Kathy Brown

Five Dimensions of Mathematical Proficiency – Podcast Episode 16 | Podcast Episode 16

Classnotes Podcast (July 13, 2007) What does it mean to be mathematically proficient? The Committee on Mathematics Learning was established by the National Research Council in 1998. In its report, Helping Children Learn Mathematics, the committee chose the term “mathematical proficiency” to capture what it means to learn mathematics successfully. The understanding is that all students need to be on the road to mathematical proficiency beginning in pre-kindergarten. Kathryn Brown, an IDRA education associate and developer of IDRA’s Math Smart! model, outlines the five dimensions of mathematical proficiency and provides tips on helping students develop their mathematical thinking. Kathy is interviewed by Aurelio M. Montemayor, M.Ed., director of the IDRA Texas Parent Information and Resource Center.

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Show length: 18:35


“Applying Math to Children’s Lives”
by Kathryn Brown, IDRA Newsletter

IDRA’s Math Smart! Model
IDRA’s Math Smart! presents a shift in mathematical thinking for instructors, that develops the five dimensions of mathematical proficiency using scientifically-based researched strategies.

Adding It Up: Helping Children Learn Mathematics – Executive Summary
By Jeremy Kilpatrick, Jane Swafford, Bradford Findell, editors; Mathematics Learning Study Committee, National Research Council

“Learning Angles with English Language Learners: The Discipline of Noticing”
By Jack Dieckmann, M.A., IDRA Newsletter

“Can Everyone Master Mathematics?”
By Jack Dieckmann, M.A., and Aurelio M. Montemayor, M.Ed., IDRA Newsletter

Making It Count – A Call for a Coordinated Approach to Math Education
National Academies inFocus

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Show Notes

  • 01:59 Aurelio introduces the show topic, “Five Dimensions of Mathematical Proficiency” – and welcomes guest Kathy Brown, an IDRA education associate and developer of IDRA's Math Smart! model. Kathy was also a guest on Episode 13 of Classnotes.

  • 03:12 Aurelio asks Kathy to name and describe each of the five dimensions.

  • 03:37 Kathy begins by discussing the meaning of “proficiency.”

  • 04:23 Kathy explains that the dimensions work in concert, and that there is no particular order to them.

  • 04:31 Dimension 1: conceptual understanding – understanding the big idea and the big picture and being able to connect big ideas in mathematics to each other.

  • 07:45 Dimension 2: procedural fluency – doing the actual math and computation.

  • 09:01 Dimension 3: strategic competence – using different strategies and tools to represent the problem and find the solution.

  • 10:58 Dimension 4: adaptive reasoning – discussion, building reflective and logical thought, and justification of solutions. Aurelio recalls a such a discussion that students had about angles, as described in an IDRA article. Kathy explains that in this dimension, “mathematics becomes a conversation.”

  • 15:43 Dimension 5: productive disposition – a recognition by the student of the immediate value of the mathematics being learned, and an empowering feeling about that learning.

  • 16:38 Kathy explains how an understanding of the five dimensions changes how a traditional math instructor views the teaching process. Graduation expectations in math also change.