An Investigation of Prospective Mathematics Teachers’ Pedagogical Content Knowledge in the Beginning of their Profession

Author(s):

Elcin Emre Akdogan(presenting / submitting)Gonul Yazgan-Sag

Conference:

ECER 2015

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 03, Teachers' Perspectives

Paper Session

Time:

2015-09-08

17:15-18:45

Room:

659.Oktatóterem [C]

Chair:

n.n. n.n.

Contribution

Bridging between theory and practice is one of the common problems in teacher education. Teaching practice offers a general solution to this problem (Oliveira & Hannula, 2005). However in order to build up knowledge of prospective teachers, observing learning environments in their complexity is important for them in the sense that they can generate interactions with students and give insightful reflections during their teaching practice (Oliveira & Hannula, 2005). Teacher knowledge has an essential role in teaching and learning (Lannin et al., 2013).

Shulman’s (1987)` theory for knowledge of teaching comprised of subject matter knowledge (SMK), general pedagogical knowledge and pedagogical content knowledge (PCK), which he defines as a “special amalgam of content and pedagogy that is uniquely the province of teachers, their own special form of professional understanding” (p. 8). Most scholars and policy makers have a consensus on Shulman’s pedagogical content knowledge (PCK) that it has an important contribution to teaching and learning mathematics (Hill, Ball, & Schilling, 2008). Shulman’s (1986, 1987) conceptions of PCK have extended by researchers in mathematics education (Lannin et al., 2013). As Hill et al. (2008) described, mathematical knowledge for teaching (MKT) is comprised of subject matter knowledge (SMK) and PCK. Subject matter knowledge consists of common content knowledge (CCK), specialized content knowledge (SCK), and knowledge at the mathematical horizon. Knowledge of content and students (KCS), knowledge of content and teaching (KCT), and knowledge of curriculum are subcategories of PCK. On the other hand the framework that Chick, Baker, Pham, and Cheng (2006) suggested is comprised of three categories: Clearly PCK includes those aspects, which are most clearly a blend of content and pedagogy; Content Knowledge in a Pedagogical Context includes those aspects drawn most directly from content; and Pedagogical Knowledge in a Content Context includes knowledge which has been drawn most directly from pedagogy (Chick et al., 2006).

After examining theoretical perspectives on teacher’s pedagogical content knowledge, we decided to determine prospective teachers’ pedagogical content knowledge based on their knowledge on (i) instruction and (ii) students’ thinking. The purpose of the study is to investigate prospective mathematics teachers’ pedagogical content knowledge in their first teaching practice. We formulate our research question as the following: What do prospective mathematics teachers have that can be considered as a pedagogical content knowledge in their first teaching experience?

Method

We conducted study with four prospective mathematics teachers in a five-year teacher education program at the Secondary Mathematics Education Department of a University in Turkey. As prospective mathematics teachers in this program completed subject matter courses related to mathematics in the first seven semesters, in the remaining three semesters, they took pedagogical courses. At the time of the study, participants were attending the fifth (final) year of the program. They had completed subject matter courses as well as most of the pedagogical courses such as Teaching Methods on Mathematics Education, Classroom Management, Instructional Technology and Material Development. We collected data during prospective mathematics teachers’ school experience course that takes 14 weeks (one-semester long), in a high school. “School experience” course aims helping prospective teachers making observations and building up teaching practice. While prospective teachers are responsible for making observations about school setting, classroom setting, and their mentors’ instructional approaches, they are also required to prepare a classroom activity and implement it in their mentor teacher’s class. The data for this study was collected through classroom observations and interviews that were videotaped. We did three focus group interviews during the “school experience” course in order to determine prospective teachers’ knowledge of pedagogical approaches on the specific content. We have done two classroom observations while four prospective teachers perform classroom activity in pairs in their mentors’ class. The qualitative data analysis, designated by Auerbach and Silverstein (2003), was adopted while analyzing the data collected throughout the research. This perspective can be defined as content analysis (Yıldırım & Şimşek, 2006). The data taken from the research were separated into meaningful units in the first step of coding, which is described by Patton (2002). The data was coded and categorized according to these units and then the categories were analyzed and interpreted.

