Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Creative Mathematical Thinking in a Numbers Game

Version 1 : Received: 14 October 2020 / Approved: 15 October 2020 / Online: 15 October 2020 (08:42:55 CEST)

How to cite: Kruis, J.; Stevenson, C.; van der Maas, H.L.J. Creative Mathematical Thinking in a Numbers Game. Preprints 2020, 2020100314 (doi: 10.20944/preprints202010.0314.v1). Kruis, J.; Stevenson, C.; van der Maas, H.L.J. Creative Mathematical Thinking in a Numbers Game. Preprints 2020, 2020100314 (doi: 10.20944/preprints202010.0314.v1).

## Abstract

Creative thinking is increasingly recognised as an essential ability that should be part of school curricula. Given the move towards online learning and assessment, we investigate whether mathematical creativity can be assessed at-scale in the Numbers game, an arithmetic game in Math Garden, a popular online math practice platform. In the Numbers game, a generalisation of the 24 Game, children are asked to figure out how to compute a target number using basic arithmetic operations and a given set of numbers. We argue that creative thinking is required when the search space is complex, and propose that the base-pattern, i.e., the sequence of the operations needed to solve a Numbers game item, indicates search space complexity. We then demonstrate that items with disordered base-patterns are more likely to require mathematical creativity to figure out. Specifically, our analysis shows that for items with only one solution sequence, those with disordered base-patterns are more difficult and take longer to solve compared to items with ordered base-patterns. For items where multiple solution sequences are possible, nine times out of ten children choose ordered over disordered base-patterns. We conclude that the Numbers game has potential for assessing mathematical creativity at-scale.

## Subject Areas

creative thinking; mathematical creativity; response processes; digital learning environment; online learning platform

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