Measuring pre-service elementary teachers’ geometry knowledge for teaching 2-dimensional shapes

Minju Yi; Jian Wang; Raymond Flores; Jaehoon Lee

doi:10.29333/ejmste/12220

Full Text (PDF)

Minju Yi ¹ ^* , Jian Wang ¹ , Raymond Flores ¹ , Jaehoon Lee ¹

More Detail

¹ College of Education, Texas Tech University, Lubbock, TX, USA^* Corresponding Author

Abstract

This paper reports our efforts to develop a measure of pre-service elementary teachers’ geometry knowledge for teaching 2-dimensional (2D) shapes and to evaluate the psychometric properties of this measure. Specifically, the GKT-2D scale was designed to assess pre-service elementary teachers’ geometry content knowledge, knowledge of geometry and students, knowledge of geometry and teaching in relation to 2D shapes, based on the van Hiele theory and mathematical knowledge for teaching framework. Using 307 pre-service elementary teachers’ responses on the instrument, we examined item- and scale-level reliability and hypothesized factor structure of the instrument. The results suggested that the GKT-2D scale is a reliable and valid measure of the three facets of pre-service elementary teachers’ geometry knowledge for teaching 2D shapes, with some limitations further addressed. This paper offers directions for future research in evaluating content-specific knowledge for teaching mathematics to unpack the complex relationship between teacher knowledge, teaching quality, and student learning.

Keywords

geometry knowledge for teaching
pre-service elementary teachers
reliability and validity
van Hiele theory

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2022, Volume 18, Issue 8, Article No: em2137

