Session USING CONCEPT MAPS AND CONCEPT QUESTIONS …ww.cdio.org/files/document/file/concept_maps_fie.pdfconceptual understanding. In particular, "muddiest-part-of-the-lecture" cards

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0-7803-7444-4/02/$17.00 © 2002 IEEE November 6 - 9, 2002, Boston, MA32nd ASEE/IEEE Frontiers in Education Conference

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USING CONCEPT MAPS AND CONCEPT QUESTIONS TO ENHANCECONCEPTUAL UNDERSTANDING

David L. Darmofal 1, Diane H. Soderholm 2, and Doris R. Brodeur 3

1 David L. Darmofal, Massachusetts Institute of Technology, Cambridge, MA 02139 [email protected] Diane H. Soderholm, Massachusetts Institute of Technology, Cambridge, MA 02139 [email protected] Doris.R. Brodeur, Massachusetts Institute of Technology, Cambridge, MA 02139 [email protected]

Abstract Conceptual understanding is the ability to applyknowledge across a variety of instances or circumstances.Several strategies can be used to teach and assess concepts,e.g., inquiry, exposition, analogies, mnemonics, imagery,concept maps, and concept questions. This paper focuses onthe last two -- concept maps and concept questions. Conceptmaps are two-dimensional, hierarchical diagrams that showthe structure of knowledge within a discipline. Conceptquestions are questions posed to students to encouragehigher order thinking and help them understand the basicprinciples of a discipline. This paper describes currentprogress at MIT in the development and use of concept mapsand concept questions in aerospace engineering.

Index Terms Aerospace Engineering, Concept Maps,Concept Questions, Conceptual Understanding.

INTRODUCTION

The Department of Aeronautics and Astronautics at theMassachusetts Institute of Technology (MIT) is engaged in anumber of educational initiatives to reform its educationalprograms. To achieve its program goals, the department hasdesigned a curriculum that parallels the context of the lifecycle of an engineering system, i.e., the Conception, Design,Implementation, and Operation (CDIO) of engineeringsystems shapes the content, scope, and sequence of theundergraduate curriculum. At the same time, the departmentis investigating the findings of educational research toimprove faculty's ability to guide student learning, with thegoal of applying best practices in teaching and learning toengineering education.

During the past two years, MIT Aero/Astro faculty haveintroduced pedagogical techniques into a variety ofaerospace engineering courses seeking to improveconceptual understanding. In particular, "muddiest-part-of-the-lecture" cards [1] and in-class concept questions [2]coupled with automated personal response systems [3] arebeing used in the sophomore core courses and in the junior-level courses in thermal energy and aerodynamics. Unliketraditional lectures, these active learning strategies engagestudents with the conceptual material during class. Whenimplemented properly, active learning improves conceptualunderstanding, decreases feedback time between faculty andstudents, encourages self-driven learning, and clarifiescommon misconceptions. [4]-[11]

CONCEPT LEARNING AND CONSTRUCTIVISM

Conceptual understanding is the ability to apply knowledgeacross a variety of instances or circumstances. It differsfrom declarative knowledge learning in that declarativeknowledge involves a memorization of an associationbetween two or more entities. Conceptual understandinginvolves the ability to apply knowledge across a variety ofpreviously unencountered instances. [12] Conceptualunderstanding is considered lasting if the concept representsa "big idea" having lasting value beyond the classroom,resides at the heart of the discipline, requires uncoverage ofmisconceptions, and offers the potential to engagestudents.[13]

Concepts can be classified as concrete concepts anddefined, or abstract, concepts. Concrete concepts are ideasof common objects, e.g., wing, jet engine, or object qualitieslike elliptical, red, smooth. Concrete concepts are learnedby the presentation of a variety of instances andnoninstances whose characteristics can be directly perceivedby the learner.[14] For most engineering students,understanding concrete concepts is usually not difficult. Onthe other hand, understanding defined concepts can be achallenge. Defined, or abstract, concepts are rules thatclassify objects or events. These concepts require verbaldefinitions if they are to be learned in an adequate way, e.g.,drag, turbulence, boundary layer. A student who hasunderstood a defined concept has learned the classifying ruleand is able to apply it to any instance of the class. It is notessential that the learner know the definition itself in order toshow that he/she has learned the concept. Students showtheir understanding of abstract concepts by using theirknowledge, adapting it, and customizing it.[15] Studentswho begin to organize their knowledge around the majorconcepts of a discipline, have begun the transformation fromnovice to expert thinker.[16] Assessment of conceptualunderstanding requires the application of knowledge to newproblems and diverse situations.

