Instructional Science 30: 379–402, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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Text editing in chemistry instruction BING HIONG NGU, RENAE LOW & JOHN SWELLER University of New South Wales, Australia Received: 6 June 2001; in final form: 29 January 2002; accepted: 12 April 2002 Abstract. In two experiments, differential performance on chemistry problems was obtained for two training strategies: text editing and conventional problem solving. Text editing requires students to scan the text of problem statements and specify whether it provides sufficient, missing or irrelevant information for solution. It was hypothesized that text editing, which emphasizes gaining familiarity with schematic knowledge, would lead to higher achievement than conventional problem solving. Experiment one indicated that text editing was superior to conventional problem solving in learning to solve molarity and dilution problems. In particular, students who were trained in text editing skipped some intermediate steps while solving molarity problems. In contrast, using stoichiometry problems, experiment two showed that students who were trained in text editing performed worse than students given conventional problems to solve. An error analysis suggested that because of its failure to direct students’ attention to the coherent problem structure in the first instance, text editing has no advantage over conventional problem solving in the domain of stoichiometry problems. It was concluded that the suitability of a text editing training strategy depends on the learning materials. Keywords: problem solving, text editing
In solving chemistry word problems involving mathematical manipulations, many college students tend to choose a formula and ‘plug’ in the values and variables without making any effort to analyze and represent the problem structure before formulating solution (Reif, 1983; Nakhleh et al., 1996). This problem-solving behavior is similar to novice problem solvers in a physics domain (Chi et al., 1981). Novices often relied on variables cited in problem statements as indicators to select equations. In contrast, experts were capable of categorizing problems based on a physics principle, and used this to construct an elaborate qualitative analysis of the problem situation before formulating quantitative equations for solutions. Chi et al. (1982) attributed this disparate problem-solving behavior exhibited by novices and experts to the presence of different schemas. Schemas are defined as cognitive constructs that allow one to categorize elements of information in the manner in which they will be used (see Low & Over, 1990, 1992; Sweller & Low, 1992; Low et al., 1994).
380 In the solution of mathematically based problems, the presence of an appropriate schema is considered crucial to the selection and application of mathematical operators (see Mayer, 1987; Kintsch & Greeno, 1985). Consider a word problem such as “If a boat traveled downstream in 120 minutes with a current of 5 kilometers per hour and the return trip against the same current took 3 hours, what was the speed of the boat in still water?”. Someone without schematic knowledge of the specific relations between speed of boat, rate of current, and time that can be expressed in a mathematical equation, is unable to solve such a problem. In the absence of such schematic knowledge, there is no context for computation and calculation. On the other hand, if someone is able to identity the problem as belonging to a given category (e.g., river current contrast), he or she could determine what information from the text should be used, in what sequence and through what operations (see Mayer, 1987). Sweller (1988) proposed that the basis for such schematic knowledge is familiarity with problem states and their associated moves. If schemas are central to problem solving skill, it makes sense to design instructional procedures that can promote schema acquisition. An instructional technique that has been demonstrated to enhance learning through schema acquisition is text editing (Low et al., 1994). Text editing requires students to classify problems with sufficient (S), missing (M) or irrelevant (I) information for solution. In addition, students must provide the information needed for solution once a problem has been identified as missing and underline the irrelevant information that was not required for solution. Examples (Low et al., 1994, p. 425) of such problems are: (a) What is the area of a rectangular park if the length is 50 metres? (missing information); (b) What is the area of a rectangular park if the length is 50 metres and the width is 30 metres? (sufficient information); (c) What is the area of a rectangular park if the length is 50 metres, the width is 30 metres, and there is a fence 2 metres high surrounding the park? (irrelevant information). In requiring students to edit problem texts, the text editing procedure encouraged them to identify the coherent problem structure, their underlying principles and the tactics for extracting relevant information from the text. In Low et al.’s study (1994), students who received text editing exercises acquired superior schemas in solving algebra problems as compared to those students who were given conventional problem solving. Apparently, text editing trained learners to focus on analyzing, and selecting relevant units of information to construct a coherent problem model for solution. Low and Over (1989) found that there was a positive correlation between performance on text editing tasks and problem solutions. This finding suggests that when students could select appropriate information from the problem texts, they had the means
