| The overall purpose of the present study was to determine if there was a relationship between Situated-Problem-Based Instruction (SPBI) and students' mathematical cognition. Further, we also wanted to advance a kind of theory conductive to students' capacities such as to pose mathematics problems, to solve problems with real situation, or to solve problems creatively.From some international mathematical performance tests reports (e.g. IAEP, 1992) and cross-national studies (e.g. Stevenson et al. , 1990; Stevenson &Stigler, 1992; Stigler, Lee, & Stevenson, 1990; Cai& Silver, 1995; Cai , 1995, 1998, 2000) we could find that there were differences in many aspects of our students' mathematical cognition. These differences showed that our students performed significantly better on routine tasks assessing computation and simple problem solving than on tasks assessing complex problem solving, the use of mathematics to solve problems related to real life, and creativity.As we knew, problem was the motive force of invention. And problem-posing was the generative aspect of mathematical thinking. A number of researchers had conducted investigations to compare the performance of students' problem-posing and problem-solving. The findings of theses studies(e. g. Cai , 1998; Bikai Nie, &Bingying Wang, 2000)provided evidence that, while our students outperformed on problem-solving tasks, the result was not the same on problem-posing tasks.Because most students learned mathematics and developed increased mathematical capacities only when they participate in instruction focused on rich and worthwhile mathematical activity. However, in the circles of mathematics education, there was a universal sense, that is: our mathematical education loses contact with reality; students solve problems not related to real life; the mathematical activity students conducted mostly focused on memorization and mechanical use of procedures rather than the use of mathematical knowledge and tools to explore patterns, frame and solve problem, etc..But how to change this situation ? Or how to change those aspects of our mathematical curriculum and teaching practice that inhibit high-level mathematical cognition? As the key role mathematical problems playing on students learning, we put forward a proposal which focusing on the problems students engaging with on mathematical class, that is: a) encourage students posing mathematical problems, b) set mathematical problems in contexts related with students' daily life, c) providestudents opportunity to solve complex problems.In order to probe the effects of SPBI on students' mathematical cognition, this study focused on two instruction experiment(Part III), one was .called Unit-Theme- Situation Experiment which created problem situation according to a unit theme; the other one was called Mini-Situation Experiment which created problem situation according to individual class. The following hypotheses were examined:1. Students receiving SPBI will perform significantly better than students receiving instruction traditionally on tasks assessing problem-posing.2. Students receiving SPBI will perform significantly better than students receiving instruction traditionally on tasks assessing the use of mathematics to solve problems related to real life.3. Students receiving SPBI will perform significantly better than students receiving instruction traditionally on tasks assessing creatively problem-solving4. Students receiving SPBI won't perform significantly better than students receiving instruction traditionally on routine-tasks assessing computation and recall of basic facts.We developed two cognition assessment instruments (CAI), one called Tasks I is for Unit-Theme- Situation Experiment, and the other one called Tasks II is for Mini- Situation Experiment. Each of the two CAI involved a variety of mathematical tasks to capture the aspects of students' mathematical cognition related with hypotheses described above.The performances of students on Tasks I confirmed the third hy...
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