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 […]
It seems like since the very inception of public education in the United States, we have been grappling with what good math instruction should look like. For example, in 1895 John Dewey wrote, “There is no subject taught in the elementary schools that taxes the teacher’s resources as to methods and devices to a greater extent […]
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 […]
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 […]