I recently had two exhilarating conversations with teachers I work with: one with high school teachers and the other with second grade teachers. First the high school conversation: I posted this problem on the board and asked the teachers to solve it on their own before sharing their thinking with the others. A few moments […]
There is substantial evidence that throughout the school years children benefit when parents are involved in their learning. What more could a school want than parents who are actively involved in supporting their children at home with their math homework? Well…it turns out the answer to that question is a bit more tricky that you […]
Recently I saw this post and it really got me thinking about the idea of everyone being a math person. If we are going to believe that EVERYONE can be a math person, we must also consider clarifying some things… Tradition has it that the phrase “Let no one ignorant of geometry enter” was […]
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 […]
