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Prospective elementary teachers hold preconceived ideas about elementary school students' attitudes toward mathematics. We found that there exists a gender bias with prospective teachers expecting girls to have negative attitudes toward mathematics and boys more likely to have positive attitudes toward mathematics. We found that these expectations exist for both prospective teachers in a traditional undergraduate degree program and prospective teachers in an alternative licensure graduate degree program. We also found that these expectations do change with the completion of a mathematics methods course and classroom experiences.

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Noelting's (1980a, 1980b) three parallel instruments on proportional reasoning—two presenting problem-solving tasks in the ratio and division interpretations of fractions and one presenting the tasks in the purely symbolic form of numerical fractions—were administered to 6 female and 41 male learning disabled students, grades four through eight. Performances on the instruments were then compared to the performances of 120 non-learning disabled students in grades five through nine of the same school district. The purpose of the study was to determine whether learning disabled students differed in their development of proportional reasoning and whether their disability was in the use of symbols and language and not in their ability to solve proportional problems. Developmental scalograms, PPR>0.93, resulted in support of the hypothesis that the proportional reasoning abilities of the learning disabled student are developmental and thus not unlike those of the non-learning disabled student. A comparison of the three means for the two groups revealed a reversal in performance with the learning disabled students more successful at problem solving and the non-learning disabled students more successful at the purely symbolic form of numerical fractions. Unlike the non-learning disabled students, the learning disabled students' inability to express a strategy did not indicate an inability to solve the problem.

“One of the most well established facts in all mathematics education literature is that performance on fraction is undesirably low” (Hope and Owens 1987, 37). One example of that performance is that less than half of the seventh graders tested in the 1986 National Assessment of Educational Progress recognized that 5 1/4 equals 5 + 1/4 (Kouba et al. 1988)! We keep trying to comprehend why so many students and intelligent adults don't understand fractions.