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888"A'888888888| : ConcepTests
Description and Purpose
The ConcepTest technique is a robust and flexible tool for promoting
collaborative student thinking, for quickly assessing conceptual understandings
class-wide, and for illuminating areas of confusion. Other names for this are
"classroom voting", "clicker questions", and "peer instruction". The idea began
with Eric Mazur at Harvard in order to increase student engagement in his large,
lecture-style physics classes. It has quickly evolved into a technique with
demonstrated efficacy in a wide variety of subjects and at many levels -- from
developmental mathematics at community colleges to professional level courses
at universities.
Responses are uninhibited because the ConcepTests are not graded and at least
in some implementations, responses are anonymous. Students learn to
articulate ideas and justify choices with expert level reasoning. The convince-your-neighbor arguments systematically increase both the percentage of correct
answers and students' confidence. Mazur says he sees the greatest
improvement when about half the students are correct initially; there can be gains
of as large as 40 percent
The ConcepTest strategy is extremely versatile. Used to introduce a topic, it can
reveal students' current levels of understanding. Used skillfully, and with
appropriate prompts and extensions it can involve students in developing key
disciplinary ideas, reducing the need for endless lecture. At the end of a topic, it
can check for desired outcomes. Perhaps the biggest challenge is coming up
with appropriate questions.
Preparation
Select a key disciplinary understanding or a concept that students frequently
have confusion over. It could be a common nave understanding. Here are
some examples: Science: that the elliptical path of the earth around the sun is
what causes seasonal change. Mathematics: When asked is -b a positive or a
negative number? students will often assume its a negative number.
Psychology: that intelligence is fixed and unchangeable.
Construct plausible alternative answers that would help to reveal developed,
partial or incorrect conceptions. When the options are well designed, student
responses also give the instructor some insight into the nature of the partial and
mis-conceptions students are working with.
Procedure
1. Pose one (or possibly a series of) multiple choice questions related to
important disciplinary concepts.
2. Give students about one minute to individually puzzle over and select one
of the alternatives.
3. Get the entire class to signal their choices all at once. You can use a
range of methods to gather this information ranging from high-tech hand
held computers, to a simple show of hands. This makes the points of
agreement and disagreement visible to the class as a whole.
4. Give students a chance to chat with their neighbors to share and clarify
information and convince their neighbors of their logic. Conversations are
typically animated and chaotic as everyone seeks to explain their
reasoning and justify their choices. Wander around the room. Eavesdrop
on conversations without interfering or helping.
5. After a minute or two, take a second "vote".
6. If you have people moving in the right direction, but still have a lot of
disagreement, you may decide to repeat #4 and #5.
Variation and Extensions
Where you go from here depends on your reason for using the strategy.
Sometimes the instructor will extend the question, or provide additional
information. Sometimes the instructor will use the test as a vehicle through
which to introduce an investigation. For example, Vosniadou et al (2001)
conducted a study on the ways inquiry in science are structured to promote
conceptual understanding. She compared student learning in a classroom
organized along principles of inquiry, and those organized around traditional text
book sequences. In the study, students examined patterns of agreement and
disagreement in their hypotheses and the rational for them. They then used
experiments to test and inform their hypotheses. These dialogues (i) created
cognitive disequilibrium which from a learning theory perspective, is a necessary
precursor to learning. (ii) the disequilibrium emerged out of carefully structured
dialogue with peers (group work) in which students needed to attend to each
others thinking; and (iii) created an authentic reason for pursuing further
exploration.
Illustrative Example Circling the Earth
Imagine there is a rope wrapped tightly about the earth at the equator. An
additional 50 foot length of rope is spliced into it. The extended rope is then held
at the equator in a circular shape so that it is at a constant height above the earth
all the way around.
Which of the following is the tallest critter that can walk underneath the rope
without touching it?
(A) An amoeba. ?
(B) A Chihuahua ?
(C) A WNBA player ?
(D) King Kong ?
Further Information
This question was designed to begin an exploration into some important
properties of circles. As described in the protocol above, students read, vote,
discuss and re-vote. At this point there is often still wide disagreement about the answer and reasons for it. If movement forward seems stuck the instructor may ask additionally:
How would you go about digging deeper here so that you can come to resolution?
What experiments could you perform?
What data, formulas, or other facts might be useful?
Either the instructor can provide what students suggest and additional time can
be spent in class, or this can be continued as a homework assignment (and to
bedevil ones friends)
Extension questions could be asked:.
What if you did this with a rope around the moon? Around a globe of the
earth? How would your answers change ?
Instead of adding 50 feet, what if you added 10 feet? 10 miles? n miles?
What patterns do you see and what generalizations can you make?
NOTE: An analytic approach to this problem benefits from small amounts of
geometric and algebraic knowledge. An experimental approach requires neither.
For more information:
Koman, K. (1995) Newton, One-on-One. Harvard Journal
http://www.columbia.edu/cu/gsapp/BT/RESEARCH/mazur.html
MAA FOCUS Newsletter, Teaching with Classroom Voting, May/June
2007, pages 22, 23)
Vosniadou et al. (2001) Designing learning environments to promote
conceptual change in science. Learning and Instruction, 11 381419.
(http://www.cs.phs.uoa.gr/en/staff/58.%20Vosniadou%20-
%20Ioannides%20-%20Dimitrakopoulou%20-%20Papadimitriou.pdf )
Five ConcepTest Questions Relating to Slope
1. A roof has a rise to run ratio of 1 to 5. The slope of the roof is.?
(a) 5 (b) EMBED Equation.3 (c) EMBED Equation.3 (d) - 20 (e) EMBED Equation.3
2. A highway caution sign indicates that a road has a 5% downgrade. The slope of the roadway is.?
(a) 5 (b) EMBED Equation.3 (c) EMBED Equation.3 (d) - 20 (e) EMBED Equation.3
3. A 20 foot ladder is leaning against a house with its bottom 4 feet from the base of the house. The slope of the ladder is.?
(a) 5 (b) EMBED Equation.3 (c) EMBED Equation.3 (d) - 20 (e) EMBED Equation.3
4. A skydiver is falling at a constant rate of 20 feet per second. On a graph, the altitude of the skydiver is plotted against time. The slope of the line graph is.?
(a) 5 (b) EMBED Equation.3 (c) EMBED Equation.3 (d) - 20 (e) EMBED Equation.3
5. Arrange the lines that have the slopes given below, in order of increasing steepness (flattest to steepest).
(a) 5 (b) EMBED Equation.3 (c) EMBED Equation.3 (d) - 20 (e) EMBED Equation.3
Follow-up Question: How much steeper is the steepest line than the flattest line?
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