Title: Conceptual testing in engineering courses: Testing students conceptual understanding of thermodynami
1Conceptual testing in engineering
coursesTesting students conceptual
understanding of thermodynamics and fluid
mechanics in a course in Energy Systems
Michael May, LearningLab DTU Technical University
of Denmark mma_at_dtv.dk
2A course in Energy Systems at DTU
- Energy Systems An introductury (1. semester)
course in - Thermodynamics
- Fluid mechanics
- Case studies of Energy Systems (ex.
Refrigerator)
3Different uses of conceptual tests
- When?
- Test of students understanding relative to the
requirements for a course - Test of students understanding of core elements
during a course - Test of students understanding at the end of the
course
- How? (-gt A typology of conceptual tests)
- Representational forms used in the test
questions - Level of learning addressed by the type of
questioning
- Why? (-gt Fuctional roles of testing)
- Test used to promote student reflection (on own
learning) - Test used as a form of measurement of learning
(information to teachers) - Test used as portfolio documentation
There seems to be a kind of progression at the
institutional level in the discovery and
acknowledgement of functional roles of testing
4Testing a conceptual requirement for the course
Example of a test borrowed from the
Thermodynamics Concept Inventory reused here
as a test of a conceptual requirement (regarding
the concept of mechanical energy which should be
well established in high school physics) for the
course in Energy Systems
Consider a marble that is held at the lip of a
bowl. The marble is released, with no force
added, and begins to roll down into the bowl.
Assuming the rolling process is frictionless,
for which of the figures below does the ball
have maximum energy?
5Distribution of answers (beginning of the course)
(43 answers)
Could there be something in the test that
promotes wrong answers?Is it valid as a measure
of understanding the concept of mechanical
energy?
6Repeating the question with variation
- At the end of the course we wanted to test
understanding of the same concept - The dilemma of testing for the same concept we
cannot use the same test, because some will
remember the correct answer (even without
understanding) - We can however tested again with a similar
question in this case we introduced specific
questions about potential and potential engergy - This way we also avoided the problem of students
being confused about the unspecific question
about energy (for which of the figures below
does the ball have maximum energy?)
7The revised test
- Consider a marble that is held at the lip of a
bowl. The marble is released, - with no force added, and begins to roll down into
the bowl. - Assuming the rolling process is frictionless, for
which of the figures below - does the ball have
- maximum potential energy?
- maximum kinetic energy?
- maximum mechanical energy?
8Distribution of answers (end of the course)
Distribution for subquestion (b) on maximum
kinetic energy
(38 answers)
9Promoting student reflection through testing
- This is another example from the same test given
in the beginning of the course on Energy Systems
(also copied from the Thermodynamics Concept
Inventory) this time testing understanding of
the Ideal Gas law
- The figure depicts a gas heated and expanding in
a sealed, frictionless, piston-and cylinder
arrangement, where the piston mass and the - atmospheric pressure above the piston remain
constant. - The pressure of the gas will
- Increase
- Remain the same
- Decrease
- Insufficient information..
10Distribution of answers
11Student in-class reflection during test feedback
- In giving feedback to students on the test a
discussion arose, - which revealed important aspects of students
reasoning - Some of the students did perhaps not recall and
fully understand theIdeal Gas law as taught in
high school physics (again a requirement forthe
course), but more importantly - Many students defended their wrong answer with
a form of (highly relevant) practical
resoning(in practice the work done in moving
the piston will correspond to a fluctuation in
the pressure, meaning that it will momentarily be
increased untill the volume is expanded and an
equilibrium is established with the atmospheric
pressure) - The nature of ideal models and the conditions
under which they are true as opposed to more
concrete physical models are not understood by
students in introductory engineering courses and
this understanding is in itself an important
objective for engineering education - The in-class discussion of the test was an
important learning experiencefor students
12Features of students conceptual understanding
- There will (allmost) always be some
preconception of core content - based on
intuitive anchoring - based on experience -
base on prior education
- Prior understanding will generally include
misconceptions - - but it will also be partially true / valid
- this should be used actively as a bridge to
scientific understanding - conflicts (experience
versus intuition or conflicting conceptualization
- among students) can be utilized to promote
conceptual change - there will generally be a
small set of prototypical misconceptions of core
content (i.e. misconceptions are not arbitrary
and chaotic but motivated and systematic) (the
phenomenographic approach)
- The misconceptions and intuitions of prior
understanding will persist in parallel with
scientific understanding (if it is not
explicitely addressed) !
