PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Learning Progressions in Mathematics and Physics: An Example for Partial Derivatives
Page: 1189
We describe the creation of a learning progression about partial derivatives that extends from lower-division multivariable calculus through upper-division physics courses for majors. This work necessitated three modifications to the definition of a learning progression as described in the literature. The first modification is the need to replace the concept of an upper anchor with concept images specific to different (sub)disciplines. The second modification is that rich interconnections between ideas is the hallmark of an expert-like concept image. The final modification is using representations in several ways to support the development of translational fluency in emerging experts. These theoretical changes are supported by examples of research and curriculum in the use of differentials in thermodynamics.