Factors Associated with Prospective Teachers’ Achievement in Quadrilateral Definitions: An Exploration of Background Characteristics

Year 2018, Volume: 47 Issue: 2, 566 - 600, 01.10.2018

Ramazan Avcu

Abstract

This study investigated the relationships
among prospective middle school mathematics teachers’ background variables and
their achievement in defining special quadrilaterals. The participants of the
study were 184 prospective teachers (49 males and 135 females) from four intact
classes (38 freshmen, 50 sophomores, 49 juniors, and 47 seniors). The special
quadrilaterals test, the Utley geometry attitude questionnaire, and the
background characteristics questionnaire were used to gather data. The results showed
that participants had low level of achievement in defining special
quadrilaterals. No significant difference was found in their achievement with
respect to gender, enrolment in an elective geometry course, and enrolment in a
teaching practicum course. On the other hand, their achievement scores
differentiated significantly in terms of their year levels. The multiple
regression correlation results showed that prospective teachers’ geometry
course scores were a significant predictor of their achievement, while CGPAs
and geometry attitude scores were not.

Keywords

special quadrilaterals, background variables, prospective teachers

References

• Avcu, R., & Avcu, S. (2015). Turkish adaptation of Utley geometry attitude scale: A validity and reliability study. Eurasian Journal of Educational Research, 58, 1-24.
• Bal, A. P. (2014). Predictor variables for primary school students related to van Hiele geometric thinking. Journal of Theory and Practice in Education, 10(1), 259-278.
• Bal, A. P. (2011). Geometry thinking levels and attitudes of elementary teacher candidates. Inonu University Journal of the Faculty of Education, 12(3), 97-115.
• Bal, A. P. (2012). Öğretmen adaylarının geometrik düşünme düzeyleri ve geometriye yönelik tutumları. Eğitim Bilimleri Araştırma Dergisi, 2(1), 17-34.
• Battista, M. T. (1990). Spatial visualization and gender differences in high school geometry. Journal for Research in Mathematics Education, 21(1), 47-60.
• Christensen, L. B., Johnson, R. B., & Turner, L. A. (2013). Research methods: Design and analysis. Boston: Pearson.
• Dochy, F.J.R.C., De Ridjt, C., & Dyck, W. (2002). Cognitive prerequisites and learning: How far have we progressed since Bloom? Implications for educational practice and teaching. Active Learning in Higher Education, 3, 265-284.
• Duatepe Paksu, A. (2013). Predicting the geometry knowledge of pre-service elementary teachers. Cumhuriyet International Journal of Education, 2(3), 15-27.
• Edwards, B., & Ward, M. (2008). The role of mathematical definitions in mathematics and in undergraduate mathematics courses. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics (pp. 223-232). Washington, DC: Mathematical Association of America.
• Ekstrom, R. B. (1994). Gender differences in high school grades: An exploratory study. New York: College Entrance Examination Board.
• Erkek, Ö., & Işiksal-Bostan, M. (2015). The role of spatial anxiety, geometry self-efficacy and gender in predicting geometry achievement. Elementary Education Online, 14(1), 164-180.
• Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). Los Angeles: Sage Publications.
• Hailikari, T., Nevgi, A., & Komulainen, E. (2008). Academic self‐beliefs and prior knowledge as predictors of student achievement in Mathematics: A structural model. Educational Psychology, 28(1), 59-71.
• Harackiewicz, J.M, Barron, K.E, Tauer, J.M., & Elliot, A.J. (2002). Predicting success in college: A longitudinal study of achievement goals and ability measures as predictors of interest and performance from freshman year through graduation. Journal of Educational Psychology, 94, 562-575.
• Higher Education Council. (2006). Eğitim fakültelerinde uygulanacak yeni programlar hakkında açıklama [Description of the new teacher education curricula]. Retrieved December 31, 2017, from http://www.yok.gov.tr/documents/10279/49665/aciklama_programlar/aa7bd091-9328-4df7-aafa-2b99edb6872f
• Leder, G. C. (1992). Mathematics and gender: Changing perspectives. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 597–622). New York: Macmillan.
