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

Morris M. Girgis

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Conference: 2011 ASEE Annual Conference & Exposition
Location: Vancouver, BC
Publication Date: June 26, 2011
Start Date: June 26, 2011
End Date: June 29, 2011
ISSN: 2153-5965
Conference Session: Modeling and Problem-Solving
Tagged Division: Educational Research and Methods
Page Count: 20
Page Numbers: 22.159.1 - 22.159.20
DOI: 10.18260/1-2--17440
Permanent URL: https://peer.asee.org/17440
Download Count: 582

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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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Abstract

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

Citation
Format

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. 10.18260/1-2--17440

TY  - CPAPER
AB  -    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 &amp; 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 &amp; 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 &amp;           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)       &amp;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
AU  - Morris M. Girgis
CY  - Vancouver, BC
DA  - 2011/06/26
PB  - ASEE Conferences
TI  - An Active Learning Environment for Enriching Mathematical, Conceptual, and Problem-Solving Competencies
UR  - https://peer.asee.org/17440
DO  - 10.18260/1-2--17440
ER  -