Show and tell activity (aka lecture method) may work for some but never in a mathematics class. Getting students to explain and ask questions are nice but only when the explanation and the questions are mathematical. Reasoning and justifying are good habits of mind but they are only productive if they are based on mathematical principles. Explaining, asking questions, and substantiating one’s conjecture or generalization make a productive class discussion but they are only productive for learning mathematics if the mathematics is kept in focus. Orchestrating a productive class discussion is by far the most challenging work of mathematics teaching. Stein, Engle, Smith, and Hughes* (https://doi.org/10.1080/10986060802229675) proposed five practices for moving beyond show and tell in teaching mathematics. I have always practiced them in my own teaching whether with students or with teachers and I find them effective especially when the lesson involve cognitively demanding tasks and with multiple solutions. Continue reading “How to orchestrate a mathematically productive class discussion”