A Study On Supporting Problem Of Mathematical Knowledge In Physics Course

In the developing history of mathematics and physics, the two disciplines have connected and been co-dependent. They, however, were separated and independent owing to the classified modern course. Although some scholars have already noticed the effects of classified course and proposed to integrate mathematics and the science course so as to harmonize the teaching of the two courses. But the system study is lacking. In educational practice, there are some problems during high school physics learning, such as lacking of mathematics basis and the difficulty of using mathematics. Affected by the examination oriented education, the majority of the academic papers in china explore the mathematical implication skills in solving physical problems. A few research the mathematical implication in teaching physics from the perspective of mathematics and physics coordination.This research conforms to the trends of "not solely working within the discipline" and "emphasis on discipline permeating" which the fundamental education reform promotes. This dissertation, from a macro review of mathematics application in physics course to a micro analysis of the problem of mathematics application, provides a deep research on supporting state of mathematics to physics course. Firstly, we respectively do a textual and contextual analysis on high school Curricular criteria and course books in order to investigate mathematics application in physics course. Then, we do a wide questionnaire on junior and senior high school physics teachers in order to know the actual situation of it and the problems. On the basis of investigation, this dissertation further explores the problems: one, to do a experimental teaching research of adding trigonometry knowledge to see whether lacking of mathematics knowledge needs improvement; two, to do a test on the question of function graph symbolizing object movement and do an analysis on 20 subjects' verbal protocol in order to discovering the way of eliminate the problem of mathematics implication. This research finally obtains the following findings:1. In junior high school physics course criteria, there are 8 physical concepts and 3 physical rules which are required to understand and learn more of them. While in senior high school physics course criteria, there are respectively 25 and 39. What's more, the complexity of senior physics course improves in a large scale. The quantitative definition, rule and the relative exercises in the senior high school physics course books are respectively 2 times, 4 times, 4 times as much as that in junior high school course books. The teaching designs also reflect that the requirement of mathematics model ability, space imaginative ability, mathematics reasoning and analysis ability, and mathematical operation ability improves a lot compared with that of junior high school physics course book.2. The needful degree is below "ordinary" for the mathematics knowledge points which are 12 items including number, proportion, formula and geometry in junior high school physics course book; while in senior high school physics course book, there are 46 items which require a degree beyond "ordinary", which shows the mathematics knowledge during physics learning extremely expands.3. Trigonometry knowledge is universally wanted in senior high school physics learning, which greatly effects physics learning. While some mathematics knowledge in senior high school learning is also lacking, such as circular measure, permutation, combination, ordered series of numbers and some of them in junior high school learning. But these lacks do not badly affect physics learning.4. The application problems mainly focus on how to solve triangle, acute triangle function, equation, inequation, function and its image, the three-dimensional image of a solid; while such knowledge as, plane geometry, solid geometry, operation of number and equation, trigonometric function equation, permutation and combination, ordered series of numbers sum, probability has no application problems. All these "application problems" affect physics learning in a higher degree than that of mathematical base weakness. According to our analysis, the main reasons of the application problem lie on the difference between physics situation and mathematics situation. The application of mathematical knowledge in physics situation demands a new process of knowledge building.5. The teaching experiment research finds out that supplementary mathematics knowledge which highly affects physics learning can prominently improve students' physics grades; while supplementary mathematics knowledge which does not affects physics learning so prominently can hardly improve students' physics grades. Supplementary mathematics knowledge can improve female students' and the high students' physics grades more effectively.6. A research, employing verbal protocol to explore students' ability of interpreting moving graph, finds out that students can easily understand the relationship between the characteristic information of moving graph and its physics concept; while they are not capable of associating graph language with real moving situation. In addition, students tend to do point to point from two graphs comparison and then to gain individual information rather than to convert graph language into mathematical symbol language. They fail to understand the actual significance of a graph in the whole. A further research discovers that this application problem relates to the innate abstractness of teaching mathematics function.