Browsing by Author "Corven, Julien"
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Item Exploring the Prevalence of Covariational Reasoning Across Mathematics and Science Using TIMSS 2011 Assessment Items(International Journal of Science and Mathematics Education, 2023-02-01) Gantt, Allison L.; Paoletti, Teo; Corven, JulienCovariational reasoning (or the coordination of two dynamically changing quantities) is central to secondary STEM subjects, but research has yet to fully explore its applicability to elementary and middle-grade levels within various STEM fields. To address this need, we selected a globally referenced STEM assessment—the Trends in International Mathematics and Science Study (TIMSS)—to investigate the extent to which covariational reasoning could be applied. Specifically, we identified the frequency of items with potential to elicit students’ covariational reasoning through a content analysis of publicly released TIMSS 2011 items in Grades 4 and 8 mathematics and science. We found that approximately one-third of items in all grades and subjects had potential for covariational reasoning, and many of these items had such potential with no viable alternative strategy. Furthermore, items in every content strand and cognitive domain had potential for covariational reasoning. We interpret these findings as indicative of the salience of covariational reasoning across STEM education, and we discuss the implications of these results for research, assessment, and instruction.Item Prospective elementary teachers' evaluations of students' solutions to division story problems(University of Delaware, 2022) Corven, JulienThis dissertation comprises two articles. In the first article, I review and synthesize literature on how prospective teachers (PTs) might evaluate students’ mathematical thinking as manifested in written work. After defining evaluation, I argue that evaluating students’ thinking in productive ways is both necessary and desirable within the context of responsive teaching. I then describe potential uses for evaluation in helping teachers respond productively to student thinking or in the enactment of responsive teaching moves. I synthesize findings of previous studies on evaluating student work into a framework of seven evaluation criteria. I then combine this framework with research on teachers’ diagnostic processes to create an elaborated process for evaluating student work. Excerpts from interviews with PTs demonstrate the utility of these products. In the second article, I describe an empirical interview study conducted with 15 elementary PTs enrolled in their first mathematics content course to ascertain the extent to which their evaluations aligned with components of the elaborated process and how their evaluations changed over time. Key findings include: (1) strategic competence was consistently the evaluation criterion PTs used most frequently, but the depth of evaluations using this criterion was inconsistent; (2) criteria PTs used for evaluation were inconsistent among solutions and appeared to reflect PTs’ perceptions of weaknesses; (3) PTs’ use of the personal preference criterion decreased significantly throughout the course; and (4) some PTs exhibited a common and productive trajectory in their evaluations on the clarity criterion. Implications for future research and teacher preparation programs are shared.