Knowledge of Student’s Understanding and The Effect on Instructional Strategies: a Case of Two Novice Mathematics Teachers

Masduki Masduki(1*), Stephanus Suwarsono(2), Mega Teguh Budiarto(3)

(1) Universitas Muhammadiyah Surakarta
(2) Sanata Dharma University, Yogyakarta
(3) Surabaya State University
(*) Corresponding Author

Abstract

Pedagogical content knowledge plays a role in learning in classroom. The study aims to 1) analyze the teachers’ knowledge of the students' errors and difficulties in solving linear equations and 2) describe the instructional strategies used by teachers to reduce their errors and difficulties. The subjects were two novice teachers who have taught the Junior High School 7th grade students with different math abilities for two years. The data collection was conducted by open questionnaire and interview. The results showed that both teachers have knowledge of students' errors and difficulties in solving linear equations. However, the teacher's learning strategies in helping students reduce students' errors and difficulties were different from one another. It can be concluded that the teacher's knowledge of the students’ errors and difficulties can help teachers determine the appropriate learning strategies to present a learning subject matter.

Keywords

pedagogical content knowledge, students’ errors and difficulties, teachers’ strategies

Full Text:

PDF

References

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

Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished Doctoral Dissertation. Michigan State Univesity, East Lansing. https://doi.org/10.1086/461626

Borko, H., & Putnam, R. T. (1996). Learning to Teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 673–708). New York: Macmillan.

Brizuela, B., & Schliemann, A. (2004). Ten-Year-Old Students Solving Linear Equations. For the Learning of Mathematics, 24(2), 33–40.

Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical Content Knowing: An Integrative Model for Teaching Preparation. Journal of Teacher Education, 44(4), 263–272.

Filloy, E., & Rojano, T. (1989). Solving Equations : the Transition from Arithmetic to Algebra, 2(June), 19–26.

Grossman, P. L. (1989). A Study in Contrast: Sources of Pedagogical Content Knowledge for Secondary English. Journal of Teacher Education, 40(5), 24–31. https://doi.org/10.1177/002248718904000504

Grossman, P. L., & Richert, A. E. (1988). Unacknowledged knowledge growth: A re-examination of the effects of teacher education. Teaching and Teacher Education, 4(1), 53–62. https://doi.org/10.1016/0742-051X(88)90024-8

Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra 1, 2. Educationa Studies in Mathematics, 27, 59–78.

Jupri, A., Drijvers, P., & Heuvel-Panhuizen, M. van den. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-013-0097-0

Krawec, J. L. (2014). Problem Representation and Mathematical Problem Solving of Students of Varying Math Ability. Journal of Learning Disabilities, 47(2), 103–115. https://doi.org/10.1177/0022219412436976

Linchevski, L., & Herscovics, N. (1996). Crossing The Cognitive Gap Between Arithmetic and Algebra: Operating on the Unknown in the Context of Equations. Educational Studies in Mathematics, 30, 39–65.

Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources, and development of pedagogical content knowledge for science teaching. In J. Gess-Newsome & G. Lederman (Eds.), Examining pedagogical content knowledge: The construct and its implications for Science Education (pp. 95–132). Dordrecht, Netherland: Kluwer Academic. https://doi.org/10.1007/0-306-47217-1_4

Magruder, R. L. (2012). Solving Linear Equations : A Comparison of Concrete and Virtual Manipulatives in Middle School Mathematics. University of Kentucky, US. Retrieved from uknowledge.uky.edu/edc_etds/2

Mancl, D. B., Miller, S. P., & Kennedy, M. (2012). Using the concrete-representational-abstract sequence with integrated strategy instruction to teach subtraction with regrouping to students with learning disabilities. Learning Disabilities Research and Practice, 27(4), 152–166. https://doi.org/10.1111/j.1540-5826.2012.00363.x

Marks, R. (1990). Pedagogical Content Knowledge: From a Mathematical Case to a Modified Conception. Journal of Teacher Education, 41(3), 3–11. https://doi.org/10.1177/002248719004100302

Miles, B. M., & Huberman, A. M. (1994). Qualitative Data Analysis (2nd Editio). California: Sage Publications.

NCTM. (2000). Principles and Standards for School Mathematics. (J. Carpenter & S. Gorg, Eds.). Reston, VA: The Natioanal Council of Teachers of Mathematics.

Papaieronymou, I. (2007). Student Difficulties in Understanding The Difference Between Algebraic Expressions and The Concept of Linear Equations. In D. Pitta – Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education 22 - 26 February 2007 (pp. 934–943). Larnaca, Cyprus: Department of Education, University of Cyprus.

Park, S., & Chen, Y. C. (2012). Mapping out the integration of the components of pedagogical content knowledge (PCK): Examples from high school biology classrooms. Journal of Research in Science Teaching, 49(7), 922–941. https://doi.org/10.1002/tea.21022

Park, S., & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Science Education, 38(3), 261–284. https://doi.org/10.1007/s11165-007-9049-6

Park, S., & Steve Oliver, J. (2008). National Board Certification (NBC) as a catalyst for teachers’ learning about teaching: The effects of the NBC process on candidate teachers’ PCK development. Journal of Research in Science Teaching. https://doi.org/10.1002/tea.20234

Rollnick, M., Bennett, J., Rhemtula, M., Dharsey, N., & Ndlovu, T. (2008). The place of subject matter knowledge in pedagogical content knowledge: A case study of South African teachers teaching the amount of substance and chemical equilibrium. International Journal of Science Education, 30(10), 1365–1387. https://doi.org/10.1080/09500690802187025

Shulman, L. S. (1986). Those Who Understand : Knowledge Growth in Teaching. Educational Researcher, 15(2), 4–14. Retrieved from http://www.jstor.org/stable/1175860

Shulman, L. S. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review, 57(1), 1–21. https://doi.org/10.1007/SpringerReference_17273

Smith, D. C., & Neale, D. C. (1991). The construction of subject-matter knowledge in primary science teaching. Advances in Research on Teaching, 2(I), 187–243. https://doi.org/10.1016/0742-051x(89)90015-2

Tamir, P. (1988). Subject Matter and Related Pedagogical in Teacher Education. Teaching & Teacher Education, 4(2), 99–110.

van Garderen, D. (2008). Middle School Special Education Teachers’ Instructional Practices for Solving Mathematical Word Problems: An Exploratory Study. Teacher Education and Special Education, 31(2), 132–144. https://doi.org/10.1177/088840640803100206

van Garderen, D., Scheuermann, A., & Jackson, C. (2013). Examining How Students With Diverse Abilities Use Diagrams to Solve Mathematics Word Problems. Learning Disability Quarterly, 36(3), 145–160. https://doi.org/10.1177/0731948712438558

Warren, E. (2003). The Role of Arithmetic Structure in the Transition from Arithmetic to Algebra. Mathematics Education Research Journal, 15(2), 122–137.

Widjaja, W., & Stacey, K. (2009). Growth of pre-service teachers’ knowledge and teaching ideas about decimals and fractions: The case of Vivi. Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia, 2(2001), 587–594.

Article Metrics

Abstract view(s): 683 time(s)
PDF: 478 time(s)

Refbacks

  • There are currently no refbacks.