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DOI: 10.1039/C0RP90012E (Paper) Chem. Educ. Res. Pract., 2011, 12, 427-433

Methods used by pre-service Nigeria Certificate in Education teachers in solving quantitative problems in chemistry†

Ibrahim Mohammed Danjuma
Science Education Programme, Abubakar Tafawa Balewa University, PMB 0248, Bauchi, Nigeria. E-mail: imdanjuma19@yahoo.co.uk

Received 4th January 2010 , Accepted 23rd August 2011

First published on 30th September 2011

Abstract

This paper reports part of the results of research on chemical problem solving behavior of pre-service teachers in Plateau and Northeastern states of Nigeria. Specifically, it examines and describes the methods used by 204 pre-service teachers in solving quantitative problems from four topics in chemistry. Namely, gas laws; electrolysis; stoichiometry and composition of substances. The pre-service teachers involved were 200 and 300 level Nigeria Certificate in Education (NCE) chemistry majors and non-majors. Data were collected from their written responses to four items of a chemistry problem solving Test (CPST) and retrospective interview. The frameworks adopted for analysing the methods used in solving the CPST items were those documented in the chemical education literature (Garafalo F. and Toomey R., (2002), www.inform.umd.edu/EdRes/Topic/Chemistry/ChemConference/Chem Con/Paper2.htm; Chemtutor, (2001), www.chemtutor.com/numbr.htm; Danjuma I. M. and Akpan E. U. U., (2000), Niger. J. Curric. Stud., 7(2), 129–135). These are plug and chug; ratio and proportion; dimensional analysis; reaction chemical equivalence and simple algebra. The results of the data analysis revealed that most of the pre-service teachers have used the appropriate methods to solve the CPST items, except that, only a few got the correct answers. Most of them indicated that their main reason for using the method of choice was the nature of the problems. Also, most of them indicated that they were not aware of other methods of solving the problems.

Introduction

Problem solving has been an aspect of chemistry teaching and learning that has attracted the attention of many chemical educators. The reasons are that chemists function best in problem situations (Bajah and Bello, 1987) and most of the difficulties encountered by chemistry students just starting out involve problem solving (Selvaratnam, 1983; Onwu and Moneme, 1986; Watts and West, 1992; Mason et al., 1997). Watts and West (1992) define a chemical problem as, any problem that uses knowledge in chemistry towards a solution. Recent work on chemical problem solving categorised a problem as either algorithmic or conceptual depending on its nature (Bowen and Bunce, 1997; Mason et al., 1997; Chiu, 2001; Stamovlasis, et al., 2005). The distinction between an algorithmic and conceptual problem is that algorithmic questions can be answered by applying a set of procedures to generate a response, while a conceptual question tries to tap into the “why” aspect of a response which indicates understanding of chemical ideas associated with the problem (Bowen and Bunce, 1997). Both algorithmic and conceptual questions can be both quantitative and qualitative. In line with this latter categorization, the type of knowledge required for solving chemistry problems has been investigated. Anderson cited in Chiu (2001) explained that such knowledge is of two types: declarative knowledge and procedural knowledge. The former, represented by propositions is knowing that something is the case (conceptual understanding), whereas procedural knowledge represented by productions is knowing how to do something. Conceptual understanding helps the problem-solver develop a meaningful representation of the problems and also narrow the search for solutions by matching the schema or “conditions” that represent the givens in the problem with a set of “actions” in procedural memory that are most likely to produce satisfactory results. Procedural knowledge on the other hand is faster to activate and more reactive to the environment. Research into the relationship between these forms of knowledge in chemical problem solving provided results that were inconclusive. For example, Nurrenbern and Pickering (1987) and Nakleh and Mitchell (1993) reported results indicating that a student’s performance in algorithmic problems has little relationship with their conceptual understanding of the chemistry principles. However, in a related study Chiu (2001) reported that when participants in her study were categorized by their performance on the algorithmic and conceptual questions, students with high achievement in both types of questions were found to be good problem solvers and were also good conceptual thinkers. They were able to appropriately retrieve relevant chemical principles and concepts for solving problems.