Constructivism presents a view of learning that isparticularly useful in describing conceptual learning. Theconstructivist view is that individuals must actively constructtheir knowledge through testing concepts on priorexperience, applying these concepts to new situations, andintegrating the concepts into prior knowledge.[17]-[18] Ifnew knowledge conflicts with past experiences, these newconcepts will be difficult to assimilate and learning isgenerally superficial and short-term. For purposes of

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teaching, a constructivist instructor must understandstudents’ pre-existing knowledge and encourage students toconfront knowledge that conflicts with the concepts beingtaught.

Traditional teaching uses a transmittal approach inwhich students are assumed to gain knowledge whilepassively listening to lectures. This style of teaching is indirect conflict with a constructivist view of learning as itdoes not actively engage students, nor does it force studentsto confront their misconceptions. In pursuing a pedagogicalapproach to enhance conceptual understanding, studentsmust 1) become dissatisfied with their pre-existingknowledge; 2) possess some minimum understanding of thescientific concept; 3) believe the concept is plausible; and 4)believe the concept is useful in explaining knownbehavior.[19] The transition to conceptual-changeinstruction from the long-standing transmittal approach isdifficult.

CONCEPT MAPS AND CONCEPT QUESTIONS IN

ENGINEERING EDUCATION

In the past ten years, concept maps and concept questionshave been used to teach and assess conceptual understandingin mathematics and science education.[20]-[24] Now, thesetools are being applied to humanities and social sciences,and to some extent to engineering education.[25]-[28]

Concept maps are useful for identifying and organizingconcepts and their relationships to each other. A conceptmap is a two-dimensional, hierarchical node-link diagramthat depicts the structure of knowledge within a scientificdiscipline as viewed by a student, an instructor, or an expertin a field. They are composed of concept labels, eachenclosed in a box or oval, a series of labeled linking linesand general-to-specific organization.[29]-[30] Cornwell hasused concept maps for defining both course-level andcurriculum-level content in mechanical engineering.[31] Hefinds that concept maps help students establish connectionsbetween the various topics and organize concepts in theirminds. He suggests using concept maps as advanceorganizers, reference guides, and assessment tools. Harmon,et al. used concept maps (constructed knowledge maps) asboth pretests and posttests to evaluate the extent to whichstudents learned key concepts in a simulated design task inenvironmental engineering.[32] In addition to course levelassessment, Turns, et al. suggest using concepts maps forassessment at the engineering program level: to characterizelevel of expertise in a domain, identify disciplineknowledge, and explore students’ conceptions ofengineering. [33] While Streveler and Miller do not use theterm ‘concept map’, their work on the use ofmultidimensional scaling to identify student misconceptionsgives insight into cognitive structures and the connectionsstudents make among series of concepts.[34]

Concept questions, also called concept tests, and coinedas “ConcepTests” by Mazur, are used extensively in active

learning and peer coaching environments, particularly inmathematics and science. According to Mazur, goodconcept questions focus on a single concept; are not solvableby relying solely on equations; reveal common difficultieswith the concepts; and have several plausible answers basedon typical student misunderstandings.[35] In engineering,Danielson & Mehta are developing banks of conceptquestions in the field of statics. They have tested theinstructional effectiveness of the use of concept questions attwo different institutions.[36]

CONCEPT MAPS AND CONCEPT QUESTIONS IN

AEROSPACE ENGINEERING AT MIT

In the sophomore multidisciplinary engineering course, weare developing concept maps to identify and organize keyengineering concepts, and map the relationships of key ideaswithin and between disciplines. The disciplines covered inUnified Engineering include materials and structures, signalsand systems, dynamics, thermodynamics, and fluids. Theconcept map of each discipline provides a means ofcommunication between and among the faculty membersteam-teaching the course, and for the teaching assistants aswell. The maps help faculty members plan class time moreefficiently by sequencing concepts correctly, building uponthe concepts taught by the other faculty members, andavoiding duplication and omission of important ideas. Themaps also highlight areas where two or more disciplineslink. The links are pointed out to students to help themunderstand how the disciplines are integrated, and are alsoused in the design of homework problems and in-classexamples. (See Figure 1 for a sample concept maps.)

