Session F1D

978-1-4244-6262-9/10/$26.00 ©2010 IEEE October 27 - 30, 2010, Washington, DC 40th ASEE/IEEE Frontiers in Education Conference F1D-1

Work in Progress – A Concept Map for Mechanics of Materials

C.J. Egelhoff, Nathan Podoll, and Kassim Tarhini

United States Coast Guard Academy, Carla.J.Egelhoff@uscga.edu, Nathan.A.Podoll@uscg.mil, Kassim.M.Tarhini@uscga.edu

Abstract – The Mechanics of Materials course is fundamental to all areas of solid mechanics in engineering. It is commonly a “gatekeeper” course and generally considered “difficult” by students. Educators across several engineering disciplines have attempted to improve learning through efforts such as: developing physical demonstration models for classroom use, writing computer programs for independent learning, and conducting concept inventory studies to uncover the underlying cause of learning difficulty. This paper describes the development of a Concept Map for Mechanics of Materials. The map serves as the focal point for discussions and questions, and is simple enough so that anyone can re-create its salient features as a hand-drawn sketch. This concept map has been used and assessed as a tool to review the Mechanics of Materials course before administering a gateway exam in the next-level course, and as a tool for the Fundamentals of Engineering Exam review course. Preliminary assessment results indicate this concept map is an effective tool to use for teaching or reviewing Mechanics of Materials. Index Terms – Concept Map, Mechanics of Materials, Mind Map, Solid Mechanics, Strength of Material

INTRODUCTION

The Mechanics of Materials course is fundamental to many engineering programs such as Mechanical, Civil, Industrial, Chemical, Biomedical, and Marine Engineering. It is also commonly a “gatekeeper” course, whereby students who don’t do well academically, (or perceive they haven’t done well) may exit the engineering major path. The course is generally considered “difficult” by students; although the math required is not particularly difficult, the content and vocabulary (unchanged in practice for decades) are new to students. Educators routinely strive to create a new approach, a new technique, or a new project to excite student interest or enhance learning. Educators across several engineering disciplines have attempted to improve Mechanics of Materials learning through endeavors such as: • development of physical demonstration models or video

for classroom use, • development of computer programs to assist, encourage

and facilitate independent learning by students,

• concept inventory research to uncover the underlying cause of learning difficulty with the content, and

• a more clearly articulated problem-solving approach has been proposed by others specifically for Mechanics of Materials to improve student learning.

Concept maps have been used to introduce new

subjects, to help students see the “big picture”, to communicate the structure of curriculum among courses and within a course, and to assess learning. This paper describes the development and preliminary assessment of a concept map for the first Mechanics of Materials course. [1-3]

PERSONAL CONCEPT MAPS FOR MECHANICS

Concept maps are not new; we initially encouraged students to develop personal concept maps as a means to learn or demonstrate understanding of the Mechanics of Materials course content. We hoped over several years that a student would produce a map so wonderful, that we would adopt it for everyone to use. This never happened, although many of the personal maps were beautiful, colorful and revealing of the students’ thinking. The student-created maps provided a wealth of rich evidence regarding student perception of the importance of topics and of student misconceptions. Ultimately, such efforts proved inadequate for several reasons, including the following: • since the student-created maps varied widely, the

instructor needed to interview virtually every student to determine the intended meaning,

• there was so little commonality among student-created maps that communication was not facilitated using the student maps, and

• since concept maps do not generally provide help with problem solution, the student-created maps also did not give much assistance about the next step or direction of the problem solution. As instructors, we need to more clearly articulate the

overarching ideas and the intended goals and applications for Mechanics of Materials because students see the many topics conveyed in the course as disjointed and unrelated. Students have difficulty solving real-world problems based on the principles presented in the course.

COMMON CONCEPT MAP

Session F1D

978-1-4244-6262-9/10/$26.00 ©2010 IEEE October 27 - 30, 2010, Washington, DC 40th ASEE/IEEE Frontiers in Education Conference F1D-2

Our hypothesis is that a “common” concept map could be used to teach and to review topics presented in Mechanics of Materials. This “common map” could become a focal point for classroom or individual discussion and questions during the semester, and could be simple enough so that anyone could re-create its basics as a hand-drawn sketch. We have intentionally chosen to use characteristics of both concept maps and mind maps because the images are powerful memory enhancers for most engineering students.

