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 […]

# Tag: teaching through problem solving

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 […]