“What does it take to be good at something in which failure is so easy, so effortless?” Atul Gawande (2007) said this in his book Better referring to the medical field, but that question can be used in the context of many fields, specifically education. The question of what it means to be an expert at teaching has taken on some urgency in the effort to reform public education (Sternberg and Hovarth, 1995). Theories of expert teaching vary throughout the educational community (Shulman, 1987; Sternberg and Hovath, 1995). Sternberg and Hovarth (1995) state that a model must be developed in teacher expertise to those teachers who are expert at teaching students from those who are merely experienced at teaching students.
Stanovich (2009) states that operationalism is simply the idea that concepts in scientific theories must in some way be linked to observable events that can be measured. To conceptualize and operationalize expert teaching, we must look into the practices and empirical evidence that the theories of expert teachers are based. The purpose of this paper is to examine the literature of the theories of expertise in teaching mathematics. First, the two theories of expertise in teaching in the context of mathematics will be discussed: teacher pedagogical content knowledge and subject matter knowledge. Then, research that has been presented relating to the two theories will be explored as research has suggested that these two theories are interconnected (Shulman, 1987).
Theories of Teacher Expertise
Shulman (1987) proposed that expertise in teaching is based on fully developing teachers on three knowledge bases: pedagogical content knowledge (PCK) and subject matter knowledge (SMK). Subject matter knowledge describes...
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...Teacher Education, 51(3), 166-173.
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...agogical content knowledge.” As long as I prepare, I know that I can teach effectively.
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Teachers should be experts in their subject field. Novice students need help from an expert to learn about concepts in a meaningful way.
Demonstrating knowledge of content and pedagogy is important and must be embedded in planning, because in order to be a great teacher you need to know what you are teaching and the best way to teach it to your students. If an instructor does not possess a deep knowledge of what they are teaching it will be difficult to successfully engage students in discussion, promote questioning, and answer their questions. Teachers with a strong knowledge of the content they are teaching are able to present new information by linking it to previous information, address misconceptions, and plan activities and exercises to successfully engage students. They also understand that not all students learn the same way and have different pedagogical techniques planned.
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Shulman, L.S. (1986) Those who understand: Knowledge growth in teaching. Educational Researcher, 15 (2), p.4-14.
Marzano, R.J. (2007). The art and science of teaching. Alexandria, VA: Association for Supervision and Curriculum Development.
Kirova, A., & Bhargava, A. (2002). Learning to guide preschool children's mathematical understanding: A teacher's professional growth. 4 (1), Retrieved from http://ecrp.uiuc.edu/v4n1/kirova.html
As a secondary subject, society often views mathematics a critical subject for students to learn in order to be successful. Often times, mathematics serves as a gatekeeper for higher learning and certain specific careers. Since the times of Plato, “mathematics was virtually the first thing everyone has to learn…common to all arts, science, and forms of thought” (Stinson, 2004). Plato argued that all students should learn arithmetic; the advanced mathematics was reserved for those that would serve as the “philosopher guardians” of the city (Stinson, 2004). By the 1900s in the United States, mathematics found itself as a cornerstone of curriculum for students. National reports throughout the 20th Century solidified the importance of mathematics in the success of our nation and its students (Stinson, 2004). As a mathematics teacher, my role to educate all students in mathematics is an important one. My personal philosophy of mathematics education – including the optimal learning environment and best practices teaching strategies – motivates my teaching strategies in my personal classroom.
Develop teaching expertise is the part of proposition from NBPTS, specifically knowing the subjects they teach and how to teach those subjects to students (1987). One of the methods is continue to pursue their professional development by joining a professional association or organization, attending a workshop, and reading a professional journal, website, or books. These ideas enhance teachers’ cognitive growth by enlarge information of the latest strategies or method, enhance cognitive growth, and learning to help the teachers to become expert in their teaching and influence on student learning.
In this course I experienced an important change in my beliefs about teaching; I came to understand that there are many different theories and methods that can be tailored to suit the teacher and the needs of the student. The readings, especially those from Lyons, G., Ford, M., & Arthur-Kelly, M. (2011), Groundwater-Smith, S., Ewing, R., & Le Cornu, R. (2007), and Whitton, D., Barker, K., Nosworthy, M., Sinclair, C., Nanlohy, P. (2010), have helped me to understand this in particular. In composing my essay about teaching methods and other themes, my learning was solidified, my knowledge deepened by my research and my writing skills honed.