A Comparative Study Of Reasoning And Proving Tasks In High School Mathematics Textbooks And Their Classroom Use

As a structured written vehicle for mathematical knowledge,textbooks are important for curriculum implementation,and TIMSS research has shown that classrooms are often centred around the tasks in textbook resources,the quality of which will have a significant impact on students’ learning in mathematics.However,teaching materials do not directly determine the quality of teaching and learning,and the mediating role of the teacher,i.e.the teacher’s use of the materials and the practices adopted by the teacher in the classroom,needs to be considered.In addition,studies have shown that reasoning and proof are a major difficulty in teaching and learning mathematics.Textbook reforms in various countries have emphasised the importance of reasoning and proof,and China’s latest curriculum standards for general high school mathematics identify logical reasoning literacy as one of the six core literacies.This study focuses on the reasoning and proof content in The Shanghai Educational Publishing House(SEPH)Edition of textbooks and the People’s Education Press(PEP-A)Edition of textbooks,examining the differences between the presentation of the tasks in the textbook and their use in the classroom,and aims to answer the following two questions:(1)What are the characteristics of the reasoning and proof tasks in the two editions of the textbook? What are the similarities and differences?(2)What are the similarities and differences in the use of the reasoning and proof tasks in the textbook resources by the teachers of SEPH and PEP-A?In order to answer these two research questions,this study selected a task analysis framework and a reasoning and justification framework to independently code two aspects of the tasks in the curriculum resources and the use of the tasks in the classroom.A content analysis approach was adopted to analyse the coding results,and a comparative research approach was adopted to firstly compare the similarities and differences between the two versions of the teaching materials,and secondly to examine the similarities and differences between the presentation of the teaching materials and the use of the teaching materials in the SEPH and PEP-A versions respectively,and then to summarise the commonalities and differences in the use of the teaching materials between the two versions.The study found that: for the function content of the two versions of textbooks(1)both editions provide students with limited opportunities to learn reasoning and proof,and the facilitation between sub-processes is weak;(2)the PEP-A provides more tasks in the inductive stage of mathematics and prefers non-rigorous proof,while the SEPH places equal emphasis on the inductive stage and the stage of supporting mathematical assertions and prefers rigorous proof;(3)both editions provide students with more opportunities to learn reasoning and proof,and the facilitation between sub-processes is weak;(4)both editions provide students with more opportunities to learn reasoning and proof.(3)both editions provide more opportunities for students to learn reasoning and proof,and emphasize mathematical induction and the law of knowing from the particular to the general in their teaching;(4)both editions follow the differences in the textbooks in terms of the rigorous required for proof in classroom use.Finally,this study suggests that(1)teachers should make full use of the textbook and its surrounding resources to design tasks that take into account students’ prior knowledge and understanding levels in order to provide more learning opportunities;and(2)the textbook writers could provide more suggestions and guidance requirements in the teacher’s book for teachers on how to design textbook tasks.