Research On The Effectiveness Of Creating Mathematical Problem Situations In Junior Middle School

The Mathematics Curriculum Standards for Compulsory Education(2022 Edition)further emphasizes the need to strengthen situational design and problem posing,and play its role in promoting students’ learning and core literacy development.What elements should be included in the effective design of mathematical problem situations in junior high school? What is the performance of the high-quality junior high school mathematics classroom that can be studied by other teachers in the design of problem situations? How to optimize the design of mathematical problem situations in junior high school? Studying these problems,on the one hand,is conducive to promoting the scientific construction of the analytical framework for the design of mathematical problem situations in junior high school;On the other hand,it provides reference for teachers to examine the effectiveness of problem context design.This study takes the teaching in the field of number and algebra as an example,and based on the analysis of situational cognitive theory,constructivist learning theory,effective teaching and relevant literature,puts forward a hypothesis framework for the analysis of the effectiveness of mathematical problem context design.Modifies the hypothesis framework based on the interviews with seven junior high school mathematics teachers and the questionnaire survey results of 108 junior high school mathematics teachers.The final analysis framework of mathematical problem context design includes two first level dimensions: effective presetting and effective generation,four secondary dimensions: effective context design,effective problem design,effective teacher elicitation and effective student response,nine specific elements:relevance with students,authenticity,interest,relevance with knowledge,hierarchy,directivity of questioning,inspiration,positive response and correct answers.Taking the constructed analysis framework of the effectiveness of mathematical problem context design as a reference,this paper analyzes the effectiveness of problem context design of 23 high-quality junior high school mathematics classroom cases involving the concept teaching in the field of numbers and algebra,evaluates the specific level of each case under the nine effective elements of mathematical problem context design,and counts the proportion of the number of cases at different levels under each element.The results show that: The merits of creating problem situations in high quality junior high school mathematics classroom are as follows: fully considering the connection with students’ real life;Pay attention to the hierarchy of the problem and its relationship with mathematical knowledge;Teachers are flexible in the directivity of questioning;The students are highly responsive.The existing problems are: the authenticity and interest of the problem situation are low;Teachers’ enlightenment is not enough;The correctness of students’ responses in the teaching of upper concepts or lower concepts that can be learnt by others with analogy under the theme of functions and equations is not ideal.Based on the above deficiencies in the design of problem situations in high quality junior high school mathematics classroom,this paper puts forward suggestions to optimize the design of problem situations in junior high school mathematics from two main aspects: improving the authenticity and interest of problem situations,and improving the correctness of students’ responses by using enlightenment.To be specific,context design should always keep in touch with the students’ reality and expand extracurricular knowledge reasonably;Make full use of real life materials to improve the level of situational authenticity;Properly enrich the content of the theme of the situation and improve the level of the interest of the situation;Skillfully use classroom questioning skills to improve teachers’ level of inspiration;Be good at analyzing the causes of negative responses and solving problems according to the situation;Elaborately design the upper concept topic to improve the students’ response level.