Diverse mathematical knowledge among indigenous Amazonians.

We investigate number and arithmetic learning among a Bolivian indigenous people, the Tsimane', for whom formal schooling is comparatively recent in history and variable in both extent and consistency. We first present a large-scale meta-analysis on child number development involving over 800 Tsimane' children. The results emphasize the impact of formal schooling: Children are only found to be full counters when they have attended school, suggesting the importance of cultural support for early mathematics. We then test especially remote Tsimane' communities and document the development of specialized arithmetical knowledge in the absence of direct formal education. Specifically, we describe individuals who succeed on arithmetic problems involving the number five-which has a distinct role in the local economy-even though they do not succeed on some lower numbers. Some of these participants can perform multiplication with fives at greater accuracy than addition by one. These results highlight the importance of cultural factors in early mathematics and suggest that psychological theories of number where quantities are derived from lower numbers via repeated addition (e.g., a successor function) are unlikely to explain the diversity of human mathematical ability.

Writing motivation and ability profiles and transition during a technology-based writing intervention.

Students exhibit heterogeneity in writing motivation and ability. Profiles based on measures of motivation and ability might help to describe this heterogeneity and better understand the effects of interventions aimed at improving students' writing outcomes. We aimed to identify writing motivation and ability profiles in U.S. middle-school students participating in an automated writing evaluation (AWE) intervention using MI Write, and to identify transition paths between profiles as a result of the intervention. We identified profiles and transition paths of 2,487 students using latent profile and latent transition analysis. Four motivation and ability profiles emerged from a latent transition analysis with self-reported writing self-efficacy, attitudes toward writing, and a measure of writing writing: Low, Low/Mid, Mid/High, and High. Most students started the school year in the Low/Mid (38%) and Mid/High (30%) profiles. Only 11% of students started the school year in the High profile. Between 50 and 70% of students maintained the same profile in the Spring. Approximately 30% of students were likely to move one profile higher in the Spring. Fewer than 1% of students exhibited steeper transitions (e.g., from High to Low profile). Random assignment to treatment did not significantly influence transition paths. Likewise, gender, being a member of a priority population, or receiving special education services did not significantly influence transition paths. Results provide a promising profiling strategy focused on students' attitudes, motivations, and ability and show students' likeliness to belong to each profile based on their demographic characteristics. Finally, despite previous research indicating positive effects of AWE on writing motivation, results indicate that simply providing access to AWE in schools serving priority populations is insufficient to produce meaningful changes in students' writing motivation profiles or writing outcomes. Therefore, interventions targeting writing motivation, in conjunction with AWE, could improve results.