A Study On Influence Of Declarative Knowledge And Mathematical Beliefs On Problem-solving

Many educationalists think that all kinds of knowledge and skills acquired are not enough, what is more important is that learner could solve problems with these knowledge and skills. In some sense, the ability to solve problem is an important object for schooling.Cognitive psychologists sort knowledge into declarative knowledge and procedural knowledge which constitute main content of every subject in school. Confronting with 'knowledge exploration', many people think that schooling should shift from 'knowledge as center' to 'ability as center' while students should shift from 'learning the knowledge' to 'learning to learn'. Many researching domains such as 'expertise' attest by means of experiments that knowledge including declarative knowledge decides problem-solving ability of learners to a large extent and declarative knowledge could make up the limitations of so-called innate ability. All these researching result can be all applied to mathematics.Learners are not studying in a 'vacuum' environments and he or she have positive or negative beliefs toward self, subject and outer environments. In mathematical domain, schoenfeld put forward 'mathematical belief at first and think that negative belief could undermine learners' performance on problem-solving tasks. After that, many researchers think that mathematical belief must exist as a system. Many researches reveal from different point of view that learners' mathematical beliefs influence their ability to solve problem.In this article, experimental material is a judging theorem of similar triangles (two triangles is similar if two sides of theirs become a set comparison and their included angles are equal). Firstly, the theorem is divided into many parts by means of competence-components analysis and then establish one question according to one component which is used all together to measure learner' declarative knowledge about this theorem. Secondly, MRBQ(students' mathematics-related beliefs questionnaire) which was worked out by foreign researchers is tested, after being revised, it become MRBQ of this article. This questionnaire is used to measure learners' beliefs related to mathematics. Thirdly, we cooperate with some mathematical teachers to establish a test comprised of seven questions according to the theorem in order to measure learner' ability to solve problems using this theorem. There are 270 students who are grade three students in two junior secondary school of Shandong Province and...