Reflections on Practice: Multiple Strategies = Multiple Challenges

Abstract

When teachers give a problem like “Find 3/4 of 60,” they can anticipate the ways in which students will respond. It is easy to tell whether the student knows how to do the problem and whether she or he got the right answer. The mistakes that students might make on this problem are also predictable. Other problems found in traditional middle school curricula might produce more variety in solution strategies, but usually few surprises greet the experienced teacher. Few judgments need to be made, because the strategy is either appropriate or not; and barring computational errors, the answer is either right or wrong. This familiarity with the mathematics, the problems, and potential student responses produces a desirable level of comfort for teachers, even for those who are sometimes uncertain about their own mathematical skill and understanding. It leaves them free to focus on preparing students for the next skill to be learned and assisting those students who need extra help to become proficient. What happens when the curriculum, some of the mathematics, the problems, and the solution strategies all seem new and unpredictable? What does this situation mean for the teacher and for the students?