This research examined the use of visual-spatial representation by deaf and hearing students while solving mathematical problems. The connection between spatial skills and success in mathematics performance has long been established in the literature. This study examined the distinction between visual-spatial "schematic" representations that encode the spatial relations described in a problem versus visual-spatial "pictorial" representations that encode only the visual appearance of the objects described in a problem. A total of 305 hearing (n = 156) and deaf (n = 149) participants from middle school, high school, and college participated in this study. At all educational levels, the hearing students performed significantly better in solving the mathematical problems compared to their deaf peers. Although the deaf baccalaureate students exhibited the highest performance of all the deaf participants, they only performed as well as the hearing middle school students who were the lowest scoring hearing group. Deaf students remained flat in their performance on the mathematical problem-solving task from middle school through the college associate degree level. The analysis of the students' problem representations showed that the hearing participants utilized visual-spatial schematic representation to a greater extent than did the deaf participants. However, the use of visual-spatial schematic representations was a stronger positive predictor of mathematical problem-solving performance for the deaf students. When deaf students' problem representation focused simply on the visual-spatial pictorial or iconic aspects of the mathematical problems, there was a negative predictive relationship with their problem-solving performance. On two measures of visual-spatial abilities, the hearing students in high school and college performed significantly better than their deaf peers.

Research tells us that academic preparation is key to deaf students' success at college. Yet, that is not the whole story. Many academically prepared students drop out during their first year. This study identified entering deaf college students' personal factors as assessed by their individual responses to both the Noel-Levitz College Student Inventory Form B and the Learning and Study Strategies Inventory, second edition (LASSI). Entering students in 3 successive cohorts (total n =437) participated in this study. Results show that in addition to entry measurements of reading and mathematic skills, personal factors contributed to the academic performance of students in their first quarter in college. The Noel-Levitz provided the comparatively better predictive value of academic performance: Motivation for Academic Study Scale (e.g., desire to finish college). The LASSI also showed statistically significant predictors, the Self-Regulation Component (e.g., time management) and Will Component (e.g., self-discipline), but accounted for relatively less variability in the students' initial grade point averages. For this group of underprepared students, results show that personal factors can play a significant role in academic success. Deaf students' personal factors are discussed as they relate to other first-year college students and to their subsequent academic performance and persistence.

One hundred and thirty-three mathematics teachers of deaf students from grades 6-12 responded to a survey on mathematics word problem-solving practices. Half the respondents were teachers from center schools and the other half from mainstream programs. The latter group represented both integrated and self-contained classes. The findings clearly show that regardless of instructional setting, deaf students are not being sufficiently engaged in cognitively challenging word problem situations. Overall, teachers were found to focus more on practice exercises than on true problem-solving situations. They also emphasize problem features, possibly related to concerns about language and reading skills of their students, rather than analytical and thinking strategies. Consistent with these emphases, teachers gave more instructional attention to concrete visualizing strategies than to analytical strategies. Based on the results of this study, it appears that in two of the three types of educational settings, the majority of instructors teaching mathematics and word problem solving to deaf students lack adequate preparation and certification in mathematics to teach these skills. The responses of the certified mathematics teachers support the notion that preparation and certification in mathematics makes a difference in the kinds of word problem-solving challenges provided to deaf students.

This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and meaning were all significantly correlated with both the ACT Mathematics Subtest and National Technical Institute for the Deaf (NTID) Mathematics Placement Test scores. Multiple regression analyses identified the best combination from among these potential independent predictors of students' performance on both the ACT and NTID mathematics tests. Additionally, the participating deaf students' grades in their college mathematics courses were significantly and positively associated with their reading grade level and their knowledge of morphological components of words.

English sentences containing the universal quantifiers each, every, and all are highly complex structures in view of the subtleties of their scope properties and resulting ambiguities. This study explored the acquisition of universal quantifier sentences as reflected in the performance of three diverse collegelevel student groups on a multipicture sentence interpretation task. The participant groups (hearing native speakers, deaf students, and second language learners of English) all exhibited fundamental knowledge of universal lexical, semantic, and syntactic properties that contribute to quantifier sentence interpretation. The native speakers outperformed the deaf and second language groups, whose performance was strikingly parallel. Performance patterns are explained in terms of the influences of derivational economy, including the option to restrict in situ indefinite noun phrases to singleton indefinites. The symmetry effect observed in child language studies was also observed among the college-aged participants in this study. It is explained in terms of a pragmatic challenge in managing contextual information that invokes an unexpected singleton indefinite interpretation. The results contribute to the understanding of sentence comprehension under conditions of restricted learner access to target language input and underscore the value of seeking correlates of theory-internal derivational economy in language acquisition and use.