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An Active Learning Environment for Enriching Mathematical, Conceptual, and Problem-Solving Competencies

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2011 ASEE Annual Conference & Exposition


Vancouver, BC

Publication Date

June 26, 2011

Start Date

June 26, 2011

End Date

June 29, 2011



Conference Session

Modeling and Problem-Solving

Tagged Division

Educational Research and Methods

Page Count


Page Numbers

22.159.1 - 22.159.20

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Paper Authors


Morris M. Girgis Central State University

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Morris Girgis is a professor at Central State University. He teaches undergraduate courses in manufacturing engineering. He recieved his Ph.D. in mechanical engineering from Hannover University, Germany. His current research in engineering education focuses on developing and implementing new educational tools and approaches to enhance teaching, learning, and assessment at the course and curriculum levels.

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A PBL Approach for Teaching Mathematical and Problem-solving Skills: Integrating Lectures, Testing, Laboratory and Case StudiesAbstractThis paper describes a Problem-Based Learning (PBL) approach that integrates multiple tasksand activities designed for enhancing students’ mathematical and problem-solving competencies.The research framework has been developed to enable comparison of pre- and post- tests of thesame group of students to determine the effectiveness of the PBL approach on their problem-solving competency. In a Strength of Materials course, the proposed approach was implementedby offering students several problem-based tasks and activities. At the onset of the PBLapproach, students were offered sessions on conceptual and procedural understanding of thetopic. They were given a pre-test to assess their initial problem-solving skills. They were thenengaged in hands-on laboratory activities. Next, students were assigned a case study based on aproblem similar to the assigned laboratory experiment to develop mathematical models of themechanical system. And finally, students were given a post-test to evaluate the effectiveness ofthe approach.During the case study project, the instructor introduced the problem and provided the studentswith the learning objectives, problem statement, case study approach, deliverables and deadlines.The instructor guided the students throughout the entire PBL activity by explaining concepts,giving hints for deriving the system mathematical equations and organizing the problem-solvingprocess. The help was carefully offered so that the students worked independently and mademost assumptions and decisions by themselves.The activities of the problem-based learning approach were structured into the following tasks orsessions: 1. Conceptual understanding and problem-solving session followed by a relativelydifficult pre-test and a survey, 2. Experimental laboratory session based on a problem that issimilar but easier than the pre-test, 3. Open-ended problem-based case study performed inmultiple sessions as assigned to students, and, 4. Post-test equivalent in difficulty to the pre-testfollowed by a second survey. The pre and post tests are designed to match the desired level ofproblem-solving competency.Post and pre test results were compared to assess the effectiveness of the entire set of activities.Surveys after both tests were designed to collect students’ reflections and feedback about thenew approach. Improved test results and positive student comments indicated the effectivenessof the approach in enhancing student conceptual understanding and problem-solving skills.Students’ comments indicated their enthusiasm regarding the new teaching and learningapproach. Students benefited from the activity through the active learning environment, teamingarrangement that strengthened their individual capacities and skills, improving conceptual,mathematical and problem-solving skills as observed in their improved test scores.The challenges of this study include the small size of the participating teams that limited theselection of a uniform group of students and the limited time within the course to perform suchan extensive program with multiple tasks and activities. Future research will includeenhancement, refinement and pilot testing of the approach as well as extending it to otherengineering domains and disciplines.References1. Newswetter, Wendy C., Fostering Integrative Problem Solving in Biomedical Engineering: The PBL Approach,Annals of Biomedical Engineering, Vol. 34, No. 2, February 2006, pp. 217-2252. Smith, K. A., S. D. Sheppard, D. W. Johnson & R.T. Johnson, Pedagogies of Engagements: Classroom-BasedPractices, J. Eng. Educ., 94(1):87-102, 2005 K1 K2 W Case Study of a Spring-Pulley SystemAdditional Supporting Material:     Conceptual & Procedural Understanding (lecture) Pre-test - A problem more difficult than the laboratory Laboratory Session based on a mechanics problem that is easier than the Pre-test Problem-Based Case Study for enhancing mathematical and problem-solving skills Post-test that is similar to the Pre-test with the same level of difficulty Determine the effectiveness of the teaching approach by test results, surveys and interviews     Figure 1. Components of the integrated PBL teaching/learning approach Activity Session/Activity Description Activity Time Planning by Weeks Conceptual & 0.4 class period Lecture procedural (20 minutes) understanding Pre-test consistingSession I Testing of a relatively difficult problem 0.6 class period Week 1 Collecting student (30 minutes) Survey feedback on the pre-test Experimental lab 2 class periods Session II Laboratory session based on a (100 minutes) similar problem Problem-based case study for enhancing 4 class periods) Week 2, 3 Session III Case Study mathematical and 200 minutes) &4 problem-solving competencies Post-test that is 0.6 class period Testing similar to the Pre- (30 minutes) test in Difficulty Questions to Session IV Week 5 identify students’ 0.4 class period Questionnaire opinions and (20 minutes) feedback on all activities Total time for all activities Spanned 8 class periods over 5 (400 minutes) weeksNotes: 1. The activities are distributed over a four-week period.2. The course design project is based on designing an improved laboratoryexperimental set-up that models the case study problem.3. An oral presentation and a written report are required for the case study. Figure 2. Planned Sessions for Conducting the PBL Case Study Approach

Girgis, M. M. (2011, June), An Active Learning Environment for Enriching Mathematical, Conceptual, and Problem-Solving Competencies Paper presented at 2011 ASEE Annual Conference & Exposition, Vancouver, BC.

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