https://doi.org/10.29333/ejmste/12220

Publication date: 12 Jul 2022

Article Views: 1536

Article Downloads: 1049

Open Access References How to cite this article

References

Abellan, M. B., & Ginovart, M. (2010). Moodle quizzes for assessing statistical topics in engineering studies. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.853.7392&rep=rep1&type=pdf
Alex, J. K., & Mammen, K. J. (2016). Geometrical sense making: Findings of analysis based on the characteristics of the van Hiele theory among a sample of South African grade 10 learners. EURASIA Journal of Mathematics, Science, and Technology Education, 12(2), 173-188. https://doi.org/10.12973/eurasia.2016.1211a
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). Information Age.
Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238-246. https://doi.org/10.1037/0033-2909.107.2.238
Bentler, P. M., & Bonett, D. C. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88, 588-606. https://doi.org/10.1037/0033-2909.88.3.588
Bleeker, C., Stols, G., & Van Putten, S. (2013). The relationship between teachers’ instructional practices and their learners’ level of geometrical thinking. Perspectives in Education, 31(3), 66-78.
Brakoniecki, A., Glassmeyer, D., & Amador, J. (2016). Examining PSTs thinking about technology-based trigonometric explorations through replacing, amplifying, and transforming framework. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38^th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (1463-1470). The University of Arizona.
Brown, T. A. (2015). Confirmatory factor analysis for applied research. Guilford Publications.
Browning, C., Edson, A. J., Kimani, P. M., & Aslan-Tutak, F. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on geometry and measurement. The Mathematics Enthusiast, 11(2), 333-384. https://doi.org/10.54870/1551-3440.1306
Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17(1), 31-48. https://doi.org/10.2307/749317
Carroll, W. (1998). Middle school students’ reasoning about geometric situations. Mathematics Teaching in the Middle School, 3(6), 388-403. https://doi.org/10.5951/MTMS.3.6.0398
Chapman, O. (2007). Facilitating PSTs’ development of mathematics knowledge for teaching arithmetic operations. Journal of Mathematics Teacher Education, 10, 341-349. http://doi.org/10.1007/s10857-007-9046-8
Charalambous, C. Y., & Pitta-Pantazi, D. (2015). Perspectives on priority mathematics education: Unpacking and understanding a complex relationship linking teacher knowledge, teaching, and learning. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (pp. 19-59). Routledge. https://doi.org/10.4324/9780203448946-8
Clements, D. H. (2003). Teaching and learning geometry. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp 15-78). National Council of Teachers of Mathematics.
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). Macmillan.
Council of Chief State School Officers & National Governors Association. (2010). Common core state standards-mathematics. http://www.corestandards.org/Math
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/bf02310555
Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. Learning and Teaching Geometry, K-12, 1-16.
Darling-Hammond, L., Holtzman, D., Gatlin, S., & Vasquez-Heilig, J. (2005). Does teacher preparation matter? Evidence about teacher certification, teach for America, and teacher effectiveness. Education Policy Analysis Archives, 13, 1-48. https://doi.org/10.14507/epaa.v13n42.2005
Ellerton, N. F., & Clements, M. A. (2011). Prospective middle-school mathematics teachers’ knowledge of equations and inequalities. In J. Cai, & E. Knuth (Eds.), Early algebraization. Advances in mathematics education (pp. 379-408). Springer. https://doi.org/10.1007/978-3-642-17735-4_21
Esendemir, O., & Bindak, R. (2019). Adaptation of the test developed to measure mathematical knowledge of teaching geometry in Turkey. International Journal of Educational Methodology, 5(4), 547-565. https://doi.org/10.12973/ijem.5.4.547
Everitt, B. S., & Skrondal, A. (2010). The Cambridge dictionary of statistics. Cambridge University Press. https://doi.org/10.1017/CBO9780511779633
Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (147-164). Macmillan.
Ferrini-Mundy, J., Floden, R., McCrory, R., Burrill, G., & Sandow, D. (2005). Knowledge for teaching school algebra: challenges in developing an analytic framework. Michigan State University.
Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60-72. https://doi.org/10.1016/j.jmathb.2011.08.003
Fuys, D., Geddes, D., & Tishler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education, 3, 1-196. https://doi.org/10.2307/749957
George, D., & Mallery, P. (2003). SPSS for Windows step by step: A simple guide and reference, 11.0 update. Allyn & Bacon.
Gonzales, P., Guzman, J. C., Partelow, L., Pahlke, E., Jocelyn, L., Kastberg, D., & Williams, T. (2004). Highlights from the trends in international mathematics and science study (TIMSS) 2003. NCES 2005-005. U.S. Department of Education. https://doi.org/10.1037/e672832007-002
Gonzales, P., Williams, T., Jocelyn, T., Roey, S., Kastberg, D., & Brenwald, S. (2009). Highlights from TIMSS 2007: Mathematics and science achievement of U.S. fourth and eighth-grade students in an international context. NCES 2009-001. National Center for Education Statistics.
Gutierres, A., Jaime, A., & Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. Journal for Research in Mathematics Education, 22(3), 237-251. https://doi.org/10.2307/749076
Halat, E. (2008). Preservice elementary school and secondary mathematics teachers’ van Hiele levels and gender differences. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1-10.
Herbst, P., & Kosko, K. (2014). Mathematical knowledge for teaching and its specificity to high school geometry instruction. In J. J. Lo, K. R. Leatham, & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 22-45). Springer. https://doi.org/10.1007/978-3-319-02562-9_2
Herbst, P., Ko, I., & Milewski, A. (2020). A heuristic approach to assess change in mathematical knowledge for teaching geometry after a practice-based professional learning intervention. Research in Mathematics Education, 22(2), 188-208. https://doi.org/10.1080/14794802.2019.1704851
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400. https://doi.org/10.5951/jresematheduc.39.4.0372
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 104(1), 11-30. https://doi.org/10.1086/428763
Hill, H., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Education Research Journal, 42(2), 371-406. https://doi.org/10.3102/00028312042002371
Hock, T. T., Tarmizi, R. A., Yunus, A. S., & Ayub, A. F. (2015), Understanding the primary school students’ van Hiele levels of geometry thinking in learning shapes and spaces: A q-methodology. EURASIA Journal of Mathematics, Science and Technology Education, 11(4), 793-802. https://doi.org/10.12973/eurasia.2015.1439a
Hoffer, A. (1981). Geometry is more than proof. Mathematics Teacher, 74(1), 11-18.
Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55. https://doi.org/10.1080/10705519909540118
Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143. https://doi.org/10.1080/07370000701798529
Knight, K.C. (2006). An investigation into the change in the van Hiele levels of understanding geometry of preservice elementary and secondary mathematics teachers. [Unpublished master’s thesis]. University of Main.
Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children’s reasoning about space and geometry. In R. Lehrer, & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137-167). Erlbaum.
Lin, C., Luo, F. Lo, J., & Yang, D. (2011). U.S. and Taiwanese pre-service teachers’ geometry knowledge and thinking. International Journal for Mathematics Teaching and Learning.