- Scientific understanding is not organized as an
axiomatic systems(it can be inconsistent,
incomplete and full of holes) - specifically
students can have advanced knowledge of core
elements even if some of the conceptual
requirements are not fully established
13Testing understanding of the Bernouilli equation
Consider a horizontal pipe with a contraction as
shown in the figure. The fluid flow from plane 1
to plane 2 takes place without loss. The
pressuere at plane 1 and plane 2 is called p1 og
p2 respectively. Indicate whether you expect (and
give your reasons for this belief) (a) p1 gt
p2 (b) p1 lt p2 (c) p1 p2
14Intuitive preconceptions of pressure
There is an intuitive preconception of
pressure that is sustained byexperience in
the sense of being under pressure, have less
space, as When the human body is under
pressure from all sides during anescape through
an emergencyexit (think of a fire in a building).
The problem of cause is that this experience /
intuition of pressure is verydifferent from
the concept of pressure in fluid mechanics, but
never the less it persists as a naïve
conception of pressure in spite of physics
teaching andit can interfere with students
reasoning (cf. diagram illustrating an
interview fragment).
15Invalid qualitative reasoning
- Many students attempt to apply a form of
qualitative reasoning to the question of fluid
flow i a pipe with contraction - but fail to give a correct answer because they
are mislead by the static nature of their
conceptualization - They are perhaps applying reasoning implied by
the Ideal Gas law (and not Bernouillis equation) -
16Testing understanding of the Bernouilli equation
The Bernoulli equation can be written Describe
the physical meaning of the terms of the
equation.
The intended answer implies an understanding the
equation as a particular expression of the
general principle of conservation of
energy pressure kinetic energy potential
energy constant A considerable part of the
students on a more advanced course could only
describe (some of) the individual parameters (not
the physical meaning of the terms)
17Understanding across forms and scenarios
- Deep understanding will be characterized by the
ability to - Apply a general law schema to different specific
situations - Use examples from one domain as analogies in
another domain - Reformulate conceptual understanding (not bound
to one specific text book formulation), i.e. it
can be stated in the students own words - Translate conceptual understanding between
(moving across) different forms of
representation (in language, in diagrams, in
equations, in graphs etc.)
Didactic consequence Variations in forms of
representation and in scenarios of application
are important for improvements in conceptual
understanding
18Graph-based sketching Testing Fouriers law
19Prototypical answers Phenomenography
- There will be a small set of distinct
prototypical answers (rather than a large
diffuse set) - The answers can be classified in a
meaningfull way - Wrong answers can be interpreted as a sign
of different types of conceptual difficulties
The 3 types of answers found among students of
chemical engineering tothe Fourier question a
is the correct answer, b is the answer given by
thosestudents who remember the linearity implied
in Fouriers law (but forgets to takearea into
consideration, and c is the answer given on the
basis of recollection ofthe shape of the graph
as a pure image (with no understanding of
model).
20A classification scheme for conceptual tests
- The following classification scheme is based on
the assumptions - that different representational forms makes a
difference for the level and type of
understanding that can be tested and - that different types of problems can be used to
probe different levels of learning and
understanding.
21Types of conceptual tests
Representational form / Problem type
(level)
Recognize(Know)
Compute (Apply)
Sketch(Understand)
Diagnose (Analyze)
Construct (Synthesize)
Construct theproblem fromthe description
Find errors inthe followingtext
Explain inyour ownwords
Text Numerical/ Algebraic Diagram Graph
Image
Indicate the unitsof the entities
Construct a model of thefollowing ..
Compute theresult of ...
Sketch asolution to ..
Indicate physicalmeaning of the terms of the
equation
Find errorsin the equation..
How will the circuit representedin this
diagramwork?
Sketch adiagram for ..
What does thediagram express ..
Sketch thegraph youexpect for ..
Find the graph for ..
Give a physical interpretation ofthe graph ..
Identify situationfrom image ormeasurement ..
A few exemples are indicated here (but all
combinations in the matrix can be explored!)