A fundamental goal of mathematics education is to develop students’ ability to engage in mathematical problem solving. Despite our textbooks supposedly including problems labeled as “problem solving”, many teachers are uncertain how to establish a classroom environment in which students’ natural problem solving inclinations can occur. There is consensus in the mathematics education community that […]
When it comes to supporting teachers in providing good mathematics instruction for their students, the 2023 California Mathematics Framework makes it abundantly clear that there are three areas of support that we need to provide teachers. The framework calls these the Three Dimensions of Systemic Change: An assets-based approach to instruction Active engagement through investigation […]
One of the things I’ve always appreciated about teaching is that each new school year feels like an opportunity to grow, try out new ideas, and build on both the successes and failures of the previous year. Amidst the hustle and bustle of starting a new school year, I hope you can find a quiet […]
I was recently talking with several math teachers. We were in agreement that it seems students today are profoundly different from students in the past…or at least how we remember them being in the past. Compared to the “good old days”, the teachers felt students… are coming to their respective grade levels less prepared than […]
About 18 months ago in March, 2024, two black teenage girls from a New Orleans high school announced they found a new proof of the Pythagorean Theorem. What makes their proof especially impressive is that out of more than 400 unique proofs of the Pythagorean Theorem, theirs is the FIRST proof that relies entirely on […]
The report, Adding It Up: Helping Children Learn Mathematics, begins with a strong statement, “All young Americans must learn to think mathematically, and they must think mathematically to learn.” Adding It Up breaks down what it means to think mathematically into several strands of proficiency. These abilities are described as five interwoven and interdependent strands. The […]
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 . . .
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 […]