The Effects of Visual Representations and Manipulatives on Reduction of Algebraic Misconceptions of Ninth-Grade Students

Representations have been identified as a factor affecting the development of mathematics by many researchers. Therefore, this study mainly aimed to investigate the effect of using visual representations and manipulatives on the reduction of algebraic misconceptions in ninth-grade students. The statistical population consisted of 650 male ninth-grade students in a high school of Ramhormoz in the academic year 2018-19. Male students (n = 87) in three ninth grade classes were selected from a single school. After a pretest, students' misconceptions were categorized into four categories of reading an inappropriate schema, new learning intervention in the previous schema, overgeneralization, and similarity of a mathematics word to a spoken word. The validity and reliability of data were confirmed by a researcher-made mathematics test. Two classes were then taught through teaching multiple strategies, visual, and manipulation, and one class via the traditional method. According to the results of qualitative and quantitative analysis, the use of multiple representations could affect the reduction of algebraic misconceptions of ninth grade students. Moreover, each of the visual representations and tools had an effect on the reduction of algebraic misconceptions in ninth-grade students. Among these representations, the mean posttest of the test group was higher than the subgroups of visual representations and manipulation. Mean scores indicated a significant effect after using visual representations and then manipulative representations.