Methods of solving chemistry problems

Also present in the chemical education literature is information on the methods or techniques that have been used to solve problems in chemistry. A method or technique means a general approach that could be used to solve a particular problem. Chemistry problems can be solved using a variety of techniques, some problems may require the use of a single method while others, especially more complex problems, may require the use of a combination of more than one method. Recent works (Danjuma and Akpan, 2000; Chemtutor, 2001; Garafalo and Toomey, 2002) have documented some of the methods that have been used by both experts and novices in solving quantitative problems in chemistry. These include ratio and proportion, dimensional analysis, plug and chug, reaction chemical equivalents and algebra. Other methods such as mole method, balance and mixed methods of solving stoichiometric problems were described in the work of Tóth and Sebestyén (2009). The methods presented are often used by both experts and novices in solving problems. The most important thing to consider when selecting a method or technique for use is the underlying concept behind the given problem and its complexity. Gabel (1986) reviewed the literature on problem solving in chemistry and commented thus,

“many chemistry teachers and most introductory chemistry texts illustrate problem-solving using factor-label method (dimensional analysis). It has been shown that this is not the best technique for high school students of high mathematics anxiety and low proportional reasoning ability”.

Tóth and Sebestyén (2009) observed that there appeared to be relatively few studies reported in the literature on “how students choose their problem solving strategy (method)”. They added that the problem solving strategy a student applies depends on several factors, for example, Tóth and Kiss (2005) found that Hungarian secondary school students applied strategies learned in schools even in the case of simple stoichiometric problems. Tóth (2004) also reports that Hungarian high school students created their own strategy (mainly trial and error) of balancing chemical equations before learning the oxidation number method at school and they stuck to their own strategies of low efficiency even in the case of complicated redox equations. Tóth and Sebestyén (2009) also observed that Hungarian students applied methods taught in schools for problem solving based on chemical equations. However, only 40% of the students used either the mole method or proportionality method to solve the problems. These two methods were found to be equivalent to each other both in their frequency of use and success in solving the problems. They also reported that none of the students used dimensional analysis to solve any of the given problems. These results provide evidence that seem to suggest that students apply a variety of methods that are accessible to them to solve chemistry problems. However, what needs to be empirically ascertained is their reason(s) for choice and/or preference for a method of solving a given problem and whether (or not) they are aware of other methods of solving the same problem.

The present study investigated the methods used by pre-service chemistry teachers in solving quantitative problems in chemistry. Their reasons for choice of methods used and awareness of other methods of solving the problems were also explored. In Nigeria, pre-service chemistry teacher education is provided at two levels: the Nigeria Certificate in Education (NCE) level provided by colleges of education and the undergraduate chemistry education level provided by the universities. A critical consideration of the content of the course offerings in chemistry at the NCE level indicates that enough opportunities have been provided for the acquisition of the basic knowledge and skills that are essential for both qualitative and quantitative problem solving. Specifically, the course contents of CHM 114 (Applications of Mathematics to Chemistry I) and CHM 126 (Applications of Mathematics to Chemistry II) contained mathematics’ topics that have wider applications in chemistry. Since the two courses are offered at the first year of the NCE (100 level), it follows that students at both the 200 and 300 levels must have had the required exposure to basic knowledge and skills for solving the four quantitative problems selected for this study.

