Attitudes of high school students towards visualization of mathematical content

Abstract

Teaching is a process for which its plan should contain reflection onto previous experience. With that in mind, teaching situations should be continuously researched and improved in accordance with the research results. Led by this thought and the fact that students are uncritically using visualization to solve mathematical problems, we defined the aim of this research–determine the attitude of students about the visualization of mathematical content (VMC). The subject of this research are the attitudes of students towards VMC. By analyzing our research subject, we have discovered the research problem–students use visual aid to solve problems uncritically. Based on this problem, we have set the aim of our research. Our aim was to determine the students’ attitudes (and their opinions) about VMC. Based on the aim of our research, we have set four research tasks. Based on these research tasks, we have established the main (leading) research question–What is the attitude of high school students towards the application of VMC? We divided the main research question into five questions: Do high school students consider that they understand the term ‘VMC’? Who considers they use more methods of solving mathematical problems using visual aid–high school male students or female students? Students of which grades consider that they use solving problems using visual aid more? What is the attitude of high school students about the relationship between the substantiality of the picture (the amount of data it encompasses) and the difficulty of solving the problem? What is the attitude of students about the use of software to solve mathematical problems? The research has been conducted with 1,240 high school students from Sarajevo, Bosnia & Herzegovina. For the purposes of this article, we employed a survey, questionnaire-based research. The research was created as part of a larger study conducted in the context of preparing a doctoral dissertation related to VMC. It is one fundamental research. An essential aspect of this research involves students’ attitudes toward VMC. After obtaining all necessary approvals from relevant institutions and parents, students proceeded to testing and surveying in their school classrooms, under the supervision of designated individuals who facilitated the conduct of the research. The distribution of the data was not normal, so we used the Pearson Chi-square, likelihood ratio Chi-square, and linear-by-linear association test to examine the association between student attitudes and categorical variables (gender and grade). In addition, we used frequencies and percentages. It has been concluded that the students are mostly positive towards applying visualization in their process of solving mathematical problems and these should be used in the direction of improving the students’ success, their confidence and their level of contentment in their mathematics class, as well as in other life situations that encompass mathematical content. In future research, it could be examined why students expressed such attitudes about the presented situations. Additionally, it would be significant to explore why students do not consider themselves successful in applying VMC, despite claiming to understand the term. The analysis could extend to the content presented in textbooks or instructional materials students use–how visualized the content is or whether students are required to visualize it themselves. It would also be worthwhile to investigate the extent to which teachers encourage students to visualize specific tasks or do so on their behalf. Given the fluctuation in results (we observe affirmative answers–partially or completely) observed across grades–initial decrease, subsequent increase, followed by another decrease–it might be explored whether this is related to the curriculum taught in each grade (such as content, volume, number of class hours, etc.). Regarding images leading to incorrect conclusions, it would be interesting to investigate the types of images students have in mind, how frequently they encounter such situations, where they use these images, who creates them, and similar aspects. These are just some questions for future research.