ERIC Number: ED655686
Record Type: Non-Journal
Publication Date: 2021
Pages: 191
Abstractor: As Provided
ISBN: 979-8-7087-2230-0
ISSN: N/A
EISSN: N/A
Young Adolescents' Opportunity to Develop Concept Images of Polygons in Middle School Mathematics Textbooks
Megan N. Cannon
ProQuest LLC, Ph.D. Dissertation, University of South Florida
Young adolescents build notions of figures through experiences. When young adolescents begin 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 adolescents' 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. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]
Descriptors: Middle School Students, Early Adolescents, Mathematical Concepts, Concept Formation, Geometric Concepts, Plane Geometry, Visual Aids, Textbook Content, Educational Opportunities, Middle School Mathematics, Instructional Materials, Textbook Evaluation
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Junior High Schools; Middle Schools; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A