An Evaluation Study On The Development Status Of Algebraic Thinking In Eighth-grade Students

The development of algebra provides a new way of understanding the world from a mathematical point of view.Compared with the intuitive and concreteness nature of elementary school mathematics,algebra can help students understand the quantitative relationship and change law in the real world,and help students to from a new way of thinking.So,junior high school is the key stage of algebraic thinking development.Seventh grade students began to learn formal algebra courses,after a year of algebra learning,students of algebraic thinking to what level?Whether the existing knowledge can support the next mathematics learning?This is the focus of our attention.Therefore,the students who have just entered the eighth grade as the research object,to explore the students to complete the first year of algebra curriculum after learning,algebra thinking development level and status quo.In this study,the eighth grade students coming from Heze City and Zaozhuang City of Shandong Province were selected as the main research objects.The literature and questionnaires were used to study.The main contents are including:1.From the cognitive and knowledge of the two dimensions to study the algebraic thinking,and to build the eighth grade students algebra thinking development level of a simple framework.The three aspects of the development of students' algebraic thinking are based on the SOLO model of algebraic cognitive level and the definition of mathematical thinking and understanding in American MIC project,including:(1)the level simple symbolic operation and conceptual understanding;(2)the level of contact and application;(3)the level algebraic reasoning and mathematicalization.2.Combined with the three levels of algebraic thinking,this paper analyzes the mathematics textbooks of the seventh edition of the Beijing Normal University Press,and determines the content range of the research,including the algebraic expression,the equation and the function.Finally,According to the algebraic thinking development framework,designed the questionnaire.3.The analysis of the collected questionnaire data using quantitative analysis and qualitative analysis of the eighth grade students in the simple symbolic operation and conceptual understanding level,contact and application level and algebraic reasoning and mathematicalization level made a briefly analysis,and examines the differences in gender at different levels and the differences in different regions.Combined with the data analysis,the following conclusions:(1)The overall development of students algebra thinking is not satisfactory.The number of people who can reach each level is gradually decreasing.(2)There was no significant gender difference in the level of development of algebraic thinking in the eighth grade students,and the gender had little effect on student achievement.There is also no significant difference in the level of algebra thinking between the two schools.This shows that the education between the two regions is more balanced.(3)The eighth grade students are not ideal for the basic concepts of algebra.(4)The basic operation ability of the eighth grade students to perform better,but in solving algebra reasoning and mathematical problems when the poor performance.According to the questionnaire analysis,three suggestions were put forward:(1)strengthen the cultivation of students' mathematics reading ability;(2)pay attention to the study of students' mathematical concepts and basic knowledge;(3)the development of students' algebra thinking should start from the cultivation of symbolic consciousness.Previous studies have focused on how to help students transition from arithmetic thinking to algebraic thinking in the seventh grade and the difficulty of transition.After a period of study,few people mentioned whether student's algebraic thinking is able to achieve our expectations.Therefore,the innovation of this paper is to examine the development of algebraic thinking after students have completed some algebraic curriculum,which can bring some reference for teachers 'follow-up teaching and students' learning.However,due to limited capacity,the definition of algebraic thinking three levels and teaching suggestions still need to be improved.