Expected Outcomes

According to the results, besides mainly having knowledge of instructional strategies, the prospective mathematics teachers have limited knowledge of students’ thinking. We examined prospective mathematics teacher’s pedagogical content knowledge in two categories: (i) knowledge of instruction and (ii) knowledge of students' thinking. Furthermore, we determined sub-categories for these categories. Prospective mathematics teachers’ knowledge of instruction consists of these sub-categories: “enabling students’ exploring”, “student-oriented”, “enabling students questionings of reasons”, “group working”, “awareness of different representations and ability to use them” and “knowledge of materials that can be used in the classroom”. Prospective mathematics teachers’ knowledge of students thinking also comprise of these sub-categories: “awareness of students prerequisite knowledge” and “allowing students to think independently”. The results of this research are consistent with the previous studies. To exemplify, some studies detected that the teachers with little experience also have little pedagogical content knowledge (Feiman-Nemsera & Parker, 1990). The more pedagogical content knowledge the teachers and / or prospective teachers have, the more they will be able to reflect their knowledge while teaching. One of the most significant components of teacher knowledge is their knowledge of students’ thinking. Teachers are expected to have the technical knowledge to evaluate the students’ thinking and understanding; and the knowledge to detect the students’ conceptual mistakes; the educational strategic knowledge to help the students associate their background information with their current information and to correct the possible conceptual mistakes the students may make (Carpenter, Fennema, Peterson, & Carey, 1988). Teachers must take into account of the current mathematical concepts and conceptual mistakes of the students while teaching. In order to do so, the teachers must have knowledge related to the students’ way of thinking (Grouws & Schultz, 1996).

References

Auerbach, C. F., & Silverstein, L. B. (2003).Qualitative data: An introduction to coding and analysis. New York: New York University Press. Carpenter, T. P., Fennema, E., Peterson, P. L., &Carey, D. (1988). Teachers' pedagogical Content knowledge of students' problem solving. Journal of Research in Mathematics Education, 19, 385-401. Chick, H. L., Baker, M., Pham, T., & Cheng, H. (2006). Aspects of teachers’ pedagogical content knowledge for decimals. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 297-304). Prague: PME. Feiman-Nemser, S. &Parker, M. B. (1990). Making Subject Matter Part of the Conversation or Helping Beginning Teachers Learn to Teach. East Lansing, MI: National Center for Research on Teacher Education. Grouws, D. &Schultz, K. (1996). Mathematics teacher education in: J. Sikula (Ed) Handbook Of Research On Teacher Education, 2nd edition. USA: Macmillan. Hill, Ball, & Schilling, (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-Specific Knowledge of Students. Journal for Research in Mathematics Education, 39 (4), 372–400. Lannin, J. K., Webb, M., Chval, K., Arbaugh, F., Hicks, S., Taylor, C., & Bruton, R. (2013). The development of beginning mathematics teacher pedagogical content knowledge. Journal of Mathematics Teacher Education, 16(6), 403-426. Oliveira, H., &Hannula, M. S. (2008). Individual prospective mathematics teachers: Studies on their professional growth. In K. Krainer & T. Wood (Eds.), Participants in mathematics teacher education (Vol. 2, pp. 13–34). Rotterdam: Sense Publishers. Patton, M. Q. (2002). Qualitative research and evaluation methods. Newbury Park: Sage Publication. Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher 15, 4–14. Shulman, L.S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review 57, 1 – 22. Yıldırım, A. & Şimşek, H. (2006).Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.

Author Information

Elcin Emre Akdogan (presenting / submitting)

Gazi University

Department of Secondary Science and Mathematics Education

Ankara

Gonul Yazgan-Sag

Gazi University, Turkey

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