Solution to Questions 1 and 2: 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-# 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 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 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.” 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. Summer Results for Pretest Questions 1 and 2: Approximately half of the students were able to give correct answers with correct explanations. Follow-up interviews were done with nine of the students, and were consistent with these results. First Pretest Explanations Over half (55%) of the students gave correct explanations based on the definition of specific heat, its inverse relationship to changes in temperature, or explicit algebra. About 30% of the students provided brief explanations suggesting alternative conceptions based on several simple “rules-of-thumb.” The percentage of responses corresponding to each of these explanations is shown in Table 3. Nearly half (49%) of all students who assigned the larger temperature change to the wrong material argued that the rate of change in temperature was directly proportional to the specific heat. This explanation indicated that these students were not merely confused about which specific heat was in fact larger, nor had they randomly selected the wrong answer. Results from Pretest Question 2: Second Pretest Explanations Exactly half of all students were able to give a correct answer with correct explanation for the second pretest question. The only common incorrect explanation offered was that the rate of temperature change should be directly proportional to the specific heat. This explanation accounted for 81% of all incorrect responses. 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 student’s 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. Q=mc  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. Intervention vs. Control Group Pretest Analysis A point of interest concerning the pretest results can be seen in the following table. The substantial discrepancy between the intervention group and control group remains unexplained. Since the pretest was given before the intervention occurred and the groups had been randomly selected, no significant difference in pretest scores should have been anticipated. Posttest: The posttest was administered as a two-part free-response test question on a midterm, whereas the pretest had been administered as a recitation quiz. 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. Additional posttest questions: Two partitioned gases The following multiple choice question was included both on the midterm and on the final exam. Responses on Final exam: [Note: No significant difference between intervention and control groups] Overall, 17% of all students chose options (A) or (B), both of which assert that the energy transfer between object and liquid is not equal. This indicates that even at the time of the final exam many students are confused about the concept of conservation of energy. In addition, 12% of all students selected option (D), which asserts that the energy transfer is equal and the temperature change is equal for object and liquid. As mentioned before, assertions of equal temperature change are likely to be closely associated with incorrect ideas about equilibrium, heat and temperature, and/or specific heat. In option (C) the energy transfer is equal, but the relative magnitude of temperature change (between high- and low-specific heat substances) is reversed from the correct answer. As seen by analysis of free response questions, this type of error is likely to be closely associated with thinking that the temperature change is directly proportional to the specific heat. Solution to Free Response Posttest: NOTE: These are approximate solutions. The actual temperature changes over time are exponential in nature. As long as graphs displayed the correct ratios over time the graph was scored as being correct with correct ratio. Water Al Insulation Temperature Time t1t1 t0t0 Water Aluminum Slope of H 2 0 = 1/8 Slope of Al = –1/2 Temperature Time t1t1 t0t0 Water Aluminum Thermal Equilibrium Slope of Al = –1 Slope of H 2 0 = 1/4 OR Secondary Questions: Object Sealed in a Container This was a qualitative calorimetry question fairly close in form to both the posttest and the pretest. t0t0 Time Temperature Liquid ALiquid B The specific heat of A is greater than the specific heat of B. Heating Plate Liquid A Liquid B and Notation:  T  absolute value of temperature change Responses to “Two Partitioned Gases” Question on the Midterm and Final: [Note: No significant difference between intervention and control groups] Between the time of the midterm and that of the final, students in both the intervention and control groups became less likely to believe that the temperatures of the two partitioned gases would remain the same (choice E); this seems to suggest a decrease in confusion between temperature and total internal energy. However, the numbers of students reversing the relative magnitude of temperature change (choice B) did not change in either group, implying stability in this particular misconception. Results from Pretest Question 1: These results are consistent with the results from summer Initial Assessment Diagnostic questions were administered in a second-semester calculus-based course during the 2002 summer session. (See Figure below; similar questions from later course are shown.) The questions were administered after the students had a standard lecture on calorimetry but before recitation instruction; results are shown in Table 1.