The overall arrangement of the common concept map was chosen judiciously so as to have only a few parts. One part of the map is a reminder of the assumptions needed for nearly all of the Mechanics equations and we draw the student’s attention to the idea that we will defy some of these assumptions in our application to real life analysis.

The central word was chosen to be “loading” because it is thought to be more vivid and visual than “Mechanics of Materials.” The layout gives visual cues regarding the solution path as well. Most mechanics-style analysis of “real” components progresses to a decision based on stress or deformation as the common design/analysis criteria. With large safety factors, perhaps only the stress calculation will be the defining factor, so stress could be the only or the final criterion for the analysis. However, many components require stress and deflection to be considered in the design or analysis, so the common concept map signals the user to think about both. The common concept map is also an indicator that all stresses (from the many possible loadings) “collect” together to be applied in the evaluation phase using the Mohr’s Circle and in calculating the principal stresses.

The deflection (and slope) portion of the common concept map is intentionally simplified, with just the list (as a memory cue) of methods learned to determine deflection (and slope) accompanied by the abbreviated singularity function table. Through additional investigations in the upper-level Machine Design course, we have determined that the singularity function approach is the most direct for complex geometry subjected to variable and/or repeated loads in possibly multiple planes. [4]

USES OF THE COMMON CONCEPT MAP

We have used portions of this concept map informally over several years as. Like many instructors, we began with lists of equations and lists of lists which evolved into images inside of circles with arrows. This year we printed and distributed the one-page map and used it as a review tool for two groups of students.

First, the junior level students in the Mechanisms course were assigned a 20-problem “gateway exam,” of which 80% covered Mechanics of Materials (primary prerequisite course). The Mechanisms gateway exam in 2010 was the same exam used in 2009; however, the average score increased from 68% to 90% (and decreased standard deviation, from 16.9 in 2009 to 10.0 in 2010). We believe that the exercise of review coupled with the use of the

common concept map is the reason for the increased average score.

The second group included seniors (from several majors) preparing for the Fundamentals of Engineering (FE) exam. Mechanics of Materials was reviewed in one, fifty-minute class using this concept map as a handout and a smart-board image which could be written on or annotated. At this point assessing the FE review is based on observations and non-scientific polling of student opinions. For students who had completed the Mechanics of Materials course, this common concept map received overwhelmingly positive feedback. Students expressed optimism because their expected understanding was placed in the context of the “bigger picture” and the map exposed the solution path for applied mechanics problems.

CONCLUSIONS

Mechanics of Materials is a challenging gatekeeper course for many engineering students, and as such it is a perennial target for efforts to improve learning. Concept maps are not new; however, creating a “common” concept/mind map as a tool specifically for use with Mechanics of Materials as described in this paper, is a novel approach. We have shown preliminary positive assessment results from its use as a focal image for FE review and for gateway exam review. Next we are planning to use the common concept map as an introduction tool, as a crib sheet for exams, and as a problem-solving map to use for individual homework.

REFERENCES

[1] Morsi, Rasha, Wael Ibrahim and Frances Williams, “Concept Maps: Development and Validation of Engineering Curricula,” Proceedings of the ASEE/IEEE Frontiers in Education Conference, Milwaukee, WI, 2007

[2] Borrego, Maura, Chad B. Newswander, Lisa D. McNair, Sean McGinnis and Marie C. Paretti, “Using concept Maps to Assess Interdisciplinary Integration of Green Engineering Knowledge,” Advances in Engineering Education, Winter 2009

[3] Sims-Knight, Judith E., Richard L. Upchurch, Nixon Pendergrass, Tesfay Meressi, Paul Fortier et al, “Using Concept Maps to Assess Design Process Knowledge,” Proceedings of the ASEE/IEEE Frontiers in Education Conference, Savannah, GA, 2004

[4] Egelhoff, C.J., E.M Odom and B.J. Wiest, “Application of Modern Engineering Tools in the Analysis of the Stepped Shaft: Teaching a Structured Problem-Solving Approach Using Energy Techniques,” Frontiers in Education Conference, Washington, DC, Oct 27-30, 2010

AUTHOR INFORMATION

C. J. Egelhoff, Professor and Section Chief, Mechanical Engineering.

Nathan Podoll, Commander, U.S. Coast Guard and former Associate Professor and Section Chief, Civil Engineering.

Kassim Tarhini, Instructor, Civil Engineering, United States Coast Guard Academy, 27 Mohegan Avenue, New London, CT 06320-8101 .