Livy, S., & Downton, A. (2018). Exploring experiences for assisting primary preservice teachers to extend their knowledge of student strategies and reasoning. Journal of Mathematical Behavior, 51, 150-160. https://doi.org/10.1016/j.jmathb.2017.11.004
Ma, H., Lee, D., Lin, S., & Wu, D. (2015). A study of van Hiele of geometric thinking among 1^st through 6^th Graders. EURASIA Journal of Mathematics, Science and Technology Education, 11(5), 1181-1196. https://doi.org/10.12973/eurasia.2015.1412a
MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130-149. https://doi.org/10.1037/1082-989X.1.2.130
Manizade, A. G., & Mason, M. M. (2011). Using Delphi methodology to design assessments of teachers’ pedagogical content knowledge. Educational Studies in Mathematics, 76(2), 183-207. https://doi.org/10.1007/s10649-010-9276-z
Marchis, I. (2012). Preservice primary school teachers’ elementary geometry knowledge. Acta Didactica Napocensia, 5(2), 33-40.
Martinovic, D., & Manizade, A. G. (2018). The challenges in the assessment of knowledge for teaching geometry. The International Journal on Mathematics Education, 50(4), 613-629. https://doi.org/10.1007/s11858-018-0934-4
Mayberry, J. (1983). The van Hiele levels of geometric thought in undergraduate preservice teachers. Journal for Research in Mathematics Education, 14(1), 58-69. https://doi.org/10.2307/748797
McCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D., & Senk, S. L. (2012). Knowledge of algebra for teaching: A framework of knowledge and practices. Journal for Research in Mathematics Education, 43(5), 584-615. https://doi.org/10.5951/jresematheduc.43.5.0584
Menon, R. (1998). Preservice teachers’ understanding of perimeter and area. School Science and Mathematics, 98(7), 361-368. https://doi.org/10.1111/j.1949-8594.1998.tb17306.x
Mewborn, D. S. (2003). Teaching, teachers’ knowledge and their professional development. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 45-52). National Council of Teachers of Mathematics.
Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. IEA TIMSS and PIRLS International Study Center. http://timssandpirls.bc.edu/timss2015/international-results/download-center/
Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 International Results in Mathematics and Science. IEA TIMSS & PIRLS International Study Center. https://timssandpirls.bc.edu/timss2019/international-results/
Muthén, B. & Muthén, L. (1998-2017). Mplus user’s guide. Muthén & Muthén.
Nason, R., Chalmers, C., & Yeh, A. (2012). Facilitating growth in prospective teachers’ knowledge: Teaching geometry in primary schools. Journal of Mathematics Teacher Education, 15, 227-249. https://doi.org/10.1007/s10857-012-9209-0
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education. https://files.eric.ed.gov/fulltext/ED500486.pdf
Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American educational research journal, 45(4), 1080-1110. https://doi.org/10.3102/0002831208320851
Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory. McGraw-Hill.
Olanoff, D., Lo, J., & Tobias, J. M. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on fractions, The Mathematics Enthusiast, 11(2), 267-310. https://doi.org/10.54870/1551-3440.1304
Pickreign, J. (2007). Rectangles and rhombi: How well do preservice teachers know them? Issues in the Undergraduate Mathematics Preparation of School Teachers, 1.
Provasnik, S., Kastberg, D., Ferraro, D., Lemanski, N., Roey, S., & Jenkins, F. (2012). Highlights from TIMSS 2011: Mathematics and science achievement of U.S. fourth-and eighth-grade students in an international context. NCES 2013-009. National Center for Education Statistics.
R Core Team. (2019). R: A language and environment for statistical computing. R foundation for statistical computing. http://www.R-project.org/
Reinke, K. S. (1997). Area and perimeter: Preservice teachers’ confusion. School Science and Mathematics, 92(2), 75-77. https://doi.org/10.1111/j.1949-8594.1997.tb17346.x
Robichaux-Davis, R. R., & Guarino, A. J. (2016). Assessing elementary preservice teachers’ knowledge for teaching geometry. International Journal of Mathematics and Statics Invention, 4(1),12-20.
Sandt, S., & Nieuwoudt, H. D. (2003). Grade 7 teachers’ and prospective teachers’ content knowledge of geometry. South African Journal of Education, 23(3), 199-205.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
Steele, M. D. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks. Journal of Mathematics Teacher Education,16(4), 245-268. https://doi.org/10.1007/s10857-012-9230-3
Steiger, J. H., & Lind, J. C. (1980). Statistically based tests for the number of common factors [Paper presentation]. The annual Spring Meeting of the Psychometric Society, Iowa City, IA, USA.
Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory-based instruction: Toward a theory of teaching. Educational Researcher, 41(5), 147-156. https://doi.org/10.3102/0013189X12442801
Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics. Allyn & Bacon.
Taie, S., Goldring, R., & Spiegelman, M. (2017). Characteristics of public elementary and secondary school teachers in the United States: Results from the 2015-16 national teacher and principal survey first look (NCES 2017-072). U.S. Department of Education. National Center for Education Statistics. https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2017072
Texas Education Agency. (2012). Texas essential knowledge and skills (TEKS) for mathematics, elementary. https://www.google.com/search?client=safari&rls=en&q=TEKS&ie=UTF-8&oe=UTF-8
Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38, 1-10. https://doi.org/10.1007/BF02291170
Usiskin, Z. (1982). van Hiele levels and achievement in secondary school geometry. CDASSG project. National Institution of Education.
van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2016). Elementary and middle school mathematics: Teaching developmentally. Pearson.
van Hiele, P. M. (1984). The child’s thought and geometry. In D. Fuys, D. Geddes, & R. Tischler (Eds.), English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele (pp. 243-252). Brooklyn College.
van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.
Welder, R. M., & Simonsen, L. M. (2011). Elementary teachers’ mathematical knowledge for teaching prerequisite algebra concepts. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1-16.
Wenglinksy, H. (2002). How schools matter. The link between teacher classroom practices and student academic performance. Education Policy Analysis Archives, 10(12). https://doi.org/10.14507/epaa.v10n12.2002
Wheaton, B., Muthén, B., Alwin, D. F., & Summers, G. (1977). Assessing reliability and stability in panel models. Sociological Methodology, 8, 84-136. https://doi.org/10.2307/270754
Yilmaz, G. K., & Koparan, T. (2016). The effect of designed geometry teaching lesson on the candidate teachers’ van Hiele geometric thinking level. Journal of Education and Training Studies, 4(1), 129-141. https://doi.org/10.11114/jets.v4i1.1067
Yi, M., Flores, R., & Wang, J. (2020). Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers' geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 103038. https://doi.org/10.1016/j.tate.2020.103038
Zambak, V. S., & Tyminski, A. M. (2017). A case study on specialized content knowledge development with dynamic geometry software: The analysis of influential factors and technology beliefs of three preservice middle grades mathematics teachers. Mathematics Teacher Education and Development, 19(1), 82-106.
Zumwalt, K., & Craig, E. (2005). Teachers’ characteristics: Research on the demographic profile. In M. Cochran-Smith, & K. M. Zeichner (Eds.), Studying teacher education: The report of the AERA panel on research and teacher education (pp. 111-156). Lawrence Erlbaum Associates Publishers.

