Investigation On The Current Situation Of Mathematical Reasoning Ability Of Senior One Students And Research On Teaching Design ——Based On MPCK Theory And New Curriculum Standard

The current "ordinary high school mathematics curriculum standard" puts forward the idea that "deductive reasoning" and "reasonable reasoning" should develop simultaneously,and the training goal of mathematics curriculum clearly puts forward to cultivate students' reasoning ability;Reasoning ability is the basis of analyzing and solving problems in mathematics,and it is an important part of the core literacy of the six mathematics disciplines.Therefore,mathematics teaching should pay more attention to cultivating students' reasoning ability.MPCK theory is the core knowledge that mathematics teachers should have in the field of mathematics teaching,that is,the knowledge of mathematics teaching.Although there have been a large number of studies on MPCK at home and abroad,most of them are differences studies with teachers as the research object.This study takes senior one students as the research object,and strives for mathematics teachers to select different PK(knowledge of general teaching method)to improve the process of knowledge generation and transformation in mathematics classroom on the basis of in-depth understanding of MK(knowledge of mathematics discipline)and CK(knowledge about mathematics learning),strengthen students' understanding and application ability of knowledge,and develop students' induction and analogy thinking in a subtle way,Achieve the purpose of improving students' mathematical reasoning ability.Specifically:Firstly,according to the requirements of the new curriculum standard,the students' mathematical reasoning ability is classified,the evaluation framework and influencing factors of students' mathematical reasoning ability are analyzed with the help of relevant literature,and a questionnaire is prepared to study the current situation of students' mathematical reasoning ability,including basic information,mathematical reasoning ability test questions and topic feedback.Secondly,307 students from six classes of senior one in X Middle School in X city were selected as the preliminary survey objects,and 6 mathematics teachers in the senior one group were selected as the interview objects for investigation and research.Through the analysis of the results of individual interviews,ability tests and questionnaires,the following conclusions are drawn: the overall level of mathematical reasoning ability of senior one students is low and the gap between classes is large;On the whole,the deductive reasoning ability of senior one students is better,the analogical reasoning ability is the second,and the inductive reasoning ability is the worst.Then,based on the above survey results,two classes are selected as the classes of the final comparative experiment.With the help of MPCK theory,this paper analyzes the teaching materials,learning situation and teaching methods,formulates the teaching design of "trigonometric function induction formula" and "trigonometric function image and property",and carries out educational comparative experiments.The experimental class adopts the teaching design based on MPCK theory,and the control class adopts the conventional teaching design;Finally,through the problem-solving test of the experimental class and the control class,and the analysis of the results with the help of SPSS software,the final conclusion is drawn:(1)there is a significant difference in the average value of mathematics scores between the experimental class and the control class.The teaching design based on MPCK theory pays attention to the generation and discrimination of concepts and the participation of students in the teaching process of formulas,which helps to deepen students' understanding and application of concepts and formulas;(2)Scientific instructional design is the basis of classroom teaching.The growth of mathematics teachers needs certain theoretical support.MPCK theory can help teachers grow scientifically and rapidly;(3)The instructional design based on MPCK theory is beneficial to the development of students' logical reasoning ability,and the lower the difficulty coefficient to a certain extent,the more it can reflect the difference between the results of the two instructional designs.