In the future, we plan to ask students to create their ownconcept maps. Students can use their maps to check theirown understanding of the concepts and plan their study time,as well as aid faculty in diagnosing and correcting studentmisconceptions.

In Unified Engineering, Thermal Energy, andAerodynamics at MIT, we use a peer instruction approachsimilar to that developed for physics by Mazur.[37] In thisapproach, concept questions are given to students in classwith time for individual thought and reflection. After acheck to see how well students have understood thequestion, small group discussions are held (if needed) inwhich student groups attempt to answer the question.Afterward, the instructor clarifies misconceptions and leadsstudents in further exploration of the concept. In the threecourses discussed above, we measured class responsethrough various techniques, including hand raising, flashcards, and, most recently, PRS, a personal response system.Interactive student response systems, such as PRS, haveseveral advantages over hand raising or flash cards, e.g.,anonymity of student responses and the generation ofassessment data to analyze aggregate performancestatistics.[38]

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FIGURE. 1CONCEPT MAP OF THERMODYNAMICS IN UNIFIED ENGINEERING

fixed but free to rotate

water stream

Given the water behaves as shown above, which direction will the cylinder rotate when the stream first makes contact with the cylinder?(a) Clockwise(b) Counter-clockwise

FIGURE. 2SAMPLE CONCEPT QUESTION USED IN AERODYNAMICS

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Figure 2 is a sample of a concept question which we haveused in our junior-level aerodynamics course. A feature ofthese questions is that they address common misconceptionswhich we have found students to possess entering the courseor common misconceptions students have when firstencountering new material. For example, the question inFigure 2 tests a misconception that a jet of water impingingon an object would tend to ‘push’ the object in the directionof the flow. This misconception we have found is quitecommon as most people have had previous experience withthe force and subsequent motion generated by a water streamimpacting an object. However, the difference in thisproblem is that the water stream has a glancing contactwhich allows the stream to be turned as depicted in thefigure. In actuality, the object will rotate clockwise (i.e.‘into the stream’) and this can be easily demonstrated byapplication of conservation of momentum to the waterstream and Newton’s Law of equal and opposite forces.When we use this concept question, we include an in-classdemonstration in which the students can clearly observe thecylinder being drawn into the stream. Another advantage ofthis question is that it has a direct analogy with the mannerin which lift is generated on an airfoil.

Our experience with the use of concept questions hasshown that a critical aspect of the successful use of thetechnique requires students to have some experience withthe material prior to class (see also Mazur for a discussion ofthe need for student preparation). In our aerodynamicscourse, we give reading assignments and homeworks whichare due prior to discussing the material in class. The use ofpre-class homework is a significant shift from traditionalengineering pedagogy in which homeworks are assigned anddue only after discussing the material in class. Not only isthe pre-class homework critical to the success of activelearning in the class room but it also encourages student self-learning. Furthermore, by scanning the homeworkassignments, student misconceptions and commondifficulties can be detected immediately rather than onlyweek(s) after discussing material. Thus, in the spirit ofactive learning, pre-class homework decreases feedback timebetween the students and teaching staff. Finally, we notethat the shift from post-class to pre-class homework forcesthe homeworks to become a tool for formative rather thansummative assessments. (See Figure 5 for a sample of aconcept question.)

PROCESSES FOR DEVELOPING CONCEPT MAPS

AND CONCEPT QUESTIONS

During our initial attempts to engage students more activelyin their own conceptual learning, we employed a variety ofapproaches for developing concept maps and conceptquestions, including

Instructor knowledge: Instructor knowledge is avaluable resource for identifying difficult concepts andwriting questions that illustrate and assess these concepts.

Instructors understand from past teaching experiences whatare the most common difficulties in their subjects. Ininformal interviews conducted by colleagues and educationspecialists, instructors identify difficult concepts in theirdisciplines, based on the learning objectives and outcomes oftheir courses. The purpose of the interviews is to developlists of concepts that are required to achieve the measurableoutcomes, to select those concepts that are most difficult forstudents to master, and to document the knownmisconceptions which lead to learning difficulties.

Instructional staff collaboration: In the large sophomoremultidisciplinary core course, a team of faculty,undergraduate and graduate teaching assistants comprise theinstructional staff. The creation of concept maps was acollaborative effort. To develop concept maps for each ofthe disciplines, key concepts were identified from coursesyllabi and written on Post-it notes. The faculty member incharge of the discipline checked the concepts and added ordeleted as necessary. A brief explanation about constructingconcept maps was given at the weekly course staff meeting.Following that, groups of faculty and teaching assistantsworked together to arrange and re-arrange the Post-itNotes into a map. Completion of the maps took place overseveral weeks during the course staff meetings. Facultymembers then refined the maps in individual sessions withthe department instructional designer. Sharing the completedmaps at a course staff meeting was an important step forcourse planning, teaching and learning activities, homeworkproblems, and identifying areas of possible studentmisconception or confusion.

