Enhancing Conceptual Understanding: Recent Experiences

1
Enhancing Conceptual Understanding Recent
Experiences

• Prof. David L. Darmofal
• Aeronautics Astronautics
• Massachusetts Institute of Technology

2
Outline

• Background on course (16.100)
• Conceptual Understanding
• Research on conceptual understanding
• Utilization of ConcepTests (following Mazur)
• Pre-class homework
• Oral exams
• Results

3
Course Overview (MIT 16.100)

• Class of about 40 students (juniors and seniors)
• Students will have previous fluid dynamics
• conservation laws
• 2-D potential flows
• some basic aerodynamics
• Not quite a required course but 2/3s take it
• Course topics include
• Incompressible, subsonic, transonic, and
  supersonic flows
• Viscous flows with an emphasis on boundary layers
• Wind tunnel testing and computational methods

4
Generic Course Objective

• A student that successfully completes course XYZ
  will be able to
• Apply the concepts from XYZ to a wide variety of
  situations beyond those previously encountered
• Engineer solutions to problems that embody the
  concepts from XYZ
• Learn related or more advanced concepts in a
  self-directed manner

5
In a final exam far far away ...
6
Outline

• Background on course (16.100)
• Conceptual Understanding
• Research on conceptual understanding
• Utilization of ConcepTests (following Mazur)
• Pre-class homework
• Oral exams
• Results

7
Barriers to Conceptual Understanding

• Misconceptions preconceptions that oppose
  principles being learned
• Traditional pedagogies stress analytic ability
  over conceptual understanding
• Traditional assessments stress analytic ability
  over conceptual understanding

8
Constructivist Model of Learning(Piaget)

• Argues that individuals learn by
• Actively constructing their knowledge,
• Testing concepts on prior experience,
• Applying these concepts to new situations,
• Integrating the new concepts into prior
  knowledge.
• Directly opposes the blank state view of how
  people approach learning

9
Sources of Misconceptions in Engineering

• Real world experience
• Education from prior courses
• Education from current course

10
Aerodynamic Concept Lift Generation by an
Airfoil

• Students possess many myths half-truths about
  lift generation
• Pressure differences generate lift
• Pressure differences from Bernoulli effect
• Upper surface longer than lower surface!
• As they learn about aerodynamics, other ideas
  muddy the situation
• Circulation creates lift
• Vortex sheets on the airfoil surface create lift

11
Lift Generation Pre-conception Data
Best answer
Half truth
Incorrect responses
12
Pedagogical Elements to Address Conceptual
Understanding

• Frequent formative assessments that make students
  conceptions evident to themselves and to teachers
• Summative assessments that target deep,
  conceptual understanding
• In-depth coverage of fewer topics (this is a
  programmatic issue as well)

13
Concept Questions(Ellis, Landis, Meeker, 2000
Mazur, 1997)

• Focus on a single concept
• Are not solvable (in time given) by relying
  solely on equations
• Reveal common difficulties with the concepts
• Have more than one plausible answer based on
  typical misunderstandings

14
Using Concept Questions

• Pose concept question
• Ask students to indicate their answers we
  currently use handheld PRS system
• If most have the correct answer, give a brief
  explanation, then move on
• Else, clarify concept
• have students discuss with neighbors,
• give mini-lecture on concept and answers
• Take another poll of students answers
• A typical class period will include about 2-3
  concept questions

15
Benefits of Concept Questions (Ellis, Landis,
Meeker, 2000)

• Provides immediate feedback on the level of class
  understanding
• Gives students practice in using terminology and
  concepts
• Confront common misconceptions
• Enhance inter-personal and communication skills
• Improve class participation and motivation

16
Processes for Developing Concept Questions

• Derive from measurable outcomes
• Instructor knowledge
• Feedback from reading and homework
• Open-ended concept questions
• Oral exams and/or interviews
• In my opinion, developing good concept questions
  is the most difficult aspect of this technique

17
ExampleLift Generation Concept Question
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?
• Clockwise
• Counter-clockwise
• Not enough information

18
Cylinder-stream questionIs it effective?

• Single concept force generation through momentum
  change of fluid (flow turning)
• Cannot be solved in 1-2 minutes by integral
  momentum
• Reveals common difficulties
• students do not connect flow turning with force
  generation
• Stream impingement on cylinder often leads to the
  conclusion of a counter-clockwise motion (i.e. a
  fire hose effect)
• Leads naturally to lift generation through flow
  turning and streamline curvature

19
Pre-class Assignments

• Problem to address conceptual understanding
  in-class, students must begin learning beforehand
• Solution Reading and homework assignments due
  prior to in-class discussion of material
• Homeworks are at same level as in past years when
  given after class.
• Same amount of work for students, but front-loaded

20
Advantages ofPre-class Assignments

• Leverage existing resources for basics
  derivations while permitting faculty to be
  value-added in classroom
• Classroom interactions can focus on concepts
• Encourage self-directed learning
• Improve feedback time
• Homeworks can be designed to demonstrate typical
  misconceptions

21
Active AssessmentOral Examinations

• Oral exams are an active assessment method
  engaging students while they are thinking
• Improves likelihood of an accurate assessment by
  its dynamic nature
• Valuable experience for students
• Opportunity for faculty to learn more about
  misconceptions

22
Oral Exam The Process

• All exams are oral (mid-term and final)
• Students given question(s) 30 minutes prior to
  oral exam
• Oral exam conducted for 30 minutes
• Grading sheet (tabular) developed listing each
  concept to be assessed and the level achieved

23
Lift Pre-conception Exam Data
Best answer
Half truth
Incorrect responses
Conceptual understanding of lift significantly
improved
24
Importance of Implementation

• Effective implementation of ConcepTests is not
  trivial and impacts entire pedagogy
• In Fall 2000, we implemented ConcepTests in-class
  but
• ConcepTests had inconsistent quality
• Pre-reading assignments were too simplistic
• Conceptual understanding was difficult to assess
  with written exams
• The Fall 2000 experience led directly to the
  current implementation

25
Exam Question for 2000 2001

• How would you model the aerodynamics of the boom
  and the boom wing?

