The Study Of Higher Mathematics Study Differentiation Points

In mathematics learning, there are some knowledge points whose learningprocess is very likely to result in a student division, which is called"differentiation point”. In the practical mathematics teaching, the differencesin the performance of students can be traced back to the emergence of learningsuccessfully or not up to some point of differentiation. For a long time, althoughmany teachers have put a lot of efforts into teaching the differentiation points,comprehensive and systematic sum maries are still not enough, so is the assessmenton psychological causes. Therefore, the in-depth study of Grade-one mathematicslearning differentiation point contributes to the improvement of teaching quality,helping students with learning difficulties and improving the training mode ofexcellent students. At the same time, since textbooks and the way teachers teachthe new curriculum have changed greatly, it also helps to explore an efficientway to train teachers.Firstly, through literature analysis, the paper describes a lot on themathematical differentiation theoretically. It defines the concept of amathematical point of differentiation, and offers a means of classification fromthree dimensions, namely teaching performance, positions as well as types ofknowledge. Meanwhile, it analyzes four characteristics of differentiation.Secondly, through a questionnaire by teachers and students and personal interviews,the paper develops appropriate indexes, identifying the differentiation pointsin Grade-one Mathematic textbook1-3(by People’s education press, Compulsory,B version), including the differentiation point that teachers and students agreeor disagree with. It also classifies them into three dimensions. Later, accordingto the responses and interviews from teachers and students on the causes ofdifferentiation point, the paper analyzes the causes of differentiation pointsthrough three aspects, which are the content and features of the differentiationpoint, the cognitive features of Grade one students as well as the teachingsituations. Based on the above, combined with the effective strategies on breaking throughdifferentiation points mentioned by teachers and students, it puts forward theteaching principles and strategies on breaking through them under the guidanceof modern education and teaching theory as well as students’ learning features.Finally, the research paradigm is given by the highest proportion ofthree-dimensional geometric point of differentiation identified in the survey.Firstly it studies three-dimensional geometric differentiation point to exploreappropriate teaching strategies, then the effectiveness of the teaching strategiesof the experimental research to test whether the causes of the differentiationpoint analysis is accurate or not and whether it is appropriate to carry out suchstrategies. I draw the following conclusions from the experiment:1. As can be seen through the several findings, differentiation certainlyshares the commonality of features;2. Due to the characteristics of the knowledge itself, the cognitive levelof students, teaching methods, points of differentiation does exist in mathematicslearning, and has impacts on students’ achievement and interest in learningmathematics;3. Through experimental class teaching practice, the analysis on causes ofdifferentiation point is appropriate, so are the teaching strategies. Mathematicaldifferentiation can be worked out. Students’ interest in learning math will beimproved with the breakthrough of differentiation point;4. The effective teaching on differentiation point is a strong starting pointfor students learning ability and creative spirit.In summary, this study wants to help front-line educators recognize thecharacteristics and causes of the differentiation point, find effective teachingstrategies. As for the breakthrough on differentiation point in the day-to-dayteaching, here come the following suggestions: investigate more complexdifferentiation points at first, figure out causes, find out a breakthrough, andmake sure about the targeted strategy with experimental research. Besides, checkwhether the breakthrough strategy is fit in with the cognitive-law and whether it can play a better role. As for how to further determine the impact of theknowledge of students’ differentiation point and what teaching strategies can bebetter able to break through the differentiation point teaching, it is necessaryfor teachers to enhance professional learning, educational research, and carryout action research and reflective practice, which is of benefit to break throughthe differentiation point and improve the quality of teaching.