Students’ Development of a Logarithm Function in Python Using Taylor Expansions: A Teaching Design Case Study
We present here the lessons learned by iteratively designing a tutorial for first-year university students using computer programming to work with mathematical models. Alternating between design and implementation, we used video-taped task interviews and classroom observations to ensure that the design promoted student understanding. The final version of the tutorial we present here has students make their own logarithm function from scratch, using Taylor polynomials. To ensure that the resulting function is accurate and reasonably fast, the students have to understand and apply concepts from both computing and mathematics. We identify four categories of such concepts and identify three design features that students attended to when demonstrating such understandings. Additionally, we describe seven important take-aways from a teaching design point of view that resulted from this iterative design process.