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ERIC Number: ED556262
Record Type: Non-Journal
Publication Date: 2013
Pages: 207
Abstractor: As Provided
Reference Count: N/A
ISBN: 978-1-3035-6510-6
Understanding Proportional Reasoning in Pre-Service Teachers
Johnson, Kim H.
ProQuest LLC, Ph.D. Dissertation, The Pennsylvania State University
The purpose of this study is to examine the proportional reasoning of pre-service teachers at the beginning of their teacher preparation program using the developmental shifts described by Lobato and Ellis (2010). They cast changes in proportional reasoning as transitions or "shifts" in students' thinking and these shifts can serve as tools to "evaluate [a] student's current thinking" (p. 61). Lobato and Ellis (2010) suggested that one needs to make the following transitions or shifts in his or her thinking in order to develop proportional reasoning: (1) from reasoning with one quantity to reasoning with two quantities, (2) from reasoning additively to reasoning multiplicatively, (3) from reasoning with composed-units to reasoning with multiplicative comparisons, and (4) from iterating a composed unit to reasoning with a set of infinitely many equivalent ratios. Twenty-five pre-service teachers, who were either elementary education majors or secondary mathematics education majors, completed a questionnaire consisting of problems that were meant to elicit the four shifts identified in the model. Based on the questionnaire responses, these twenty-five were placed into four groups. Eleven of these pre-service teachers (2 from Group 1, 3 from Group 2, 3 from Group 3 and 3 from Group 3) were then interviewed to examine how their reasoning related to the shift model. The analysis of the data suggests that model was hierarchical for those in Group 1 (participants who seemed to exhibit all four shifts) and Group 4 (participants who only provided evidence of shift 1). For those in Groups 2 and 3, the model did not appear to remain hierarchical given that the participants in these groups seem to inconsistently exhibit characteristics of the shifts. This means that when solving some proportional problems they would provide evidence of making all four shifts and on other problems they would revert back to evidence of making shifts 2,3, and 4. Groups 2 and 3's reasoning was inconsistent with the shifts because they were in the process of making the transitions as they learned to be proportional reasoners. The findings in this study provide teacher educators with knowledge about the nature of pre-service teachers' proportional reasoning. In particular, this study highlights four assumptions and misconceptions about proportional reasoning seem necessary for pre-service teachers to transform. These four assumptions include: reasoning quantitatively, recognizing ratios as measurement, misconceptions about the concept of ratio and fraction, and the obstacle of linearity. Mezirow's theory requires a disorienting dilemma in order to help individuals engage in rational discourse and critical reflection about previous assumptions. This study illustrates how four problems (Lemon/Lime problem, Dog/Cat problem, Housing problem and Track problem) were able to provide pre-service with a disorienting dilemma causing them to engage in rational discourse with the researcher and critically reflect on their previous assumptions in order to revise their strategies for solving these problems. By helping these pre-service teachers become aware of the assumptions they have about ratio, proportion and proportional reasoning through these disorienting dilemmas (i.e., thought-provoking problem solving tasks) they were able to think about proportional problems in new ways and make shifts in their proportional reasoning. This knowledge can be used to develop courses that can transform pre-service teachers' understandings of ratio and proportion and enhance their proportional reasoning so that future teachers can ultimately improve their students' learning. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Higher Education; Postsecondary Education; Elementary Education; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A