381 to integrate the information in an equation for solution. It seems that the text editing task focuses attention on acquiring schematic knowledge in the course of representing coherent problem structure. Mayer (1987) suggested that a problem solver needed to be able to represent a problem before he or she could implement a solution strategy for the problem. Accordingly, in solving word problems, acquiring skill in problem representation promotes schema acquisition. Kintsch and his colleagues (Greeno & Kintsch, 1985; van Dijik & Kintsch, 1983) suggested that solving word problems entails an interaction between comprehending text and building a situation model (a coherent problem structure) of the problem domain, on which a problem solution can be generated. Text editing exercises require students to assess and select relevant information in the problem texts conforming to a situation model of the domain. Thus, text editing encourages schema acquisition because it emphasizes the comprehension of problem texts, and indirectly the construction of a situation model in which the relations among values and variables needed to be specified. Notice that the building of a situation model is similar to construction of a coherent problem structure whereby the emphasis is on expressing the structure of the problem in a mathematical equation suitable for computation. The text editing procedure was originally devised as a measure of schema acquisition (Low & Over, 1989, 1990, 1992). Its use as an instructional tool has been limited to algebraic word problems (Low et al., 1994). The purpose of this study was to extend Low et al.’s (1994) findings to a chemistry domain. The basic intention was to replicate those findings, isolate some of the conditions under which such results are obtainable and to investigate conditions under which the reverse findings might be obtained. In the experiments reported in this paper, two types of chemistry word problems were used: dilution and molarity and stoichiometry chemistry word problems. These chemistry problems are similar to algebra word problems in some aspects. The following outlines the similarities between algebra word problems and chemistry word problems. Consider the following example of a dilution word problem: A 50 ml HCL of a 2.0 M solution was accurately diluted to 500 ml. Calculate the molarity of the diluted solution. This problem is similar to an algebra word problem in three aspects. First, the dilution word problem consists of problem statements similar to an algebra word problem. Second, the problem can be solved using the formula M1 V1 = M2 V2 . Usually a mathematical formula represents an integral part of a solution procedure for an algebra word problem. Third, the goal is to find an
382 unknown quantity, in this case, M2 . In most algebra word problems, the goal is to find an unknown quantitative variable. However, mere knowledge of the formula, M1 V1 = M2 V2 , is insufficient to become proficient in solving the above dilution word problem. A problem solver needs to know what chemical concepts govern that formula. That is, the number of moles of solute remains unchanged before (M1 V1 ) and after (M2 V2 ) dilution or evaporation. Molarity word problems are concerned with finding the molarity (concentration), volume and mass related to a chemical solution. An example of a molarity problem is given below. 25 g of sodium sulphate, Na2 SO4 were dissolved in sufficient water to obtain 500 ml of a solution. Calculate the molarity of the solution (Na = 23, S = 32, O = 16). To solve the molarity problem, two ratios have to be combined into a single mathematical equation for solution. Each ratio represents the number of moles of solute (n). The first ratio is related to the conversion of mass to moles: number of moles of solute, n = mass/RFM. To be able to calculate this correctly, students need to know the chemical formula of the chemical substances involved, and the calculation of RFM (relative formula mass). In the above example, the RFM for Na2 SO4 is the sum of the compound’s relative atomic mass, (2 × 23) + 32 + (4 × 16). The second ratio is related to finding the molarity (M) of the solution by dissolving some chemical substance (represented by n) in a definite volume (V in millilitre) of water (n = MV/1000). The solution of a molarity problem lies in extracting relevant variables and values from the problem statements and constructing a coherent mental representation so that the two ratios are equated to form the single equation (mass/RFM = MV/1000). Like the dilution word problem, a stoichiometry word problem is similar to an algebra word problem in three aspects. Consider an example of a stoichiometry problem: Sodium metal, Na, reacts with chlorine to produce sodium chloride, NaCl, according to: 2Na + Cl2 → 2NaCl (Na = 23; Cl = 35.5) If 23 g of sodium, Na, react with chlorine gas, Cl2 , what mass of sodium chloride, NaCl, will be formed? Once again, the stoichiometry problem contains problem statements; part of the solution procedure involves a simple proportion mathematical formula;
383 and the goal is to find an unknown quantitative variable. To solve the problem, a student needs to know how the various chemical substances are related in a simple proportion formula. In sum, like algebra word problems, solution of chemistry word problems requires the skill of extracting the relevant quantitative variables from the problem statements and integrating them in a coherent mathematical equation. This skill is unlikely to be acquired through conventional problem solving. Many studies have demonstrated the ineffectiveness of conventional problem solving as a learning tool (Cooper & Sweller, 1987; Owen & Sweller, 1985; Sweller & Cooper, 1985). The findings suggest that conventional problem solving tends to induce a means-ends solution strategy as a problem solver attempts to search for a solution path. This may put a strain on the learner’s limited working memory. Apart from the reasons suggested by Sweller and his co-workers, training on conventional problem solving does not include the extraction of the relevant information, and the integration of such information to form mathematical formulae appropriate for solution. Rather, conventional problem solving emphasizes how to carry out arithmetic calculation and algebraic transformation to obtain the solution. The present two experiments were designed to investigate the effectiveness of the text editing training strategy in the context of chemistry problems. It was predicted that students would acquire schemas by doing text editing exercises that emphasized the representation of the problem in a coherent problem structure. Experiment one compared text editing training with conventional problem solving in dilution and molarity word problems. It was predicted that students who received text editing training would acquire schemas leading to superior problem solving skill over those who were given the traditional learning technique, practice in problem solution. Experiment two examined the effectiveness of text editing training in learning a different type of chemistry problem – stoichiometry problems. The expectation was that text editing training which emphasized the construction of coherent problem structures, would be superior to conventional problem solving in learning to solve stoichiometry problems.
Experiment one Experiment one compared the performance of students who were given text editing training with another group who were engaged in conventional problem solving. It was hypothesized that text editing training would be superior to conventional problem solving.
