A Study On High-school Students' Mathematical Application Representations

This research mainly takes the object by the representation of high-school students' mathematical applications. The article in carries on the summary to the domestic and foreign mathematical application' study mathematics in the foundation,had discovered that the existing researches on the characterization of high-school students' mathematics applications have no in-depth characterization of the nature revealed or is only thoroughly mostly simple migrates the lower grade findings to the high school. These are not tally with the reality. Therefore, on the basis of the research results from other subjects and the re-analysis from mathematical application, I re-interoperated of the representation state' change process in the mathematical applications solution process. Finally, I have obtained the results on representation state' change process: (1) when the problem known conditions extract information zero, nodes have not been activated between nodes without mutual association. (2) When the problem known conditions extract information on the scene, the memory about scenarios in the minds is activated, and students in the brain construct of the problem initial state. (3) When the problem known conditions extract information on explicit information, the memory about explicit information in the minds is activated. (4) When the problem known conditions extract information on implicit information, the memory about implicit information in the minds is activated and students have require input information and can construct of a completely network. (5) When the problem known conditions extract information on critical thinking, the memory about critical thinking in the minds is activated and students can extract all the information, mutual exchange of information in the minds and construct of the completely state. In fact, the problem solving process is to establish link between the states constantly changing, and finally achieve the most stable process.Subsequently, the empirical into the research stage. In Experiment 1,I use self-made table to find high-school students representational states' charge ,and sum up students'five representational states: representational state of zero messages, representational state of text messages, representational state of data and critical information, representational state of low-seated structural and representational state of deep-seated structural. Experiment 2 is on the basis of the experimental 1'results and the self-made questionnaire .Firstly I make data analysis, and make stratified random taken based on an analysis. Then, I make oral report experimentation for the students from the three levels. Finally, I find out differences of three students in characterization to the same type problems. Sum up these different and named: (1) Oral report shows that outstanding students use the concept-drive mode, bias from the overall structure. So, outstanding students are better in the speed and accuracy than medium students and poor students are obvious advantage who use data-driven mode. (2) Oral report also shows that outstanding students and medium students in solving problems will performance repeated situation, and the number outstanding students are more than medium students.In the final chapter, on the basis of the Experiment 1 and Experiment 2'conclusion, I propose corresponding strategies for existing curriculum design and teaching: (1) Teachers can use of hierarchical instructional design model in mathematics teaching. (2) Teachers should advise their students to solve problems starting with the structure of topics that includes of mathematical knowledge and mathematical methods. (3) Teachers must pay attention to the students'emotion. (4)Teachers should focus on the development of students'mathematical language sense.The article innovation lies in that research to that high school student solve the algebra application problems from the nature of problem representation.Due to the time and energy is limited; this study can only progress to here. There are a large number of issues that are needed to complete in the future. The recommendations of whether to play in the reality; how to further refinement the concept about three types of students ,main body state , and to identify the key issues characterization of the main factors. Whether the same method can be used to study other types of applications on, and so forth.