June 15, 2014
June 15, 2014
June 18, 2014
24.920.1 - 24.920.23
Multi-Course Alignment for 1st Year Engineering Students: Mathematics, Physics, and Programming in MATLABBackgroundHistorically, siloed courses utilizing traditional, deductive, teaching methods have struggled toeffectively promote conceptual understanding. Gains students achieve are usually modest and notstatistically significant; usually students are able to increase their factual knowledge only. Thesegains are predicated on students having either no preconceptions or correct but incomplete ones.However, students who have incorrect preconceptions do poorly as they must change theirexisting cognitive structure. Inductive teaching methods better enable students to achieve thischange.PurposeOur first year students struggle to synthesize concepts across Programming for Engineers,Calculus I, and Physics I courses. While calculus and physics are the tools to be utilized byengineers to solve problems, our students are often unable to see that the knowledge presented inthe mathematical and physics context can be transferred to solve engineering problems. Studentsalso tend to think of programming as an isolated component of engineering, while they shouldview programming as yet another tool to verify results or to solve more complex problems.Design/MethodThree faculty members have linked their classes so that students are in a STEM (science,technology, engineering, and mathematics) small-learning-community (SLC). The same set ofstudents is registered for all three courses simultaneously. All three faculty have collaborativelydeveloped several real-world application problems that require leveraging knowledgehorizontally across all three courses. For example, to solve the physics problem, students mustuse calculus concepts (summations, integrals, derivatives, and vectors) and implement them in aprogramming context (loops, decisions, vectors).At the beginning of the semester, students have not yet learned the mathematical theorems usedto solve the physics equations. This is where MATLAB’s plotting capability can be used to solvethe problems. For example, students have not yet learned that the maximum of a function can befound by setting the derivative equal to zero, and solving for the unknown. By plotting the curve,students can visually determine the x-coordinate of the curve’s peak. The complexity of theproblem increases when solving a system of equations. If the equations are those of straightlines, students tend to do well mathematically. When the system uses polynomial equationsinstead, students are more hesitant, which leads to algebra errors and poor results. Plotting thetwo curves with MATLAB allows students to visually solve for the (x,y) coordinates of theirintersections, thus answering actual physics concepts of trajectories. Later in the semester,students learn the theoretical process to solve those systems. Having solved the problemgraphically increases their confidence in solving it mathematically.At mid-semester, the mathematical concepts become more challenging, such as integrals.However, this concept can be programmed using loops. Each step of the integration process hasto be coded separately, thus reinforcing the student’s conceptual understanding of thefundamentals.In both cases, students have solved the physics problem graphically and therefore have a deeperunderstanding of the solution than those who did not utilize MATLAB.ResultsTo measure the impact of the integrated multi-disciplinary problems on student learning, a pre-and post-concept inventory was given both in Calculus and Physics classes. These tests weregiven to students, whether or not enrolled in the small learning community group.A mid-term focus group comprised of the STEM SLC students was interviewed by a memberfrom the Center for Teaching and Learning Excellence to measure the satisfaction of thestudents. The gathered feedback was taken into account to improve course structure and delivery.An end-of-semester feedback survey was given to all students, both those in and out of theSTEM SLC, to evaluate the overall program success and identify the areas for improvement.Final semester grades between the STEM SLC and the control group were compared to measurethe impact of the program. Longitudinal Math, Physics, and Statics data will be collected for thestudents who participated in the STEM SLC and compared to students who did not.ConclusionsTypically students see one way to solve a problem. By linking the assignments across the threeclasses, students are presented with multiple course specific solutions for solving the problems.Through this repetition process, from different viewpoints (calculus, physics, and programming),it is expected that different learning styles will be addressed, increasing student understandingand cross concept connections.As students are presented with multiple methods of solving a problem, it is expected thatstudents understanding, problem-solving ability, and critical thinking skills will be significantlyimproved.The overlap between the three classes might play a role in their overall satisfaction. Students aremore likely to understand a concept if they know it is applied to other classes.
Liron, C., & Steinhauer, H. M., & Raghavan, J., & Berhane, B. (2014, June), Multi-Course Alignment for First-Year Engineering Students: Mathematics, Physics, and Programming in MATLAB Paper presented at 2014 ASEE Annual Conference & Exposition, Indianapolis, Indiana. https://peer.asee.org/22853
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