384 Method Participants Participants were 23 male students from an eleventh-grade single-sex school in Sydney who had no previous experience in solving molarity and dilution problems. Data were collected in group sessions in the classroom supervised by the chemistry teacher together with a researcher. Materials and procedure In session one, the chemistry teacher taught the topic of molarity and dilution to all students as part of the chemistry course requirement. Session two began the following day. The students were randomly assigned to two groups: text editing and conventional problem solving. At the beginning of the session, students were told about the procedure of the experiment. First, both groups read the materials in the instruction phase for five minutes. The instruction phase included definitions of molarity and dilution along with an illustrative worked example of each. The aim was to refresh students’ memory about the concepts related to the molarity and dilution problems which they had studied the previous day. This phase was followed by acquisition phases, which were matched for time (22 minutes for each group). The text editing group read the instructions for carrying out the text editing exercise and also studied three text editing practice problems together with correct answers. Then, they were required to classify up to 20 problems in terms of whether each problem presented sufficient, missing or irrelevant information in relation to solution. When a student identified the missing component in the problem, he had to provide additional information that the problem had to contain in order for solution to be possible. Similarly, upon discovering any irrelevant information within the problem, the student’s task was to underline the irrelevant information. Examples of the problems are provided in Table 1. The acquisition phase for the conventional problem solving group began with the students studying three problems together with their illustrative worked-out examples. These three problems were identical to the text editing practice problems except each problem contained sufficient information for solution. They were then required to solve up to 11 problems which were a subset of the 20 problems used in text editing but modified so that each problem contained only sufficient information for solution. No student from either group was expected to complete the acquisition problems within the time allocated. Both groups were allowed access to the instruction phase materials during the acquisition phase. Also, students were free to ask questions. All the acquisition problems were selected by the
385 Table 1. Examples of molarity and dilution problems containing missing, sufficient, or irrelevant information in Experiment one Missing information A 50 ml HCl solution was accurately diluted to 500 ml. Calculate the molarity of the diluted solution. (Additional information: the molarity of the initial HCl solution was missing) Calculate the molarity of the solution made by dissolving 31.8 g of sodium carbonate, Na2 CO3 , in water (Na = 23, C = 12, O = 16) (additional information: volume of water). Sufficient information How many moles of sodium chloride, NaCl are in 500 ml of a 2 M solution? If we wish to prepare 20 ml of 1. 2 M KCl, how many ml of 2 M KCl would be required? Irrelevant information 20 g of sodium sulphate, Na2 SO4 were dissolved in sufficient water to obtain 500 ml of a solution with a density of 1.11 g/ml. Calculate the molarity of the solution (Na = 23, S = 32, O = 16). A solution was prepared by diluting 20.0 ml of a 4.0 M solution of ammonia to a total volume of 100 ml. The exact amount of water added was 80 ml. What is the molarity of the resulting solution.
researcher and reviewed by two local chemistry teachers for appropriateness. Most of these problems resembled regular chemistry text book exercises. Session three followed four days later. The first 25 minutes were devoted to feedback. Feedback was provided for the text editing group by identifying the correct response for each training problem. At times, students were simply asked “Which formula is used to solve this problem?” No problems were solved nor were any solution steps worked through. The aim of the feedback was to direct students’ attention to the structure of the problems by assisting them to recognize the problem types and their associated formulae. For the conventional problem solving group, feedback focused on the working required to reach solution of the problem. The test phase began immediately after the feedback. Two subsets of tests were given: seven similar problems and five transfer problems with 12 minutes in total for each subset. Similar problems consisted of four dilution problems and three molarity problems which resembled the training problems in the acquisition phase. The five transfer problems were sub-divided into three single transfer problems and two combination transfer problems (see Table 2). The single transfer problems were isomorphic to the similar test problems. Isomorphic problems have similar solution procedures but a different story context (Reed, 1987). For instance, a drug problem was a molarity problem but it had a medical context cover story (see Table 2).
386 Table 2. Examples of similar problems and transfer problems in Experiment one Similar problems A NaCl solution is 2.0M. How many millilitres(ml) of this solution will contain 10.0 g of NaCl? (Na = 23, Cl = 35.5). What is the molarity of KCl in solution made by adding 325 ml water to 255 ml 2.0 M KCl. Transfer problems Single transfer problem Phenobarbitone, C12 H12 N2 O3 , is commonly used in medicine as a long-acting sedative. A patient may take 5.0 ml of phenobartitone as a dose. If the concentration of the phenobartitone is 0.017 M, what mass of the drug is present in one dose? (C = 12, O = 16, N = 14, H = 1). Combination transfer problem A NaCl solution is 2.0 M. What is the molarity when an additional 10.0 g of solid NaCl is dissolved in 2.0 litres of the solution (Na = 23, Cl = 35.5).
A single transfer problem involved a solution procedure of either a dilution or a molarity problem only. The combination transfer problems were considerably more difficult than the single transfer problems because they involved solution procedures comprising solution steps of both the dilution and molarity problem. Instruction for the test phase required students to show their working in reaching solution on their answer sheets. In summary, the whole experimental procedure involved three separate sessions. In session one the chemistry teacher taught the topic of molarity and dilution. In session two, the students completed the instruction phase and the acquisition phase. Finally, feedback was given and the students undertook two tests in session three. Results and discussion One of the students from the text editing group was absent in session two and the data analysis was thus based on the remaining 22 students: 11 from the text editing group and another 11 from the conventional problem solving group. It was hypothesized that students involved in text editing training would have higher achievement scores on tests of the dilution and molarity problems than students who were given conventional problem solving training. For the achievement tests, one mark was awarded for each correct solution generated. When a student made arithmetical rather than logical errors, the answer was scored as correct. The 0.05 level of significance was used for all analyses except where otherwise stated.
