Developing Elementary Teachers’ Pedagogical Content Knowledge of Rate-of-Change in Engineering Thermodynamics: A Design Study

The developing pedagogical content knowledge of elementary-certified teachers was supported in a course on concepts in algebra and calculus. Engineering thermodynamics was used as a domain through which participants could model rate-of-change for a variety of functions. The design of the professional development course is examined, and teachers’ struggles and triumphs with course content described. Results show teachers’ backgrounds in elementary algebra proved a barrier to their ability to treat relationships among variables as mathematical objects. Once these barriers were overcome rate-of-change served as a powerful support to model complex thermal applications that utilized rate-of-change as an index of efficiency.