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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 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. 

It has been well documented that students face difficulties in transferring their knowledge and skills learned in prior courses to other areas of the curriculum. These problems with transfer are exacerbated by foundational courses being taught outside the major, as well as the fact that many engineering courses are taught in silos, with little connection being made to the engineering curriculum as a whole. Work is needed to better enable students to see the connections between their courses and transfer the requisite knowledge and skills from prior classes to other areas of the curriculum, and in their careers. This study builds on prior work (published at the ASEE Annual Conference last year) which used a series of think aloud, problem-solving interviews to assess the barriers and challenges students face in transferring knowledge from prior mathematics courses into an applied engineering setting. In this prior work, participants were tasked with solving a rigid body equilibrium problem typical of an engineering statics course but which required integration skills, as well as knowledge of the centroid, to solve. In the course of this study it was found that participants could not solve the problem as they could not determine the centroid of the object in question. Participants cited issues such as a lack of applied problems being taught that used centroids, the use of tabulated data for centroids, and forgetting governing equations as major barriers to being able to solve the problem. A majority of participants did however believe that being shown a general equation used to calculate centroids would have improved their problem solving success. Grounded in the results of this prior study, two separate interventions designed to promote the transfer of knowledge and skills from prior courses were developed and tested with the goal of aiding students in determining the location of the centroid. In order to examine the potential effectiveness of these interventions, a series of (n=11) think aloud interviews were conducted based around the same statics problem as had previously been used. One of these interventions used a mathematical, equation-based-prompt in an attempt to promote knowledge transfer, while the other used a similar prompt but provided in a more applied, engineering context - in this case an excerpt from the notes made by the instructor of the department’s engineering statics class. Findings suggested that an equation-based-prompt was largely unsuccessful at promoting problem solving success. The applied prompt based on prior course notes was more successful in enabling participants to solve the problem and find the centroid. It was unclear however if students truly understood the equations and methods presented in this prompt or whether they were simply able to correctly interpret the prompt and copy the pattern onto their solution. Persistent problems with (English) units and a lack of utilizing a formal problem solving method were also observed. A broader analysis of the study also suggests that students do not fully understand the conceptual underpinnings of the calculations used to determine the location of the centroid of an object. 

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.