387 Table 3 shows means and standard deviations for the similar problems test scores. A 2 (group: text editing vs. conventional problem solving as a between-subject factor) × 2 (problem type: dilution vs. molarity as a repeated measured within-subject factor) analysis of variance was performed. The main effect of group was significant, F(1,20) = 4.41, MSE = 4.45. The text editing group outperformed the conventional problem solving group for the dilution and the molarity problems combined. The main effect for problem type was also significant, F(1,20) = 9.68, MSE = 11.00. The molarity problems were significantly more difficult than the dilution problems for both groups. The group × problem type interaction was not significant, F(1,20) = 2.00, MSE = 2.27. Table 3 also shows the means and standard deviations of the non-attempted problems and errors made for the similar test. No difference was detected between the two groups for the non-attempted problems, t(20) = 0.96, SE = 0.29. In contrast, the conventional problem solving group made significantly more errors than the text editing group, t(20) = 1.78, SE = 0.46. Note that if a student made a similar error more than once across all problems, it was counted as one error score only. Essentially there were two types of errors for Experiment one – conceptual and unit errors. A conceptual error refers to the assignment of incorrect values to the variables or using a wrong formula. For instance, if a student used M = nV nM MV or V = 1000 , instead of n = 1000 for the molarity problems (note that n = 1000 no. of moles of solute); and used M1 V2 = M2 V1 rather than M1 V1 = M2 V2 for solving the dilution problem, he had committed a conceptual error of assigning a value to the wrong variable. Additionally, if students used n = MV to calculate a dilution problem and M1 V1 = M2 V2 to calculate a molarity 1000 problem, this constituted a conceptual error of using a wrong formula to solve the problem. A Fisher exact probability test indicated a possible real difference between the two groups with respect to the conceptual errors made on molarity problems, p = 0.074 but not on the dilution problems (see Table 3). The second type of error was a unit error. According to Bassok (1990), students have greater difficulty in matching intensive quantities than extensive quantities between two problems having an identical structure. An example of the former is km/hour while an example of the latter is km. Some students in the conventional group could not distinguish mole/L (intensive) from M (extensive). A Fisher exact probability test detected a significant difference between the two groups with respect to unit errors made on both molarity problems, p = 0.045 and dilution problems, p = 0.045 (see Table 3). Data for the transfer problems are shown in Table 3. As the transfer problems were divided into single transfer problems and combination transfer problems, a 2 (group) × 2 (problem type) ANOVA was performed. The
388 Table 3. Means, (standard deviations) of correct solutions, non-attempted problems, errors made, no. of students who made specific errors and no. of students who generated correct solutions during the test phases in Experiment one
Similar test Correct solutions Dilution problems Molarity problems Non-attempted problems Errors made Dilution and molarity problems No. of students who made errors Specific conceptual errors Dilution problems Molarity problems Specific unit errors Dilution problems Molarity problems Transfer test Correct solutions Single problems Combination problems Errors made Single and combination problems No. of students who generated correct solutions All single problems correct At least one combination problem correct
Text editing M (SD)
Conventional problem solving M (SD)
3.18 (1.08) 2.64 (0.67) 0.27 (0.47)
3.00 (1.00) 1.55 (1.29) 0.55 (0.82)
0.64 (0.67)
1.45 (1.37)
5 1
6 5
0 0
4 4
2.81 (0.60) 0.73 (1.00)
2.36 (0.81) 0.55 (0.82)
1.45 (1.29)
1.91 (1.30)
10 4
6 4
Note: n = 11 for both groups; Fisher exact probability tests significant at 0.05 level.
main effect for the problem type was significant, F(1,20) = 74.56, MSE = 42.02. The combination transfer problems were far more difficult than the single transfer problems. In contrast, the main effect for the group was not significant, F(1,20) = 1.41, MSE = 1.11, nor was the group × problem type interaction, F(1,20) = 0.36, MSE = 0.20. However, there were 10 students from the text editing group who could solve all the single transfer problems compared to six students from the conventional problem solving group. A
389 Fisher exact probability test indicated a possible real difference between the two groups in solving the single transfer problems, p = 0.070. No significant difference was detected for the combination transfer problems. As only two students from the conventional problem solving group had one non-attempted problem each, no statistical analysis was performed on the non-attempted transfer problems. Table 3 also shows the means and standard deviations of the number of errors made by the students for the transfer problems. Once again, no significant difference was observed between the two groups, t(20) = 0.83, SE = 0.553. Therefore, for the transfer problems, the text editing group possibly outperformed its conventional counterparts in solving the single transfer problems but not the combination transfer problems. In addition to scores and errors, the manner in which students solved the molarity problems also was analyzed in order to investigate any evidence for differential schema acquisition. Consider the following molarity problem which was used in the acquisition phase: A solution contains 1.1 g of sodium nitrate, NaNO3 in 250 ml of solution. What is the concentration of this solution? (Na = 23, N = 14, O = 16). This problem can be solved using the following steps. Note that RFM means relative formula mass. mass (1) No. of moles = RF M (2) Calculate RFM of NaNO3 (3) Calculate the no. of moles MV (4) No. of moles of solute = 1000 (5) Equate (1) & (4) (6) Calculate M Alternatively, students can skip some intermediate steps, condensing the six steps (multi-step) into two steps if they have the appropriate schema: mass MV = 1000 (1) RF M (2) Calculate M Table 4 shows the number of students from each group who used a 2-step solution strategy and a multi-step solution strategy in the acquisition and test phases. Note that for the acquisition phase, the data were matched only for the common training problems. During the acquisition phase, students in the text editing group were required to edit but not solve the training problems, however, they were not penalized if they chose to provide a solution. A Fisher exact probability test showed a significant difference between the two groups in using the 2-step solution strategy, p = 0.017 and the multi-step solution strategy, p = 0.005. For the similar test, a Fisher exact probability test again indicated a significant difference for the 2-step solution strategy, p = 0.006 but not the multi-step solution strategy, p = 0.33. With respect to the single transfer test, a similar result was obtained by a Fisher exact probability test:
390 Table 4. No. of students who used the two different solution strategies (2-step and multi-step) in Experiment one Text editing
Conventional problem solving
Acquisition phase 2-step Multi-step
5 0
0 8
Similar test 2-step Multi-step
6 3
0 5
Transfer test Single transfer problems 2-step Multi-step Combination transfer problems 2-step incorrectly applied
6 3
0 6
5
0
Note: n = 11 for both groups; Fisher exact probability tests significant at 0.05 level.