From the review of the literature made so far, there seem to be very few empirical studies conducted on the general problem solving behaviors of this category of pre-service NCE teachers. The few that were reported (Bello, 1990; Adigwe, 1993a; 1993b) dwelt largely on identifying the difficulties encountered by pre-service teachers in solving chemical problems rather than isolating and describing the specific methods used by the pre-service teachers in solving chemical problems. For instance, Bello (1990) reports that pre-service NCE teachers experienced various forms of difficulties in solving stoichiometry problems, such as misconception in terminology, errors in the use of quantities, inability to carry out mathematical calculations, and inability to comprehend the mathematical link between stoichiometric concepts. Adigwe (1993a, 1993b) reported several forms of misconceptions held by pre-service NCE chemistry teachers in chemical equilibrium and chemical kinetics, respectively. It therefore becomes imperative to carry out more empirical research on the problem solving behavior of this category of pre-service teachers in Nigeria.

The problem for this study, therefore, was to explore and describe the methods used by the pre-service NCE teachers in solving four quantitative numerical problems in chemistry. Specifically, the study sought answers to three research questions.

1. What methods do pre-service teachers use in solving selected quantitative problems in chemistry?

2. What are their reasons for the choice of the methods used in solving the selected quantitative problems in chemistry?

3. Are the pre-service teachers aware of other alternative methods of solving the selected quantitative problems in chemistry?

Design of the study

In this study, an attempt has been made to examine the methods used by pre-service NCE chemistry teachers in solving some quantitative problems in chemistry. The design involved both a quantitative methodology and a qualitative methodology. The quantitative method was used to determine the frequency and proportion of the methods used by the pre-service teachers in solving the selected problems. While the qualitative method which involved semi-structured interviews was used to analyze particular aspects of their thinking in using the methods of choice to solve the problems and their reasons for choosing the methods, as well as determining whether they are aware of other alternative methods of solving the same problems.

Participants

The population for the study comprised eight hundred and seventy nine 200 level and 300 level NCE pre-service teachers majoring in chemistry and those that have taken chemistry as a minor/non-major teaching subject from eight colleges of education located in the Plateau and six states of the Northeast geopolitical zone of Nigeria. The sample for the study comprised two hundred and four pre-service-teachers drawn from the population. Specifically, fifty seven 200 level NCE chemistry majors, sixty six 300 level NCE chemistry majors, forty 200 level NCE non-majors and forty one 300 level NCE non-majors. One of the reasons for choosing this group of pre-service teachers was that, at their present academic levels, they must have taken enough chemistry courses that have equipped them with some basic knowledge and skill needed for solving the selected quantitative problems. Secondly, experience shows that after completing their studies, this category of pre-service teachers are being employed (in places to supplement graduate teachers) to teach chemistry at the secondary schools in Nigeria because the number of chemistry teachers is grossly inadequate especially in the Northern part of the country. Thirdly, prior to the administration of the CPST, their performance on a chemistry achievement test and a mathematics skill test has indicated that they possess an appreciable knowledge of chemistry and mathematical skills required for solving the CPST items. A stratified random sampling technique was employed to select the sample. Four strata were formed based on their academic level and subject specialisation. A random sample of 10 pre-service teachers from each stratum from each of the eight colleges of education was drawn [except for one college where the population of 200 level NCE chemistry majors was less than 10; in this case, the whole population (N = 7) was sampled].

Data analysis

The instrument for data collection was a four-item free response chemistry problem solving test (CPST) developed by the researcher. Each item in the test represents one of the four topics in chemistry (i.e. composition of chemical substances, stoichiometry, gas laws, and electrolysis) found in the foundation chemistry courses of most of the colleges of education and at first-year undergraduate level of Nigerian Universities. The participants took the test and no time limit was assigned. Their written responses were analysed using frequency and percentage. Judgement on the methods that they have used to solve the CPST items was based on the frameworks documented in the literature (Peters, 1990; Danjuma and Akpan, 2000; Chemtutor, 2001; Garafalo and Toomey, 2002). (Excerpts on how these methods have been used to solve the four CPST items by a sample of the pre-service NCE teachers have been presented in Appendices A–D of the ESI†). At the end of the testing session, a semi-structured interview with each respondent was conducted by the researcher and the research assistants to collect the qualitative data. During the interview session the respondents were asked to explain in detail their solutions including reasons for prefering to use their chosen method(s) in solving the CPST items and whether they were aware of other alternative methods of solving the items. Notes on their responses were taken during the interview. As stated earlier the semi-structured type of interview was employed. The technique requires the use of research assistants because of the large sample involved and a total of eight research assistants were employed by the researcher to assist in conducting the interviews. Each research assistant was trained by the researcher on the technique. They all possessed a minimum of a Bachelors Degree in Science or Science Education. The interview transcripts were analysed by the researcher using a content analysis method.

