(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?

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?

she has been conditioned to reach for a calculator whenever she has to compute.

Maybe this is not a big deal, but it really made me think.

ability to easily calculate 7^2 + 6 and 55 + 9 did not interfere with her answering the question correctly. But, is that OK? Should she have been able to calculate those without a calculator? She might have been able to calculate them without a calculator if she was asked to do so. It might be that

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

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…

tadwatanabe.wordpress.com/2025/09/11/c...

Critique The standards for mathematical practice in the Common Core State Standards describes “varieties of expertise that mathematics educators at all levels should seek to develop in their students.…

tadwatanabe.wordpress.com/2025/08/05/c...

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…

tadwatanabe.wordpress.com/2025/08/01/i...

Division of Fractions In the previous post, I discussed how the common denominator algorithm for dividing fractions can be derived. In one example, I shared that 7 1/2 ÷ 3/4 can be calculated as follows: 7 1/2 ÷ 3/4 = 1…

tadwatanabe.wordpress.com/2025/07/28/d...

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…

Is the common denominator algorithm enough?
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…

I'm on a roll :-)
tadwatanabe.wordpress.com/2025/07/24/c...

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…

tadwatanabe.wordpress.com/2025/07/21/q...

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…

tadwatanabe.wordpress.com/2025/07/17/d...

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…

My first blog post in a long while.
tadwatanabe.wordpress.com/2025/07/08/m...

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.

MAT programs for people with undergraduate degrees are often one year (one year plus summer?) programs. Some may be fully online.

I haven't been able to do this in great part because a lot of my connections with Japanese colleagues through that platform. I guess it is not as toxic over there.

I would love to hear more about it.

How to make the access to high-quality teacher equitable when we know not all teachers are high-quality (or equally high-quality) may be the second most important job. Should teachers be rotated every N years across different schools?

Although I agree that visual representations may be great support for students' learning, I'm a bit troubled by this image that shows numbers without any unit.

Took me while to register myself, but I think I am now registered.

Is this open to people outside of UK?

That’s more than 11,000 steps a day. When I am in the U.S., if I get to 8000, that’s a lot. When I am in Japan, I easily make 10,000 though.

There is nothing in the “old”(?) way that says you can’t work toward the correct answer.

Some are good (?) at making things sound good.

“Gradual release of responsibility” is basically I Do We Do You Do, right?