a significant difference for the 2-step solution strategy, p = 0.006 but not for the multi-step solution, p = 0.19. Table 4 also shows that five out of the six students who used the 2-step solution strategy to solve the single transfer (molarity) problem successfully incorrectly applied the 2-step solution strategy to attempt to solve the combination (dilution and molarity) transfer problems. None of the students from the conventional problem solving group did likewise. A Fisher exact probability test yielded a significant difference between the two groups, p = 0.017. Thus, most students in the text editing group tended to use a 2-step solution strategy while the conventional problem solving group used only a multi-step solution strategy for solving the molarity problems. In fact, the text editing group tended to use the 2-step solution strategy for solving not only the single transfer (molarity) problems but also the combination (dilution and molarity) transfer problems. Possibly, this is an example of the Einstellung phenomenon which reflects a negative aspect of using schemas whereby the problem solvers occasionally pay the price of incorrect classification of problem types (Sweller, 1989). In contrast to molarity problems, a typical dilution problem has two solution steps. Consider the following:
391 6.0 M of HCl is diluted from initial volume of 1.0 L to 3.0 L. What is the final concentration? M1 V 1 = M2 V 2 Calculate M2 There is less scope for reducing the number of steps and accordingly, no difference in solution strategies was observed for the two groups in solving the dilution problems. Both groups used the above two solution steps to solve the dilution problems. The results of Experiment one support the hypothesis that a text editing training strategy was more effective than conventional problem solving in assisting students to acquire skills in solving the similar test problems and, to a lesser extent, the single transfer problems. Presumably, students who received training in text editing were familiar with the schematic knowledge of both the dilution and the molarity problems and were not as easily distracted as their conventional problem solving counterparts when the story context of the test problems altered. However, of particular interest was the different solution strategies commonly adopted by the two groups in solving the molarity problems: a 2-step solution strategy for the text editing group and a multi-step solution strategy for the conventional problem solving group. As mentioned earlier, the molarity problems involve multiple solution steps. The ability to condense the multi-step to the 2-step calculation to solve the molarity problems is a reflection of expert-like performance. Koedinger and Anderson (1990) demonstrated that experts who had schematic knowledge for geometry problems used key solution steps and skipped the less important ones. Similarly, the same evidence of step skipping by experts can be found in the work of Blessing and Anderson (1996). The problems used by Blessing and Anderson (1996) are similar to the molarity problems presented in Experiment one. In both cases, the problems involved procedural knowledge which required the application of a rule for each solution step. In their studies, Blessing and Anderson (1996) found that experts noticed the relationship between solution steps (recognize any sort of pattern contained in the solution steps) and generated a new single operator that skipped steps. In our case, steps 1, 2, 3 and 4 mass MV = 1000 . Note that step 5 contains can be skipped and replaced by step 5, RF M the relations among variables required for solution. It seems that text editing training assists some students to recognize the principal equation necessary (step 5) to solve the molarity problem. In summary, the strength of the text editing training strategy lies in facilitating the acquisition of the schemas for solving chemistry problems, in particular, the molarity problems. Students who practiced conventional
392 problem-solving probably acquired inferior schemas as they were not told of the logic underlying the steps taken to solve problems. They were thus not given the opportunity to realize the importance of relating essential variables, and to practice relating such variables.
Experiment two Experiment one demonstrated that text editing training was superior to conventional problem solving in learning dilution and molarity problems. Experiment two compared text editing training and problem solving using stoichiometry problems. In some aspects, stoichiometry problems are similar to dilution and molarity problems. In both cases, the variables cited in the problem are related in a mathematical formula. A stoichiometry problem (see Appendix) consists of problem statements and a balanced chemical equation. The solution procedure involves a simple proportion mathematical formula. To be able to edit a stoichiometry problem, students need to know how the various chemical substances are related in a simple proportion formula. This schematic knowledge would enable students to provide the additional information required to solve a problem presenting insufficient information. Likewise, any irrelevant information would be noticeable. Experiment two considered whether solution of stoichiometry chemistry problems was facilitated by training students to assess whether information provided within the text of a problem was necessary and sufficient for solution. The expectation was that text editing training would facilitate schema acquisition and hence, problem solving when compared with conventional problem solving. Method Participants Twenty-three male students from tenth-grade at a single-sex school in Sydney participated in the experiment. (These students differed from those who participated in Experiment one.) All the students had only limited exposure to the stoichiometry chemistry problems used in this study. A pilot study indicated that students’ skills in solving stoichiometry problems could be improved with instruction. Group testing was conducted in the classroom supervised by the chemistry teacher together with a researcher. Materials and procedure Students were randomly assigned to two groups: a text editing group and a conventional problem solving group. First, both groups read the instruction
393 phase materials for 10 minutes. There were three parts in the instruction phase. Part one explained how to interpret a balanced chemical equation. Part two provided an illustrative worked example of a moles-moles calculation. Part three provided another worked example of a mass-mass calculation (Appendix). Lastly, the steps involved in calculating stoichiometry chemistry problems from a balanced chemical equation were summarized. Students were free to ask questions whenever they encountered any difficulty in understanding the materials. The acquisition phase followed the instruction phase. Both groups read the information sheet for four minutes before they proceeded to do their respective training problems. Within that four minutes, the text editing group studied the instructions for carrying out text editing and studied three text editing practice problems with correct answers. The conventional problem solving group studied three problems together with their workedout examples. The three problems were the same as the three text editing practice problems but modified so that each problem contained sufficient information only. Thereafter, the training exercise began. For the text editing group, each student was given a booklet containing six training problems and their respective solutions. Students first classified each problem according to whether it contained sufficient, missing or irrelevant information in relation to the solution. In addition, they: (a) solved the problem if it contained all the necessary information to reach a solution; (b) provided additional information if a missing component of the information was discovered; (c) underlined any irrelevant information within the text of the problem once it was identified and then solved the problem accordingly (see Table 5). Students were required to spend two minutes in answering a problem, a further one minute to study a correct response (sufficient (S), missing (M) and irrelevant (I)) and a correct solution which was located on the next page. No student could study the solution without first attempting the problem. No additional time was provided if the students could not complete the acquisition phase within the time limit. The text editing group solved 2/3 of the total number of problems as it was not possible to solve problems with missing information. Students in the conventional problem solving group were given the same six training problems but modified so that each problem contained only sufficient information for solution. They were given two minutes to solve a problem and a further one minute to study its solution. All students could refer to the examples in the instruction phase while solving the training problems. When students finished the acquisition phase, the test phase began. The test phase comprised eight problems which resembled the problems used in the acquisition phase. Students were given five minutes to answer as many questions as they could.