Results

Research question 1: what methods do pre-service teachers use in solving the selected quantitative problems in chemistry?

Tables 1–4 present the frequencies and percentages of the methods used by the pre-service teachers in solving the four CPST items. The tables also contain data on the proportion of those that attempted an item, and those that did not. (“Attempted” here indicates a response that was relevant and some meaning can be derived from it. “Not attempted”, on the other hand, indicates no response or a work that was completely irrelevant and meaningless). The tables also contained data on the percentage of those that used the correct method and got a correct answer, and those that used the correct method and got a wrong answer.
CPST item 1. A gas at a pressure of 5.00 atm was heated from 0 °C to 546 °C and simultaneously compressed to one third of its original volume. What will be the final pressure in atm?
Table 1 Frequencies and percentages of the methods used by the pre-service teachers in solving CPST item 1 (percentage in parenthesis)
Method used to solve CPST item 1 200 Level NCE 300 Level NCE 200 Level NCE 300 Level NCE  
Majors Majors Non-majors Non-majors Total
n = 57 n = 66 n = 40 n = 41 n = 204
a Correct method for solving the item.
Attempted 51(25) 60(29.4) 32(15.7) 37(18.1) 180(88.2)
Not attempted 6(2.9) 6(2.9) 8(3.9) 4(2) 24(11.8)
aPlug and chug 50(24.5) 58(28.4) 29(14.2) 35(17.1) 172(84.3)
Simple algebra 1(0.50) 2(1) 3(1.5) 2(1) 8(3.9)
Correct method correct answer 11(5.4) 5(2.5) 6(2.9) 8(3.9) 30(14.7)
Correct method incorrect answer 39(19.1) 53(25.8) 23(11.3) 27(13.2) 142(69.6)

CPST item 2. When aqueous copper(II)tetraoxo-sulphate (VI) was electrolyzed between copper electrodes, the masses in grams of the electrodes before the experiment were 9.20 g (anode) and 7.75 g (cathode) . After the experiment, it was found that the mass in grams of the copper anode was 6.00 g. Calculate the mass in grams of the copper cathode at the end of the experiment.
Table 2 Frequencies and percentages of the methods used by the pre-service teachers in solving CPST item 2 (percentage in parenthesis)
Method used to solve CPST item 2 200 Level NCE 300 Level NCE 200 Level NCE 300 Level NCE  
Majors Majors Non-majors Non-majors Total
n = 57 n = 66 n = 40 n = 41 n = 204
a Correct method for solving the item.
Attempted 33(15.7) 44(21.6) 11(5.4) 23(11.3) 110(53.4)
Not attempted 24(12.3) 22(10.8) 29(14.2) 18(8.8) 94(46.8)
Reaction chemical equivalents 1(0.5) — — — 1(0.5)
Ratio and proportion 5(2.5) 11(5.4) 4(2) 6(3) 26(12.3)
aSimple algebra 27(13.2) 33(16.2) 7(3.4) 17(8.3) 84(41.2)
Correct method correct answer 6(2.9) 5(2.5) 2(1) 6(2.9) 19(9.3)
Correct method incorrect answer 21(10.3) 28(13.7) 5(2.5) 11(5.4) 65(31.9)

