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DOI: 10.1039/C2RP20084H (Paper) Chem. Educ. Res. Pract., 2012, 13, 484-489

Mental capacity and working memory in chemistry: algorithmic versus open-ended problem solving

Helen St Clair-Thompson a, Tina Overton b and Myfanwy Bugler a
aDepartment of Psychology, University of Hull, Hull, HU6 7RX, UK. E-mail: H.St-Clair-Thompson@hull.ac.uk; Tel: +44 1482 465339
bDepartment of Chemistry, University of Hull, Hull, HU6 7RX, UK

Received 2nd July 2012 , Accepted 6th September 2012

First published on 27th September 2012

Abstract

Previous research has revealed that problem solving and attainment in chemistry are constrained by mental capacity and working memory. However, the terms mental capacity and working memory come from different theories of cognitive resources, and are assessed using different tasks. The current study examined the relationships between mental capacity, working memory, algorithmic and open-ended problem solving, and A level chemistry grades. The results revealed that the best predictor of algorithmic problem solving and A level grades was performance on a counting recall task, which requires the simultaneous processing and storage of information within working memory. The best predictors of open-ended problem solving were backwards digit recall and the figural intersection test. The results therefore demonstrated a dissociation between the cognitive resources underlying algorithmic and open-ended problem solving. The results are discussed in terms of both theoretical and practical implications.

An important constraint on the abilities and achievements of science students is ‘mental capacity’ or ‘working memory capacity’ (e.g.Danili and Reid, 2004; Tsaparlis, 2005; Vaquero et al., 1996). Researchers have often used these terms interchangeably, although they arise from different theoretical conceptualisations of cognitive resources (e.g.Niaz and Logie 1993; St Clair-Thompson and Botton, 2009). Theories of ‘mental capacity’ and ‘working memory’ may be in part complimentary (e.g.de Ribaupierre and Bailleux, 1994; Kemps et al., 2000; Pascual-Leone, 2000). However, within the context of science education few researchers have attempted to specify the nature of mental capacity or working memory resources (see also Niaz and Logie, 1993; St Clair-Thompson and Botton, 2009).

Mental capacity is often conceptualised within the framework of the theory of constructive operators (Pascual-Leone, 1970, 1987). According to this theory a participant is unlikely to be successful at problem solving if the number of procedures that need to be activated to solve a problem is greater than their M-capacity (e.g.Boujaoude et al., 2004; Johnstone, 1984; Johnstone and El-Banna, 1986; Niaz, 1988, 1989; Tsaparlis, 2005; Tsaparlis and Angelopoulos, 2000). M-capacity has commonly been assessed using the figural intersection test (Pascual-Leone and Burtis, 1974), in which participants have to locate one area of common intersection in a set of given overlapping shapes. It has also been assessed using backwards digit recall (Wechsler, 1955), in which participants are asked to recall sequences of digits in reverse order. Performance on both of these tests serves as a useful predictor of problem solving in chemistry. This has been demonstrated using many types of algorithmic problem solving (e.g.Boujaoude et al., 2004; Tsaparlis, 1998; Tasparlis and Angelopoulos, 2000) as well as overall exam success (e.g.Johnstone and El-Banna, 1986; Danili and Reid, 2004).

The concept that participants fail on problem solving tasks due to cognitive demand is also sometimes referred to as the working memory overload hypothesis (e.g.Chandran, 1987; Johnstone and El-Banna, 1986; Niaz, 1987; Opdenacker et al., 1990). Although there are several theoretical models of working memory, according to one of the most widely accepted models (e.g.Baddeley, 2000; Baddeley and Hitch, 1974) working memory is a multiple-component system for both processing and storing information. At the heart of working memory is a central executive system, a domain-general limited capacity system often likened to attentional-control. The central executive is supported by two domain-specific storage components; the phonological loop that is responsible for the maintenance of auditory information, and the visuo-spatial sketchpad that is specialised for dealing with visual and spatial information. Baddeley (2000) identified the episodic buffer as a further subcomponent of working memory, responsible for integrating information from the subcomponents of working memory and long-term memory.

