On the Shoulders of Giants: Helping Students Understand Mathematics through its History

Abstract

The IDEAS curriculum and instruction model was designed to help secondary students better understand mathematics by incorporating the historical development of the subject into classroom instruction. IDEAS is an acronym that describes the components of the model: I (Introduce the concept through a hands-on activity); D (Discover the historical, cultural, and human context through biography); E (Examine the primary sources through inquiry); A (Actualize the learning through written reflection); and S (Synthesize the understanding through practice and application). This study examined the effectiveness of the IDEAS model in a secondary setting, with 107 students enrolled in a pre-calculus course at a large suburban Title I public school in the southeastern United States. The IDEAS model was studied in both a classroom (face-to-face) context and a digital (online) context. A mixed methods approach was used, employing a quasi-experimental design, to determine the effectiveness of the intervention (the implementation of the IDEAS model). Quantitative data included pre- and post-intervention questionnaires, content assessments, and written reflections. Qualitative data included written reflections and one-on-one interviews. The main findings of this study were that the IDEAS model (1) increased participants’ understanding of the nature of mathematics (p < .02; d = .66); (2) helped participants develop a more positive attitude toward mathematics and its history; and (3) increased participants’ academic achievement in mathematics (p < .05; d = .33). These results have implications for secondary students, teachers, administrators, and researchers.