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The Opportunity Costs of Procedures vs Understanding
For those who have followed my writing, my apologies if you’ve heard this before: I majored in math, but didn’t know why the invert and multiply rule…
Apr 21, 2024 • 
Barry Garelick
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The Opportunity Costs of Procedures vs Understanding
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Procedures vs Understanding in Math
This article is excerpted from “Math Education in the U.S.” (Chapter 10)
Sep 2, 2023 • 
Barry Garelick
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Procedures vs Understanding in Math
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Effective Math Instruction: Hiding In Plain Sight
An earlier version of this article appears in “Math Education in the U.S.” Footnotes appear after the list of references at the end of the article.
May 23, 2023 • 
Barry Garelick
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Effective Math Instruction: Hiding In Plain Sight
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Foreword for "Traditional Math" Good evidence-informed education is the new progressive!
by Paul A. Kirschner
Sep 3, 2022 • 
Barry Garelick
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Foreword for "Traditional Math" Good evidence-informed education is the new progressive!
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Thoughts on Conceptual Understanding
In a previous post, I talked about different beliefs held by math teachers and others regarding when the standard algorithm for multi-digit addition and…
Apr 23 • 
Barry Garelick
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Thoughts on Conceptual Understanding
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An Example of Contextual Understanding
Or "concepts" as they are sometimes called
Jan 13 • 
Barry Garelick
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An Example of Contextual Understanding
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Reform Math: The Symptoms and Prognosis
(Originally published in Education News, February 27, 2014; co-authored with Robert Craigen)
Feb 21, 2023 • 
Barry Garelick
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Reform Math: The Symptoms and Prognosis
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Teachers Must Be Teaching Math Wrong (Again)
I just finished reading this article in Hechinger Reports. I also just finished writing a comment about the article, which follows:
Sep 6, 2024 • 
Barry Garelick
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Teachers Must Be Teaching Math Wrong (Again)
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The Fetish Over Conceptual Understanding in Math
Conceptual understanding in math has served as a dividing line between those who teach in a conventional or traditional manner, and those who advocate…
Apr 9, 2023 • 
Barry Garelick
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The Fetish Over Conceptual Understanding in Math
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Conceptual Understanding vs Vague, Transitory Notions
“Conceptual understanding” is one of those terms, that despite many definitions that have been provided, often remains more as Andrew Old once described…
Jan 6 • 
Barry Garelick
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Conceptual Understanding vs Vague, Transitory Notions
Thoughts on Conceptual Understanding
In a previous post, I talked about different beliefs held by math teachers and others regarding when the standard algorithm for multi-digit addition and…
Mar 13, 2024 • 
Barry Garelick
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Thoughts on Conceptual Understanding
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Teaching Math With "Fidelity"
I recently saw a discussion among parents on the internet which included a note that one parent received from his son’s teacher:
Mar 12, 2024 • 
Barry Garelick
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Teaching Math With "Fidelity"
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