There are two types of assessment based on its goals or use. One is what I call assessment in the service of teaching. The second is what I call assessment in the service of learning. Assessment in the service of teaching refers to the use of assessment information to improve teaching while assessment in the service of learning refers to the use of assessment information in the form of feedback to keep the learners to the task of learning. This post is about assessment in the service of learning. Continue reading “Six ways to give feedback to students to keep them in the task of learning”
How to orchestrate a mathematically productive class discussion
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”
Prerequisite knowledge for calculus
This post describes foundational reasoning abilities and mathematical knowledge students need to develop before beginning a course in calculus.
1. Covariational reasoning
Ideas and strategies for teaching math algorithms
It is a bunch of procedures. That’s how people perceive algorithms are. And they are right. Algorithm has been defined as 1) “step-by-step procedures that are carried out routinely”; 2) “a precisely-defined sequence of rules telling how to produce specified output information from given input information in a finite number of steps”. It is no wonder then that teaching algorithms is perceived by many as teaching for rote learning and produces not conceptual knowledge but procedural knowledge. Continue reading “Ideas and strategies for teaching math algorithms”