A Study On The Correlation Between CPFS Structure And Problem-Solving Ability Of Sequence Among High School Sophomores

Modern learning theory indicates that the learning process involves the formation,development,and refinement of cognitive structures.The Cognitive Process Framework for School Mathematics(CPFS)is a unique and superior cognitive structure used by mathematics learners.Understanding the current state of students’ CPFS structure is essential for math learners,and providing teaching recommendations to enhance it is of great significance.The college entrance exam continues to focus on problem-solving,making it a crucial component of course objectives and a key area assessed in the exam.Therefore,exploring the correlation between students’ CPFS structure and problemsolving ability is a critical issue that requires attention.As learners’ mathematical learning is closely related to cognitive structures,improving students’ CPFS structure can enhance their problem-solving abilities.Since sequence is significant in high school mathematics,this paper will examine the relationship between CPFS structure and problem-solving ability using the sequence unit as an example.Using the method proposed by Professor Yu Ping to detect the CPFS structure of students,we compiled the "CPFS Structure Test Paper of Sequence of High School Sophomores" and the "Test Paper of Sequence Problem Solving Ability of High School Sophomores." We processed the students’ test paper scores using Excel 2007 and SPSS27.0 to analyze the current situation of CPFS structure and problem-solving ability of sequence among high school sophomores.Our analysis focused on overall trends and gender differences.We conducted Pearson and regression analyses to explore the correlation between CPFS structure and problem-solving ability,drawing the following conclusions:(1)The CPFS structure of high school sophomores regarding sequence was not perfect,with most students demonstrating intermediate-level CPFS structures,and no significant gender differences in the establishment and improvement of CPFS structure were found.(2)High school sophomores’ ability to solve sequence problems was not perfect,with most demonstrating intermediate-level problem-solving abilities,and no significant gender differences were found in problem-solving ability.(3)The CPFS structure of high school sophomores was correlated with problem-solving ability at a 0.01 level,indicating a causal relationship.The non-standardized regression equation between CPFS structure and problem-solving ability of sophomore students is Y=1.284X+22.547,while the standardized regression equation is Y=0.763 X.In order to learn more about the situation of high school mathematics and teaching,we conducted interviews with students and teachers.Combining the survey and interview results,we offer the following suggestions for improving students’ CPFS structure of sequence:(1)Guide students to experience the complete learning process of concepts and propositions,helping them establish conceptual and propositional domains.(2)Emphasize the internal and external connections of the concepts and propositions of sequence,assisting students in establishing the concept and proposition departments.(3)Foster students’ habit of knowledge integration and encourage them to take the initiative in improving their individual CPFS structure.Finally,drawing from CPFS structure theory and the suggestions for improving students’ CPFS structure of sequence,we have developed a teaching design focused on the concept of arithmetic sequence.Our aim is to provide practical guidance for front-line teachers in the teaching of sequence unit.