Muddiest-point-in-the-lecture[39]/reading/homework:In the aerospace engineering curriculum at MIT, we usestudent feedback to identify the part of the lecture, reading,and/or homework that is most confusing or difficult. Duringthe next few years, the "muddy part" data will be continuallycollected, analyzed, and compared with the lists of keyconcepts and associated misconceptions.

Open-ended concept questions: Once an initial set ofconcepts is selected, students are asked to respond to open-ended concept questions, either in-class or as part of awritten homework assignment. Student responses frequentlycontain a few consistent misconceptions that can then beused as the focus of new concept questions.

Student-developed concept questions: Taking the open-ended concept question technique a step farther, we askstudents to generate concept questions as part of a pre-classhomework assignment on new concepts. Students are givena description of a good concept question, shown a fewexamples, and asked to develop new concept questionsbased on the assigned reading. Students must also provide asolution (or set of reasonable solutions) to each question.Many of the students’ concept questions can be used withonly minor changes. More often, the student identifies adifficult concept and, through his/her answers to the conceptquestion, demonstrates some of the underlying reasons forthe conceptual difficulty. Often, the answer that the student

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believes is the “correct” answer to the concept question is, infact, somewhat or completely incorrect. This occurrence canalso be very useful in writing concept questions

CURRENT PLANS

We are currently focusing on the development of acomprehensive set of concepts in aerodynamics andthermodynamics and related aerospace disciplines. We planto develop and refine corresponding concept maps andconcept questions. In another year, we anticipate having afairly comprehensive database of concept questions. Thedatabase will be continually refined and extended and theuse of the open-ended and student-developed conceptquestion strategies will also be explored.

With the extended use of concept maps and conceptquestions in the classroom, more systematic assessment ofstudent conceptual understanding will be implemented.While we have data on student perceptions of theirunderstanding and their satisfaction with their learningexperiences, we have little evidence documenting students’growth in conceptual understanding as a result of usingconcept maps and concept questions. Our initial efforts withoral examinations of aerodynamics concepts are leading inpromising directions.

SUMMARY

The Department of Aeronautics and Astronautics at MIT ismaking progress in its methods to enhance conceptualunderstanding with the use of concept maps and conceptquestions. At the present time, concept maps and conceptquestions have been developed in basic thermodynamics,structures, signals and systems, dynamics, controls,advanced aerodynamics and thermal energy, and are beingused by several undergraduate instructors in their courses.We have collected data on their use, and have initiated plansfor a concept questions database. Our next steps are toimplement a more systematic approach to assessment of theeffectiveness of concept maps and concept questions in theimprovement of students’ conceptual understanding.

REFERENCES

[1] Angelo, T. A., and K. P. Cross, “Classroom Assessment Techniques:A Handbook for College Teachers”, 2nd ed., Jossey-Bass, SanFrancisco, 1993.

[2] Mazur, E., Peer Instruction: A User's Manual, Prentice-Hall, UpperSaddle River, NJ, 1997.

[3] Personal Response System, PRS, http://www.educue.com

[4] Felder, R. M., and R. Brent, "Navigating the Bumpy Road to Student-Centered Instruction", College Teaching, 1996, pp. 43-47.

[5] Hake, R. R., "Interactive-Engagement vs. Traditional Methods: A Six-Thousand-Student Survey of Mechanics Test Data for IntroductoryPhysics Courses", American Journal of Physics, v. 66 no. 1, 1998, pp.64-74.

[6] Heller, P., and M. Hollobaugh, "Teaching Problem Solving ThroughCooperative Grouping, Part 2: Designing Problems and StructuringGroups", American Journal of Physics, v. 60 no. 7, 1992, pp. 637-644.

[7] Heller, R., R. Keith, and S. Anderson, " Teaching Problem SolvingThrough Cooperative Grouping, Part 1: Group vs. Individual ProblemSolving", American Journal of Physics, v. 60 no. 7, 1992, pp. 627-636.

