Mono- and Multi-Representational Learning of the Covariational Aspect of Functional Thinking

Using multiple external representations is advocated for learning in STEM education. This learning approach assumes that multiple external representations promote richer mental representations and a deeper understanding of the concept. In mathematics, the concept of function is a prototypical content area in which multiple representations are used. However, there are hardly any experimental studies investigating the effect of learning functional thinking with multiple representations compared to learning with only one form of representation. Therefore, this article reports on a quasi-experimental intervention study with students from Grade 7, using three measurement time points. The study compared the multi-representational learning of functional thinking with both tables and graphs with mono-representational learning with either tables or graphs. The results show that multi-representational learning led to advantages in learning qualitative functional thinking. However, in quantitative functional thinking, learning with both graphs and tables did not result in higher learning gains than learning exclusively with graphs. Furthermore, students were better able to transfer their knowledge from graphs to tables than vice versa. The results also indicate that multi-representational learning requires more time than mono-representational learning but can lead to higher learning gains. In sum, the results show that the effect of learning with representations is a complex interaction process between learning content and the forms of representation.

Improved and Sustained Graduate Programs Diversity Outcomes: a 10-year Analysis and Summary of the Brown University IMSD Program

This report describes the 10-year outcome of implementing practices that support and foster success of underrepresented students in science, technology, engineering, and math (STEM) graduate training at Brown University. The results show sustained improvements in compositional diversity, retention, and degree attainment of supported students relative to their peers. Among the outcomes is an increase in enrolled student diversity from 19 (35 of 179) to 26% (58 of 223) for historically underrepresented minority (URM) students and an increase in Ph.D. degree attainment from 4 (1 of 25) to 14% (6 of 44) for this group. These achievements follow the introduction and coordination of academic and co-curricular practices through the National Institutes of General Medical Sciences–funded Brown University Initiative to Maximize Student Development (IMSD) Program. At the center of these outcomes is the alignment of IMSD practices with recent diversity initiatives launched by the university. The outcomes described result from long-term commitments to building a culture that includes: (1) development of relationships that serve underrepresented students, (2) provision of a personalized education program of support and skills-based learning that supplements discipline-based research and coursework, and (3) investments in processes that build a culture that values and benefits from diversity. These practices may yield similar outcomes and success for students when applied elsewhere.