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Pedagogical Content Knowledge and Self-Efficacy

Classroom teaching is a very complex, challenging, demanding, frightening, and nuanced activity (Shulman, 2004). Notably, teachers receive and teacher education in learning institutions in a specific field, general knowledge, and pedagogical formation (Abell, 2008). As such, pedagogical content knowledge is based on both pedagogical and content knowledge. It incorporates pedagogical knowledge, teaching processes, content knowledge, and realizing teaching, which determines teachers’ knowledge in a certain subject (Shulman, 1986).

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By definition, pedagogical content knowledge is the mastery in which a teacher knows how to teach the desired content. Content knowledge is the amount of actual knowledge and the organization in the mind of a teacher (Shulman, 1986). On the other hand, pedagogical knowledge is the knowledge that entails the strategies and principles of classroom management and organization in education (Shulman, 1987). Yilmaz (2011) notes that mastery experience influences pedagogical knowledge and content during teaching. This essay paper reviews the effect of pedagogical content knowledge on preservice mathematics teacher self-efficacy.

The teachers’ astuteness of self-efficacy is an essential characteristic of effective teaching and creates a positive relationship between teachers and students (Swackhamer, Koellner, Basile & Kimbrough, 2009). The findings of a study done by Swackhamer et al. (2009) show that self-efficacy levels are positively influenced by the content-specific knowledge through pedagogical emphasis. Pedagogical content knowledge enhances teachers’ ability to succeed in teaching mathematics through improved astuteness of self-efficacy. Notably, it enables preservice teachers to formulate and represent the subject to students in a comprehensible manner. Besides, it enables teachers to comprehend what makes certain hard or easy to understand (Graeber, 1999). Further, it enables preservice teachers to acknowledge the models and pre-concepts that students from diverse backgrounds and ages bring in the classroom (Graeber, 1999).

Pedagogical content knowledge enhances preservice mathematics teachers’ belief that students will have positive learning outcomes. Steele and Hillen (2012) note that preservice teachers with common pedagogical instructions can teach students much better. However, content knowledge of certain topics influences the manner in which a preservice teacher should teach mathematics. Therefore, mixing mathematical and pedagogical tasks will enhance mathematics knowledge among preservice teachers (Steele & Hillen, 2012).

Notably, pedagogical content knowledge is the way of understanding, which is unique to preservice teachers. In this regard, preservice teachers can take the subject matter and transform their understanding into instructions that students can comprehend (Shulman, 1986). In this case, pedagogical content knowledge entails the amalgam of pedagogy and content, which differentiates “teachers” from “knowers” (Balboa & Stiehl, 1995). One way to amalgamate pedagogy and content is through group discussions, as they introduce strong feelings and commitment. According to Shulman (1984), teachers must involve themselves in deliberation, debate, and decision making on how to teach because it is the only way in which sufficient knowledge or pedagogical content knowledge can arise. In this regard, deliberation, debate and decision participation improves teachers’ self-efficacy regarding content delivery.

According to Ball (1990), the mathematical understandings that potential teachers bring are insufficient to teach understandable mathematics. Although teachers claim to learn subject matter from teaching it, they do not establish the principles and concepts underlying numerous rules and their connections (Ball, 1990). As such, preservice teachers without pedagogical content knowledge cannot revolutionize the ideas about mathematics because they assume that self-efficacy will happen automatically through teaching (Ball, 1990). In this regard, pedagogical content knowledge enhances and transforms the understanding of mathematics among preservice teachers hence better comprehensiveness of students (Ball, 1990).

The connection between content and pedagogy is the key to understanding knowledge base of mathematics (Shulman, 1989). This intersection enables teachers to transform content knowledge they possess into pedagogically powerful and adaptive variations, which is comprehensible to students from different backgrounds (Shulman, 1987). To transform the content knowledge into students, a preservice teacher needs to understand and be sensitive to aspects such as zero, fractions, odd and even numbers, and the manner in which students perceive mathematics in general (Ball & Bass, 2000). Mainly, pedagogical content knowledge brings knowledge and sensitivity among preservice teachers. Knowledge and sensitivity provide teachers with credible reason why a student does not understand the subject taught. In retrospect, pedagogical content knowledge improves the understanding of teachers about the manner in which students should be taught to comprehend certain topics in mathematics.

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Abell, S. K. (2008). Twenty years later: Does pedagogical content knowledge remain a useful idea? International Journal of Science Education, 30(10), 1405-1416.

Balboa, J. M. & Stiehl, J. (1995). The generic nature of pedagogical content knowledge among college professor. Teaching & Teacher Education, 11(3), 293-306.

Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466.

Ball, D. L. & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83-104), Westport, CT: Ablex.

Graeber, A. O. (1999). Forms of knowing mathematics: What preservice teachers should learn. Educational Studies in Mathematics, 38, 189–208.

Shulman, L. S. (1984). The practical and the eclectic: A deliberation on teaching and educational research, Curriculum Inquiry, 14(2):183-200.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

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Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-21.

Shulman, L. S. (1989). Aristotle had it right: On knowledge and pedagogy. The Holmes Group, Occasional Papers Series Based on Keynote at Annual Meeting, Atlanta, Georgia.

Shulman, L. S. (2004). The wisdom of practice: Essays in teaching, learning and learning to teach. San Francisco: Jossey-Bass, Inc.

Steele, M. D. & Hillen, A. F. (2012). The content-focused methods course: A model for integrating pedagogy and mathematics content. Mathematics Teacher Educator, 1(1), 1-36.

Swackhamer, L., Koellner, K., Basile, C. & Kimbrough, D. (2009). Increase the self-efficacy of in-service teachers through content knowledge. Teacher Education Quarterly, 36(2), 63-78.

Yilmaz, C. (2011). Teachers’ perceptions of self-efficacy, English proficiency, and instructional strategies. Social Behavior & Personality: An International Journal, 39(1), 91-100.

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