Solution to Questions 1 and 2:

1
Students' Use of Rule-based Reasoning in the
Context of Calorimetry and Thermal Phenomena
Ngoc-Loan P. Nguyen, Warren M. Christensen, and
David E. Meltzer Iowa State University Supported
in part by NSF Grant DUE-9981140
Introduction Calorimetry, the measurement of
heat, is a basic part of most introductory
science courses in physics and chemistry. The
goal of this project is to investigate student
learning difficulties in calorimetry, create
focused worksheets and tutorials to improve
learning, and test them in classes. The initial
step involved identifying a baseline of student
understanding using diagnostic questions and
interviews. Initial testing was carried out in
summer 2002. Preliminary versions of a worksheet
were developed and tested, and further testing
was carried out in spring 2003 in Physics 222, a
second-semester calculus-based introductory
physics course. One group (Control) received
standard instruction, while a second group
(Intervention) received instruction using the
worksheet. Examination of the performance of the
two groups indicates that further innovative
development is needed to make improvements over
standard instruction.
Follow-up Investigation  Additional testing was
done in a second-semester calculus-based physics
course during spring 2003. The same type of
pretest was administered to all recitation
sections about a week after lecture instruction
on calorimetry, on the day that homework
involving calorimetry questions was due. Seven
recitation sections had been randomly chosen
using a random number generator to form the
intervention group after the pretest, they
received instruction with our calorimetry
worksheet during the normal recitation period.
All other sections received standard instruction.
Here are two representative explanations offered
to justify an incorrect answer to Pretest
Question 2 Student 1 A has a higher specific
heat so it takes less time to reach the same
temperature. Student 2 Since the specific
heat of A is two times that of liquid B, and
everything else is held constant (the initial
temperature and mass and the heating rate), the
liquid of solution A will heat up two times as
fast as liquid B.
The pretest and posttest questions are not
completely equivalent the posttest question
requires a calculation of the slope ratio,
whereas Pretest Question 1 does not. If one
overlooks this difference and considers the gains
in score from pretest to posttest, the
intervention group seems to show a better
performance than the control group. However,
performance on other questions (see below) did
not support this conclusion.
A notable feature of the responses to Question 2
is that one category of erroneous explanations
from Question 1 almost completely disappeared,
despite the similarities between the problems.
The proportion of students claiming that
temperature changes would be equal because energy
transfers were equal (the largest category in
Question 1) fell from 9 to 1, suggesting that
application of this rule-of-thumb depends on
the context in which the problem is presented.
Solution to Questions 1 and 2
Of the students who said that the temperature
changes of the two materials would be equal, 70
justified this conclusion either by the fact that
the system was moving toward equilibrium, or with
the argument that equality in energy transfers
implied equality of temperature changes. For
example, here is one students argument "Same.
The system will reach an equilibrium since the
copper will gain the heat that the water gives up
they will both change the same amount of ?C." A
different justification was offered by this
student The temperature change of the copper
and the water will be the same. Any heat lost by
the copper will be gained by the water, or any
heat gained by the copper will lost from the
water. So ?T of both are the same. Here a
student argues (incorrectly) that the temperature
change is dependent on initial conditions More
than, since it has to go from a lower initial
temperature to a higher system temperature.
Qmc?T Students written explanations suggested
that most of their answers were linked to certain
specific rules (either correct or incorrect)
which allowed rapid responses without requiring
extensive reasoning.