(1) If you are teaching Calculus I, out of 10 points, how many points would you give to this student and why? (2) Is this a reasonable assessment question for Calculus I?
Tad Watanabe
@tadwatanabe.bsky.social
Professor of Math Education at Kennesaw State University, Kennesaw, GA, USA.
I've been sitting in a Calculus II class where students are learning various integration techniques - u-substitution, integration by parts, trig substitution, partial fraction decomposition, etc. But so much of exercises are really just algebraic manipulation. Is that normal?
I was helping a student in College Algebra. She was working on a problem that asked her to evaluate a composition of functions u and w when x = 7, where u(x) = x^2 + 6 and w(x) = SQRT(x + 9). As she calculated, she used her calculator to calculate 7^2 + 6 and once again 55 + 9. Clearly her lack of
tadwatanabe.wordpress.com/2025/09/11/c...
Common Core Possible Revisions 5: Division of Fractions
Division of fractions is one of the most challenging topics for upper elementary/early middle school mathematics. It (and multiplication of fractions) is also one of my favorite topics to discuss a…
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tadwatanabe.wordpress.com/2025/08/01/i...
Invert-and-Multiply Algorithm for Division of Fractions
As I have discussed, in the Common Core State Standards, division of fractions by fractions is a grade 6 standard. Specifically, 6.NS.1 states: Interpret and compute quotients of fractions, and sol…
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I'm on a roll :-) tadwatanabe.wordpress.com/2025/07/24/c...
Common Denominator Algorithm for Division of Fractions
In a previous post, I mentioned that interpreting division as quotitive leads naturally to a division algorithm often called common denominator algorithm. I have written a post about that algorithm…
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tadwatanabe.wordpress.com/2025/07/21/q...
Quotitive Division of Decimals (and Fractions)
When discussing division of fractions, some mathematics educators suggest that we start with quotitive division problems. So, they may ask students to solve a problem like this: There are 12 pounds…
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tadwatanabe.wordpress.com/2025/07/17/d...
Division of Decimals (and Fractions)
As I mentioned in my previous post, multiplication and division are typically introduced in equal group situations. Thus, if 3 quantities, A (number of groups), B (group size), and C (total), are i…
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My first blog post in a long while. tadwatanabe.wordpress.com/2025/07/08/m...
Multiplication and Division of Decimals (and Fractions)
I observed 2 Grade 5 lessons that were on division of decimals recently, and they made me think a lot about division. In particular, I was wondering why we teach multiplication and division of deci…
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There is an interesting article, What is a Mathematical Concept?", by Martin Simon in the recent issue of Mathematics Teacher: Learning & Thinking. I wonder what people think about Simon's idea.