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ILUSTRATION OF A CONSTRUCTIVISTIC APPROACH TO TRANSFORM AND
ASSESS THE TEACHING AND LEARNING PROCESS IN INTRODUCTORY
PHYSICS
MOISÉS ORENGO-AVILES
University of Puerto Rico at Mayaguez
Physics Department, PO Box 9016, Mayaguez, PR 00680-9016
[email protected]
The behavior of falling objects was used to assess students’ misconceptions about
acceleration and a think-pair-share constructivistic strategy was used in the
classroom to promote the discovery of the underlying physical explanation. A set
of 3 different questions were posed at the final examination to determined the
gain in students understanding of the acceleration concept. The results and
possible explanations for the discrepancies are explored in this article.
Introduction
Students commonly misinterpret the concept of rate of change and ratio, especially when
they deal with the change of a rate of change as in the concept of acceleration. Acceleration is
the result of a change in velocity, which in turn is the rate at which the position of an object
changes. The traditional approach is to tell the students the definition or to pose it as a
mathematical equation. The efficiency of the teaching by telling approach has been questioned
[1] due to the fact that students’ previous experiences influence their understanding of the
physical world around them. The behavior of falling objects was used to assess students’
misconceptions about acceleration and a think-pair-share constructivistic strategy that
emphasized peer learning [2] was used to promote the discovery of the underlying physical
explanation.
The students where confronted in class with three questions. First they have to answer
individually, and then revise their responses with their neighbor and finally the professor carried
out the experiment and guided the discussion. This inquiry-based process was performed for
each question, in sequential order. The questions and most common answers are summarized in
Table 1.
Results and discussion
In order to illustrate that the direction of the acceleration for the object in questions 1 and
2 is always downward two methods were used. A vector diagram was drawn to represent the
change in velocity and a numerical calculation stating the change in velocity as positive or a
negative number. The direction of the acceleration is the same as that of the change in velocity,
not that of the velocity. In the second case the direction of the change in velocity is the same as
the direction of the velocity.
To demonstrate that the acceleration at maximum height is not zero two more questions
were posed. What is the velocity of the object at its maximum height? All the students agreed
Table 1: Questions for falling objects
Questions
Think: Individual
response
Pair: Revised
response
Share:
Response after
experiment
Discussion:
Correct
answered after
discussion
1. A ball is thrown
upward, after
leaving the hand,
what is the
direction of the
acceleration while
it is moving up?
Justify your
answer.
Out of 3
possibilities given
(up, down, other)
most of the
students indicated
up as the direction.
Most of the
students did not
change their
responses. But
they supplied
more
justifications.
The
experiment
consisted of
throwing the
object. Only a
couple of
students
change their
answer to the
correct one.
Acceleration
points down.
2. A ball is thrown
downward, after
leaving the hand,
what is the
direction of the
acceleration while
it is moving down?
Justify your
answer.
Out of 3
possibilities given
(up, down, other)
most of the
students indicated
down as the
direction.
Most of the
students did not
changed their
responses.
The
experiment
consisted of
throwing the
object. Only a
couple of
students
change their
answer to the
correct one.
Acceleration
points down.
3. A ball is thrown
upward, what is
the acceleration
when it reaches its
maximum height?
Justify your
answer.
All the students
answered zero.
None of the
students changed
their response.
The object was
thrown
upward.
None of the
students
changed their
response.
The correct
answer is not
zero.
it was zero, which is the right answer. The second question was: does the velocity stay at zero
after a second have passed? Of course not, the students agreed. Then the acceleration can’t be
zero because this will imply constant velocity, but the velocity is zero, then the object will
“float” there forever. The later is a contradiction, the experiment clearly shows that the object
doesn’t stay “floating” at the maximum height it comes back to the ground. In conclusion, the
acceleration for a falling object, no matter if it is moving up or down is always downward
including when it is at the maximum height where the acceleration is not zero.
In order to assess the students understanding of this basic behavior of falling objects, 3
different questions were posed in the final examination. The questions and the percentage of
right answers are summarized in Table 2.
Table 2: Final examination questions
Questions
Percentage of students
with correct answer
1. A ball is thrown upward, after leaving the hand, draw the forces
acting on the ball while it is moving up.
20%
2. A ball is thrown downward, after leaving the hand, draw the
forces acting on the ball while it is moving down.
85%
3. A ball is thrown upward, draw the forces acting on the ball when
it reaches its maximum height.
60%
By the end of the course it have been illustrated that acceleration is due to a net force and
the direction on the acceleration is that of the net force. Thus, it was expected that the students,
knowing the behavior of the falling ball, were able to draw a unique force pointing downward for
the 3 questions posed in the final examination.
Based on the responses in the final examination the following misconceptions were
identified: (1) when the ball is moving up there is a force pointing up, (2) when the ball is at the
maximum height there is a force pointing up. The first misconception apparently comes from the
idea that the force that was used (by the hand) to throw the ball up “stays” with it while the ball
is rising. The force in the second misconception was identified as the normal force. The normal
force is the reaction force of the surface acting on the object normal (perpendicular) to the
surface, it only exist when there is a surface. The air might be mistaken as a surface, or the
students got used to drawing a normal force in so many examples given in class. The other
possibility is that they still think that the acceleration is zero at that point and they need a force to
balance the weight so that no net force produced zero acceleration. Which is obviously wrong.
These possible explanations need further analysis and exit interviews might help to
elucidate the students reasoning.
Acknowledgments
The PR-CETP alliance was instrumental in providing stimulus and guidance through its
evaluators and course revision specialists to explore this alternative way of teaching these
concepts and others.
Bio
Moises Orengo-Aviles is Associate Professor of Physics and Science Coordinator for
CETP at the Mayaguez Campus of the University of Puerto Rico. He collaborated in writing
student centered activities in Physics for the K-12 PR-SSI (Systemic Statewide Initiative). He
served as mentor for the LS-AMP (Louis Stoke Alliance for Minority Participation) to counsel
student in pursuing graduate studies. He is coauthor of a handbook written in Spanish that
promotes the used of cooperative learning at the university level.
References
[1] L.C. McDermott, Guest Comment: "How we teach and how students learn -- A mismatch?"
Am. J. Phys.60 (4) 295 (1993).
[2] Catherine H. Crouch and Eric Mazur, “Peer Instruction: Ten Years of Experience and
Results”, Am. J. Phys. 69, 970-977 (2001)