Research On The Current Situation Of Mathematics Problem Posing Strategy And Mathematics Understanding Of Senior One Students

China ’s mathematics curriculum standards clearly point out that ’ putting forward mathematical problems ’,improve students ’ ability to put forward mathematical problems in practical teaching activities,and develop a reflective and questioning learning attitude.However,the current classroom teaching is mainly to solve problems,and there are few links for students to ask questions independently.Students do not know much about how to put forward mathematical problems.Problem posing can be used as a cognitive activity in teaching,and it can also be used as a teaching method to transform and connect different contents to promote students ’understanding of concepts.Students have more connections between existing cognitive structure and new knowledge through problem posing,which shows that this mathematical concept and mathematical thought become a part of personal internal network knowledge.Therefore,problem posing is the basis of mathematical understanding,and the use of strategies is a subjective and internal psychological process of mathematical understanding.The purpose of this study is to explore the current situation and relationship between mathematical problem-posing strategies and mathematical understanding performance.Among them,problem-posing strategies are used as an assessment of students ’ mathematical understanding,and the process of students ’ mathematical thinking and understanding is deeply explored.This study mainly focuses on the following three questions :(1)What is the current situation of high school students ’ problems ?(2)The current situation of mathematics understanding of high school students ?(3)The relationship between problem-posing performance and students ’ mathematical understanding ?This study mainly uses :(1)literature analysis,(2)questionnaire survey,(3)interview,(4)statistical analysis.The questions of the test paper are mainly selected from three test questions of Dr.Shaixia ’s thesis.There are three different types of situations(free situation,semi-structured situation,structured situation).Each question is compiled into a test paper.The test paper mainly involves the difficulty of the problem,how to think about and put forward the content,and make minor modifications to the type-related questions.The test paper also evaluates the performance of students ’ mathematical understanding on the basis of the problem.Research question one,high school students ’ ability to put forward mathematical problems is general,most students can put forward reasonable mathematical problems.However,there are still a small number of students who have unclear questions(no mathematical characteristics)and no answers.From the performance of the three situations,the number of students ’ answers to the free situation is the largest,followed by the semi-structured situation,and the structured situation is the last;the semi-structured situation is the best,and the free situation and the structured situation are not much different.At the performance level of challenge difficulty and strategy,students tend to use known strategies to raise questions on simple questions,with the largest number,followed by supplementary strategies and modification strategies for medium difficulty problems,and expansion strategies for higher difficulty problems.From the students ’ written performance,each strategy has a connecting role in the problem of different difficulty,and also verifies that Silver & Cai ’s method presents a symmetrical response to the mathematical problems raised by students(according to the conditions or objects of the previous problem).Research question two,through the students to ask questions after the assessment of students ’ mathematical understanding,students in the situation two and three of the overall situation procedural understanding quantity is better than the conceptual understanding quantity;the problem of procedural understanding in structured context is better than that in semi-structured context,and the conceptual understanding of semi-structured context is higher than that of procedural understanding.However,the performance of students ’ conceptual understanding is relatively single,and there is less interconnection between knowledge points.The distribution of the relationship between problem-posing strategies and mathematical understanding of senior one students.In semi-structured and structured situations,the number of procedural understanding and conceptual understanding using known strategies is the largest.In the semi-structured situation,the addition strategy and modification strategy perform better in procedural understanding than conceptual understanding.In the structured situation,the performance of supplementary strategy and modification strategy in procedural understanding and conceptual understanding is evenly distributed.The expansion strategy is not prominent in the mathematical understanding of the two situations.According to the research results,this study puts forward the following suggestions : pay attention to the training of students ’ mathematical problems,improve the students ’ subject knowledge structure system,cultivate students ’mathematical problem structure understanding,strengthen students ’ conceptual understanding and focus on substance.