Physical Experiments to Enhance Model-eliciting Activity Implementation

Model-Eliciting Activities (MEAs) use open-ended case studies to simulate authentic, real-world problems that small teams of students address. Our approach for this Phase 3 CCLI Project took the theoretical framework from mathematics education to create a strategic, scalable approach which addressed crucial goals in engineering education. As part of a multi-year and multiUniversity effort, California Polytechnic State University, San Luis Obispo (Cal Poly) has developed and tested several MEAs which use experiments (or other physical/hands-on activities) to enhance student learning within the mechanical engineering curriculum. The three primary areas in which we have incorporated hands-on physical activities include a) using laboratory experiments to collect data for the models, b) as a method to provide self-assessment of the student models, and c) as a reinforcement tool to help students better understand the concepts being covered in the MEA. Background Model-Eliciting Activities (MEAs), which were developed in the mathematics educational community, require teams of students to attack open-ended problems. MEAs are distinctly different from “textbook” problem-solving activities in terms of length of time, access to information resources, number of individuals involved in the problem-solving process, and type of documentation required. However, the most important difference is the emphasis on building, expressing, testing and revising conceptual models. The six guiding principles of MEAs try to maximize the learning potential of these activities: Reality Principlecontains a realistic client with engineering context Model Construction Principlea mathematical model and/or decision algorithm must be developed Model Documentation Principlea deliverable, often in the form of a memo to the client, should reveal student thinking Self-Assessment Principlestudents should be able to know when their model is “good enough” Generalizability Principlethe model should apply to multiple related situations Effective Prototype Principlethe MEA should involve important concepts that are critical in future classes and engineering practice. Of these six principles, we found that physical experiments most specifically address the Model Construction Principle and the Self-Assessment Principle. The Model Construction Principle P ge 25041.2 requires students to create a mathematical system to reasonably address the needs and purpose of a given client. We specifically use the hands-on experiments to create data that the students can use to build their models, and then to test the validity of their models. The Self-Assessment Principle requires that as students develop the model, they must be put in a position that encourages self-evaluation of their work. The hands-on activities that we describe here encourage students to test and revise their models by pushing them past their initial ways of thinking to create a model that better meets the needs of the client. Finally we have also found that it can be beneficial to use physical laboratories and demonstrations that are not directly related to the MEA, but can still be used to reinforce the concepts that are being stressed. Using Physical MEAs to Help with Model Construction Several of the MEAs developed at Cal Poly utilize hands-on physical activities to collect data to help with model construction. We will describe two such MEAs, both of which are used in a senior level thermal systems design course which is taken by all of our mechanical students. Key topics for this course include engineering economics, pumps/piping, heat exchangers, and system simulation/optimization. These MEAs are implemented during a weekly 3-hour laboratory meeting associated with this course. Typically, two such lab meetings are utilized to complete one MEA. Energy Efficiency Rebate Program Design MEA Here, an electricity utility has hired the student teams to develop an electricity rebate program which encourages customers to undertake measures to make their homes more energy efficient. This MEA is intended to reinforce concepts from engineering economics, thermodynamics, and system optimization. The desired model is an optimized rebate structure which returns the greatest electricity savings per dollar invested in the program. At its simplest, anyone can easily note that a $20 rebate for compact fluorescent light bulbs (CFLs) would save the customer more money (and conserve more electricity) than a $40 rebate for a new microwave. To develop the framework for their rebate structure model, students use a provided $30 plug-in power meter (Kill-a-Watt model 4460), the utility electricity meter (smart meter or conventional), and their electricity bill to measure and estimate the electricity usage by all major appliances and lighting in multiple residences. At a minimum, they are asked to determine instantaneous power (kW), average power (kW), and estimated energy per month (kWh) of each device. One specific goal here is to directly address commonly held misconceptions regarding energy and power and their associated dimensions. Each group uses their electricity usage measurements to design the framework of an energy efficiency rebate program for our local electricity utility. The model they develop should provide recommendations, based on economics and electricity usage, which obtain the most “bang for the buck.” In keeping with other MEA principles (specifically the Generalizability Principle), the model they develop needs to be general enough that it could quickly be modified for other types of homes, other price structures, different time frames, and different quantities of available rebate money. P ge 25041.3 This MEA, with only minor modification, has been used successfully in three consecutive years of this course. After one week, students bring in their electricity measurements to class and we compare values. Through coordinated discussion lead by the instructor, we try to ensure that all groups are on a trajectory for success. We also compare measurement values at this meeting. Some appliances due to their size (refrigerators) or voltage (electric dryers) are more difficult to measure, so we share measurements throughout the class as necessary. Students are provided a grading rubric for their rebate program deliverable, and typical scores earned for this activity are 7-10 points out of a possible 10. Obviously, appliance electricity consumption data is readily available via the internet, so it could be argued that the first half of this MEA (the data acquisition portion) is unnecessary. In fact, our experience is the opposite. Engineering students are very excited about the opportunity to make measurements of their own appliances. Inevitably, we hear students sharing their experiences of surprise at some of their measurements. Several students have even volunteered that the MEA encouraged them to modify their behavior regarding electricity usage. Their enthusiasm for the measurements helped motivate effort during the calculation-intensive model development portion of the activity. Viscosity Measurement MEA Here, a petroleum company has hired the student teams to develop a small, robust device for measuring fluid viscosity quickly in the field. The viscometer is supposed to work over a wide range of viscosities (1-1000 cP), although the device does not necessarily have to measure dynamic viscosity. The projects are evaluated (with lower scores being better) based on the volume of liquid required to make a measurement, the time required per measurement, the measurement error (compared to an unknown standard), and the variability of their measurements. In an attempt to not bias their creativity, no equipment is provided for this MEA. The first week was occupied with brainstorming and refining their ideas. By the second week, students have developed a working prototype and use the lab period to calibrate their device. It is during this meeting that the students utilize their measurements to develop an appropriate engineering model of their measurement principle. For instance, many students develop devices that involve dropping a mass through a column of the measurement liquid and measuring the descent time (i.e., a “falling ball viscometer”). So based on their measurements and device characteristics, they have to decide how to model the behavior they observed (laminar vs. turbulent, wall effects, is terminal velocity achieved, etc.). This MEA has been used successfully in two years of this course. A key learning objective was to improve student understanding of the similarities and differences of kinematic and dynamic viscosity. Later in the course, when we discussed pumping of viscous fluids, it was clear to the instructor that student understanding of the two viscosities was greatly enhanced. Also, we wanted to give students an intuitive feeling of the “thickness” of a 1 cP fluid versus a 1000 cP fluid. While not particularly surprising, students commented on how helpful it was to touch fluids of varying viscosity, in order to develop this level of familiarity. P ge 25041.4 On a downside, our efforts to foster creativity and diversity in their designs were initially unsuccessful. In our first year of implementation, every group came up with methodologies which measured dynamic viscosity, so there was less discussion of the two viscosities than expected. Also, only two groups out of 18 designed anything other than a “falling ball viscometer.” Consequently, in the second year of implementation, we adjusted the scoring rubric to encourage diversity of designs. By providing a small adjustment of their score based on the complexity of their methodology, we were able to encourage a wide range of solutions in addition to falling ball viscometers. New solutions developed by students included a) pouring of the liquid, b) sliding glass on a layer of the fluid, c) measuring torque and speed of a motor mixing the liqu