| The operation of rational numbers is not only the initial part of mathematicscurriculum of the third stage (7-9 grade), but also an important foundation for othersections of mathematics curriculum as well. Learning it well will be a good start forarousing students’interest and confidence of mathematical learning. However, thissection has been neglected in either actual teaching or educational research. As adults,mathematics teachers and educational researchers rarely realize what a big challengeit is for 7 grade students to do operations with negative numbers. Therefore, 7 gradestudents are less seriously treated than pupils who are beginners of the field of numberand operation. Also, there has been a long lack of researches on teaching and learningof the operation of rational numbers in junior middle school.This study aimed to elucidate the misconceptions held by 7 grade students aboutthe operation of rational numbers and the possible causes of these misconceptions,using the tool of three tests for students along with classroom observations andinterviewing. A grade-7 class of 38 students was the subject of this study. Qualitativeanalysis was the main method to analyze data collected by field investigation in orderto identify the subjects’misconceptions and their possible causes. The major studyresults are as follows.At least four misconceptions about the operation of rational numbers were heldby 7 grade students: M1, addition means increasing, while subtraction meansdecreasing. M2, in one formula, if there is only one mathematical symbol (‘＋’or‘－’) between two numbers, then this symbol is a sign indicating the operation ofaddition or subtraction; if there are two or more mathematical symbols‘(＋’o‘r－’)between two numbers, then the symbol which a number closely follow is a signshowing positive or negative numbers, other symbols are the sign indicating theoperation of addition or subtraction. M3, parenthesis is used to highlight the selectiononly in sense of writing. M4, adjacent numbers can be associated with priority.Four major factors related to the development of misconceptions about theoperation of rational numbers were identified: Students’prior knowledge andexperience, Non-formal daily language of students and their teacher, vague details inlearning materials and teacher’s explanations, students’intuition. In this paper for the specific performance: (1) Prior knowledge and experience may result in students’misunderstanding of the essence of addition and subtraction of rational numbers. (2)The customary manner of reading a mathematical formula may result in students’misunderstanding of the meaning of the＋and－symbols. (3) Vague explanationsabout the usage of parenthesis do not benefit students in construction of correct andstrong knowledge of parenthesis. (4) Students’preference for easiness may contributeto their abuse and generalization of the tricks of the calculations.The paper concluded by providing some recommendations for educators andresearchers. The suggestions for persons who write the textbooks are noted below: (1)Adding necessary specification of the process of problem-solving, and adjusting theorder and manner of the textbook content. (2) Enhancing the pertinence andusefulness of the textbook, and organizing the textbook in a new way. The suggestionsfor mathematics teachers are listed as follows: (1) Teachers should permit andencourage students to explore calculation methods. (2) Introducing to studentsmulti-representation of the operation of rational numbers in order to deepen students’understanding of mathematics concept. (3) Teachers should keep track of students’learning and correct students’misunderstanding. (4) Raising students’Metacognitionability in mathematics teaching. |
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