Annotated Bibliography of Resources for Educational Reform, Coherent Teaching Practice, and Improved Student Learning

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• Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist, 23 (2), 145-166. 

How can students be successful at school mathematics without understanding how to apply it to the real world? Schoenfeld reports on a qualitative study of a geometry class in which he examined the instruction and results of that instruction. The class was well managed and well taught, and the students did well on standardized tests. It appeared to be a very successful class. The author explicates how, from a mathematicians' point of view, the class may have actually done as much harm as good to the students. Specifically, he explores the way students gain proficiency at doing the procedures of mathematics without understanding. He found that the students failed to connect the processes of formal mathematics (e.g., geometry proofs) with other kinds of problems such as geometric constructions. Instead, the focus was on accurately performing a series of steps. The students believed that getting the right answer and expressing it in the right form was what counted. They believed that all problems could be solved in just a few minutes. And finally, they viewed themselves as passive consumers of others' mathematics. The subject matter was presented, explained, and rehearsed. There was little sense of exploration or of the importance of understanding. Schoenfeld concludes that reexamination of curricular goals, materials, and tests is needed if the purpose of mathematics instructionÑto help students think mathematically rather than simply master algorithmic proceduresÑis to be fulfilled. 

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