By Dr. Randall I. Charles
“First instruction” describes the teaching used to introduce new mathematics ideas to students for the first time. The instructional model used for first instruction and the fidelity of its implementation may be the most important influences on the learning of new mathematics concepts and procedures. One purpose of this paper is to describe what research has shown to be a highly effective model for first instruction called Problem-Based Teaching and Learning (PBTL). A second purpose is to dive deep into one aspect of PBTL critical to implementing this instructional approach with fidelity—supporting productive struggle.
This paper has three major parts. Part 1 describes the key elements of PBTL and explains why it is highly effective. Part 2 describes the meaning of productive struggle and identifies key ways teachers can support productive struggle. Part 3 uses a classroom example to illustrate ways of supporting productive struggle.