The Role of Visualization Approach on Students\' Attitudes Towards and Achievements in Mathematics

The purpose of the study is to determine the effect of visualization approach on the students' attitudes towards and achievements in mathematics. It is an experimental research based on an experimental pre-test post-test model. The experimental and control groups consist of the 8 th grade students of a secondary school in Izmir during the 2010-2011 academic year. The experimental group was formed of 21 students, while the control group was formed of 22 students. The data were collected using the ´´Mathematics Attitudes Scale´´ which was prepared by Nazlicicek ve Erktin (2002) and ´´Algebraic Expressions and Equations Achievement Test´´ which was developed by the researchers. Results showed that the visualization approach affects the studentsattitudes towards mathematics and achievements in mathematics lessons positively. SUMMARY Purpose and significance: The purpose of the study is to determine the role of visualization approach which is an alternative way to algebraic approach on the students' attitudes towards and achievements in mathematics. In this study, both difficulties and strengths associated with visualization usage in mathematics education as well as its cognitive and affective aspects were investigated. Methods: It is an experimental research based on an experimental pre-test post-test model. The experiment and control groups consist of the 8 th grade students of a secondary school in Izmir during the 2010-2011 academic year. The experimental group was formed of 21 students, while the control group was formed of 22 students. In this study ´´Mathematics Attitudes Scale´´ developed by Nazlicicek ve Erktin (2002) was used as data collecting tool. This scale consisted of three factor structure with 20 items. Possible scores on the scale ranged from 20 to 100. ´´Algebraic Expressions and Equations Achievement Test´´ developed by the researchers was also used in the study. After the item analysis 14 items were omitted. The number of items was decreased to 31. The reliability (Cronbach Alpha) of the Achievement Test was found 0.81. Results and Discussion: Results showed that visualization approach affects the studentsattitudes towards mathematics positively. Also visualization is more effective than the traditional mathematics teaching. This finding is consistent with the research results of Aktumen ve Kacar, 2003; Konyalioglu 2003; Agathangelou ve ark. , 2008; Oguz, 2008. This finding is inconsistent with the findings of Ġpek, 2003; Uygun, 2008; Korukcu, 2008. Because they found that visualization does not affect students' attitudes towards mathematics even though it affects students' mathematical achievements positively. Another result of this research is that visualization approach affects the studentsmathematics achievements. This finding is consistent with research results of Aktumen ve Kacar, 2003; Drijvers, 2003; Ġpek, 2003; Korukcu, 2008; Oguz, 2008; Tuncer, 2008; Konyalioglu, 2003; Afamasaga-Fuata, 2004; IĢik, 2007; Pulido ve Salinas, 2008. Very often one believes that learning how to construct graphs of geometrical figures is enough to learn visualization in mathematics. Moreover, in this kind of task students get satisfactory results. But a task of construction requires only a succession of local apprehensions: one needs to focus on units and not on the final configuration. In other words, a student can succeed in constructing a graph or a geometrical figure and being unable to look at the final configurations other than as iconic representations. That is easy to observe and to explain (Duval, 1999). Visualization is no longer related to the illustrative purposes only, but also being recognized as a key component of reasoning (deeply engaging with the conceptual and not the merely perceptual) problem solving, and even proving (Arcavi, 2003). For that reason visualization approach can be used as an alternative way to algebraic one in mathematics, especially in mathematical problem solving. It allows us to see the abstract concepts as they are concrete. Conclusion: Many research (Bloom, 1979) showed that the core of the differences between individuals´ learning processes arise from their affective characteristics. Self confidence, anxiety and attitude have large portion in these characteristics (Baykul, 2005). By all means visualization approach is very important in terms of individualscognitive evolution in mathematics education. To teach students how to use the visualization in mathematics and to show them that "problem solving could be easier by using visualization approach" are not only important for cognitive side but also in terms of affective evolution.  This research was based on the Doctoral Dissertation (of the first author) directed by Asist. Prof. Dr. NeĢ'e BaĢer.