trying things out, making mistakes, and not having to get everything right; (b) encouraging students to tackle “challenge problems” for homework in collaboration with classmates, putting the premium on how well they describe the mathematics in each problem and communicate with peers, versus getting the right answer. 


    Shame, Shame Go Away: Fostering Productive Struggle with Mathematics” by Joel Amidon, Ann Monroe, David Rock, and Candies Cook in Kappa Delta Pi Record, April-June 2020 (Vol. 56, #2, pp. 64-69).

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  • Interleaving in Math: A Research-Based Strategy to Boost Learning

    Posted by Thad Wilhelm on 4/1/2020 10:00:00 AM


    In this article in American Educator, cognitive scientist Pooja Agarwal and Chicago math teacher Anne Agostinelli examine the all-too-common phenomenon of students seeming to master math concepts in classroom quizzes and unit tests – and then forgetting them months later. 

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  • US students lag other countries in math. The reason likely lies in how schools teach it.

    Posted by Thad Wilhelm on 2/27/2020 8:00:00 AM

    The latest results of a respected international exam given to teenagers ranked the U.S. ninth in reading, but 31st in math literacy out of 79 countries and economies. America has a smaller-than-average share of top-performing math students, and scores have essentially been flat for two decades.

    How the U.S. compares on science, math and reading scores

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  • Steve Levitt: America’s Math Curriculum Doesn’t Add Up

    Posted by Thad Wilhelm on 11/26/2019 7:00:00 AM

    Freakonomics Radio

    Most high-school math classes are still preparing students for the Sputnik era. Steve Levitt wants to get rid of the “geometry sandwich” and instead have kids learn what they really need in the modern era: data fluency.  The high-school math curriculum in the U.S. predates the age of modern computers. Can educators and policymakers be convinced it’s time for an overhaul?

    See a related Op-Ed in the LA Times, written by Jo Boaler and Steve Levitt.

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  • Summary of Big Ideas from Learning Theory and Science

    Posted by Thad Wilhelm on 8/19/2019 4:00:00 PM

    Below are some of the theoretical and empircal underpinnings of our mathematics program.

    • Learning happens against the backdrop of existing knowledge
    • Constructing one’s own knowledge is central to deeper understanding, more generalizable knowledge, and greater motivation (Piaget’s Constructivsm)
    • Scaffolding provides prompts and hints that help learners to figure things out on their own (Vygotsky’s Zone of Proximal Development)
    • Externalization and articulation enhance learning (Vygotsky’s theory of learning in social interaction that gets internalized)
    • Reflection and meta-cognition support deep understanding
    • Learning builds from concrete to abstract knowledge – visual representation can support this progression (Piaget’s theory of cognitive development)

    List compiled by Dr. Hakim.

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  • Keith Devlin: All The Mathematical Methods I Learned In My University Math Degree Became Obsolete In My Lifetime

    Posted by Thad Wilhelm on 6/24/2019 8:00:00 AM

    Keith Devlin

    If you are connected with the world of K-12 mathematics education, it’s highly unlikely that a day will go by without you uttering, writing, hearing, or reading the term “number sense”. In contrast everyone else on the planet would be hard pressed to describe what it is. Though entering the term into Google will return close to 38 million hits, it has yet to enter the world’s collective consciousness. Stanford mathematician Keith Devlin explains what it is.

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  • How Do You Want to Be When You Grow Up?

    Posted by Thad Wilhelm on 5/28/2019 9:45:00 AM

    On Being

    Abraham Verghese and Denise Pope

    Today young people are trying to balance the question of “What do I want to do when I grow up?” with the question of “Who and how do I want to be in the world?” Physician and writer Abraham Verghese and education researcher Denise Pope argue that’s because the way we educate for success doesn’t support the creation of full, well-rounded humans. And they see the next generation challenging our cultural view of success by insisting that a deeply satisfying life is one filled with presence, vulnerability, and care for others.

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  • Eddie Woo: How math is our real sixth sense

    Posted by Thad Wilhelm on 1/10/2019 1:00:00 PM

    Eddie Woo

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  • NCTM's Principles to Actions

    Posted by Thad Wilhelm on 12/15/2018 10:00:00 AM

    The National Council of Teachers of Mathematics (NCTM) introduces Principles to Actions: Ensuring Mathematical Success for All, setting forth a set of strongly recommended, research-informed actions, based on the Council’s core principles and intended for all educational leaders and policymakers, all school and district administrators, and all teachers, coaches, and specialists of mathematics.  Click here to read the exective summary.  

    Effective Mathematics Teaching Practices

    • Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.
    • Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
    • Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.
    • Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.
    • Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.
    • Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.
    • Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.
    • Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.
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  • Mathematics Education Through the Lens of Social Justice: Acknowledgment, Actions, and Accountability

    Posted by Thad Wilhelm on 1/26/2018 12:00:00 PM

    From A joint position statement from the National Council of Supervisors of Mathematics and TODOS: Mathematics for All:


    The National Council of Supervisors of Mathematics (NCSM) and TODOS: Mathematics for ALL ratify social justice as a key priority in the access to, engagement with, and advancement in mathematics education for our country’s youth. A social justice stance requires a systemic approach that includes fair and equitable teaching practices, high expectations for all students, access to rich, rigorous, and relevant mathematics, and strong family/community relationships to promote positive mathematics learning and achievement. Equally important, a social justice stance interrogates and challenges the roles power, privilege, and oppression play in the current unjust system of mathematics education—and in society as a whole.

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