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Within the profession, there is a desire for graduating engineers to be “T-shaped” professionals who have a deep subject knowledge (the vertical of the “T”), with the ability to apply that knowledge across a broad range of contexts (the horizontal of the “T”). The ability to transfer knowledge between courses in the undergraduate curriculum, and then into one’s career, is, therefore, an important skill that should be developed in engineering curricula. Based on prior work in this area, and with the goal of developing adaptive problem solvers who can transfer their knowledge across a range of contexts, we compare the problem solving approaches taken by both experts (faculty) and novices (students) when faced with problems that require knowledge to be transferred in order to be solved. Transcripts and artifacts generated through a series of think aloud protocols are analyzed using an a priori coding scheme and thematic analysis based around a sense-making framework of knowledge transfer. A comparison of expert (faculty) and novice (student) approaches to problem solving demonstrated 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 observed to be a differentiating factor in their approach as compared to novices. 

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. 

I initially became interested in knowledge transfer after observing my students’ general inability to use mathematical knowledge and skills in an applied (engineering) context. My personal belief was that the students should have an understanding of basic basic mathematical concepts, like integration, and be able to use them correctly to solve problems. Clearly, something was missing in my students’ understanding or perhaps memory that was causing them problems in this regard. In my initial work on knowledge transfer, I found that many students did not even recognize the need to transfer knowledge and for example, to integrate to solve a problem framed in an engineering context unless they were prompted to do so. Concerned by this troubling observation, coupled with my belief that engineers should be able to both understand and apply mathematical concepts in their coursework and careers, I determined to investigate the cause of the problem and, if possible, evidence a potential solution to help students transfer mathematical knowledge into an applied (engineering) context. In this study, I examine an expert (faculty) approach to problem solving using a semi-structured, think-aloud interview protocol coupled with a thorough thematic analysis for phenomenological themes. This analysis, grounded in an existing framework of knowledge transfer, provides a rich, thick description of the knowledge transfer, and problem solving process employed by the faculty expert and serves as a useful comparative case against which student approaches to problem solving and knowledge transfer can be judged. Important findings of this study relate to the extensive use of reflective and evaluative practices employed by the faculty member at all stages of the problem solving process. These internal checks and balances are rarely observed among novice problem solvers and perhaps represent behaviors that we, as educators, should seek to impart in our students if they are to become more adaptable engineers who are better equipped to transfer their knowledge and skills across a range of contexts. 

Students often face difficulties in transferring concepts, knowledge and skills between their courses. This difficulty is especially true of the fundamental math and science courses that are often taught outside the major of the student and without engineering context. At the same time, graduating engineers are moving into an increasingly interdisciplinary workplace that values the ability to work broadly across a range of contexts. More work is needed to better prepare students to adapt their knowledge and skills to new situations and to demonstrate how the various courses and concepts within their curricula relate. In this study, we ask students, teaching assistants and faculty to “think aloud” through their solution to a statics problem that requires mathematical knowledge to be transferred in order to be solved. Two faculty, two teaching assistants and seven undergraduate students are interviewed as they think aloud through the problem. Interview transcripts and solutions to the statics problem are then examined for themes and patterns in responses in order to draw conclusions about the challenges different populations face in transferring knowledge and solving such problems. Observations indicated that students could apply simple integration skills to find the area of a shape when given a curve describing its shape, but could not use integration to find the centroid. The participants did however recall being taught how to calculate centroids in the past and discussed a lack of usage of this skill causing their inability to recall it correctly. Student participants in general displayed simple approaches to problem solving based on reading the problem statement rather than following an engineering approach starting with governing equations. A potential barrier to problem solving success was identified in the varying symbols used by different research participants which could lead to a lack of understanding if these symbols are not clearly explained and defined in a classroom setting. Future work will further examine these themes, as well as developing prompts and activities to promote knowledge transfer and problem solving success.