The Practical Research On The Teaching Of Linear Equation With One Unknown From The Perspective Of HPM

Linear equation with one unknown is the starting point and key point for students’ equation learning,laying a solid foundation for later learning of binary equations,quadratic equations and primary functions.At primary level,arithmetic thinking is mainly used to solve problems.For students who have just entered the first year,it is a difficult task to make the leap from arithmetic to algebraic thinking.The field of History of Mathematics and Mathematics Education(HPM)has attracted much academic attention in recent years,and studies have shown that the integration of the history of mathematics into mathematics teaching and learning can help improve students’ cognition and enhance their interest in learning.This study provides a HPM perspective to help students overcome their learning difficulties and also to provide teachers with new teaching ideas.The main research questions are as follows:(1)What learning difficulties do students have in learning linear equation with one unknown?(2)How does the use of the history of mathematics in a lesson on linear equation with one unknown help students to overcome their learning difficulties?(3)How does the use of the history of mathematics in a lesson on linear equation with one unknown affect students’ emotional attitudes?Through the study,we found that students’ difficulties in learning linear equation with one unknown include:(1)understanding of the meaning of unknowns;(2)easy to make mistakes when shifting terms and understanding the idea of shifting terms;(3)conversion from arithmetic to algebraic thinking;(4)the role and importance of learning linear equation with one unknown;(5)lack of interest in learning linear equation with one unknown;(6)lack of thinking and carelessness,relying on mechanical solutions prone to calculation errors;(7)unable to sort out the correct equation relationship;(8)too chaotic and unorganized steps in solving problems.Based on the practical research of HPM case teaching,the following conclusions were drawn from the analysis of the data collected:(1)Regarding the use of the history of mathematics to help students overcome learning difficulties: the history of mathematics gives students a deeper understanding of the meaning of unknowns and shifting terms;the history of mathematics helps students make a smooth transition from arithmetic to algebraic thinking;the use of the history of mathematics is better in helping students recognize the role and importance of learning equations,but some students still think that they are learning for exams.(2)On affective attitudes: the history of mathematics allows students to experience the joy of inquiry;the history of mathematics has a moral effect on students;the history of mathematics creates good motivation for students to learn;the history of mathematics can better demonstrate the appeal of mathematics and influence students’ perceptions of mathematics.