394 Table 5. Examples of stoichiometry problems containing sufficient, irrelevant and missing information in Experiment two Sufficient information Given that 2Cu + S → Cu2 S (Cu = 56, S = 32) How many moles of S are needed to react with 1.0 moles of Cu ? Irrelevant information Magnesium reacts with sulphuric acid (H2 SO4 ) according to: Mg + H2 SO4 → MgSO4 + H2
(Mg = 24, H = 1, O = 16)
How many moles of Mg react with 0.5 moles of sulphuric acid if 1 mole of hydrogen, H2 occupied 22.4 L at STP? Missing information Given that 4Al + 3O2 → 2Al2 O3
(Al = 27, O = 16)
What mass of oxygen is required to react with aluminium?
Results and discussion The objective of this study was to compare the performance of students who were given two different kinds of training strategies: text editing which focused on gaining familiarity with the schematic knowledge required to solve problems and conventional problem solving which emphasized computation and calculation. The achievement scores were based on the number of correct solutions generated. Scoring was identical to Experiment one. Table 6 shows the means and standard deviations of correct solutions, nonattempted problems and errors made for the acquisition phase and the test phase. For the acquisition phase, the conventional problem solving group produced significantly more correct solutions on problems from which a solution was available for both groups (i.e. excluding the two text editing problems with missing information), t(21) = 3.19, SE = 0.41; and made significantly fewer errors than the text editing group, t(21) = 2.44, SE = 0.43. Since only two students from each group did not attempt two problems during the acquisition phase, the data on non-attempted problems were not analyzed. The test phase indicated a similar result. The conventional problem solving group produced significantly more correct solutions, t(21) = 2.36, SE = 0.09; and had a significantly lower number of non-attempted test problems than the text editing group, t(21) = 2.49, SE = 0.86. However, a difference was
395 Table 6. Means and (standard deviations) of correct solutions, non-attempted problems and errors made during the acquisition phase and the test phase in Experiment two
Correct solutions Errors made Non-attempted problems No. of students who made errors Given-and-asked-for chemical substances Coefficients and subscripts Mass mass/mole-mole problems
Acquisition phase Text Conventional editing problem solving
Test phase Text editing
Conventional problem solving
1.18 (0.98)∗ 2.45 (1.04) –
2.50 (1.00) 1.42 (0.10) –
0.91 (1.14)∗ 1.73 (0.65) 4.73 (1.56)∗
3.00 (2.70) 1.33 (0.49) 2.58 (2.50)
8 5 4
3 6 3
8 6 6
4 6 5
Note: n = 11 (text editing group); n = 12 (conventional problem solving group) ∗ t-test significant at 0.05 level; Fisher exact probability tests significant at 0.05 level.
not detected between the two groups for the errors made on the test problems, t(21) = 1.63, SE = 0.24 though the conventional problem solving group made fewer errors than the text editing group. Overall, the test results favored the conventional problem solving group. Apparently, training in text editing did not give students practice in the skills required to solve stoichiometry problems. According to Savoy (1988), many high school students are not able to correctly balance chemical equations because they misunderstand several chemical concepts such as chemical formulae, atomicity and the meaning of subscripts of formulae and the coefficients in the balanced chemical equations. Many cannot differentiate the real purpose of coefficients (number of molecules) and the meaning of subscripts (law of definite proportion). Moreover, they are unable to express the quantities of chemical substances in different units (moles, grams), and how they are related in a balanced chemical equation. Consider a stoichiometry problem used in the study: Given that 4Al + 3O2 → 2Al2 O3
(Al = 27, O = 16)
What mass of oxygen reacted with aluminium will produce 2 grams of aluminium oxide? In order to reach solution, students need to know: (1) how to identify the given-and-asked-for chemical substances (2) the meaning of subscripts of a formula and the coefficients in the balanced chemical equation (3) that the chemical formula represents a definite quantity of substance which can be expressed in moles and mass
396 (4) how to recognize the mole-mole (chemical substances expressed in mole) and mass-mass (chemical substances expressed in grams) relations in the equation (5) how to apply a simple proportion It was possible that the text editing procedure was unable to cater for the learning of these chemical concepts because of the nature of the text within the stoichiometry problem itself. The text editing exercise did not direct students’ attention to chemical concepts such as coefficient, subscripts, chemical formulae, and mole-mole and mass-mass relations because the problem statements do not provide any avenue for these chemical concepts to be edited. In addition, text editing acts as a hindrance to learning the givenand-asked-for chemical substances. This explanation was supported by an analysis of the types of errors committed. The errors made included three conceptual errors: (1) inability to identify the given-and-asked-for chemical substances, (2) inability to differentiate the coefficients and subscripts and (3) inability to differentiate mass-mass or mole-mole problems. The three types of errors are illustrated below. Consider a stoichiometry problem used in the study: Magnesium reacted with water according to: Mg + 2H2 O → Mg(OH)2 + H2
(Mg = 24, H = 1, O = 16)
When 12 g of magnesium reacted with water, what mass of magnesium hydroxide, Mg(OH)2 was produced? First, an attempt to incorporate 2H2 O, H2 or both in the calculation reflected students’ inability to identify the given-and-asked-for chemical substances. Second, when students calculated the molar mass (Mg(OH)2 ) incorrectly, they could not distinguish between the coefficient and the subscript of the chemical formula. Third, if students applied the simple proportion procedure before they expressed the quantities of the given-andasked-for chemical substances in the same unit (gram or mole), this implied that they could not recognize it as a mass-mass or a mole-mole problem. Table 6 shows the number of students who made the different types of errors across all problems. For the acquisition phase, eight students from the text editing group were unable to identify the given-and-asked-for chemical substances whereas only three students from the conventional problem solving group shared the same difficulty. A Fisher exact probability test indicated a significant difference between the two groups, p = 0.01. Similarly, a Fisher exact probability test showed that the text editing group made significantly more errors on the given-and-asked-for chemical substances than the
