Forms and Presentations of Circle Proofs and Tasks in Geometry Textbooks, 1891-2010

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Abstract

Since the nineteenth century, emphasis on proof in high school geometry has evolved from student reproductions of proofs to student generation of proofs and knowledge construction through proving. Presently, the Common Core State Standards for Mathematics not only specifies theorems for students to prove, but also recognizes the mathematical practice of proving. We present an historical analysis of 24 high school geometry textbooks from 1891-2010, specifically examining the presentation and forms of proofs and student proof tasks relating to circles. Results indicate that textbooks have decreased the proportion of complete proofs while increasing the proportion of illustrations and supports for student proof tasks. Furthermore, paragraph proofs have declined while two-column and alternative proof forms increased during twentieth century.

Authors

• Amanda Thomas, University of Missouri

• Victor Soria, University of Missouri