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Proof is central to mathematics and has drawn substantial attention from the mathematics education community. Yet, valid and reliable measures of proof comprehension remain rare. In this article, we present a study investigating proof comprehension via students’ summaries of a given proof. These summaries were evaluated by expert judges making pairwise comparisons, which were used to generate a score for each summary. This approach, known as comparative judgement, has been demonstrated to generate reliable and valid scores when assessing other mathematical constructs. Our findings suggest that comparative judgement can produce valid and reliable assessments of the quality of student-produced proof summaries. We also explored which features of students’ proof summaries were most valued by the expert judges, and found that high-scoring summaries referenced a proof’s logical structure and the mechanism by which it reached a contradiction.

This report represents the results of a preliminary study to determine if there is a valid cause to question the positional relationship of brake and accelerator pedals in contemporary automobiles. Ten subjects were tested to determine how long it takes to move the foot from the accelerator to the brake pedal (a) in the same horizontal plane, and (b) with a 6-in. height differential. Experimental results indicated that at high speeds, a reduction in stopping distance of upwards of 14 ft. could be affected for the case tested.

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