Physics Union Mathematics
An Emphasis on Mathematics
Adaptation of ISLE and the ALG in the PUM curriculum with the emphasis on mathematics
The PUM curriculum utilizes ISLE logic and specifically focuses on a system and modeling approach for constructing knowledge. Students will start by identifying a system undergoing a process and then learn how to simplify this process for the analysis. The process repeats for each conceptual area and has two components: (1) a logical path analogous to the processes that scientists and mathematicians use to construct knowledge and (2) multiple representations. Both approaches are based on research on how the human brain works and on the nature of science and mathematics. When interacting with the world, a human brain proceeds through cycles of concrete experiences, reflection, formation of hypotheses, and active testing. Similar processes on a bigger scale occur when scientists construct knowledge: they collect observational data, reflect on the patterns, devise hypotheses, and actively test them. The process takes years but can be simplified and shortened with appropriate scaffolding and bridging analogies. Representing knowledge in multiple ways links abstract representations (words and equations) to more concrete ways of understanding (sketches of processes and diagrams). It helps students reason about physical processes with understanding and serves as an aide in problem solving. Different representations allow multiple exposures and engage different learners. This approach is likely to benefit special needs and underserved students as they might have difficulties learning if only more abstract representations are used.
