Graduation Year

2021

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Curriculum and Instruction

Major Professor

Eugenia Vomvoridi-Ivanovic, Ph.D.

Co-Major Professor

Cheryl R. Ellerbrock, Ph.D.

Committee Member

Darlene DeMarie, Ph.D.

Committee Member

Catherine Bénéteau, Ph.D.

Keywords

Content Analysis, Geometry, Images, Middle Grades, Visualization

Abstract

Young adolescents build notions of figures through experiences. When young adolescentsbegin middle school mathematics, they already have prior assumptions and conceptualizations about shapes (Herbst, Fujita, Halverscheid, & Weiss, 2017). Over years of experiences, interactions, and exposures with a particular concept, these students develop concept images consisting of all the visual information, pictures, mental images, or properties associated with the particular mathematical concept (Vinner, 1983). Seminal works in the field of mathematics education research found that without an opportunity to engage with varied representations, young adolescent students may not develop robust concept images (Aspinwall, Shaw & Presmeg, 1997; Hasegawa, 1997; Mesa, 2004; Presmeg, 1986, 1992; Tall & Vinner, 1981; Vinner, 1983; Vinner & Dreyfus, 1989).

Therefore, in this study, I analyzed young adolescents’ opportunities to develop concept images of polygons in middle school mathematics textbooks (grades 6-8). I chose to analyze convex polygons in nine textbooks: Pearson enVisionmath2.0 Grades 6, 7, 8 (Berry et al., 2017), Houghton Mifflin Harcourt Go Math! Grades 6, 7, 8 (Burger et al., 2014), and McGraw Hill Education Glencoe Math Course 1, 2, 3 (Carter et al., 2015). This sample of textbooks represents one series from each of the three major textbook publishers: Pearson, Houghton Mifflin Harcourt, McGraw Hill Education (Banilower et al., 2018).

I explored young adolescent’s opportunity to develop concept images of polygons in middle school mathematics textbooks in terms of the exposure to a variety of polygons represented, exposure to a variety of polygon orientations, exposure to non-prototypical images, exposure to a variety of contexts, exposure to a variety of image roles, and exposure to developmentally responsive tasks. The results of this study indicate that within three published middle school mathematics textbook series, students do not have adequate opportunities to develop robust concept images of polygons. In all three textbook series, students have more exposure to images of convex polygons in eighth-grade textbooks, followed by sixth-grade textbooks, and the finally seventh-grade textbooks, however, all three textbook series contained little variety in terms of types of convex polygons represented. The three textbook series did not provide ample opportunities for students to engage with images of convex polygons in a variety of orientations and did not provide many opportunities for students to engage with non- prototypical images of convex polygons. Additionally, the three textbook series did not provide much variety in terms of contexts and roles of images with a majority of convex polygons set in purely mathematical contexts and as interpretive images. Further, all three textbook series provided little to no developmentally responsive tasks containing images of convex polygons in terms of young adolescents' physical, psychological, social-emotional, and moral needs.

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