Category: BlogPosts

Learning multiplication with flashcards

Hey folks…I recently came across this article about learning multiplication facts. Here is my summary of it with some addition thought sat the end… A 2022 study from the Netherlands compared two methods of practicing multiplication facts: reciting equations displayed on a whiteboard and singing songs practicing with flash cards. Teachers used the same scripted […]

Inserting Productive Failure into your Mathematics Lessons

Check this out! Students were randomly assigned to experience 1 of 2 conditions: Productive Failure (PF), in which students collaboratively solved complex problems without any instructional support or scaffolds; or Direct Instruction (DI), in which the teacher provided strong instructional support, scaffolding, and feedback. Findings showed that although PF students generated pictorial representations and methods for solving […]

Learning to Count – part 2

In this previous post, I proposed a new way of counting things. If you haven’t already read it, please do so. Otherwise this post won’t make much sense. In that post I ended with the following problem… How many rectangles are in this 3-by-4 figure? I promised you an answer to this problem, so here it […]

Should we adopt new textbooks yet?

So yesterday I was asked a totally reasonable question: Is it time for districts to start thinking about adopting updated materials…especially since the California Math Framework has been revised. I provided an answer, but I feel like my answer changes weekly. Read on and let me know your thoughts about my response: QUESTION:  “Our district […]

Learning to Count

Counting is hard. It is far more involved than just saying one, two , three. After all, claiming that saying one, two, three means you are counting…is like claiming you can spell just because you know how to say a, b, c . Sometimes, however, counting does feel as easy as saying one, two, three. Counting […]

Designing Ambitious Instruction

As a math coach who serves schools in multiple districts, I need to be clear on what I am aiming for during my coaching. What am I helping the teacher to do or learn or improve upon? I’ve decided my focus is to support teachers implement AMBITIOUS math instruction for their students. Ambitious instruction deliberately […]