Understanding Math Pedagogy

The understanding mathematics teaching is one kind of teaching whose goal is to promote the knower to understand mathematics fully. From the understanding objection, it needs to excavate the intrinsic significance of the understanding object diligently; but from the main body for comprehension, in order to establish the relation between the knowledge and consummate the cognitive structure that is in knower's brain; Mathematics comprehension may be divided into six levels: the sensation, the image, the connection, the inference, the method, the thought; The characteristics of mathematics comprehension are the individual difference, the hierarchical and the cycle of operations; The fundamental process of mathematics comprehension is "deconstruction" and "construction"; The intrinsic mechanism of mathematics comprehension is the circulation of mathematical language, mathematical reflection and mathematics comprehension; The supreme good of mathematics comprehension is the understanding of mathematics idea and method.From the present situation of mathematics comprehension, there usually are four types: the memorial comprehension, the operational comprehension, the intuitive comprehension and the analytical comprehension, but the most main type about mathematics comprehension is the union of the problem solving, memory and comprehension(the union of the operational comprehension and the memorial comprehension). In general, student's mathematics comprehension is in the lower level in our country. There are the comprehension disabilities. The reasons for the comprehension disabilities are multiple, as follows, the improper knowledge contacts way, the improper method utilizes, the improper representation method, even the bad manners and so on.If you want to reduce student's comprehension disabilities and promote student's mathematics comprehension that, from three dimensions as follows longitudinal, crosswise and the process, you need to follow three fundamental principles as follows perception, rich and circulative in mathematics teaching;The fundamental strategies to implement these three principles mainly are the recurrence strategy, multi-representation strategy and the metacognitive problem-presented strategy and so on.Promoting student's mathematics comprehension relates closely with the evaluation about students' understanding level. From three dimensions as follows longitudinal, crosswise and the process, there are separately the CILDWI method for classifying, the concept map method for evaluating and external language method for evaluating and so on.