Examining Two Middle School Mathematics Teachers’ Knowledge for Teaching Manipulation of Algebraic Expressions during Lesson Planning and Instruction

Year 2019, Volume: 10 Issue: 3, 588 - 616, 13.12.2019

Dilek Girit Yıldız , Didem Akyüz

https://doi.org/10.16949/turkbilmat.487243

Abstract

Teachers use
their content and pedagogical content knowledge for teaching algebra. For this
reason, the examination of how teachers use this knowledge may help shed light
on how students learn algebra, especially in determining why they usually have
difficulties. The aim of the current study is to reveal what teachers know, and
propose what they actually need to know for teaching the simplification and
equivalence of algebraic expressions. The multiple-case study design was used
for this study to compare and contrast the two middle school teachers’ lesson
planning and instruction. The data corpus included lesson plans, actual
instruction records, and post-observation interviews. Data analysis was
conducted using the Mathematical Knowledge for Teaching (MKT) model. The
findings indicated that both teachers had a lack of specialized content
knowledge about mathematical representations such as algebra tiles. They did
not use algebra tiles effectively and could not link algebraic and geometric
representations that underlie the idea of multiplication. It was observed that
both teachers generally used unknowns and variables interchangeably indicating
the inadequacy of their common content knowledge. In the planning process, the
two teachers were able to state the common misconceptions that the students
generally had and the ways of addressing them. Through the cases of these two
teachers, it was observed that teachers need to have a good conceptual
mathematical understanding and also knowledge of students’ thinking in order to
design effective lessons. Based on the findings, the types of knowledge that
the teachers need to have are outlined and the theoretical and practical implications
of the study are discussed.

Keywords

Equivalence of algebraic expressions, mathematical knowledge for teaching, simplification of algebraic expressions, middle school mathematics teacher

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