CPST item 3. Given the equation below, what mass of ammonia would be produced from 1.0 mole of H2 and excess nitrogen?
N2(g) + 3H2(g) → 2NH3(g)
Table 3 Frequencies and percentages of the methods used by the pre-service teachers in solving CPST item 3 (percentage in parenthesis)
Method used to solve CPST item 3 200 Level NCE 300 Level NCE 200 Level NCE 300 Level NCE  
Majors Majors Non-majors Non-majors Total
n = 57 n = 66 n = 40 n = 41 n = 204
a Correct methods for solving the item.
Attempted 38(18.6) 36(17.7) 23(11.3) 26(12.8) 123(60.3)
Not attempted 19(9.3) 30(14.7) 17(8.3) 15(7.4) 81(39.7)
Plug and chug 10(4.9) 5(2.5) 10(4.9) 7(3.4) 32(15.7)
aReaction chemical equivalents 19(9.3) 20(9.8) 3(1.5) 14(6.9) 56(27.5)
aDimensional analysis — — — — —
aRatio and proportion 9(4.4) 11(5.4) 10(4.9) 5(2.5) 25(17.2)
Correct method correct answer 6(2.5) 3(1.5) 3(1.5) 3(1.5) 15(7.4)
Correct method incorrect answer 22(10.8) 28(13.7) 10(4.9) 16(7.8) 76(27.3)

CPST item 4. A strip of pure copper having a mass of 3.178 g was strongly heated in a stream of oxygen until it was converted to the black oxide. The resultant black oxide has a mass of 3.978 g. Calculate the percentage composition of the black oxide?
Table 4 Frequencies and percentages of the methods used by the pre-service teachers in solving CPST item 4 (percentage in parenthesis)
Method used to solve CPST item 4 200 Level NCE 300 Level NCE 200 Level NCE 300 Level NCE  
Majors Majors Non-majors Non-majors Total
n = 57 n = 66 n = 40 n = 41 n = 204
a Correct method of solving the item.
Attempted 45(22.6) 57(27.9) 32(15.7) 36(17.7) 170(83.3)
Not attempted 12(5.9) 9(4.4) 8(3.9) 5(2.5) 34(16.7)
aRatio and proportion 42(20.6) 54(26.5) 30(14.7) 32(15.7) 158(77.5)
Simple algebra 3(1.5) 3(1.5) 2(1) 4(2) 12(5.9)
Correct method correct answer 5(2.5) 4(2) 1(0.5) 2(1) 12(5.9)
Correct method incorrect answer 37(18.2) 50(24.5) 29(14.2) 30(14.7) 146(71.5)

Research question 2: what are their reasons for the choice of the methods used in solving the selected quantitative problems in chemistry?

The results of content analysis of the qualitative data generated from the retrospective interviews with each of the participants on their solutions to the CPST items were collated and summarised as follows:
CPST item 1. Most of the participants, including those that employed the wrong methods, stated that they used the methods because the question involved a gas law.
CPST item 2. The main reason given by some of the participants for using their selected methods to solve this question was that all the data necessary for solving the question were given and there was only one unknown. Another reason given by some was the nature of the question (i.e. electrolysis). However, a few others could not advance any definite reason.
CPST item 3. The participants' main reason for using the varying approaches (including those that were not successful) was the nature of the question (i.e. mole ratios were involved and the question involved calculating the mass of NH3 from the given stoichiometric equation). Few of them that also attempted the question could not give any definite reason.
CPST item 4. Most of the participants stated that the nature of the question (i.e. determination of percentage composition) made them decide to use the percentage method (i.e. ratio and proportion, which was the correct method). The same reason was also given by the few that used the incorrect method.

Research question 3: are the pre-service teachers aware of other alternative methods of solving the selected quantitative problems in chemistry?

The results content analysis of the qualitative data generated from the retrospective interviews was also collated. The analysis revealed that most of the participants could only think of the method they used to tackle the problems and no alternative.