• Leikin, R., & Winicki-Landman, G. (2000). On equivalent and non-equivalent definitions: Part 2. For the Learning of Mathematics, 20(2), 24-29.
• Levenson, E., Tirosh, D., & Tsamir, P. (2012). Preschool geometry: Theory, research and practical perspectives. Boston: Sense Publishers.
• Linchevsky, L., Vinner, S., & Karsenty, R. (1992). To be or not to be minimal? Student teachers’ views about definitions in geometry. In W. Geeslin & K. Graham (Eds.), Proceedings of the 16th Conference of the International Group for the Mathematics Education (Vol. 2, pp. 48-55). Durham, NH: University of New Hampshire.
• Ma, X. (1995). Gender differences in mathematics achievement between Canadian and Asian education systems. The Journal of Educational Research, 89(2), 118-127.
• Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analysis. Journal for research in mathematics education, 28(1), 26-47.
• McGraw, R., Lubienski, S. T., & Strutchens, M. E. (2006). A closer look at gender in NAEP mathematics achievement and affect data: Intersections with achievement, race/ethnicity, and socioeconomic status. Journal for Research in Mathematics Education, 37(2), 129-150.
• Ministry of National Education (2013). Ortaokul matematik dersi 5-8.sınıflar öğretim programı [Middle school mathematics curriculum: Grades 5-8]. Ankara: Directorate of State Books.
• Mogari, D. (2010). Gender differences in the learners’ learning of properties of a rectangle, African Journal of Research in Mathematics, Science and Technology Education, 14(3), 92-109.
• Movshovitz-Hadar, N., Zaslavsky, O., & Inbar, S. (1987). An empirical classification model for errors in high school mathematics. Journal for Research in Mathematics Education, 18(1), 3-14.
• Oral, B., & İlhan, M. (2012). İlköğretim ve ortaöğretim matematik öğretmen adaylarının geometrik düşünme düzeylerinin çeşitli değişkenler açısından incelenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 6(1), 201-219.
• Pallant, J. (2016). SPSS survival manual: A step by step guide to data analysis using IBM SPSS (6th ed.). Maidenhead: Open University Press.
• Parsons, R. R. (1993). Teacher beliefs and content knowledge: Influences on lesson crafting of pre-service teachers during geometry instruction (Unpublished doctoral dissertation). Washington State University, USA.
• Reynolds, D., & Teddlie, C. (2000). The processes of school effectiveness. In D. Reynolds & C. Teddlie (Eds.), The international handbook of school effectiveness research (pp. 134-159). London: Farmer Press.
• Rumberger, R.W., & Palardy, G.J. (2004). Multilevel models for school effectiveness research. In D. Kaplan (Ed.), The Sage handbook of quantitative methodology for the social sciences. Thousand Oaks, CA: Sage.
• Selden, A., & Selden, J. (2008). Overcoming students’ difficulties in learning to understand and construct proofs. In M. Carlson, & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics (pp. 95-110). Washington, DC: Mathematical Association of America.
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
• Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169.
• Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. B. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.
• Usiskin, Z., & Griffin, J. (2008). The classification of quadrilaterals: A study of definition. Information Age Publishing, Inc.
• Utley, J. (2007). Construction and validity of geometry attitude scales. School Science and Mathematics, 107(3), 89-93.
• Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2016). Elementary and middle school mathematics: Teaching developmentally (9th ed.). New York, NY: Pearson Education.
• Van Dormolen, J., & Zaslavsky, O. (2003). The many facets of a definition: The case of periodicity. The Journal of Mathematical Behavior, 22(1), 91-106.
• Vinner, S. (2002). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Boston, USA: Kluwer Academic Publishers.
• Wilkins, J. L. M., Zembylas, M., & Travers, K. J. (2002). Investigating correlates in mathematics and science literacy in the final year of secondary school. In D. F. Robitaille & A. E. Beaton (Eds.), Secondary analysis of the TIMMS data (pp. 291-316). Boston: Kluwer.
• Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal for Research in Mathematics Education, 36(4), 317-346.
• Zazkis, R., & Leikin, R. (2008). Exemplifying definitions: A case of a square. Educational Studies in Mathematics, 69(2), 131-148.