Creative and algorithmic mathematical reasoning: effects of transfer-appropriate processing and effortful struggle

ABSTRACT

Two separate studies, Jonsson et al. (J. Math Behav. 2014;36: 20–32) and Karlsson Wirebring et al. (Trends Neurosci Educ. 2015;4(1–2):6–14), showed that learning mathematics using creative mathematical reasoning and constructing their own solution methods can be more efficient than if students use algorithmic reasoning and are given the solution procedures. It was argued that effortful struggle was the key that explained this difference. It was also argued that the results could not be explained by the effects of transfer-appropriate processing, although this was not empirically investigated. This study evaluated the hypotheses of transfer-appropriate processing and effortful struggle in relation to the specific characteristics associated with algorithmic reasoning task and creative mathematical reasoning task. In a between-subjects design, upper-secondary students were matched according to their working memory capacity.

The main finding was that the superior performance associated with practicing creative mathematical reasoning was mainly supported by effortful struggle, however, there was also an effect of transfer-appropriate processing. It is argued that students need to struggle with important mathematics that in turn facilitates the construction of knowledge. It is further argued that the way we construct mathematical tasks have consequences for how much effort students allocate to their task-solving attempt.

KEYWORDS:

• Creative mathematical founded reasoning
• algorithmic reasoning
• effortful struggle
• transfer-appropriate processing

Acknowledgments

We thank Tony Qwillbard for help with parts of the data collection and computer programming. We also thank all the students for being part of this study and the teacher for helping out organizing the data collection

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. $\widehat{\psi }=\sum w_j{\bar{Y}}_j$

Additional information

Funding

Kempe foundation to Johan Lithner; Umea University to Bert Jonsson