I’ll bet you are wondering two things: What does the title mean? What the heck is a nutria? Today I did a demonstration with a wonderful 6th grade class. We were comparing and ordering rational numbers. I grabbed this lesson from Open Up Resources. (It is an amazing free curriculum, but you might need to […]
Recently I was asked why it is important for students to experience productive struggle during a math lesson. This is a very fair question, since historically the role of math teacher has been to explain math concepts so clearly that students can’t help but understand. Why would we ever want to intentionally cause students to […]
Here are a couple of things I’m digging into: Responsive Math Teaching: https://www.gse.upenn.edu/academics/research/responsive-math-teaching Teaching Through Problem Solving: https://lessonresearch.net/wp-content/uploads/2020/07/Characteristics-of-Japanese-Mathematics-Lessons-2.pdf . . .
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 […]
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 […]
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 […]
As I continue reading through the newly revised California Mathematics Framework, I will occasionally post some of my thoughts. In Chapter 9: Structuring School Experiences for Equity and Engagement, they describe methods of teaching that enable all students to be appropriately challenged while also expanding access to rigorous mathematics for all students. Here I will […]
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 […]
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 […]