History of mathematics as context for improving strategy flexibility in cubic equations

Abstract

Studies show that using original historical sources as a context for teaching problem-solving enhance students problem-solving skills and mathematical understanding. Despite, the extent to which it can improve students’ strategy flexibility in problem-solving is not well reported. This paper present quasi-experimental study that sought to examine whether history-integrated lessons on cubic equations improves senior high school students’ strategy flexibility. Participants were 128 Form 2 science students from two senior high schools in the Ashanti Region of Ghana, assigned to an experimental group or a control group. The experimental group was taught original historical approaches to solving cubic equations. Lessons emphasised the algebraic methods developed by early mathematicians such as del Ferro, Tartaglia, and Cardano. The control group, on the other hand, were taught the standard algebraic methods such as rational root test and factorisation. Afterwards (i) post-test data was collected using strategy flexibility test and was analysed to identify if there was statistically significant difference between the flexibility scores of the control and experimental groups; and (ii) qualitative data was collected from selected students using an interview to explain the reasons behind the difference observed within the post-test data. Findings showed that the experimental group had improved flexible and innovative first-step strategy use than the control group. Thematic analysis of the qualitative data revealed three themes that support the observed difference in strategy flexibility (i) expansion of strategy repertoire, where students reported that they now have knowledge of alternative methods for solving cubic equations, (ii) situational strategy selection where students reported of having improved ability to select strategies appropriate to a given equation structure, and (iii) motivational dispositions where students reported of becoming interested, enjoyed, engaged and confident. The results suggest that teaching students’ non-linear equation-solving by history-integration can meaningfully enhance strategy flexibility. These findings align with the theory of adaptive expertise and findings of existing empirical studies in the history and pedagogy of mathematics. The study recommends that teachers should teach problem-solving in algebra using the historical context of concepts. The study is limited in the sense that participants were assigned to groups non-randomly, lessons were short in duration, and sample was not larger enough. Future research should employ more rigorous designs, larger samples, extended lesson periods, and follow-up assessments to evaluate long-term retention and transfer of strategy flexibility.