The study of six graders' problem-solving performance, teachers' problem posing and teaching beliefs in different algebra problems

This paper presents three investigations related to algebra problems; (1) Taiwanese sixth graders' problem-solving performance on story problems, word-equation problems, and equation problems; (2) Taiwanese mathematics teachers" posing sequences towards these problems and their hidden teaching beliefs; and (3) the relationship between student's performance and teachers' beliefs. These analyses revealed that sixth graders performed the best on equation problems and the worst on story problems. Further investigation indicated that although students performed better on equal ton problems, their algebraic thinking was still not well-developed. Second, about 80% mathematics teachers posed problems with the sequences of equation problems, word-equation problems, and story problems, respectively; they preferred the symbol-precedence view. They thought equation problems were easiest for students, and that word -equation problems should teach students how to directly find Hebraic solutions and the procedures of algebraic operations. They also agreed that algebraic equations were the most effective way to solve story problems and word-equation problems. The remaining teachers, who expressed a non-symbol-precedence view, believed that story problems should be taught first. Third, the comparisons showed the inconsistency between students "performance and teachers" predictions, especially those teachers with a non-symbol-precedence belief made the worst predictions.