Development of Visual Mathematics Literacy Self-efficacy Scale for Prospective Teachers
Author(s):
Başak Çalık (presenting / submitting) Yeşim Çapa Aydın (presenting)
Conference:
ECER 2014
Format:
Paper

Session Information

22 SES 04 JS, Teaching, Learning and Assessment in Higher Education

Paper Session, Joint Session NW 22 and NW 24

Time:
2014-09-03
09:00-10:30
Room:
B030 Anfiteatro
Chair:
Tamás Kozma

Contribution

In the last century, new thoughts and inventions come to life day by day as a result of knowledge transmission and production which are important elements in people’s lives while teachers’ roles are prominent in this process. They should have some capabilities to be good role models for individuals. This assumption brings some terms and concepts to minds that should be acquired by every teacher. In this perspective, “literacy” term obtains a concession over others explained as the capacity of individuals to find and use of knowledge, skills besides analyzing, judging and also solving and making sense of problems in different areas (OECD, 2012). Mathematics literacy has become one of the goals of mathematics teaching due to changes at technology and mathematics as a result of transition from industrial to information society (Kaiser& Willander, 2005). It is defined as “an individual’s capacity to identify and understand the role that mathematics play in the world, to make well founded judgements and to use and engage with mathematics in ways that meet the needs of that individual’s life as constructive, concerned and reflective citizen” (OECD, 2006).On the other hand, visual literacy as a different type of literacy defined by  Wileman (1993) as” the ability to turn information of all types into pictures, graphics or forms that help communicate the information”. It is an interrelated concept integrating theory, visual language and presentational perspective and technological development (Kordigel Abersek, 2008). The importance of integration of various disciplines in education to provide meaningful learning is emphasized (Taşkın Can, Cantürk & Öngel, 2005) so interdisciplinary relations and looking the problems from multi-perspectives gains high attention. Hence, two literacy types will be considered as one type of literacy, visual math literacy. Each individual makes use of visual images in their daily lives, especially solving mathematical problems and concretizing the abstract concepts with this way is supported by many researchers (Polya 1973; Humbree, 1992; Kar& İpek, 2009) having positive effect on mathematics achievement of students. Duchastel (1980) mentioned the functions of visuals under different category names such as logical- mathematical and data presentation implying the relationship of visual literacy with mathematical literacy. Use of diagrams and charts in order to explain mathematical relationship is described in the former category while visual presentation of data is given as an example of the latter one. Bekdemir and Duran (2012) studied on this concept and defined it as “the mastery to define, interpret, evaluate and use the problems in daily life within visual framework and to define, interpret, evaluate and use the visual or spatial information in mathematical terms.” To be literate in visual mathematics, individuals’ affective characteristics play a prominent role due to the nature of the constructs. Self -efficacy is one of the affective constructs described by Bandura (1997) as “the beliefs in one’s capabilities to organize and execute the courses of action required producing given attainments” (p. 3). Since visual math literacy is a novel term, teachers and prospective teachers’ self efficacy beliefs toward this concept should be considered beforehand because they should have required capabilities toward the given era before assessing how students are. Teachers’ self efficacy perceptions are considered one of the factors which directly influence their quality of instructions in the long run (Tschannen-Moran, Woolfolk Hoy, 2007). There is no such a scale which assesses efficacy beliefs of teachers or teacher candidates toward visual mathematics literacy term that might be due to its recent use in the literature. Thus, the purpose of this study is to develop a valid and reliable scale to assess self efficacy beliefs of prospective teachers toward visual mathematics literacy.

Method

The accessible population of the study is undergraduate students in Education Faculty of Middle East Technical University in Ankara, Turkey. Convenience sampling procedure was utilized. The sample consisted of 319 teacher candidates including different fields of study and grade levels. For the instrument development part, the literature related to mathematics, visual, visual mathematics literacy and self efficacy constructs were examined carefully to generate initial item pool. Besides looking the literature, eight open ended questions were asked to six mathematics education graduates. After reviewing the literature and obtaining the responses to questions, the elementary and secondary school mathematics curricula were analyzed because content of the subject was concerned as one of the dimension for the given construct (Bekdemir &Duran, 2012). Based on the literature review, current scales and responses to open ended questions, 42 items were written in the initial item pool. Then, cognitive interviews were done with two teacher candidates; expert opinion was taken from one expert in the field and one measurement and education specialist with PhD degrees to provide content validity of the instrument. Based on the expert opinions and cognitive interviews, 16 items were eliminated and some of the items were revised due to content irrelevance, problems related to wording and organization of items for the sake of the instrument’s clarity and understandability. Consequently, the scale as a self-report instrument comprised of 26 items on a nine point Likert scale ranging from (1) “insufficient” to (9) “very sufficient”. The first part of the scale is about the demographic information asking questions about gender, field of study, grade level, the graduated high school, GPA and the status of taking a math course during university education. The second part involves items pointing out prospective teachers’ self efficacy beliefs toward visual math literacy.Sample items might be given as, How well can you estimate the perimeter of a place? ; How well can you develop a project in your discipline by getting benefit from mathematics and visual disciplines?; How well can you determine the similarities of geometrical shapes around?

