Please enter verification code
Clustering Analysis on Teachers’ Perceptions of Mathematics Pedagogical Content Knowledge
American Journal of Applied Psychology
Volume 5, Issue 2, March 2016, Pages: 6-11
Received: Jul. 18, 2016; Published: Jul. 19, 2016
Views 4321      Downloads 161
Yuan-Horng Lin, Department of Mathematics Education, National Taichung University of Education, Taichung City, Taiwan
Yuan-Shun Lee, Department of Mathematics, University of Taipei, Taipei City, Taiwan
Article Tools
Follow on us
The purpose of this study is to cluster the perceptions of mathematics pedagogical content knowledge (MPCK) for teachers. The subject is 259 primary school teachers in Taiwan. This study constructs dimensions of MPCK according to the review and conclusions of literature. The MPCK assessment includes six dimensions, which are mathematics content knowledge (MCK), students’ cognition knowledge (SCK), mathematics instruction knowledge (MIK), mathematics instruction practice (MIP), mathematics assessment knowledge (MAK) and teacher professional responsibility (TPR). The MPCK questionnaire is 4-points Likert scale and its reliability and validity are acceptable. Fuzzy clustering is adopted to cluster the subject based on these six dimensions. Results show that all teachers could be properly classified into six clusters. Each cluster has its own features of mathematics pedagogical content knowledge. There are also significantly differences in the dimensional scores among clusters. Besides, teachers who have more years of in-service tend to have higher dimensional scores on MPCK. These results could provide references for cultivating pre-service teachers and professional promotion for in-service teachers. Based on the findings of this study, some suggestions and recommendations are discussed for future research.
Fuzzy Clustering, Mathematics Pedagogical Content Knowledge, Pedagogical Content Knowledge
To cite this article
Yuan-Horng Lin, Yuan-Shun Lee, Clustering Analysis on Teachers’ Perceptions of Mathematics Pedagogical Content Knowledge, American Journal of Applied Psychology. Vol. 5, No. 2, 2016, pp. 6-11. doi: 10.11648/j.ajap.20160502.11
Ball, D. L., & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2002 annual meeting of the Canadian Mathematics Education Study Group (pp. 3-14). Edmonton, AB: CMESG/GCEDM.
Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics enough to teach third grade, and how can we decide? American Educator, 14-22, 43-46.
Bezdek, J. C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithm. NY: Plenum.
Bjelica, M. & Rankovic, D. (2010). The use of fuzzy theory in grading of students in math. Turkish Online Journal of Distance Education, 11(1), 13-19.
Carpenter, T. P., Fennema, E., Peterson, P. L., CareySource, D. A. (1988). Teachers' pedagogical content knowledge of students' problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19, 385-401.
Cobb, P., & Smith, T. (2008). District development as a means of improving mathematics teaching and learning at scale. In K. Krainer & T. Wood (Eds.), The International Handbook of Mathematics Teacher Education (Vol. 3, pp. 231-254). Rotterdam, The Netherlands: Sense.
Darling-Hammond, L. (2000). Teacher quality and student achievement: A review of state policy evidence. Educational Policy Analysis Archives, 8(1), 1-48.
Fennema, E., & Franke, M. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning: A project of the National Council of Teachers of Mathematics (pp. 147-164). New York, NY, England: Macmillan Publishing.
Greeno, J. (2003). Situative research relevant to standards for school mathematics. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics (pp. 304-332). Reston, VA: National Council of Teachers of Mathematics.
Grossman, P. (1990). The Making of a Teacher: Teacher Knowledge and Teacher Education. New York, NY: Teachers College Press
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, 372-400.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
Inyang, U. G., & Joshua, E. E. (2013). Fuzzy clustering of students’ data repository for at-risks students identification and monitoring. Computer and Information Science, 6(4), 37-50.
Karaman, A. (2012). The place of pedagogical content knowledge in teacher education. Atlas Journal of Science Education, 2 (1), 56-60.
Mewborn, D. (2001). Teachers content knowledge, teacher education, and their effects on the preparation of elementary teachers in the United States. Mathematics Education Research Journal, 3, 28-36.
Mewborn, D.S. (2003). Teaching, teachers’ knowledge, and their professional development. In J. Kilpatrick, W.G. Martin, & D. Schifter (Eds.), A Research Companion to the Principles and Standards for School Mathematics (pp. 45-52). Reston, VA: National Council of Teachers of Mathematics.
Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, 108(6), 1017-1054.
Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and Teacher Education, 21(5), 509-523.
Shulman, L. S. (1986). Those who understand: Knowledge of growth in teaching. Educational Researcher, 15(2), 4-14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
Shulman, L.S., & Grossman, P.L. (1988). Knowledge Growth in Teaching: A Final Report to the Spencer Foundation. Stanford, CA: Standford University.
Siller, H. S., Kuntze, S., Lerman, S., & Vogl, C. (2011). Modelling as a big idea in mathematics with significance for classroom instruction–How do pre-service teachers see it. In Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 990-999).
Thompson, A. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics (pp. 127-146). New York, NY: England: Macmillan Publishing Co, Inc.
Van Driel, J. H., & Verloop, N. (1999). Teachers' knowledge of models and modelling in science. International Journal of Science Education, 21(11), 1141-1153.
Verloop, N., Van Driel, J., & Meijer, P. (2001). Teacher knowledge and the knowledge base of teaching. International Journal of Educational Research, 35(5), 441-461.
Wu, K. L., & Yang, M. S. (2005). A cluster validity index for fuzzy clustering. Pattern Recognition Letters, 26(9), 1275-1291.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-353.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186