In this study, we interviewed eighteen middle school students to see how they used prior instruction to think about a geometric pattern and construct its corresponding linear equation. All students

were given the same task to complete and were questioned about their thinking during the interview.

We found that the recording of pattern recognition plays a substantial part in helping students recognize and write explicit patterns. By having students decompose the total perimeter into how they saw the pattern growing, students were more successful in making the connection to the numeric representation of growth. In addition, they were better able to explain how they set up the equation, and the connection of each part of the equation to the original pattern.

As teachers work with their students in developing a conceptual understanding of linear equations, it is critical that students are exposed to geometric patterns. The results of this study will help mathematics teacher educators better prepare teachers to develop their students’ develop rich and connected mathematical understanding.

References:

Zazkis, R. & Liljedahl, P. (2002a, March). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379-402.

Zazkis, R. & Liljedahl, P. (2002b). Arithmetic sequence as a bridge between conceptual fields.

Canadian Journal of Science, Mathematics and Technology Education, 2(1), 93-120.

]]>The number of mathematics content courses provided to support the development of early childhood education majors understanding of mathematics varies across universities. Some wonder whether it is necessary to have a series of four mathematics content courses or if a fewer number of courses would suffice. This study is intended to determine if there is a significant difference in how pre-service teachers think about teaching mathematics at each stage of a progression of four-course content courses, as well as to determine if there seems to be a ceiling effect when students no longer feel these courses are continuing to improve their content knowledge and subsequent teaching ability.

Cohen and Hill (2001) describe teacher beliefs as, “Teachers’ ideas about mathematics teaching and learning” and note that these beliefs may shape their teaching. One aspect of a teacher’s beliefs includes her sense of self-efficacy. Researchers have recognized teacher’s sense of self-efficacy as an important attribute of effective teaching which is related to positive teacher and student outcomes (Tschannen-Moran, Woolfolk Hoy, & Hoy; 1998). In this study we explore the effects of a series of four mathematics content courses on pre-service teachers’ beliefs about teaching mathematics and their own self efficacy beliefs. These classes were designed to improve understanding and self-efficacy in a subject that many students have the most difficulty with. Our study provides a snapshot of students from each of the four content courses in the series by exploring their beliefs about teaching mathematics and their own self-efficacy and beliefs they hold at the end of each course.

References:

Cohen, D. & Hill, H. (2001). Learning policy: When state education reform works. New Haven, CT: Yale University Press.

Swackhamer, L.E., Koellner, K., Basile, C., & Kimbrough, D. (2009). Increasing the self- efficacy of inservice teachers through content knowledge. Teacher Education Quarterly, Spring, 63-78.

Tschannen-Moran, M., Woolfok-Hoy, A., & Hoy, W. K. (1998). Teacher efficacy: Its meaning and measure. Review of Educational Research, 68(2), 202-248.

]]>One of the critical components of edTPA is academic language. Academic language is the formalized language of school to help students communicate, define and form concepts, and construct knowledge (Gottlieb & Ernst-Slavit, 2014). According to World-Class Instructional Design and Assessment (WIDA), emphasis on academic language will also benefit linguistically diverse populations of students because academic language is “a vehicle for communicating and learning within sociocultural contexts; the interaction between different situations and people in the learning environment (WIDA, 2014, p. 4).”

In edTPA, teacher candidates should demonstrate how they create opportunities (i.e., language functions) for students to use academic language such as vocabulary, syntax, and discourse to achieve the learning objective. As teacher educators, it is our responsibility to prepare our candidates for the edTPA by preparing them to support their students’ mathematics learning through these language demands.

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Letter from the President

Table of Contents

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