Expected Outcomes

After the administration of the scale, factor analysis was conducted to observe the interrelationships among the variables and to discover factor structure of the scale. Exploratory Factor Analysis (EFA) was utilized. Based on the multivariate normality assumption, Principal Axis Factoring extraction method was used. Then, the correlation matrix was examined to see the relationships between items. Each item correlated each other with a value of .30 or higher. Barlett’s Test of Sphericity findings were significant indicating the difference of correlation matrix from the identity matrix while Kaiser Meyer Olkin (KMO) value is .95 >.60 and the sample size is ten times greater than the number of items. Three factors were observed according to scree plot results.Oblique rotation was used to simplify and clarify the data based on the assumption that factors are correlated with each other. Pattern matrix was examined and according to results, item 5 and 25 were decided to be eliminated due to cross loadings and uninterpretable contribution of items to related factor and EFA was executed again which revealed three factors. The final version of the scale involves 24 items clustered around three dimensions named as “comprehension of visual mathematics knowledge”, “actuality” and “geometrical figures & shapes”. Actually, findings correspond with the literature in a way that confirms the validity of the scale. 62.64% of variance is explained by these three dimensions which also show that self-efficacy of visual mathematics literacy is a multidimensional construct. Factors are also intercorrelated while reliability coefficients of each factor as .94, .86 and .89 are considerably high. All in all, although the “Visual Mathematics Literacy Self Efficacy Scale” displays the basic properties of a reliable and valid scale for teacher candidates, it needs to be validated in the long run due to continuity of validation process of the scale development.

References

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman. Bekdemir, M. & Duran, M. (2012). Development of a visual math literacy self efficacy perception scale for elementary students. Journal of Ondokuz Mayıs University Education Faculty, 31(1), 89-115. Duchastel, P. C. (1980). Research on Illustrations in Instructional Texts. Bryn Mawr, Pa.: The American College, Department of Research and Evaluation. (ERIC Document Reproduction Service No. ED 215 324) Humbree, R. (1992). Experiments and relational studies in problem solving: A meta-analysis. Journal for Research in Mathematics Education, 23 (3), 242-273. Kaiser, G. & Willender, T. (2005). Development of mathematical literacy: Result of an empirical study. Teaching Mathematics and its Applications, 24(2-3), 48-60. Kar, T. & İpek, A. S. (2009). Matematik tarihinde sözel problemlerin çözümünde görsel temsillerin kullanılması [ Use of visual representations on solving word problems on mathematics history]. Journal of Qafqaz University, 28, 138-147. Kordigel Abersek (2008). Visual literacy-one of 21st century literacies for science teaching and learning. Problems of Education in the 21st Century, 5, 9-17. OECD ( Organization for Economic Co-operation and development). (2006). Assessing scientific, reading and mathematical literacy, A Framework for PISA 2006. Retrieved from the World Wide Web: http://www.oecd-ilibrary.org/docserver/download/9806031e.pdf?expires=1391258249&id=id&accname=ocid43023559&checksum=9B5AD6DD52CBC334DDD9F55C05F8CBEA OECD ( Organization for Economic Co-operation and development). (2012). PISA 2012 asessement and analytical framework, matehematics, reading, science, problem solving and financial literacy. Retrieved from World Wide Web: http://www.oecd.org/pisa/pisaproducts/PISA%202012%20framework%20e-book_final.pdf Polya, G. (1973). How to solve it, a new aspect of mathematical method. New Jersey: Princeton University Press. Taşkın Can, B., Cantürk Günhan, B.& Öngel Erdal, S. (2005). Fen bilgisi öğretmen adaylarının fen derslerinde matematiğin kullanımına yönelik özyeterlik inançlarının incelenmesi [The examination of self efficacy beliefs of science teacher candidates toward the use of mathematics on science lessons]. Jouırnal of Pamukkale University Education Faculty, 17, 47–52. Tschannen-Moran, M. & Woolfolk Hoy, A. (2007). The differential antecedents of self efficacy belşefs of novice and experienced teachers. Teaching & Teacher Education, 23(6), 944-956. Wileman, R.E. (1993). Visual communicating. Englewood Cliffs, New Jersey: Educational Technology Publications.

Author Information

Başak Çalık (presenting / submitting)
Middle East Technical University
Educational Sciences
Ankara
Yeşim Çapa Aydın (presenting)
Middle East Technical University, Turkey

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