The relationship between mathematics and language: academic implications for children with specific language impairment and English language learners.

PURPOSE: The present study examined the relationship between mathematics and language to better understand the nature of the deficit and the academic implications associated with specific language impairment (SLI) and academic implications for English language learners (ELLs). METHOD: School-age children (N = 61; 20 SLI, 20 ELL, 21 native monolingual English [NE]) were assessed using a norm-referenced mathematics instrument and 3 experimental computer-based mathematics games that varied in language demands. Group means were compared with analyses of variance. RESULTS: The ELL group was less accurate than the NE group only when tasks were language heavy. In contrast, the group with SLI was less accurate than the groups with NE and ELLs on language-heavy tasks and some language-light tasks. Specifically, the group with SLI was less accurate on tasks that involved comparing numerical symbols and using visual working memory for patterns. However, there were no group differences between children with SLI and peers without SLI on language-light mathematics tasks that involved visual working memory for numerical symbols. CONCLUSION: Mathematical difficulties of children who are ELLs appear to be related to the language demands of mathematics tasks. In contrast, children with SLI appear to have difficulty with mathematics tasks because of linguistic as well as nonlinguistic processing constraints.

Adaptive user displays for intelligent tutoring software.

Intelligent tutoring software (ITS) holds great promise for K-12 instruction. Yet it is difficult to obtain rich information about users that can be used in realistic educational delivery settings--public school classrooms--in which eye tracking and other user sensing technologies are not suitable. We are pursuing three "cheap and cheerful" strategies to meet this challenge in the context of an ITS for high school math instruction. First, we use detailed representations of student cognitive skills, including tasks to assess individual users' proficiency with abstract reasoning, proficiency with simple math facts and computational skill, and spatial ability. Second, we are using data mining and machine learning algorithms to identify instructional sequences that have been effective with previous students, and to use these patterns to make decisions about current students. Third, we are integrating a simple focus-of-attention tracking system into the software, using inexpensive, web cameras. This coarse-grained information can be used to time the display of multimedia hints, explanations, and examples when the user is actually looking at the screen, and to diagnose causes of problem-solving errors. The ultimate goal is to create non-intrusive software that can adapt the display of instructional information in real time to the user's cognitive strengths, motivation, and attention.