An investigation of elementary school 4-7th grade students' ability to link equivalent fractions' symbolic and graphical representations

The aim of this study was to determine elementary school 4-7th grade students' ability to link equivalent fractions' symbolic and graphical representations. The sample of the study consisted of 4, 5, 6 and 7th grade elementary school students in 2010-2011 academic year in the district of Geyve in Sakarya Province. The pilot study was implemented with 257 students from three elementary schools and the main study was conducted with 1111 students from 11 elementary schools. Representational Fluency Test (RFT) developed by Niemi (1996) was used as a data collection tool in the study. The RFT included items involving regional areas, line segments, and set representations to assess the part?whole meaning and those involving number lines to assess the measure meaning of rational number. In the test, there were 5 different fraction symbol which were simple and equivalent fractions. There were 18 graphical representation including regional, line segment, set and number line with distractors for each of the five fractions. In RFT, there were 90 graphical representations in total. Of a total of 90 items, 35 were distractors associated with each graphical representation except for set representation. The content validity of the test was determined by expert opinions and the reliability of the test was assured bu calculating KR-20 internal consistency coefficient. The values of the coefficient were 0,933 in the pilot study and 0,928 for the main study. The 90 items were dichotomously scored. Because the numbers of items were unequal across the categories, in all analyses the raw scores were divided by their own maximum possible scores. This scoring places all scales in a similar 0 to 1 metric but does not alter the original scale distributions or correlations. Scores in the subcategories of the data collection tool and the scores of grade levels were compared. Non-parametric tests were used because the distribution of the scores in all categories and grade levels was not normal. The results of the analyses showed that the students' performance to link equivalent fractions' symbolic and graphical representations changed significantly with respect to the representation type (region-line segment, region-number line, set-line segment, set-number line, line segment- number line) and with respect to simple and equivalent fractions. In the meantime, it was seen that as the classroom levels increased, the success rates in overall scores, representation types, except region-line segment, and simple and equivalent fractions increased. The findings of the research were discussed in the light of literature review. This study fills the gap in mathematics education research related to the field of fraction subconstructs, representations and equivalences. Also, some suggestions were made for the researchers studying in the field of mathematics teaching. Suggestions for pre-service and in-service education designers and programme developers are included in terms of fair sharing, fractions' meanings, representations and equivalences.