An investigation of the relationship between 6th grade students' images, misconceptions and academic achievement about fraction

This research was conducted to investigate the relationship between 6th grade students' concept images, misconceptions and academic achievement about fraction. The research was designed in accordance with the parallel pattern converging from mixed method designs. The population of the study consists of the 6th grade students of secondary schools affiliated to the Ministry of National Education in Battalgazi and Yesilyurt districts of Malatya province in 2018-2019 academic year. The sample of the study was determined by stratified random sampling method from schools in the universe and consisted of 633 students. The research data were obtained by using "Fraction Concept Image Questionnaire", "Three-Thier Fraction Misconception Test" and "Fraction Achievement Test". The fraction concept image questionnaire is designed to determine students' concept images and consists of 3 open-ended questions. Since the data obtained from fraction concept image questionnaire are qualitative data, they were analyzed by descriptive analysis method. To determine students' misconceptions about the fraction, the three-thier fraction misconceptions test consists of 10 questions each consisting of 3 stages. In step 1 of the questions, there are options that include the correct answer of the test item and the incorrect answers to the possible misconceptions. In the second stage, the reason of the answer given in the first stage was asked and the options were given with the correct explanation and explanations of the possible misconceptions. In addition, for those who have an explanation other than these options, a blank option is left for them to write. In the third stage, the students were asked whether they were sure of their answer. The data obtained from this test were evaluated in terms of both fraction concept success and fraction misconceptions and analyzed separately for each stage. The fraction achievement test consists of 20 questions, each with 4 options, on average difficulty, to determine students' academic achievement in fractions. As a result of the research, it was determined that the misconceptions and achievement scores of the 6th grade students differ significantly according to the concept images of the students. It was found that the students who had piece-whole concept image were more successful and had fewer misconceptions than the other students. It was found that the most common concept images of students were division, piece-whole and numerator-denominator concept images, respectively. The number of students with other concept images is quite low compared to these three concept images. The most common misconceptions that students have are, respectively, "all considering that the same fraction referenced is the same regardless of all referenced fractions.", "consideration of multiplication in fractions should always increase the value of the number, as in whole numbers", "while showing the whole shape, dividing the whole into pieces". Key Words: 6th Grade Students, Fraction, Concept Image, Misconception