397 conventional group for the test phase, p = 0.03. In contrast, there were no significant differences between the two groups for either the acquisition phase or the test phase on errors relating to distinguishing between coefficients and subscripts with Fisher exact probability tests showing p = 0.4 for the acquisition phase and p = 0.5 for the test phase. Nor were there significant differences between errors relating to distinguishing between the mass-mass and mole-mole problems with Fisher exact probability tests showing p = 0.44 for the acquisition phase and p = 0.3 for the test phase. In summary, the analysis of errors revealed that students who received the text editing training committed more errors associated with the given-andasked-for chemical substances. Indirectly, this showed that the text editing training acted as a hindrance for learning the given-and-asked-for chemical substances. Typically, a stoichiometry problem consists of three or more chemical substances expressed in a balanced chemical equation. Whenever the quantity of one chemical substance is given, the quantities of other chemical substances can be derived from it. The following demonstrates how a stoichiometry problem (used in the acquisition phase) containing irrelevant information can hinder the understanding of the given-and-asked-for chemical substances. Given that Mg + 2HCl → MgCl2 + H2
(Mg = 24, H = 1, Cl = 35.5)
Calculate the mass of MgCl2 produced when 24 g of magnesium reacts with 10 ml of HCl. Some students attempted to use the irrelevant information (10 ml HCl) to calculate the mass of MgCl2 produced instead of the 24 g of magnesium. This is because both chemical substances (10 ml of HCl and 24 g of magnesium) appeared to be equally probable relevant information for solution. The text editing technique was unable to assist students in distinguishing the subtle difference between the two given chemical substances. Similarly, missing information can also act as a hindrance for learning the given-and-asked-for chemical substances. Consider the following missing information problem used in the acquisition phase: Given that C + O2 → CO2
(C = 12, O = 16)
What mass of O2 is required to react with carbon?
398 In order to solve the problem, the quantity of carbon (missing information) is required. But some students given training in text editing incorrectly generated the molar mass of carbon (relative atomic mass) to substitute for the missing quantity of carbon. In other words, the text editing technique failed to alert students to the missing quantity of the chemical substance because they could always rely on generating the molar mass to substitute for the missing quantity. Therefore, the text editing procedure did not achieve its purpose by making students aware of the given-and-asked-for chemical substances. In summary, both groups were given similar treatments except students in the text editing training group were given an extra task - editing the given-and-asked-for chemical substances. As noted previously, the analysis of errors revealed that students who received text editing training committed significantly more errors of the given-and-asked-for chemical substances than students given conventional problem solving. Therefore, the text editing procedure may have acted as a hindrance in the learning of the concept relating to the given-and-asked-for chemical substances. It should be noted that the text editing group solved 2/3 of the total number of problems during the acquisition phase, because they could not solve problems with missing information. Since the conventional problem solving group solved more problems during the acquisition phase, this might have enhanced their performance in the test phase.
General discussion Our research focused on the role of schematic knowledge in problem solving. The text editing technique was used as an instructional tool to assist students in acquiring schematic knowledge of chemistry problems. In Experiment one, students in the text editing group performed significantly better than the conventional problem solving group on the similar problems and, to a lesser extent, the single transfer problems. Moreover, they also made fewer conceptual errors on the molarity problems and no unit errors for both the dilution and molarity problems. The most impressive result was the capability of some students in the text editing group to generate a two-step solution strategy for solving the molarity problems. No one in the conventional problem solving group used a similar solution. Furthermore, these statistically significant results were obtained using a relatively small number of participants, indicating a very strong effect. In contrast, Experiment two showed that the conventional problem solving group outperformed the text editing group in solving stoichiometry problems. Moreover, the conventional group also made fewer errors and had fewer non-attempted problems than the text editing group.
399 The main goal of this study was to enhance students’ problem-solving skills in the domain of chemistry. The text editing technique was used to assist students in acquiring schematic knowledge necessary for solution. The success of the text editing technique was evident in Experiment one. Presumably, students who were trained in text editing were encouraged to represent the problem structure and to plan solution procedures simultaneously. When students edited the text of a problem, they were confronted with complete, incomplete or irrelevant information for solution. This exercise might have encouraged them to visualize each variable separately in their minds and fit them in an equation for locating the unknown variable. For instance, any missing information in the problem text will serve as a ‘gap’ for the students to add additional information (e.g., a value) so that a coherent problem structure (mathematical equation used to solve the problem) can be generated. Similarly, any irrelevant information (e.g., an unwanted value) will need to be discarded in accordance with the problem structure. A problem text with sufficient information contains all the values and an unknown variable required to solve the problem. Since cognitive resources were being appropriately directed to learning the different variables and their relationship in the problem, students acquired schemas to solve the problems. Once the students acquired the schemas, they could go a step further; they skipped some intermediate steps to generate a 2-step solution strategy to solve the conceptually more difficult molarity problems. However, additional techniques such as the use of verbal protocols are required to find out how exactly students benefited from the text editing technique. The results of the two experiments have implications for designing effective instruction. Providing students with text editing exercises benefited them in learning to solve molarity and dilution problems. Students were encouraged to represent a coherent problem structure before applying other mathematical skills to generate a problem solution. Since text editing attends to the problem structure, it facilitates the acquisition of schemas. In contrast, conventional problem solving which focuses on computation at the expense of learning the problem structure did not benefit schema acquisition. However, when dealing with stoichiometry problems, text editing has no advantage over conventional problem solving because it fails to direct students’ attention to the coherent problem structure. Not only did text editing fail to assist students in identifying the given-and-asked-for chemical substances from the problem texts, it did not help students to extract relevant values from the chemical equations. Hence, instructional designers need to take into consideration the nature of learning materials when devising instructional tools.