Discussion

The results presented in Table 1 indicate that a high percentage of the pre-service teachers have used the correct method to solve CPST item 1 involving gas laws. Their awareness and understanding that plug and chug was the correct method was also supported by the results from the analysis of their interview response to the item. The results from the table also show that only a few (14.7%) of the pre-service teachers got the correct answer (among them was pre-service teacher S107 in Appendix A of the ESI†). Others that got it wrong could partly be attributed to the inability of some of them (47.6%) to correctly define and use the variables V1 (initial volume) and V2 (final volume) from the information given in the item. It could also be as a result of the inability of about 8.9% of them to express their answers in the correct unit, that is, atmospheres (atm). Hence, the difficulty in solving the item is more of a conceptual problem rather than an error in arithmetic.

The results in Table 2 indicate that a high percentage of the pre-service teachers that attempted CPST item 2 on electrolysis had used the appropriate method, i.e., simple algebra to solve the item. Also the results from the analysis of their interview responses showed that most of them are not aware of any other method of solving this problem. From the table, only 9.3% of the pre-service teachers got the answer correct. The fact that most of them got it wrong suggests a failure to understand how to construct the correct numerical relationship involved. This type of hurdle has been identified by earlier researchers such as Krammers-Pals et al. (1982) as one of the major difficulties experienced by students in solving numerical problems in chemistry.

Table 3 presents results of analysis on the methods used by the pre-service teachers in solving CPST item 3 which involves stoichiometry. Basically, there are three correct methods of solving this item. These are, reaction chemical equivalence method, dimensional analysis, and ratio and proportion. Interestingly, two of these methods (i.e. reaction chemical equivalence and ratio and proportion) have been used by the pre-service teachers to solve the item. The results showed that, on the whole, about two thirds (44.6%) of those (60.3%) that attempted the item used two (out of the three) correct methods to solve the item. However, they seemed to have preferred the use of reaction chemical equivalence method to ratio and proportion. It is also interesting to note that this practice was contrary to what has currently being advocated by chemical education researchers such as Garafalo and Toomey (2002) who have discouraged the use of the reaction chemical equivalence method. They argue that the corresponding equation established for the chemical equivalence from stoichiometric equations often leads students to write incorrect mathematical equations. For instance, the stoichiometric equation in CPST item 3 was

N2(g) + 3H2(g) → 2NH3(g)
From this chemical equation, the corresponding equation will be 3 mol of H2 = 2 mol of NH3. Thus, if x = number of moles of H2 and y = number of moles of NH3 given, from this information a student could mistakenly take 3x = 2y to be the correct mathematical equation, instead of 3y = 2x. Garafalo and Toomey (2002) further argue that mathematically equating different physical quantities is incorrect, but rather students should be encouraged to create and interpret ratios as this will set the stage for the correct set up and interpretation of equations. Thus, the case in CPST item 3 is y/x = 2/3, and it more easily follows that y = 2x/3. Incidently, most of the pre-service teachers that got the correct answer to CPST item 3 used this method.

Again, the observation that none of the pre-service teachers used dimensional analysis indicates that, though they were aware of the other two methods, they didn't know about dimensional analysis. This is probably because it was not one of the methods taught to them in the school. Studies (Tóth and Kiss, 2005; Tóth and Sebestyén, 2009) have reported that students used methods taught in school to solve chemistry problems. These students relied on what they had been taught in school rather than what they had been taught more recently at university. However, Tóth and Sebestyén (2009) have found that none of the participants in their study used dimensional analysis to solve both simple and complex stoichiometric problems. This observed behaviour is interesting and also an issue that needs further consideration. The method has the advantage of reducing the amount of errors that may be committed during calculation (Chemtutor, 2001). Examples of such errors include incorrect mathematics and omission of units. It had popularly been used to solve numerical problems in most general chemistry textbooks, particularly foreign textbooks that are mostly used by students at the tertiary level of education in Nigeria.

