Contrasting cases are collections of problems or examples that help students understand the quantitative structure of empirical phenomena. They are designed to present optimal variation for learning functional structures that capture how distinct quantifiable elements combine to make new properties (e.g. density is a ratio of mass over volume).
Based on prior research, contrasting cases can foster an appreciation of deep structure, flexibility, transfer, and preparation for future learning. We (and others) have had demonstrated success using contrasting cases to help students learn functional structures across a variety of STEM domains ranging from statistical variance to electromagnetic fields. In a recent publication (Schwartz et al., 2011), for example, we reported that inducing the functional structure of ratio over a series of contrasting cases about speed and density caused transfer to a semantically unrelated problem (spring constant) several weeks later.
- Schwartz, D. L., Chase, C. C., Oppezzo, M. A., & Chin, D. B. (2011). Practicing versus inventing with contrasting cases: The effects of telling first on learning and transfer. Journal of Educational Psychology, 103(4):759-775.
- Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for learning: The hidden efficiency of original student production in statistics instruction. Cognition and Instruction, 22, 129–184.