400 Acknowledgements The work reported in this paper was supported by an Australian Research Council Grant. We would like to thank Dr. Chris Acland, the Science Headmaster of Trinity Grammar School; Chai Mee Macindoe, chemistry teacher, The Narwee High School.
Appendix Stoichiometry Problem Mass-mass calculation Question Given that 2Zn + O2 → 2ZnO (Zn = 65, O = 16) What mass of zinc oxide, ZnO, is formed when 13 g of zinc, burns completely in oxygen? Solution Step 1: Under the balanced chemical equation, write the quantity given and the quantity required below the chemical formula of the substances involved 2Zn + O2 13 g
→ x g
2ZnO (Zn = 65, O = 16) actual mass
Step 2: From the equation, 2 moles of Zinc reacts with oxygen to give 2 moles of ZnO. Convert the moles to mass and write down the molecular mass 2Zn + O2 13 g 2(65) g
→ x g 2(65 + 16) g
2ZnO (Zn = 65, O = 16) actual mass molecular mass
Step 3: Therefore, by simple proportion, 13 x = 2(65) 2(81) 13(2(81)) x = = 16.2 g 2(65) Answer: Mass of ZnO is 16.2 g. Note: If we are asked to calculate the mass of oxygen required to react with 13 g of zinc, we proceed as follows:
401 2Zn + O2 13 g 2(65) g
→ x g 2(16) g
2ZnO (Zn = 65; O = 16) actual mass molecular mass
Again, by simple proportion x 13 = 2(65) 2(16) 13(2(16)) x = 2(65) x = 3.2 g Answer: The mass of oxygen required to react with 13 g of zinc is 3.2 g.
References Bassok, M. (1990). Transfer of domain-specific problem-solving procedures. Journal of Experimental Psychology: Learning, Memory, and Cognition 16: 522–533. Blessing, S.B. & Anderson, J.R. (1996). How people learn to skip steps. Journal of Experimental Psychology: Learning, Memory, and Cognition 22: 576–598. Chase, W.G. & Simon, H.A. (1973). The mind’s eye in chess. In W. Chase, ed., Visual Informational Processing. New York: Academic Press. Chi, M., Glaser, R. & Rees, E. (1982). Expertise in problem solving. In R. Sternberg, ed., Advances in the Psychology of Human Intelligence, pp. 7–75. Hillsdale, NJ: Erlbaum. Garvie, D., Robertson, A., Hughes, J. & Reid, J. (1979). Concise Chemistry. Oxford: Oxford University Press. Kintsch, W. & Greeno, J. (1985). Understanding and solving arithmetic word problems. Psychological Review 92: 109–129. Koedinger, K.R. & Anderson, J.R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science 14: 511–550. Lewis, M. & Walter, G. (1980). Thinking Chemistry. Oxford: Oxford University Press. Low, R. & Over. R. (1992). Hierarchical ordering of schematic knowledge relating to area-ofrectangle problems. Journal of Educational Psychology 84: 62–69. Low, R. & Over, R. (1989). Detection of missing and irrelevant information within algebraic story problems. British Journal of Educational Psychology 59: 296–305. Low, R. & Over, R. (1990). Text editing of algebraic word problems. Australian Journal of Psychology 42: 63–73. Low, R., Over, R., Doolan, L. & Michell, S. (1994). Solution of algebraic word problems following training in identifying necessary and sufficient information within problems. American Journal of Psychology 107: 423–439. Mansfield, G. (1981). Making Sense of Science Chemistry. London, England: AddisonWesley. Mayer, R.E. (1987). Educational Psychology: A Cognitive Approach. Little, Brown and Company. Nakhleh, M.B., Lowrey, K.A. & Mitchell, R.C. (1996). Narrowing the gap between concepts and algorithms in freshman chemistry. Journal of Chemical Education 73: 758–762. Pendlebury, J.N. (1972). Every Chemistry. Milton, Q: Jacaranda.
402 Reed, S.K. (1987). A structure-mapping model for word problems. Journal of Experimental Psychology: Learning Memory, and Cognition 13: 124–139. Reif, F. (1983). How can chemists teach problem solving? Journal of Chemical Education 60: 948–953. Savoy, L.G. (1988). Balancing chemical equation. School Science Review, 69: 713–719. Sweller, J. & Low, R. (1992). Some cognitive factors relevant to mathematics instruction. Mathematics Education Research Journal 4: 83–94. Sweller, J. (1989). Cognitive technology: Some procedures for facilitating learning and problem solving in mathematics and science. Journal of Educational Psychology 81: 457–466. van Dijik, T.A. & Kintsch, W. (1983). Strategies of Discourse Comprehension. New York: Academic. Author for correspondence: Renae Low, School of Education Studies, University of New South Wales, Sydney, 2052, Australia Phone: +61 (2) 93851940; Fax: +61 (2) 93851946; E-mail:
[email protected] 