Research On The Transition From Arithmetic To Algebra

Algebra plays as a gatekeeper to future educational and employmentopportunities. The transitional stage from arithmetic to algebra is the very importantstage during students' learning of mathematics. Because of the great changes ininstructional contents, teachers' instructional methods and learning environments,7th-grade students face tremendous challenge. In this study we focus on this stage andexplore the different patterns of 7th-grade students in the transitional stage fromarithmetic to algebra.The thesis is mainly composed of six chapters.Chapter One is the proposal of the problem. From the perspectives of the history ofalgebra, mathematics contents and psychology, it claims the necessity and the importanceof the study.Chapter Two makes a brief introduction of the background of the study. Through theoverview of the relevant literature, it is founded that the former researches put lessattention on this special stage from the angle of the acquisition and understanding ofalgebraic knowledge. Therefore, the research space was found and the theme was definedthat we investigate the performance and features of 7th-grade students in the transitionalstage.Chapter Three is the introduction of the relevant theories: the theory of schema andthe theory of the duality of mathematics concepts which was put forward for the specialtyof mathematics by Anna Sfard. The theory of schema provides us for the powerful tool todepict students' understanding of the algebraic knowledge, and the theory of the dualityof mathematics concepts can be the framework to explain students' understanding ofalgebraic concepts.Chapter Four introduces the method and the procedure of the research.Chapter Five serves as the core of the thesis. We investigate arithmetic and algebraword problems strategies of the 7th,grade students. The results show that the studentsfrom the different schools have significant difference in the understanding of thealgebraic concepts, and with the increase of the problems' difficulty come an increase ofthe students of using algebraic method. Furthermore, on the basis of the detailed analysis of the test and the interview, wesummarize three different patterns of students' transition: (1)Refusing the newknowledge; (2)The close relationship is formed between the new and the old knowledge;(3) The old and the new is scattered in the brain.Chapter Six is implications for instruction and curricular design. We put forwardseveral pointed implications for curriculum decision-makers, mathematics teachers and7-th grade students.The innovation of the study lies in that focusing on the transitional stage fromarithmetic to algebra, exploring the features of 7th-grade students in this transitionalstage and summarizing the three different patters from the angle of cognitive psychology.