| By studying the present state of mathematics problem solving of students and in terms of emphasizing the students' initiative, self-consciousness and subjectivity in mathematics problem solving, the essay points out that the mathematics problem solving is a kind of complex thinking activity and the key factors in solving mathematics problem is the self-regulated ability of students. On the basis of making the specific definition on self-regulated ability in mathematics problem solving, first of all, the essay analyzes its essence and points out that self-regulation in mathematics problem solving is the self-consciousness of problem solvers. It belongs to subsystem of thinking regulation and it can direct, control, adjust the solvers' whole thinking process. Self-regulation dominates the whole thinking activity, also, it can reflect the level of development on solvers' thinking and intelligence. Except that, the essay chiefly sets forth the following opinions:1. Self-regulation in mathematics problem solving shows differently in different stage of the whole problem solving which includes four aspects: plan making before problem solving, practice control in problem solving, results checking before the end of activity and making remedying steps after results checking.2. The study on the self-regulated ability in mathematics problem solving is of great importance to fully understand the structure of mathematics ability. We must study the structure of mathematics ability again, put self-regulated ability into it and regards self-regulated ability as an important component of mathematics ability. At the same time, study on the self-regulated ability in mathematics problem solving not only urges us to analyze the process of mathematics studying further from a new and static point and to grasp further essence of it, but also can help students study from blindly and rigidly to strategically and more efficiently and help us to solve the problem "teach students how to study" in mathematics.3. The thinking quality on mathematics of students has obvious relevance to self-regulated ability. The essence of this relevance is a relation of cause and effect. Self-regulation is "cause" and the thinking quality is "effect". They are bothimportant component of the whole thinking structure. The thinking quality represents the top layer of it and the self-regulation represents the deep layer of it. The diversity resulting from different level on self-regulation shows in the thinking quality obviously.4. The cognitive factors of students includes the theoretical knowledge, the prerequisite knowledge and the empirical knowledge of mathematics which construct the "material basis" of the students' self-regulation in mathematics problem solving. On the base of possessing proper and necessary theoretical knowledge, the empirical knowledge and the prerequisite knowledge of mathematics are key cognitive factors that affect the students' self-regulated ability in problem solving. Besides this, the motives of students and the factors on teachers are also important factors to self-regulated ability.5. With the increase of age, the maturation of mentality and the improvement of self-consciousness, the enrichment of experiment on solving mathematics problems, students' self-regulated ability in mathematics problem solving displays the developing rule of arousing from nothing to something and from a lower level to a higher level.6.To train and improve students' self-regulated ability in mathematics problem solving, we must adopt suitable teaching strategy in mathematics teaching in order to arouse students' initiative and enthusiasm of self-regulation. Teachers should emerge their complete thought process of problem solving for students because this can provide good demonstrate for students' self-regulation in their process of problem solving. Besides this, to train students' self-regulated ability in mathematics problem solving, we can also adopt special training way. Some studies show the effect of... |
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