Author Archives: Bill McCallum

About Bill McCallum

I was born in Australia and came to the United States to pursue a Ph. D. in mathematics at Harvard University, met my wife, and never went back. I am a professor at the University of Arizona, working in number theory and mathematics education.

Misconceptions about Multiple Methods

You may have noticed that I am back to publishing regular blog posts! My goal for now is a blog post every second Wednesday. I am now also trying to answer forum questions promptly. I want to thank the readers … Continue reading

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Curricular Coherence Part 3: Using Deep Structures to Make Connections

In this post I’d like to describe the third aspect of coherent content that Al Cuoco and I have been thinking about. In my fourth and final post on this subject I will talk about coherence of practice. A difficult … Continue reading

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Curricular Coherence Part 2: Evolution from Particulars to Deep Structures

In my previous post on curricular coherence I talked about how the principle of logical sequencing can determine the ordering of a set of topics. Since time is one-dimensional, and curriculum occurs over time, some principle for ordering is necessary. … Continue reading

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What Does It Mean for a Curriculum to Be Coherent?

Al Cuoco and I have been thinking about this question and have developed some ideas. I want to write about the first and most obvious one today, the principle of logical sequencing. I’ll write about others in the weeks to … Continue reading

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Quantity progression

The last remaining progression, the quantity progression, is here. Comments in the forums welcome!

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Catching up

The site was down for a few hours today because of a malware attack, but I think we have it fixed now. I took the opportunity to catch up on comments in the forums; I was way behind! Thanks to … Continue reading

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Geometry Progression Grades 7 to High School

It’s been a while coming, but here is the draft Geometry Progression for Grades 7 to High School. As usual, please make comments and corrections in the relevant forum.

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Transformations and triangle congruence and similarity criteria

While we are all waiting eagerly for the geometry progression I thought people might be interested in this article by Henri Picciotto and Lew Douglas on a transformational approach to the criteria for triangle congruence and similarity. There is also … Continue reading

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Yesterday’s post on the Noyce-Dana essays

I don’t think the normal notifications went out about this, so I’m adding this to let people know about the collection of essays about secondary mathematics that I posted yesterday.

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Essays from the Noyce-Dana project: clarifying the mathematical underpinnings of secondary school

In 2008–2009 Dick Stanley and Phil Daro, with the help of Vinci Daro and Carmen Petrick, convened a group of mathematicians and educators to write essays clarifying the mathematical underpinnings of secondary school mathematics in the United States. At the … Continue reading

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