Algebraic Functions, Computer Programming, and the Challenge of Transfer

Abstract

Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems. A common refrain about word problems is that “the equations are easy to solve - the hard part is setting them up!” A student of algebra is asked to identify functional relationships in the world around them - to set up the equations that describe a system- and to reason about these relationships. Functions, in essence, mark the shift from computing answers to solving problems. Researchers have called for this shift to accompany a change in pedagogy, and have looked to computer programming and game design as a means to combine mathematical rigor with creative inquiry. Many studies have explored the impact of teaching students to program, with the goal of having them transfer what they have learned back into traditional mathematics. While some of these studies have shown positive outcomes for concepts like geometry and fractions, transfer between programming and algebra has remained elusive. The literature identifies a number of conditions that must be met to facilitate transfer, including careful attention to content, software, and pedagogy. This dissertation is a feasibility study of Bootstrap, a curricular intervention based on best practices from the transfer and math-education literature. Bootstrap teaches students to build a video game by applying algebraic concepts and a problem solving technique in the programming domain, with the goal of transferring what they learn back into traditional algebra tasks. The study employed a mixed-methods analysis of six Bootstrap classes taught by math and computer science teachers, pairing pre- and post-tests with classroom observations and teacher interviews. Despite the use of a CS-derived problem solving technique, a programming language and a series of programming challenges, students were able to transfer what they learned into traditional algebra tasks and math teachers were found to be more successful at facilitating this transfer than their CS counterparts.