Applying Design-Based Research Findings to Improve the Common Core State Standards for Data and Statistics in Grades 4–6

Abstract

The Common Core State Standards for Mathematics have a widespread impact on children's statistical learning opportunities. The Grade 6 standards are particularly ambitious in the goals they set. In this critique, experiences helping children work toward the Grade 6 Common Core statistics expectations are used in conjunction with previous research to identify ways in which the Grades 4-6 standards might be supplemented or revised to help maximize learning. It is suggested that opportunities for children to perceive datasets as aggregates and to draw reasonable conclusions about statistical data by attending to context should be purposefully introduced in Grades 4-5. Currently, the Common Core does not have explicit learning standards for these activities in fourth and fifth grade. It is also suggested that teachers help students question their natural tendencies to focus extensively on the mode when summarizing data. The current standards do not specifically mention the mode. Revising or supplementing the Common Core in the suggested ways holds potential to make the Grade 6 statistical learning standards more attainable for children and to help teachers better anticipate the statistical thinking tendencies that are likely to emerge during classroom discourse.

Fifth-grade Students’ Quantitative Modeling in a STEM Investigation

“…The importance of context in working with data, and in modeling in particular, has been well documented-conclusions only become meaningful when they are interpreted in light of the context in which they were generated (Zapata-Cardona, 2018). For modeling problems, problem interpretation draws on both disciplinary content and general knowledge, which can both enhance and detract from an investigation (Gil & Ben-Zvi, 2011;Groth, 2019). Identifying an appropriate context in designing STEM investigations can present challenges when students "have ways of thinking about particular combinations of topic, context, and task that are difficult to foresee" (e.g., assuming that data trends follow the shape of a volcano; Lehrer & Schauble, 2021).…”

“…Given that informal inference is a foundational component of statistical literacy and a precursor to formal inference (Lehrer, 2011;Makar, 2016;Makar et al, 2011), it is of concern that many curricula ignore or downplay informal inferential reasoning as important learning in the elementary grades. This lack of early attention, in contrast to the secondary years and adult population, results in poor foundations for older students who frequently apply statistical methods without understanding or appreciating why, when, or how these are applied sensibly to a range of contexts (Garfield et al, 2008;Groth, 2019).…”

“…As such, they may be viewed as natural progressions towards line graph models. On the other hand, as Groth (2019) indicates, case value bars can sometimes be less effective in displaying certain distributional features, in contrast to those where aggregated data appear more compact (e.g., line graph). Questioning students on how they could improve their representations to facilitate data interpretation could be a step in advancing their progression towards more compact quantitative models.…”

“…The ability to generate more sophisticated representations, however, does not always mean that students can detect aggregates and their characteristics (Groth, 2019). Students had some difficulty in explicating a global view of covariation.…”