Engineering Education and the Development of Expertise - Classes

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Journal of Engineering Education 100 (January 2011) 1 Context-rich, multifaceted problems. Using context-rich, multifaceted problems has been advocated by several groups as an approach to having students develop more sophisticated problem solving skills than those developed when solving typical textbook exercises. This approach supports the development of key skills and the ability to apply conceptual knowledge both of which are needed to address the complex problems typical of engineering practice. Thus, this learning experience acts as a bridging strategy from textbook problems to realistic problems. The contexts of the problems can be chosen to link to students’ interests and career plans, increasing students’ motivation as well. Ogilvie (2009) describes multifaceted problems as problems that “lie somewhere between well-structured problems found in textbooks and large, ill-defined, open-ended challenges in the degree-of-difficulty these pose to students” (p. 3). A key characteristic of multifaceted problems is that they require students to integrate multiple concepts to construct a solution. Thus, students cannot use usual strategies of seeking examples in textbooks to identify the particular algorithm to solve the problem. Ogilvie (2009) presents the following example of a multifaceted problem related to thermodynamics: You are in charge of drinks at a picnic that will start at 3pm. You place ice inside a cooler at 6am, when the temperature outside is 10C. The day is forecast to warm up steadily to reach 30C by 3pm. Estimate how much ice you will need (p. 3). Because students are likely to have little experience in solving such problems, teaching in the course should include specific instruction on how to approach these problems. The complexity of the problems makes them well-suited to group problem solving activities. In describing his use of context-rich, multifaceted problems in an introductory physics course, Ogilvie (2009) indicates that he uses these strategies. The problems serve as a “capstone” experience for each of the main sections of the course; over the course of the semester the students solve six such problems. The instructor solved several of these problems during class to model strategies that students could apply in their own problem solving. The students worked in groups of two or three to solve the multifaceted problems during recitation with support from a graduate teaching assistant (GTA). The GTAs received training on how to use questions that prompted thinking by the students rather than giving direct answers. In addition to solving context-rich, multifaceted problems in recitation, students had to solve this type of problem on two group exams. They were graded on their use of appropriate strategies, e.g., “representing the problem with a diagram and their description of ongoing monitoring of the progress of the solution” (Ogilvie, 2009, p. 4). The approach described by Ogilvie is well aligned with the characteristics of effective learning experiences listed in Table 1. It offers students a challenge that forces them to use their prior knowledge in new ways. It also presents problems in more realistic contexts that enhance the interest of students and uses collaborative approaches that encourage deeper engagement. Ogilvie evaluated the impact of this approach on students’ analysis strategies by collecting students’ reflections at the beginning and end of the semester in response to the following questions: Please reflect on how you approach physics problems. What methods do you use? What mistakes do you have to watch for? And are these approaches similar to skills that you will need in your future studies or career? (p. 4) 132
100 (January 2011) 1 Journal of Engineering Education Two hundred sixteen students submitted both reflections. Their responses were analyzed by Ogilvie and an experienced colleague based on a scheme that divided the problem solving approaches students described into two categories: “limiting” and “expansive.” Limiting strategies included equation matching, listing knowns and unknowns, and using prior examples. Expansive strategies included thinking about re-representing the problem with a diagram, thinking about concepts first, using qualitative analysis, and identifying sub-problems. The major conclusion from the analysis is that using the multifaceted problems led to significant and substantial increases in the number of students who described themselves as using expansive strategies in solving problems. Model-eliciting activities. Model eliciting activities (MEAs) that promote deep approaches to learning were first developed in mathematics education (Lesh & Doerr, 2003). MEAs are being adapted to engineering education by several groups, see e.g., Diefes-Dux and Imbrie (2008) and Moore et al. (2008). The overall goal of MEAs is to facilitate the development of conceptual foundations of knowledge that will support deeper understanding (Lesh et al., 2000). Diefes-Dux, Verleger, Zawojewski, and Hjalmarson (2009) define MEAs as “open-ended, realistic, client-driven problems set in engineering contexts requiring teams of students to create a generalizable (shareable, reusable, modifiable) mathematical model for solving the client’s problem.” One of the distinguishing features of the MEA approach is that it incorporates multiple points of formative feedback and iteration to help students develop strategies and methods to solve such problems (Verleger & Diefes-Dux, 2008). The design of the problems themselves is guided by six principles from Lesh, Hoover, Hole, Kelly, and Post (2000): (1) Reality: the activity provided should occur in “real life”; (2) Model construction: the activity must create the need to develop, revise, refine, and extend a mathematical model; (3) Self-assessment: students should determine themselves if their solution meets the criteria for success, often described as needs of a client; (4) Model documentation: the documentation required of the students should reveal their thinking; (5) Generalizability: the activity should guide students to develop their model in a way that will allow others to not only use it to solve the immediate problem but also use it for their own purposes; (6) Effective prototype: the activity should involve learning processes and knowledge that students will use in their academic and professional careers. MEAs encourage deep engagement by demanding production and justification of a mathematical model. The problems are cast in a realistic context that should enhance student interest and motivation. The method also helps students to develop the ability to assess their progress toward a successful solution, an important meta-cognitive skill. (MEAs can be considered a specific type of problem-based learning, which we address directly in the next section.) Purdue University began the process of integrating MEAs in a required first-year engineering class in 2002. Diefes-Dux and Imbrie (2008) describe the implementation process, which continues today with cycles of assessment and improvement. The overall goal for the implementation of MEAs was to “bring engineering content and contexts into the first-year to help students better understand the nature and practice of engineering and to better prepare students for the sophomore year while addressing a number of ABET criteria” (p. 56). The learning objectives for the course that are fulfilled through the use of MEAs were: develop a logical problem solving process, translate a written problem statement into a mathematical model, solve fundamental engineering problems using computer tools, and work effectively and ethically as a member of a technical team. The implementation presented many challenges because the enrollment of the class is typically in excess of 1,400 students. The class format includes two 50-minute lectures and 133
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