Academic journal article Education

Teacher Candidates and Master Math Teachers Personal Concepts about Teaching Mathematics

Academic journal article Education

Teacher Candidates and Master Math Teachers Personal Concepts about Teaching Mathematics

Article excerpt

Literature Review

Teacher Beliefs Personal Concepts

Teacher personal concepts for this study is defined as how teacher candidates view the study of elementary mathematics content and processes and their confidence to teach elementary mathematics. How teacher candidates view the nature of mathematics and how it should be taught is worth discussing with future educators. According to Hersh, "... issue, then, is not, what is the best way to teach? But, what is mathematics really about?" (1986, p. 13). Essentially, Hersh believes that math is about ideas and not just writing down answers on paper or identifying geometrical shapes. Subject matter ideas form a belief system that teachers should use to reflect, make predictions, and construct their views about a particular subject matter (Telese, 1997).

Teacher Candidates Beliefs Personal Concepts About Teaching Mathematics

The Committee of Inquiry into the teaching of mathematics in schools (1983) emphasizes the idea that if one knows mathematics one can make mathematics. In order to really know mathematics, teacher candidates must develop their mathematic belief system even if it varies in a matter of degrees from the belief system of other teachers or teacher candidates. It is the varying degrees of confidence about a subject matter that allow teacher candidates to construct personal conceptions on that subject matter. These personal conceptions regarding mathematics consist of components such as: definitions, procedures, mental descriptions preferences regarding the content area of math (Thompson, 1992) and metacognitive awareness of mathematical processes (Desoete & Roeyers, 2000).

A primary indicator of how a teacher candidate will teach mathematics in the classroom is how well he/she understands the nature of mathematics (Hersh, 1986) and if the teacher candidate is aware of the metacognitive processes needed to accurately complete a math problem (Desoete & Roeyers, 2000). This understanding is significantly linked to how teacher candidates' personal conceptions of mathematics impacts their teaching in that content area (Madison-Nason, and Lanier, 1986; Carpenter, Fennema, and Peterson, 1986; Thompson, 1984; Dougherty, 1990). Many teacher candidates do not see themselves as actively engaging in the creation of mathematical knowledge. Rather they view a math teacher as someone who merely delivers facts, procedures and math formulas that should be memorized (Seaman, Nolan, and Dwyer, 2001; Corbin-Dwyer and Patterson, 2001). Teacher candidates are not aware of the metacognitive nature of teaching mathematics and its impact on effective instruction. Unfortunately, teacher candidates maintain a more traditional belief about the teaching and learning of mathematics (O'Laughlin, 1990 and Wilson, 1990).

In several research studies, it was reported that mathematics method courses can have a significant impact on the perceptions of teacher candidates and their pedagogical practices that they employ in the classroom (Wilcox, Schram, Lappan, and Lanier, 1991; Simon and Schifter, 1991; Ball, 1990). In other words, how a teacher candidate's personal concepts about his/her math knowledge, how he or she understands the metacognitive nature of mathematics, and his or her confidence in the content area of mathematics will impact the pedagogical practices employed in the classroom.

Mathematics and Metacognition

Since the early 2000's, researcher suggest that metacognition is essential for mathematics understanding (Desoete & Roeyers; Verschaffel, Opt Eynde, and De Corte, 2002). Teacher candidates are under the misconception that teaching mathematics in an elementary classroom is easy because they believe that they have mastered elementary school mathematic concepts. Elementary math situational problems (word problems) with illustrations seem to be an easy task for a teacher candidate, according to their personal opinions, because they have mastered the mathematical content and processes need to arrive at an accurate answer. …

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