A number of tasks requiring both processing and storage have been developed to assess the central executive component of working memory. For example, in counting recall (Case et al., 1982) participants count the number of items in a series of arrays and then recall the successive tallies of each array. Due to the requirement to reverse the digit sequence, backwards digit recall has also been employed as a complex working memory task (e.g.St Clair-Thompson, 2010). Such tasks can be distinguished from short-term memory tasks involving storage with no supplementary processing, for example digit recall is assumed to assess the phonological loop, and block recall is assumed to assess the visuo-spatial sketchpad (e.g.Pickering and Gathercole, 2001). Research has revealed that scores on such working memory tasks, particularly tasks tapping the central executive, are a useful predictor of a number of cognitive skills. For example, scores are significantly correlated with performance on tasks of comprehension, mathematics, and reasoning (e.g.Baddeley, 2003; Baddeley and Logie, 1999), and serve as a useful predictor of children’s attainment in national curriculum assessments of English, mathematics, and science (e.g.St Clair-Thompson and Gathercole, 2006).

There has been some research exploring relationships between scores on working memory tasks and problem solving in science. Roth (1990a) found that scores on a complex working memory task were significantly related to scores on science exams, and more so than performance on the figural intersection test (see also Roth, 1990b; Roth and Milkent, 1991). However, Vaquero et al. (1996) found that scores on a listening recall task did not significantly predict science attainment, and suggested that this was a result of listening recall not being sufficiently cognitively demanding to predict problem solving (see also St Clair-Thompson, 2007). However, problem solving in chemistry has not yet been fully examined within the context of the multiple component model of working memory. For example, links between the phonological loop and visuo-spatial sketchpad and problem solving have yet to be explored (see also St Clair-Thompson and Botton, 2009).

The first aim of the current study was therefore to examine relationships between measures of the central executive, phonological loop, and visuo-spatial sketchpad components of working memory and algorithmic problem solving in chemistry. Of particular interest was whether scores on tasks assessing these constructs were better predictors of problem solving than scores on the figural intersection test assessing M-capacity (e.g.Roth, 1990a). The second aim was to explore whether the same cognitive factors that underlie algorithmic problem solving are also related to success in solving open-ended problems.

Developing problem solving skills has been a topic of much research in science education (e.g.Barak and Dori., 2005; Zoller, 1993, 1999, 2012). The types of problems set in examinations or assessments in chemistry are largely algorithmic (Bennett, 2004). These employ lower order cognitive skills, such as the recall of algorithms and application of the problem to those algorithms (Johnstone,1993; Zoller and Tsaparlis, 1997). However, the types of skills that employers seek in chemistry graduates are higher order cognitive skills including critical thinking, connection making and analysis (e.g.Mason, 1998; Zoller and Tsaparlis, 1997). These skills are called upon by open-ended problem solving (Duch et al., 2001; Zoller, 1999). Open-ended problems are those for which there is no given data and ill-defined goals, and a need for the participants to use unfamiliar methods.

Although it is well established that algorithmic problem solving is constrained by participants’ mental capacity or working memory (e.g.Danili and Reid, 2004; Tsaparlis, 2005; Vaquero et al., 1996), at present little is known about the cognitive resources underlying open-ended problem solving. Overton and Potter (2011) examined relationships between scores on the figural intersection test (M-capacity), backwards digit recall (working memory), and algorithmic and open-ended problem solving. They found that scores on algorithmic and open-ended problems were not significantly related. Similarly, scores on measures of lower-order and higher-order cognitive skills are not closely related (e.g.Zoller, 2002; Zoller and Tsaparlis, 1997). Overton and Potter also revealed that M-capacity was more closely related to algorithmic than to open-ended problem solving. Working memory was not significantly related to either type of problem solving. However, they attributed this to methodological issues that made it easy for students to cheat on the backwards digit recall task. In addition, it is worthy of note that the backwards digit recall task may not be a suitable measure of working memory in participants of a high ability. For example, St Clair-Thompson (2010) found that backwards digit recall loaded on to the same factor as forwards digit recall in undergraduate students, and suggested that this was a result of the requirements to reverse the digit sequence not being demanding enough to require executive-attentional resources in this participant group. Open-ended problem solving has also not been examined within the context of the multiple component model of working memory.

