Interactive engagement in reasoning about variance
DOI:
https://doi.org/10.52041/iase2023.110Abstract
Students’ reasoning about variation is often inconsistent with the normative logic underlying statistical procedures such as ANOVA, even after formal training. This study introduced an interactive classroom activity intended to support normative reasoning about variance. In small groups, students were shown a small dataset from a hypothetical, between-groups, experiment and asked to collaboratively consider how the within- and between-group variance could provide evidence about an effect of an independent variable. Before engaging in the interactive activity, most students considered between- and within-group variability in a non-normative manner. Following the activity, nearly all students’ reasoning shifted to a normative pattern, recognizing the relevance of the ratio of between- to within-group variation for making judgements about group differences. The findings support Chi’s ICAP theory of cognitive engagement and presents a novel interactive activity to support students’ developing understanding of ANOVA, which can be very difficult to achieve in introductory courses.References
Chi, M. T. H. (2009). Active-Constructive-Interactive: A conceptual framework for differentiating learning activities. Topics in Cognitive Science, 1, 73–105.
Chi, M. T. H., & Wylie, R. (2014). The ICAP framework: Linking cognitive engagement to active learning outcomes. Educational Psychologist, 49(4), 219–243.
Reid, J., & Reading, C. (2008). Measuring the development of students’ consideration of variation. Statistics Education Research Journal, 7(1), 40–59.
Trumpower, D.L. (2013a). Formative use of intuitive analysis of variance. Mathematical Thinking and Learning, 15(4), 291-313.
Trumpower, D.L. (2013b). Intuitive analysis of variance - A formative assessment approach. Teaching Statistics, 35(1), 57-60.
Trumpower, D.L. (2015). Aspects of first year statistics students’ reasoning when performing intuitive analysis of variance: Effects of within- and between-group variability. Educational Studies in Mathematics, 88(1), 115-136.
Trumpower, D.L. & Fellus, O. (2008). Naïve statistics: Intuitive analysis of variance. Proceedings of the 30th Annual Conference of the Cognitive Science Society, 499-503. (Washington, DC).
