A Research On Mental Models Construction During Learning Mathematics

Teaching mathematics ought to inspire students' activity of learning, provide them adequate chances of doing mathematics, help them clearly understand and master the basic mathematics knowledge and skill, idea and method, get wide experience, by free exploring and collaborative communication. Recently, the socio-culture view on mathematics learning becomes mainstream of mathematics instruction theories gradually. Nonetheless, we are still a long way from having an integrated theoretical perspective that provides an adequate unified view of the ways we think and act. There is still, in large measure, a schism between "fundamentally cognitive" and "fundamentally social" studies of human thought and action. These bring the development of mathematics instruction negative effect.In the first section of this research, we reviewed the literatures including mathematics ability, mathematics representation, and small group collaborated learning. At the end of 20 century, the mainstream model of subject matter ability emphasizes the fundament role of "generalization", which suggest that the prominence character of think is "generalization". Being good at generalization is the trait of thinking profoundness, and of mathematics too. The Product View on mathematics nature is apt to take out the mathematical conception beyond the human's consciousness. Obviously, this mathematics generalization is experience-exceeded. Mathematics thinking is abstract thinking beyond domain. Mathematics generalization become thinking exercise. But mathematics domain is not as the imagines that their cognition performance is not effect by the domain content. Some researchers to suggest that content and context are fundamental to reasoning. Human learning is conservative, with representations that are tied to the initial learning situation. Many instances of domain-specific cognition result from domain-general processes operating on domain-specific representations. The distinction between abstract and concrete cognition often behaves as a continuum rather than as a dichotomy Furthermore, the continuum is learning related.A mental model is a representation of some domain or situation that supports understanding, reasoning, and prediction. One prominent explanation for the way people perform logical reasoning is that they form a mental model of the situation. Mental models are related to several other kinds of representational structures. One way people employ their mental models is to perform mental simulations-to imagine the future trajectory of a system given a set of initial conditions. These predictions involve qualitative estimates and often neglect some of the information relevant to thebehavior of a system. An important aspect of these mental simulations is that they are qualitative. That is, people reason about relative properties of physical systems. People do not estimate values of specific quantities, nor do they carry out mathematical simulations of the behavior of a system. Mental simulation often involves the use of imagery. Mental simulations may also have a motor component. Because the simulation process is effortful, with increasing experience people shift to using learned rules or cached results.Different kinds collaborative learning fit different learning objection. They have different construction. The all have some question need to solve and have different resolution. Collaborative learning situation must have a corporate and acceptable aim as the reward for the efforts from everybody. Some researcher investigated the function of giving/receiving explanation in small group. Pupils can't use the help they received maybe the critical factor of the irrelative between receiving help and performance. The notion than use the help they received is important is consistent with the constructivism learning view of learner constructing the new understanding. In collaborative group situation, effective construction strategies include: summary or recall the information for others, response others critical reflect question, propose t...