[8] Johnson, D. W., and R. T. Johnson, Cooperation and competition:Theory and Research, Interaction Book Company, Edina, MN, 1989.

[9] Johnson, D. W., and R. T. Johnson, Meaningful and ManageableAssessment Through Cooperative Learning, Interaction BookCompany, Edina, MN, 1996.

[10] Johnson, D. W., R. T. Johnson, and K.A. Smith, Active Learning:Cooperation in the College Classroom, Interaction Book Company,Edina, MN, 1991.

[11] Meltzer, D. E., and K. Manivannan, "Promoting Interactivity inPhysics Lecture Classes", Physics Teacher, v. 34, 1996, pp. 72-76.

[12] Smith, P. L., and T. J. Ragan, Instructional Design, 2d ed., Merrill,Upper Saddle River, NJ, 1999.

[13] Wiggins, G., and J. McTighe, Understanding By Design, Associationfor Supervision and Curriculum Development, Alexandria, VA, 1998.

[14] Gagne, R. M., “The Conditions of Learning”, 3rd ed., Holt, Rhinehart,and Winston, New York, 1977.

[15] Reference 13

[16] National Research Council, How People Learn: Brain, Mind,Experience, and School, National Academy Press, Washington, DC,2000. Available athttp://books.nap.edu/books/0309070368/html/index.html.

[17] Reference 12

[18] Reference 2

[19] Posner, G., K. Strike, P. Hewson, and W. Gerzog, "Accommodationof a Scientific Conception: Toward a Theory of Conceptual Change",Science Education, v. 66, 1982, pp. 211-227

[20] Reference 2

[21] Mintzes, J. J., J. H. Wandersee, and J. D. Novak (Eds.), TeachingScience for Understanding: A Human Constructivist View, AcademicPress, New York, 1998.

[22] Novak, J. D., Learning, Creating, and Using Knowledge: ConceptMaps as Facilitative Tools in Schools and Corporations, LawrenceErlbaum Associates, New York, 1998.

[23] Plotnik, E., Concept Mapping: A Graphical System for Understandingthe Relationship Between Concepts, 1997. (ERIC DocumentReproductions Service No. ED407938). Available athttp://ericir.syr.edu/plweb-cgi/obtain.pl

[24] Novak, J. D. and D.B. Gowin, Learning How to Learn, CambridgeUniversity Press, Cambridge, UK, 1984.

[25] Cornwell, P. J., "Concept Maps in the Mechanical EngineeringCurriculum", Proceedings of the 2000 American Society ofEngineering Education Annual Conference and Exposition, 2000.Available at http://www.asee.org/conferencessearch.

[26] Danielson, S., and S. Mehta, "Statics Concept Questions forEnhancing Learning", Proceedings of the 2000 American Society ofEngineering Education Annual Conference and Exposition, 2000.Available at http://www.asee.org/conferencessearch.

[27] Harmon, T. C., G. A. Burks, G. Chung, and E. Baker, "Evaluation of aSimulation and Problem-Based Learning Design Project Using

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Constructed Knowledge Mapping", Proceedings of the 2001 AmericanSociety of Engineering Education Annual Conference and Exposition,2001. Available at http://www.asee.org/conferencessearch.

[28] Turns, J., C.J. Atman, and R, Adams, “Concept Maps for EngineeringEducation: A Cognitively Motivated Tool Supporting VariedAssessment Functions”, IEEE Transactions on Education, v. 43, no.2, 2000, pp. 164-173.

[29] Reference 21

[30] Zeilik, M., Concept Mapping, 2000. Available athttp://www.wcer.wisc.edu/nise/cl1/flag

[31] Reference 25

[32] Reference 27

[33] Reference 28

[34] Streveler, R. A., and R. L. Miller, “Investigating StudentMisconceptions in the Design Process Using MultidimensionalScaling”, Proceedings of the 2001 American Society of EngineeringEducation Annual Conference and Exposition, 2001. Available athttp://www.asee.org/conferencessearch.

[35] Reference 2

[36] Reference 26

[37] Reference 239]

[38] Reference 3

[39] Mosteller, F., “The ‘Muddiest Point in the Lecture’, as a FeedbackDevice,” In Teaching and Learning:The Journal of the Harvard-Danforth Center, Vol. 3, 1989.

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Session USING CONCEPT MAPS AND CONCEPT QUESTIONS …ww.cdio.org/files/document/file/concept_maps_fie.pdfconceptual understanding. In particular, "muddiest-part-of-the-lecture" cards