A Practical Study On Teaching Problem Chains In High School Mathematics Based On Mathematical Understanding

The famous mathematician Halmos once said that “problems are the heart of mathematics”.Students’ learning is in the process of problem identification,problem analysis and problem solving.The cultivation of problem awareness and problem solving ability is an important goal of mathematics education,and the realization of mathematical understanding is one of the important goals of students learning mathematics.Teaching mathematical problem chains helps stimulate students’ learning interest,cultivate their inquiry ability and innovation consciousness,and provide more possibilities for students to achieve mathematical understanding.Therefore,it is worthwhile for educators to explore and study how to integrate the concepts related to mathematical understanding into problem chain teaching in order for students to get better learning results.First,this paper analyzes the existing research on mathematics problem chain teaching and mathematical understanding,discusses the research background,research significance,literature review and research ideas,summarizes the relevant concepts and theoretical foundations,and discusses the feasibility of integrating mathematical understanding into mathematics problem chain teaching.After investigating the level of students’ mathematical understanding and the current situation of problem chain teaching in high school mathematics classrooms,it is found that students have difficulty in achieving mathematical understanding in the process of learning mathematics,but when teachers teach with the help of problem chains students can quickly adapt and participate in the classroom.Second,this paper proposes the principles of teaching design of problem chains in high school mathematics based on mathematical understanding,as well as three teaching strategies of “designing problem situations to achieve instrumental understanding”,“designing inspiring problems to achieve relational understanding” and“designing related problems to achieve creative understanding”.Based on the teaching design process of designing,implementing,reflecting and evaluating problem chains,we present a concrete example of problem chain teaching design and conduct a practical lesson using “basic inequality” and “induction formula” as examples.Finally,this paper investigates the effectiveness of classroom teaching through classroom observation,questionnaire survey and comparative experiment,and develops a detailed analysis and discussion of the findings.Based on the above research,teaching suggestions are made and it is concluded that mathematical problem chain teaching can effectively help high school students achieve mathematical understanding and improve their test-taking ability.