It is well-established that students have difficulty transferring theory and skills between courses in their undergraduate curriculum. At the same time, many college-level courses only concern material relating to the course itself and do not cover how this material might be used elsewhere. It is unsurprising, then, that students are unable to transfer and integrate knowledge from multiple areas into new problems as part of capstone design courses, for example, or in their careers. More work is required to better enable students to transfer knowledge between their courses, learn skills and theory more deeply, and to form engineers who are better able to adapt to new situations and solve “systems-level” problems. Various authors in both the cognitive and disciplinary sciences have discussed these difficulties with the transfer of knowledge, and noted the need to develop tools and techniques for promoting knowledge transfer, as well as to help students develop cross-course connections. This work aimed to address these barriers to knowledge transfer, and crucially develop the needed activities and practices for promoting transfer by answering the following research questions: (1) What are the primary challenges experienced by students when tasked with transferring theory and skills from prior courses, specifically mathematics and physics? (2) What methods of prior knowledge activation are most effective in enabling students to apply this prior knowledge in new areas of study? In this paper we present a holistic summary of the work completed under this award. Initially, findings from a series of n=23 think aloud interviews, in which participants were asked to solve a typical engineering statics problem, is presented. These interviews evidenced multiple barriers to knowledge transfer (lack of prior knowledge, accuracy of prior knowledge, conceptual understanding, lack of teaching of applications, language of problem, curricular mapping) that hindered participant success in terms of using their mathematical skills to solve the problem. Findings also indicated the importance of reflective thinking on behalf of the participants to their problem solving success. Based on this initial work using think alouds, a further set of interviews (n=8) were conducted to more deeply examine student conceptions of important mathematical topics that are transferred into engineering such as integration and centroids. Findings indicated that participant knowledge and understanding of centroids in particular was generally based around more intuitive or geometrical conceptions rather than concrete physical or mathematical models. Following up on the initial study of problem solving, the importance of reflection on behalf of the problem solver was also examined in more detail. Comparison of expert (faculty) and novice (student) approaches to problem solving demonstrates how often experts reflect on their progress during the solving process and the manner in which they are able to connect problems in one context to similar problems they have encountered in the past in other areas of engineering. The ability of experts to “chunk” problems into smaller stages and reflect on individual elements of the problem at hand rather than the problem as a whole was also seen to be a differentiating factor in their approach as compared to novices. Similar to this paper, the associated poster presentation will cover a holistic representation of the findings of this study.
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Engineering - a context for learning mathematics: the case of guitar fret spacing
An example of how middle-school engineering projects can be used as contexts for students’ exploration of previous and new mathematics topics is shared here. In this example, students algebraically determined where to place frets on the fretboard of a stringed instrument they were designing and along the way made use of a fractional exponent that was beyond what they experienced in prior courses. Students engaged in reasoning and problem solving, had extended meaningful discourse with each other, stayed motivated through productive struggle, and actively built new mathematical understandings from new experiences and prior mathematical knowledge.
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- Award ID(s):
- 1842342
- PAR ID:
- 10394187
- Date Published:
- Journal Name:
- Technology and engineering teacher
- ISSN:
- 2158-0502
- Page Range / eLocation ID:
- 14 - 19
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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It is well-established that students have difficulty transferring theory and skills between courses in their undergraduate curriculum. At the same time, many college-level courses only concern material relating to the course itself and do not cover how this material might be used elsewhere. It is unsurprising, then, that students are unable to transfer and integrate knowledge from multiple areas into new problems as part of capstone design courses, for example, or in their careers. More work is required to better enable students to transfer knowledge between their courses, learn skills and theory more deeply, and to form engineers who are better able to adapt to new situations and solve “systems-level” problems. Various authors in both the cognitive and disciplinary sciences have discussed these difficulties with the transfer of knowledge, and noted the need to develop tools and techniques for promoting knowledge transfer, as well as to help students develop cross-course connections. This work will address these barriers to knowledge transfer, and crucially develop the needed activities and practices for promoting transfer by answering the following research questions: (1) What are the primary challenges experienced by students when tasked with transferring theory and skills from prior courses, specifically mathematics and physics? (2) What methods of prior knowledge activation are most effective in enabling students to apply this prior knowledge in new areas of study? Here, we present a summary, to date, of the findings of this investigation. These findings are based on an analysis of the problem solving techniques employed by students in various years of their undergraduate program as well as faculty experts. A series of n=23 think aloud interviews have been conducted in which participants were asked to solve a typical engineering statics problem that also requires mathematical skills to solve. Based on participant performance and verbalizations in these interviews, various barriers to the knowledge transfer process were identified (lack of prior knowledge, accuracy of prior knowledge, conceptual understanding, lack of teaching of applications, language of problem, curricular mapping). At the same time, several interventions designed to promote the transfer of knowledge were incorporated into the interviews and tested. Initial results demonstrated the potential effectiveness of these interventions (detailed in the poster/paper) but questions were raised as to whether participants truly understood the underlying concepts they were being asked to transfer. This poster presentation will cover a holistic representation of this study as well as the findings to date.more » « less
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