Relation between students’ problem-solving performance and representational format

Abstract

An analysis is presented of data on students' problem-solving performance on similar problems posed in diverse representations. Five years of classroom data on 400 students collected in a second-semester algebra-based general physics course are presented. Two very similar Newton's third-law questions, one posed in a verbal representation and one in a diagrammatic representation using vector diagrams, were given to students at the beginning of the course. The proportion of correct responses on the verbal question was consistently higher than on the diagrammatic question, and the pattern of incorrect responses on the two questions also differed consistently. Two additional four-question quizzes were given to students during the semester; each quiz had four very similar questions posed in the four representations: verbal, diagrammatic, mathematical/symbolic, and graphical. In general, the error rates for the four representations were very similar, but there was substantial evidence that females had a slightly higher error rate on the graphical questions relative to the other representations, whereas the evidence for male students was more ambiguous. There also was evidence that females had higher error rates on circuit-diagram problems in comparison with males, although both males and females had received identical instruction.

Role of mental representations in problem solving: Students’ approaches to nondirected tasks

“…Previous studies concerned with multiple representations [26,32] have evoked the key importance of students' fluency with different kinds of representations and in translating information among them. In the context of chemistry, Kozma [44] reported that when novice students are presented with multiple depictions, they attended to these representations on an individual basis.…”

“…Students' difficulties in handling particular representations such as diagrammatic and graphical representation in specific topics were investigated [21][22][23][24][25]. Studies were also geared towards exploring problem solving performance and hence differences in strategies with a change in representation [26][27][28]. The application of multiple representations for conceptual understanding [29,30] and enhancing problem solving performance [31,32] was additionally explored.…”

Unpacking physics representations: Towards an appreciation of disciplinary affordance

“…For example, Meltzer [10] notes that "the instructor's view of the ease or difficulty of a particular representation in a particular context might not match the views of a large proportion of students" (p. 473). This inability of physics teachers to judge the difficulties that a given representation may pose for students has also been reported by other researchers [15,48,49].…”

“…This theoretical article is about the teaching and learning challenges that arise from students experiencing this partiality of representations, where important physics aspects are not initially discernible. These issues are educationally important because what creates a powerful communicative system for physics at the same time manifests in the difficulties students experience in terms of becoming "fluent" [2] (p. 28) in the disciplinary-specific representations [2,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Theoretical details from the literature, together with the concept of disciplinary affordance [11,12], are used to underpin a case that physics representations need to be "unpacked" for students.…”

Using cluster analysis to identify patterns in students’ responses to contextually different conceptual problems

“…These interventions use multiple contexts to augment graphical skill. Differences in the representation of physics problems were found to produce strong differences in performance [21][22][23]. Differences in performance based on representation were also influenced by the context of the problems [22,23].…”