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Justin K. Dimmel and Patricio G. Herbst

Geometry diagrams use the visual features of specific drawn objects to convey meaning about generic mathematical entities. We examine the semiotic structure of these visual features in two parts. One, we conduct a semiotic inquiry to conceptualize geometry diagrams as mathematical texts that comprise choices from different semiotic systems. Two, we use the semiotic catalog that results from this inquiry to analyze 2,300 diagrams from 22 high school geometry textbooks in which the dates of publication span the 20th century. In the first part of the article, we identify axes along which the features of geometry diagrams can vary, and in the second part of the article, we show the viability of using the semiotic framework to conduct empirical studies of diagrams in geometry textbooks.

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Justin K. Dimmel and Patricio G. Herbst

We investigated how secondary mathematics teachers check student geometry proofs. From video records of geometry teachers checking proofs, we conjectured that teachers have different expectations for details that follow from written statements than for details that are conveyed by diagrams. To test our conjectures, we randomly assigned 44 secondary mathematics teachers to 1 of 3 experiment groups (n & 13, n & 15, n & 16) in which they viewed and rated representations of instructional practice. Participants in each group viewed treatment or control versions of instructional scenarios and rated the appropriateness of the teachers' work in different segments of each scenario. We compared participants' ratings across and within experiment groups. We found that participants rated lower instruction that deviated from what we hypothesized to be their expectations, confirming our hypotheses.