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Author Archives: Bill McCallum
Talking about fractions, decimals, and numbers
When students first learn about fractions, we want them to learn that they are just numbers; new numbers, but numbers nonetheless, that fit into the same system as the whole numbers they are familiar wtih. The number line can help … Continue reading
Posted in Curriculum, Illustrative Mathematics, Language
2 Comments
Ways of thinking and ways of doing
Somewhere back in days of Facebook fury about the Common Core there was a post from an outraged parent whose child had been marked wrong for something like this: $$ 6 \times 3 = 6 + 6 + 6 = … Continue reading
Posted in Standards
13 Comments
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
Posted in Algorithms
11 Comments
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
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 onedimensional, and curriculum occurs over time, some principle for ordering is necessary. … Continue reading
Posted in Curriculum
2 Comments
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
Posted in Curriculum
3 Comments
Quantity progression
The last remaining progression, the quantity progression, is here. Comments in the forums welcome!
Posted in Progressions
1 Comment
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
Posted in Uncategorized
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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.
Posted in Progressions
1 Comment
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
Posted in Curriculum
1 Comment