Tanker wing
 
 
Attachment point
Boom

• Concepts include
• Use of non-dimensional parameters (Re, M)
• Sources of drag (friction, induced, wave,
  separation)
• Transonic drag rise, critical Mach, and sweep
  effect
• Drag due to separation (on boom)
• Interference (downwash from tanker wing)

Boom wing
26
Comparison of 2000 Written 2001 Oral Exam
Tanker wing
Attachment point
 
 
Boom
Boom wing

• In 2000 Written, other problems were given
• In 2001 Oral, a short supersonic airfoil problem
  was also discussed if time remained
• In either case, students were given similar time
  to respond to this question

27
Assessment of Student Conceptual Performance
Fall 2000 vs 2001
A significant shift occurred but many confounding
factors (written vs. oral, multi- vs. single-part
exam, grading, etc)
28
Student Evaluations of Pedagogy
Very Effective
Effective
Not Effective

• Lecture, In-class exercises, and
  reading/assignments all show gains
• Interesting point lecture gains occurred even
  with shift to more student-directed learning
• Wind tunnel same ratings new team project caused
  dip in Fall 2002

29
Student Comments A Learning Transition Occurred

• I was initially opposed to the idea that I had to
  do reading homework before we ever covered the
  subjects. Once I transitioned I realized that it
  made learning so much easier!!
• I was skeptical at first of new techniques like
  PRS, hw on material that hasnt been learned in
  lecture. In the end, it worked out very well.
  This has been a course where I really felt like I
  got my moneys worth.
• I really like the format of the class, I think
  its actually a very good way to format a course.
  At first I didnt like how the homework was
  really tricky and it always came before we went
  over the material in lecture, but after a little
  bit I didnt mind it.
• Doing homework before the lectures is good makes
  actual learning in lectures possible.

30
Student Comments Oral Exams

• The oral exams are an excellent measure of
  understanding.
• Oral exams are the best part of the subject, I
  think these gave a good opportunity to show what
  you understand.
• Oral exams are also good. Pretty nerveracking,
  but good overall.
• I really like the idea of the oral final. Even
  though it is scary, it really shows how much you
  know about the subject, better than any exam
  would.
• The oral exams allow a true assessment of
  understanding better than pretty much anything
  else.

31
Take-away Messages

• Improving conceptual understanding requires a
  pedagogy that addresses misconceptions including
  frequent formative assessments.
• While effective pedagogies exist that can improve
  conceptual understanding, implementation is
  critical. Consider using pre-class assignments
  and oral exams.
• Students recognize the benefits of these
  pedagogies when effectively implemented.

32

• Extra Slides Follow

33
16.100 Learning Objectives

• Formulate and apply aerodynamic models to predict
  the forces on and performance of realistic
  three-dimensional configurations
• Assess the applicability of aerodynamic models to
  predict the forces on and performance of
  realistic three-dimensional configurations and
  estimate the errors resulting from their
  application
• Design and execute a computational and
  experimental aerodynamic analysis together with
  members of a team.

34
16.100 Measurable Outcomes

• We have developed 17 measurable outcomes for
  16.100. Some examples are (with assessment
  methods listed)
• Apply flow similarity, non-dimensional
  coefficients such as the lift and drag
  coefficient, and non-dimensional parameters such
  as the Mach number and Reynolds number in
  aerodynamic modeling of realistic configurations
  (homework, team project reports, exams)
• Apply integral momentum conservation to explain
  the relationship between flow turning, the
  generation of lift on an airfoil, and the
  subsequent loss of lift upon stall (homework,
  exams)
• Explain the sources of friction, induced, wave,
  and pressure drag (homework, exams)

35
Project Focus Model-based Design
Develop Baseline Geometry
Validate/Calibrate Aerodynamic Models on Baseline
Geometry
Design with Calibrated Aerodynamic Models (Trade
studies, optimization, etc.)
Basis for Case Study
36
Wind Tunnel Experiments

• Wind tunnel tests for validating low-speed
  modeling
• Flow visualization
• Some students involved in building model
• Emphasis given to
• Assumptions
• Applicability
• Sources of error

37
Advanced Computational Methods

• Exposure to modern computational aerodynamic
  methods
• Emphasis given to
• Fundamental fluid dynamics
• Assumptions
• Applicability
• Sources of error

M 1.2, Angle of Attack 7 degrees
38
Synthesis of Theory, Experiment Computation
Mach 0.9
Theory
CL
Computation
Model
Experiment
CD
39
Impact of Homework and Lectures
From Schwartz et al (1999)
Only analyzed data
Analyzed data then attended lecture
Read, summarized then attended lecture
Post-test abilities to predict outcomes
Students were studying how people organize
knowledge using schema and then were asked to
predict outcomes