Problem solving processes in high school geometry

The theoretical basis for this investigation is drawn mainly from the information processing theories of human problem solving developed by Newell and Simon with the addition of ideas from Bernard on mathematical problem solving. Using a clinical paradigm, a descriptive study is made of the processes used by high school students while solving geometry proofs. "Think aloud" protocols for student solutions to specific problems are analyzed extensively and individual solution sequences are tabulated. The individual solution sequences are used to construct an Empirical Problem Space and the applicability of the search representation and the heuristic search methods to geometry problem solving is investigated. Regular patterns of analysis, synthesis, and heuristic usage are indicated. Existing relationships between Analysis-Synthesis-Heuristic sequences, heuristic usage, problem solving efficiency, and total solution time are discussed. Indications of the effectiveness of the early introduction of goal oriented heuristics and of optimal heuristic usage were found. Comments regarding possible applications to instruction in geometry problem solving and suggestions for additional research are included