Post hoc discernment of developmental mathematics noncognitive factors and concept transfer
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One purpose of this study was to determine if students in a non-traditional developmental mathematics course improved on five developmental mathematics noncognitive factors—math equanimity, math mindset, math self-efficacy, math belongingness, and college belongingness—believed to be relevant to student success. I also examined if changes in these factors predicted course achievement. Another purpose was to explore whether or not Foundations students would transfer their knowledge to place value problems involving varied bases and contexts. A final purpose was to investigate the utility of then-surveys that retrospectively measure participants’ pre-intervention noncognitive factors. In response to policy pressures to increase completion rates, community colleges are experimenting with research-based strategies that create demand for learning, increase students’ competence valuation, and improve their productive persistence. The New Mathways Project’s Foundations of Mathematical Reasoning course is built around one such strategy. In this exploratory study (N = 597), I investigated the impact of using Foundations on the development of students’ noncognitive factors and on mathematical success. My student measures included: pre-post-then-surveys of noncognitive factors, math course grades, math final exam grades, percent attendance, a place value assessment of transfer, and one-on-one interviews. I used multilevel models to analyze my quantitative research questions and created evidence markers for qualitative analysis of the transfer assessment. I conducted interviews to provide additional insight. Students significantly improved their math equanimity, but had stable, mid-range scores on the other factors. Positive changes in math self-efficacy and low initial math equanimity were associated with higher grades. Pre-surveys of equanimity may be more accurate than then-surveys, but pre-surveys of math mindset, math self-efficacy, and math belongingness may be interchangeable with then-surveys. Contrary to popular findings, the then-surveys did not provide larger estimates of program effects than pre-surveys. Overall, students evidenced minimal transfer. Interviewees exhibited greater changes in noncognitive factors and evidenced more transfer than other students. This study provides valuable information for the potential users of the NMP materials. It contributes to, and points out complications with, transfer research. Lastly, it adds to research on retrospective measures, which are rarely used in mathematics education research.