Comparison of mathematical problem-solving processes using haptic and digital learning media

Abstract

Problem solving is a core competency in math education and as a process-oriented skill, it is essential across all mathematical topics. Not only the Austrian curriculum but also international studies such as PISA, highlight its importance. Digital materials can be effective when it comes to supporting problem solving. This study aims to examine the difference of haptic and digital mathematical problem-solving processes of 7th grade learners, thereby also focusing on differentiation. For that, the following aspects will be considered: types and number of phases, linearity, additional support, challenges and problem-solving strategies, so-called heuristics. The processes, documented by videography, were analyzed using Schoenfeld’s protocol analysis method. 
The results of the qualitative study indicate that problem-solving processes differ in type and number of phases, regardless of whether they happen in a haptic or digital setting. Moreover, three quarters of the processes were non-linear, possibly caused by offering additional support. Furthermore, support was used more frequently within the digital setting and led to an increased number of verification phases, which are essential for successful problem solving. Therefore, this study highlights that differentiation within a problem-solving setting influences the structure of the process. Focusing on the heuristic strategies, the following differences were found: The heuristics Measuring and Transformation are characteristics of the haptic setting. As a result, the haptic setting, alongside the digital one, creates an effective learning environment for initiating problem solving.
Based on a master’s thesis, this article summarizes the most important findings of the study.