Cognitive Model Of Multivariate Mathematical Characterization Of Learning And Teaching And Research

Ever since 1990s, research on multi-representations has become a hot topic in fields such as cognitive science, education with integration of ICT in education. Theme of research has also gradually shifted from experimental environment to the learning from multi-representations and with multi-representations in daily teaching environment.Likely, with integration of ICT in Mathematics instruction, representation, especially multi-representations has now become the main subject of the international group for the psychology of mathematics education (PME). However, the research on multi-representations is needed to extend both in theory and its application.In domestic, in theory some research on multi-representations in mathematics learning is discussed only in scattered research on mathematics problem-solving. In actual daily teaching and learning environment, the research of relating to the research on multi-representations such as integration of ICT in mathematics instruction which is discussed prospectively in the sight of multi-representations. Cognitive theory of learning from/with multi-representations can provide substantial theory basis for teaching with multi-representations. So, the research has value very much.The thesis consists of theory research and practical research. Triangulation research method is adopted to verify reliability and validity of the research.In theory, firstly based on the theories such as new dual coding theory, dual coding theory, cognitive theory of multimedia learning, Semiotic system of representation, CPFS theory, the thesis employs theory analysis as a main method supplemented by experience and case analysis, in order to establish a cognitive model of learning of multi-representations of mathematics and elaborate on the characteristic of cognitive process and cognitive product of learning of multi-representations of mathematics. And then, the thesis discussed significance and value of the cognitive model.Secondly, based on cognitive load theory and the cognitive model, the thesis employs theory analysis that is main method supplemented by experience and case analysis, in order to probe into significance and value of the principles and strategies of instructional design optimizing the learning of multi-representations of mathematics.In practices, firstly, the thesis employs multi-factors experiment that is main method supplemented by investigation, interview, case study and other research methods, taking learning of multi-representations of mathematics concept and worked-example in high school for examples, in order to probe into the "Ought to be" significance and value of the principles and strategies of instructional design optimizing the learning of multi-representations of mathematics.Secondly, the thesis employs quasi-experiment that is main method supplemented by investigation, interview, case study and other research methods, taking learning of multi-representations of mathematics concept and problem-solving in high school for examples, in order to probe into the "actual" significance and value of the principles and strategies of instructional design optimizing the learning of multi-representations of mathematics.The main contributions of the research are as follows:1. Pose cognitive model of learning of multi-representations of mathematics. The cognitive system of learning of multi-representations of mathematics mainly consists of two sub-systems called working memory and long-term memory. The working memory is a place where multi-representation information is processed. It may process the information into logogens and imagens, and develop from superficial code into deep code, then construct integrated code, and finally accumulatively stored in long-term memory which is made up of verbal system and non-verbal coding system. Much phenomena of learning of multi-representations of mathematics can be interpreted extensively by the cognitive model.2. Pose eight principles of instructional design for optimizing learning of multi-representations of mathematics: firstly, it poses five principles which optimize the multi-representations information: (1)information package principle: namely.try best to package multi-representations information into meaning information unit.(2)spatial contiguity principle: namely, depictive and descriptive representations should be near each other in the space, not apart from each other.(3)temporal contiguity principle: namely, depictive and descriptive representations should be isochronous, not asynchronous.(4)coherence principle: namely,try best to keep coherence between the information structure of multi-representations and the structure of mathematical object, eliminate irrelevant information.(5)double-channel principle: namely, try best to package information with double channel senses, not only with one sense channel. Secondly, it poses three principles for improving the instructional strategy: (1)strategy cognition principle: namely, try best to promote or enhance students to apply the cognitive strategy and metcognitive strategy to process.(2)positive affection principle: namely, try to create learning environment to promote students' positive affection devotion.(3)active behavior principle: namely, try to promote students to write by hand and speak by mouth.3. The outcome of the experimental research shows:(1)instructional design and strategy for optimizing learning of multi-representations of mathematics can improve the process and product of mathematical concept and worked example.(3)The student's level and level of instructional design can influence the process and product of mathematics learning significantly.(3)Compared with instructional design of static group, one of the dynamic groups is better in improving the learning process and product, and dynamic-written group is best fit for the learning of high level student, while the dynamic-teacher group is best fit for the low level student. 4. The outcome of the experimental research shows: (1)Compared with the ordinary fashion of instructional design, the optimized one can reduce cognitive load in the mathematical concept learning, and upgrade learning efficiency, although it cannot improve learning effect (understand achievement).(2)the optimized one can improve effect and efficiency of mathematical problem solving significantly, and can also reduce cognitive load.