A Research On Cognitive Organization Of Mathematical Literacy

During the development of the Literacy Education concept, Many Chinese mathematical teachers and researchers have probed the phenomena of mathematical thinking or mathematical literacy, and tried to discover how to foster it. These works prove that the process of mathematical thinking is the core of mathematical literacy. But few educators concentrated on the internal mechanism of mathematical literacy's acquiring. This caused that the specific instructional countermeasure teachers selected was based more on experience than on theory. However, many foreign researchers have deeply unveiled the process of mathematics learning and problem solving, according to theories of contemporary cognitive psychology. For example, Schoenfeld, Goldin, and De Corte analyzed mechanism of mathematics learning and problem solving, respectively. These researches are closely related to mathematical literacy, and will reinforce our theories.The author discussed the dilemma of current theories of mathematical literacy and analyzed its theoretical causes. According to the development of views of knowledge and ability, the author suggests we can foster mathematical literacy by acquiring mathematical expertise. From De Corte's perceptive of mathematical disposition, a 3-dimensioned frame of the cognitive organization of mathematical literacy was proposed. The frame includes dimensions of component, level and performance, and each of dimensions also consists of many elements. Furthermore, the author emphasizes the interaction among the elements, because mathematical literacy is a comprehensive system.To test the feasibility of the frame, the author conducted some empirical researches by the methods of interview, questionnaire and case study. The results implied that (1) mathematical literacy education should derive from everyday classroom; (2) selecting appreciate form of instruction should be in light of components of mathematical literacy's cognitive organization; (3) scientific teacher training should help teachers to make informed decisions rather than train them to perform in a specified way; (4) assessment should be reformed to adapt mathematical literacy education.