İLKÖĞRETİM ÖĞRENCİLERİ İÇİN GÖRSEL MATEMATİK OKURYAZARLIĞI ÖZ YETERLİK ALGI ÖLÇEĞİ (GMOYÖYAÖ)'NİN GELİŞTİRİLMESİ

: There are several descriptions of literacy including, “the ability to read written texts by using alphabet” (Reinking, 1994); “students’ awareness of quantitative, logical, and mathematical operations in addition to the activities related to read-write” (NRC, 1989); and “individual’s ability to find, evaluate, and use the necessary written resources with the aim of improving his knowledge as well as potential to participate to the society effectively” (Akyüz & Pala, 2010). With reference to these different descriptions it is seen that literacy can differ according to tools used and acquired knowledge; what is more, there will be the need to describe more different literacy descriptions in parallel with the developments in daily life, science, and technology (Sanalan, Sülün & Çoban, 2007). For example, there are different types of literacy such as computer literacy, art literacy, media literacy (Altun, 2003), visual literacy (Anderson, 2002), and math literacy (Ersoy, 2003). In fact in information societies it becomes a mandatory feature to define new literacy types like artistic math or visual math literacy, which were emerged through the intersection of these different types of literacy. On the other hand, it is of vital importance to remember that other literacy types like visual and math literacy are not alternatives of the general literacy, but parts or supportive elements of it (Chauvin, 2003; Reinking, McKenna, Labbo & Kieffer, 1998; Sims, O’Leary, Cook & Butland, 2002). In addition, Visual Literacy (VL), which is defined as the ability to read and evaluate information presented in the forms of table, picture, and graphic; and the skill to create new visual images (Debes, 1968; Heinich, Molenda, Russell & Smaldino, 1996; Hortin, 1980; Wileman, 1993); is in close relation with other types of literacy in terms of being a supporter or a part of them (Kellner, 1998). This relationship is even closer to Math Literacy (ML) due to its opportunities for individuals such as supporting them to better understand abstract thoughts by presenting these thoughts in a living and familiar way and bringing the experience to process the same thought in different ways (Feinstein & Hagerty, 1994; İpek, 2003). This close relationship reveals a new concept of literacy, “Visual Math Literacy (VML)”. VML can be described as, “the proficiency to perceive, signify, interpret, evaluate, and use the problems encountered in daily life within visual or spatial frameworks; and, to perceive, signify, interpret, evaluate, and use visual or spatial information in mathematical terms”. In Turkey there is no scientific research about VML, which is described as mentioned above, conducted at the elementary school level; hence, this study is very important for being the first to cover VML and integrate types of literacy. The purpose of this study is to develop a valid, reliable, easy to apply and easy to evaluate scale that can measure the self-efficacy of elementary students concerning their visual math literacy. This is a general survey study in which it is aimed to develop a scale. Participants of study are composed of 151 6th grade, 142 7th grade, and 135 8th grade students. Totally 428 students (220 girls and 208 boys) were selected randomly from two elementary schools in the Eastern Anatolian region of Turkey, and one elementary school from the Black Sea region. For the VMLSEPS first of all, 15 open ended questions were formed with reference to expert opinions, and these questions were asked to 6th, 7th, and 8th grade students (103 students in total) from two elementary schools in a large city in Eastern Anatolian region for the first semester of 2009-2010 academic year. Researchers created an item pool composed of 159 items by using students’ answers to these questions and considering the Elementary Education Mathematic Program 2005. With reference to the pool and based on the elementary school students’ successes on mathematics, an 58-item draft scale that can measure the self-efficacy of elementary students concerning their visual math literacy was prepared by a group of six experts, among which four were elementary school math teachers and two were faculty members at department of mathematics, by taking into account the majority of votes; and it was decided to entitle the scale as the Visual Math Literacy Self-efficacy Perception Scale, and abbreviated as VMLSEPS. Researchers decided to prepare a Likert type scale because it is a direct and the easiest way to determine VMLSEPS’ self-efficacy perceptions of visual math literacy, and in order to make it more sensitive and useful 5 point scale was developed. Out of the 58 items, 19 were stated as negative and the rest, 39 items, were stated as positive. Having obtained necessary permissions, the scale was tested on 428 students at 6th, 7th, and 8th grades in related schools. The test took a course hour. It was revealed that students can answer the scale generally between 15 to 25 minutes. VMLSEPS scale was basically analyzed regarding its extent and structural validity. Considering the structural validity of the VMLSEPS, experts were consulted if visual math literacy of each statement is related to its self-efficacy perceptions or sub-dimensions, and if elementary education mathematic program and students’ levels are congruent; and related corrections were made in accordance with experts’ opinions. Factor analysis was done for the structural validity of scale. For the adequacy of the sample, KMO value was calculated as 0. 959 and this value showed that the adequacy of the selected sample is perfect. Bartlett-Sphericity test was conducted in order to determine if the sample provides a normal range, and the value of significance was found as .000. The value of significance showed that the sample provides a normal range within the population. At the end of the factor analysis the items were clustered around three factors, “Field Content”, “Process”, and “The Places of Use”; and, it was showed that the total variance explained by these three factors was 41.81 %. On the other hand, for the sake of reliability, Cronbach Alpha was calculated as the criteria of the internal consistency of both the scale and each factor; and the Cronbach’s Alpha internal consistency score of the scale was calculated as 0.943. According to this analysis results, the VMLSEPS, which was designed as a 5 point Likert Scale with 38 items (36 positive and 2 negative), was finalized. The lowest score of the scale is 38 points, while the highest is 190 points. High scores indicate high level of self-efficacy perceptions of visual math literacy and low scores indicate low level of self-efficacy perceptions. Last but not least, cluster analysis was conducted in order to determine how to group the scores obtained through the scale. Accordingly, groups and the scores after the analysis are; good or good group (GG) (between 190 and 148 points), Average or Average Group (AG) (between 147 and 84 points), and Bad or Bad Group (BG) (between 83 and 38 points). As a consequence, it can be argued that VMLSEPS is a valid, reliable, easy to use and easy to answer scale that can determine elementary students’ self-efficacy perceptions of visual math literacy either individually or in group. Also, it is thought that this scale can easily be used on 6th and 8th grade elementary school students so as to determine their levels of visual math literacy