For our second session of Embolden Your Inner Mathematician, we focus on Numeracy and Visual Learning: Elicit and use evidence of student thinking.
What is we use powerful tools to elicit student thinking? How might we learn about students to deeply understand them as mathematicians? And then, what actions do we take to ensure mathematical success for all?
This week’s session began with a gallery walk using Amy Lucenta and Grace Kelemanik’s first five Contemplate then Calculate (#CthenC) lessons found on at Fostering Math Practices.
From Ruth Parker and Cathy Humphreys in Making Number Talks Matter:
No matter what grade you teach, even high school, so-called “dot” cards (which may not have dots) are a great way to start your students on the path to mathematical reasoning. We say this because, from experience, we have realized that with dot cards, students only need to describe what they see— and people have many different ways of seeing! Arithmetic problems, on the other hand, tend to be emotionally loaded for many students. Both of us have found that doing several dot talks before we introduce Number Talks (with numbers) helps establish the following norms:
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There are many ways to see, or do, any problem.
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Everyone is responsible for communicating his or her thinking clearly so that others can understand.
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Everyone is responsible for trying to understand other people’s thinking.
To embolden mathematicians and to prepare to elicit and use evidence of student thinking, teaching teams must practice to develop the habits put forth in 5 Practices for Orchestrating Productive Mathematics Discussions.
You can see our teacher-learner-leaders working to deepen their understanding of and commitment to the Making Number Talks Matter: norms, Smith and Stein’s 5 Practices for Orchestrating Productive Mathematics Discussions, and NCTM’s Principles to Actions: Ensuring Mathematical Success for All.
How might we continue to deepen our understanding of NCTM’s teaching practices? What if we team to learn and practice?
From Principles to Actions: Ensuring Mathematical Success for All
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.
And, from Taking Action: Implementing Effective Mathematics Teaching Practices in K-Grade 5
In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners. The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy. (Smith, 4 pag.)
Worth repeating:
The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy.
We continue to foster creativity, visual and algebraic representation to strengthen our mathematical flexibility as we learn together.
When mathematics classrooms focus on numbers, status differences between students often emerge, to the detriment of classroom culture and learning, with some students stating that work is “easy” or “hard” or announcing they have “finished” after racing through a worksheet. But when the same content is taught visually, it is our experience that the status differences that so often beleaguer mathematics classrooms, disappear. – Jo Boaler
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“Seeing as Understanding: The Importance of Visual Mathematics for Our Brain and Learning.” Journal of Applied & Computational Mathematics 05.05 (2016): n. pag. Youcubed. Standford University, 12 May. 2016. Web. 18 Mar. 2017.
Humphreys, Cathy; Parker, Ruth. Making Number Talks Matter (Kindle Locations 339-346). Stenhouse Publishers. Kindle Edition.
Kelemanik, Grace, and Amy Lucent. “Starting the Year with Contemplate Then Calculate.” Fostering Math Practices.
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.
From our earlier work with 
After working through Humphreys and Parker’s strategies (and learning new strategies), we transitioned to the number string from 
The goal for the next part of the learning session offered teaching teams the opportunity to select a number string from one of the Minilessons books shown below. Each team selected a number string and worked to anticipate according to Smith and Stein’s 