It was also observed from Table 3 that only 7.4% of the pre-service teachers got the correct answer. This percentage is very low. A possible explanation for this could be inferred from the results of the analysis of their interview responses. Most of those who attempted to solve the item and used the correct method could not proceed beyond establishing the chemical equivalence from the given stoichiometric equation. This observation has serious implications, especially in the NCE chemistry teacher education programme.

From the results presented in Table 4, it could be observed that a very high percentage of the pre-service teachers have used the appropriate method (i.e. ratio and proportion) to solve the problem and the 200 level and 300 level NCE chemistry majors did better than the corresponding 200 level and 300 level NCE non-majors. The results of the interview responses to the item indicated that the pre-service teachers were very much acquainted with the approach as the appropriate method for solving the item because of their long time experience in the use of the approach (i.e. calculating percentages) in solving similar problems in the past. From this observed high percent usage of the correct method, it was expected that most of the respondents would get the correct answer. However, this was not the case, because only 5.9% got the correct answer. A possible explanation for this observed behaviour could be inferred from analysis of their answer scripts and interview responses, that only this low percent were able to reason that the percentage composition of black oxide (that the question was asking for) was equal to the sum of the percentage composition of copper and the percentage composition of oxygen determined from the given masses of Cu and CuO. The majority who could not reason this way, resorted to calculating only the percentage of copper or that of oxygen in the oxide, or used other incorrect percentage formula and considered what they had obtained to be the percentage composition of the black oxide (see solutions of pre-service teachers S192, S16 and S59 in Appendices B, C and D, respectively, of the ESI†). This observation also has serious implications in the NCE chemistry teacher education programme. It implies that the pre-service teachers had not fully conceptualized the problem, meaning that though they are acquainted with the procedural knowledge required for solving the problem, they lacked the conceptual knowledge.

Conclusion and recommendation

Based on the analyses and discussion of the findings of the study, it was concluded that most of the pre-service teachers have used the appropriate methods to solve the CPST items. However, the use of correct methods was more pronounced among the chemistry majors as one would expect. Irrespective of their academic level and subject specialization only a few of the pre-service teachers obtained correct answers to the CPST items. Most of the difficulties were not arithmetic errors, but mainly in failure to understand the logical reasoning required, and also applying the chemical principle underlying a problem. This is a conceptual problem that needs to be tackled. It, therefore, suggests the need for chemistry teacher educators at this level to review their approaches to teaching quantitative problem solving in chemistry. They should give more emphasis on understanding the qualitative meaning of the chemical and mathematical principles of a given problem before embarking on calculations. This could be done using content reading instruction suggested by Danjuma and Akpan (2000) whose recommendations are as follows.

In content reading instruction, students are taught reading comprehension skills that are applicable to chemical and mathematical problem solving. The skills include, seeking the meaning of chemical and mathematics terms, words, phrases and implied relationship in the context of the given problem; identifying relevant and irrelevant data; recognizing ideas presented, translating verbal symbols and relationship into chemical or mathematical statements or equations. When a problem is given to the students to solve, the teacher asks them to read through the problem slowly, pausing at commas or at the end of a single idea to decide what it means, and to go back and re-examine it as many times as possible by asking more questions such as what does the problem ask for? What are the given conditions? What are the relevant data? And what are the key relations in the problem? Answers to these would provide qualitative meaning of a given problem.

The pre-service teachers gave several reasons for the selection and use of the correct methods of solving the problems. However, most of them were not aware of other methods of solving the problems. Their reason for the choice of methods and awareness of alternative methods has implication for chemical education research and practice. Some of the reasons given were not conceptual, hence, the need for further research on these findings.

The observed lack of awareness and use of dimensional analysis as a method of solving stoichiometric problems is also an issue that needs further consideration. More so, a similar observation was made by Tóth and Sebestyén (2009). Pre-service teacher educators should teach the use of dimensional analysis and other methods of solving chemistry problems that have been documented in the chemistry education research literature.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c0rp90012e
This journal is © The Royal Society of Chemistry 2011