Date of Graduation

12-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

Dingman, Shannon W.

Committee Member

Madison, Bernard L.

Second Committee Member

Kent, Laura B.

Third Committee Member

Harriss, Edmund O.

Keywords

CCSSM; Curriculum; Geometry; Standards; Textbooks; van Hiele

Abstract

The goal of this study is to investigate K-8 geometry curriculum standards and textbooks for their effectiveness in preparing students for high school geometry. The basis for the study is van Hiele theory pioneered by the Dutch educators and researchers of geometric understanding in adolescents, Dina van Hiele Geldof and Pierre van Hiele. Another driving force for this dissertation is research into mathematics textbooks and curriculum standards of school mathematics as seen in CCSSM and state specific standards documents, both of which influence the mathematics students have the opportunity to learn.

The K-8 geometry curriculum standards and textbook instructional segments suitable for van Hiele analysis were isolated and compared by their van Hiele levels. There were differences in CCSSM and non-CCSSM standards documents, with the overall trend indicating lower van Hiele levels as asserted by van Hiele researchers. However, a few textbooks had some higher levels interspersed in their instructional segments. Examples of level 4 activities in middle grade textbooks are provided in Chapter 3, while van Hiele level 4 tasks are not emphasized in any standards documents. The results of this study indicate that if standards and textbooks can consider young minds as they develop knowledge of the space around them then there could be more effective ways to develop geometrical understanding, and consequently raise the success rate of students in high school geometry.

The curricular materials were separated into two groups: K-5 and 6-8. The various percentages of van Hiele levels were noted in all the materials analyzed as a guide to investigate the rigor and opportunity students are provided with in grades K-8. South Carolina and Texas standards’ documents have higher percentages of level 3 tasks (31% and 22% respectively) than CCSSM (15%) in K-5 grades. Among K-5 textbooks Ready Math with 21% van Hiele level 3 content fared better than other K-5 textbooks and also better than CCSSM. For grades 6-8 neither CCSSM nor any state specific standards’ documents contain van Hiele level 4 tasks, while all the 6-8 mathematics textbooks analyzed have level 4 content. Eureka Math has 49% tasks consisting of levels 3 and 4 and this makes it better than CCSSM document (40% level 3, 0% level 4). The other textbooks analyzed have lower level 3 + level 4 content (13% for Math in focus and 20% for Open up Resources).

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