Algorithmic and conceptual stoichiometry problem solving

Chui (2001) investigated the difference in learners’ ability to solve algorithmic and conceptual problems in Chemistry and found that learners who were good at solving both algorithmic and conceptual problems were better at solving conceptual problems than algorithmic problems. Chui (2001) also noted that there is a positive correlation between algorithmic skills and conceptual understanding. The strength of this study was that the participants were asked to either explain their answers or support their answers by calculations. All this eliminated guessing. The other strength of this study was that the learners were tested in a natural environment which reduced reactive effects. However, the sample used in this study had fewer females compared to males inferring that the sample was not representative of the population from which it was drawn from. The limited scope of the test (one problem per topic) comprised its content validity.

Chui’s (2001) results were confirmed by Yilmaz, Tuncer and Alp (2007). The high algorithmic and conceptual achievement that was reported by Yilmaz, Tuncer and Alp (2007) may be due to the fact that the learners had practised the topics that were in university selection test hence the tasks were no longer problems but

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exercises. The other factor that might have contributed to this finding is that the participants may have guessed the answers since the instruments consisted of multiple choice problems or the use on constructive teaching to teach stoichiometry that could have promoted conceptual understanding and reduced alternative conceptions.

The similarity of the results of the two studies mentioned above may be attributed to the samples of these studies that were not representative of their respective populations since they were drawn from one school and two schools respectively.

Contrary to the results of the two studies above were the results reported by BouJaoude and Barakat (2003), Okanlawon (2008) and Stamovlasis, Kamilatos, Papavikonomau and Zarotiadou (2005) who found that algorithmic achievement was higher than conceptual achievement. The difference between the results reported by Stamovlasis et al and the results reported by Yilmaz, Tuncer and Alp (2007) and Chui (2001) may have stemmed from the fact that Chui (2001) and Yilmaz et al (2007) used samples that were non-representative of the populations from which they were drawn from whereas Stamovlasis et al (2005) used a sample that was almost representative of its population. However, BouJaoude and Barakat (2003) who used a sample that was non-representative

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as Chui (2001) and Yilmaz, Tuncer and Alp (2007) but got different results. The corresponding findings between the results reported by BouJaoude and Barakat (2003) and the result of Stamovlasis et al (2005) may be because the participants in these studies were all Grade 11 learners. This means that they might have had almost the same experience in solving algorithmic and conceptual problems and were at the same cognitive level. The other problem solving strategies that is reported in literature is unidentified strategies.

Unidentified strategies

Unidentified strategies are strategies that do not have a pattern nor found in textbooks. Several researchers have observed that these strategies are used learners to solve stoichiometry problems. Schmidt (1993) found that learners who use unidentified strategies to solve stoichiometry problems have a high achievement. This was supported by Schmidt and Jigneus (2003) in Sweden. However, Toth and Sebestyen (2009) found that learners used unidentified strategies to solve easy stoichiometry problems and used efficient strategies to solve difficulty problems. The other result these researchers reported was that the achievement of learners who use unidentified strategies was low. The low achievement may be caused by the fact that the learners who use these strategies apply them when they are not applicable (Cai,

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Mayer, & Grochowski, 1999). The implication of the result reported by Toth and Sebestyen (2009) is the strategies are dependent on the level of difficulty of the problem. The difference between the former result and the latter result may be because in the former two studies volunteers who are normally motivated were used and this made the samples non-representative of their respective population because volunteers. On the other hand Toth and Sebestyen (2009) did not use volunteers. However, results of Schmidt (1993) and Schmidt and Jigneus (2003) would be only possible if the sample was made up of imaginative problem solvers. But, creative problem solvers are rarely found in the population because achievement is a normally distributed variable. The other strategies used to solve stoichiometry problems that are systematic and outlined in textbooks are the mole and proportional methods.

Mole and proportional methods

It was found out that Hungarian learners used the mole and the proportional methods to solve stoichiometry problems and there was significant difference between the achievement of the learners who used the mole and proportional methods by Toth and Sebestyen (2009). This concurred with the finding of Toth and Kiss (2005). On contrary to the two findings mentioned above were Fach, de Boer and Parchmann (2007). Fach, de Boer and

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Parchmann (2007) found that achievement of learners who use the mole method was low because they tend to misconstrue the numerator and the denominator hence obtaining incorrect solutions. The difference between the reports of Toth and Sebestyen (2009) and Fach, de Boer and Parchmann (2007) was that the sample of the former was representative of the population because sampling error was minimized by random sampling whereas the sample of the latter was not representative of the population from which it was drawn. This is because participants were selected by teachers and furthermore selected learners who volunteered formed the sample. The other cause of the difference was that Fach et al (2007) used interviews which allowed them to get in-depth information whereas Toth and Sebestyen (2009) used pen and paper test. The disadvantage of pen and paper is that they do not gather much information. Toth and Sebestyen (2009) also disagreed with Gabel and Sherwood (1983) who found that learners who used the label factor method produce results that surpassed the results of learners who used the proportional method.