Interdisciplinary TPACK: A Case Study Using Variables, I/O, and Loops with Graduate Teacher Candidates in a Methods Course

This research paper describes the mathematics teacher knowledge transformation when computer science concepts are integrated with mathematics. During the last decade, schools and educators made a significant effort to introduce Computer Science (CS) and Computational Thinking (CT) in K-12. While this effort produced some positive results in schools where resources and specialized educators are available, there are school districts where creating new classes and/or hiring specialized teachers is not a sustainable option. This creates a need for teachers that are specialized in one subject area to expand their knowledge into CS and CT, and teach these concepts in their classes. This knowledge expansion and integration should result in creating integrated curricula using their subject matter knowledge and the newly acquired CS knowledge. This implies that the teacher should be able to identify the intersection of concepts between the two fields, and leverage their difference and similarities to promote deep learning for their students. The current study explores how the teacher candidates' technological, pedagogical content knowledge (TPACK) in mathematics is affected when mathematical concepts are integrated with CS and CT. This study is a three-day intervention in a graduate level secondary mathematics education methods course, where utilizing Math + CS integrated modules we infuse CS concepts into mathematics. The already known mathematics context reduced the cognitive load for familiarizing the teacher candidates with CS, and the integration of the CS concepts provided a different perspective for thinking about mathematics and teaching. After having the teacher candidates reflecting on the concepts of Variable and Equal Sign (=), our results showed that they started noticing the differences and nuances between the two fields, developing this way their interdisciplinary Math + CS TPACK (I-TPACK) knowledge. Furthermore, the study showed that representing multiplications using repetition structures illuminated the internal mechanic of multiplication and its properties. Finally, the experience with the strict grammar and syntax rules of programming illuminated the areas in the teacher candidates mathematics instruction that were ambiguous in the way they teach variables, equations, percentages, and multiplication.