How to cite this article

APA

Yi, M., Wang, J., Flores, R., & Lee, J. (2022). Measuring pre-service elementary teachers’ geometry knowledge for teaching 2-dimensional shapes. Eurasia Journal of Mathematics, Science and Technology Education, 18(8), em2137. https://doi.org/10.29333/ejmste/12220

Vancouver

Yi M, Wang J, Flores R, Lee J. Measuring pre-service elementary teachers’ geometry knowledge for teaching 2-dimensional shapes. EURASIA J Math Sci Tech Ed. 2022;18(8):em2137. https://doi.org/10.29333/ejmste/12220

AMA

Yi M, Wang J, Flores R, Lee J. Measuring pre-service elementary teachers’ geometry knowledge for teaching 2-dimensional shapes. EURASIA J Math Sci Tech Ed. 2022;18(8), em2137. https://doi.org/10.29333/ejmste/12220

Chicago

Yi, Minju, Jian Wang, Raymond Flores, and Jaehoon Lee. "Measuring pre-service elementary teachers’ geometry knowledge for teaching 2-dimensional shapes". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 8 (2022): em2137. https://doi.org/10.29333/ejmste/12220

Harvard

Yi, M., Wang, J., Flores, R., and Lee, J. (2022). Measuring pre-service elementary teachers’ geometry knowledge for teaching 2-dimensional shapes. Eurasia Journal of Mathematics, Science and Technology Education, 18(8), em2137. https://doi.org/10.29333/ejmste/12220

MLA

Yi, Minju et al. "Measuring pre-service elementary teachers’ geometry knowledge for teaching 2-dimensional shapes". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 8, 2022, em2137. https://doi.org/10.29333/ejmste/12220