Zhangtao Xu, Na Li, Bo Li


This study is to provide a better understanding of pre-service teachers’ knowledge of students’ mathematics learning through the rubrics of trigonometric function. Participants are 6 pre-service teachers from a level normal university. The method of TELT is considered in this study to analyze the factors which can have effect on their understanding. The results show that pre-service teachers always take for granted students’ learning and cannot predicate the possible difficulties during their learning and cannot grasp the keystone for breaking through difficulties. It because they cannot know the process of mathematics genesis and development and mathematics essence hidden in the formulas. The results also show that pre-service teachers cannot ascertain the students’ mistakes in cognition. And, without the proficiency of mathematics history, pre-service teachers cannot predict and understand students’ mathematics learning process.


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China mathematics knowledge, teaching mathematics, mathematical content, mathematical learning, student thinking / 中国数学知识;数学教学;数学内容;数学学习;数学思维

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Akkaş, E. N., & Türnüklü, E. (2015). Middle School Mathematics Teachers’ Pedagogical Content Knowledge Regarding Student Knowledge about Quadrilaterals. İlköğretim Online, 14(2):744-756.

An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7(2), 145-172.

An, S., & Wu, Z. (2012). Enhancing mathematics teachers’ knowledge of students’ thinking from assessing and analyzing misconception in homework. International Journal of science and Mathematics Education, 10(3):717-753.

An, S., & Wu, Z. (2014). Using evidence-based MSA approach to enhance teacher knowledge in student mathematics learning and assessment. Journal of Mathematics Education, 7(2), 108-129.

Barbara M., Kinach (2002). A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics course: Toward a model of effective practice. Teaching and Teacher Education, 18(1), 51-71.

Ausubel, D. P. (1968). Educational Psychology: A Cognitive View. New York: Holt, Rinehart and Winston.

Ball, D. L., Thames, M. H. & Phelps (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 5, (5), 389-407.

Blackett, N., & Tall, D. O. (1991). Gender and the versatile learning of trigonometry using computer software. In F. Furinghetti (Ed.), Proceedings of the 15th conference of the International Group for the Psychology of Mathematics Education. Assisi, Italy: PME.

Bogden, R. C., Biklen, S. K. (1992). Qualitative research for education. Allyn & Bacon, Boston.

Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(3), 247-285.

Clark, K. M. (2012). History of mathematics: Illuminating understanding of school mathematics concepts for prospective mathematics teachers. Educational Studies in Mathematics, 81(1), 67-84.

Jankvist, U. T., Mosvold, R., Fauskanger, J., Jakobsen, A. Mathematical knowledge for teaching in relation to history in mathematics education[J]. The conference paper of 12th International Congress on Mathematical education, Seoul, 2012.

Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34(4), 12-25.

Deng, A. (1995). Estimating the reliability of the questionnaire used in the Teacher Education and Learning to Teach study. Technical Series Report 95-1. East Lansing, MI: National Center for Research on Teacher Education.

Dlice, A. (2003). A comparative study of students’ understanding of trigonometry in The United Kingdom and Turkish Republic, PhD thesis, University of Leeds.

Empson, S. B., & Jacobs, V. R. Learning to listen to children’s mathematics. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Vol. 2. Tools and processes in Mathematics teacher education (pp.257-281). Rotterdam, The Netherlands: Sense Publishers.

Fauvel, J., & Van Maanen, J. A. (Eds.). (2000). History in mathematics education. Dordrecht: Kluwer Academic Publishers.

Fennema, E. & Franke, M. (1992).Teachers’ knowledge and its impact. In D. A. Grouws(Ed). Handbook of Research on Mathematics Teaching and learning. New York: Macmillan.

Graeber, A., & Tirosh, D. (2008). Pedagogical content knowledge: Useful concept or elusive notion. In P. Sullivan & T. Wood (Eds.), The international handbook of mathematics teacher education: Vol.1. Knowledge and beliefs in mathematics teaching and teaching development (pp.117-132). Rotterdam, The Netherlands: Sense Publishers.

Gencturk, Y. C. & Lubienski, S. T. (2013). Measuring mathematical knowledge for teaching: a longitudinal study using two measures. Journal of Mathematics Teacher Education, 16(3):211-236.

Grossman, P. L. (1990). The making of a teacher: Teachers’ knowledge and teacher education. New York: 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(4), 372-400.

Hill, H. C., Blunk, M., Charalambous, Y. C., Lewis, J., Phelps, G. C. Sleep, L. & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511.

Kennedy, M. et al. (1993). A guide to measures used in the Teacher Education and Learning to Teacher study. East Lansing, MI: National Central for Research in Teacher Education.

Kilic, H. (2011). Pre-service Secondary Mathematics Teachers' Knowledge of Students. Online Submission, 2(2), 17-35.

Morris, A. K., Hiebert, and J. & Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can pre-service teachers learn? Journal for Research in Mathematics Education, 40(5), 491-529.

National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatick, J. Swafford, & B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education

Orhun, N. (2004). Students’ mistake and misconception on teaching of trigonometry.

Park, S., Oliver. (2008). Revisiting the conceptualization of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand Teachers as Professionals. Research Science Education, 38(3), 261-284.

Peng, A. & Luo, Z. (2009). A framework for examining mathematics teaching knowledge as used in error analysis. For the Learning of Mathematics, 29(3):22-25.

Rajan P., Patil P., Anjane K., Srinivas P. (1990). The trigonometry tutor. Lecture Notes in Computer Science, Springer Berlin.

Schoenfeld, A., H. (1998). Toward a theory of teaching-in-context. Issues in Education, 4(1),1-94.

Shulman, L. S. (1986). Those who understand: Knowledge 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.

Xu, Z. Gu, L. (2011). Mathematics knowledge for teaching in China. Journal of Education Development Research, (6):52-57.

Yang, Y. D. (2007). Mathematics teaching reform for 30 years: Reality and implementation------the new century action from the Qingpu experiment. Journal of Shanghai Education Scientific Research, (12):4-9.

Zhang, J. Z. (2004). What is education mathematics? Journal of Higher Mathematics, (6):2-6.



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