A Game-based Approach to Improving the Learning of Arithmetic

Learning arithmetic requires developing both fluency and understanding in tandem [1]. However, a curricular emphasis on fluency risks prioritising algorithmic practice at the expense of other learning activities and can be boring and therefore off-putting to children [2]. Moreover, if practice is not carefully designed then fluency can come at the cost of understanding, resulting in stubborn misconceptions [3], and highly situated knowledge that does not transfer readily to other contexts [4]. Many computer games purport to help children learn arithmetic operations, but tend to prioritise fluency through algorithmic practice over understanding, e.g. [5].

In contrast, the App Stick and Split (SaS) is ground-breaking because it embodies subordination, a learning approach developed by the first supervisor that harnesses the notion new skills are acquired when necessary for tasks that we are motivated to complete [6]. The approach involves target learning being subordinated to task goals that learners can readily understand. SaS embodies subordination because, unlike many educational games where mathematics is an aside to the main game play [5,7], arithmetic practice drives game progress. Importantly, SaS allows learners to make mistakes and immediately see the consequences in terms of game progress. As such, it potentially provides motivation for sustained practice, thereby developing fluency, with inherently meaningful feedback, thereby developing understanding.
RQ1. How is arithmetic practised and learned when children interact with SaS?
RQ2. How does the arithmetic learned within SaS transfer to more traditional symbolic contexts?
RQ3. What principles can be given to games which involve subordination of learning and how can these be applied to new areas of mathematics?
To address RQ1, two methods will be used. First, children will be observed using SaS to understand how arithmetic is practised. Second, Sunflower will provide hundreds of thousands of interaction logs that track the progress of thousands of children over time. Longitudinal analyses of interaction logs will help understand how progressing through game levels relates to arithmetic learning.

To address RQ2, there will again be two methods used. First, standardised arithmetic tests (e.g. WIAT-II) will be used to samples of SaS users to identify learning transfer to traditional symbolic contexts. Second, drawing on these findings, refinements to SaS will be made to optimise learning transfer, and test these refinements through further standardised testing.

To address RQ3, general principles from the findings to RQ1 and RQ2 will be used. With Sunflower Learning, application of those principles will be applied to a novel mathematical area to develop a new App. Evaluation of the new App's initial success will be made.

References
[1] Rittle-Johnson et al. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27, 587-597.
[2] Foster (2018). Developing mathematical fluency: Comparing exercises and rich tasks. Educational Studies in Mathematics, 97, 121-141.
[3] McNeil (2008). Limitations to teaching children 2 + 2 = 4: Typical arithmetic problems can hinder learning of mathematical equivalence. Child Development, 79, 1524-1537.
[4] Chesney & McNeil (2014). Activation of operational thinking during arithmetic practice hinders learning and transfer. The Journal of Problem Solving, 7, 24-35.
[5] Jay et al. (2019). Game-based training to promote arithmetic fluency. Frontiers in Education, 4, 118.
[6] Hewitt (1996). Mathematical fluency: the nature of practice and the role of subordination. For the Learning of Mathematics, 16, 28-35.
[7] Lowrie & Jorgensen (2015). Digital games and learning: what's new is already old? In Digital Games and Mathematics Learning (pp. 1-9). Springer.