In the current study, undergraduate chemistry students were therefore asked to complete a number of cognitive tasks, including measures of the central executive, phonological loop, and visuo-spatial sketchpad components of working memory, backwards digit recall and the figural intersection test. They also completed tasks of algorithmic and open-ended problem solving and supplied their previous A level chemistry grade. Analyses were used to examine relationships between measures of mental capacity, working memory, and algorithmic and open-ended problem solving. The main aims were to establish whether tasks of mental capacity or working memory are the best predictors of problem solving, and whether similar patterns of findings emerge for solving open-ended and algorithmic problems. It was predicted that mental capacity and working memory would be better predictors of algorithmic than open-ended problem solving, due to the reliance of algorithmic problem solving on lower-order rather than higher-order cognitive skills.

Methodology

Participants

Seventy-seven undergraduate chemistry students took part in the study. There were students from each of the first, second, and third years of the undergraduate degree course. Each student was paid a small fee upon completion of the study, in order to assist with recruiting participants.

Materials and procedure

All participants took part in a single testing session in which they completed measures of working memory, a mental capacity task, and an open-ended problem-solving task. The working memory tasks were presented on a computer using E Prime software. The tasks were programmed for the purposes of this study but were all based on well-established working memory measures (e.g.Pickering and Gathercole, 2001; St Clair-Thompson, 2012). The figural intersection test and problem solving task were pen-and-paper based.

The phonological loop component of working memory was assessed using digit recall. Participants were presented with a series of digits one at a time in the centre of the computer screen, and were then asked to recall them in the same order as they were presented by entering their response using the computer keyboard. Following two practice trials participants completed three trials each with 2,3,4,5,6, and 7 digits to remember. Set Sizes were presented in an ascending order i.e. the number of items to remember increased throughout the task. The digits were presented at the rate of one per second, but there was no time limit for recalling the digit sequences. The score awarded was the total number of digits recalled correctly throughout the task. Several studies have reported good reliability of digit recall (e.g.Pickering and Gathercole, 2001).

The visuo-spatial sketchpad component of working memory was assessed using block recall. There were nine blocks or squares on the computer screen, and these were highlighted one at a time for one second each. Participants had to remember the sequence and then click on the squares in the same order by using the computer mouse. Following two practice trials participants completed three trials each with 2,3,4,5,6, and 7 blocks to remember. Again, the score awarded was the total number of blocks recalled correctly throughout the task. Several studies have reported good reliability of block recall (e.g.Alloway et al., 2006).

The central executive component of working memory was assessed using counting recall. In this task participants were asked to count the number of red circles in a series of arrays. The circles were embedded amongst distracters which were red squares and blue circles. At the end of each trial they were then asked to recall the count totals in the same order as they were presented. As for the other working memory tasks there were two practice trials, and then three trials each with 2,3,4,5,6, and 7 counting arrays. Again the score awarded was the total number of correct responses given throughout the task. Counting recall has repeatedly been reported to have good reliability (e.g.St Clair-Thompson, 2012).

After counting recall, participants also completed the backwards digit recall task. This task had the same structure as the digit recall task described above, with the exception that participants were instructed to recall the digit sequences in reverse order. Backwards digit recall has consistently been shown to be a reliable measure of the central executive component of working memory (e.g.St Clair-Thompson, 2010). Importantly, computer presentation ensured that participants did have to maintain the digits to be remembered and reverse the sequence. Following digit presentation, participants had to type their response beginning with the first item (the last that was presented). They could not backspace or return to previously entered items. Participants were also prevented from using pens and paper. Therefore, they could not note the digits during presentation, nor recall them in forwards order by entering their response from right to left.

In the figural intersection test (Pascual-Leone and Burtis, 1974), participants are presented with two sets of geometric shapes. In one set a group of shapes are each presented independently, and in the other they are presented in an overlapping manner so that there is one common area of intersection (see also Overton and Potter, 2011). A participant’s task is to identify and mark the common area of intersection. An example of the figural intersection test is shown in Fig. 1. The test consists of 36 tasks of varying degrees of difficulty. Participants were given a time limit of 20 minutes, and scores were calculated as the number of correct answers given within this time.


Example of the figural intersection test.
Fig. 1 Example of the figural intersection test.

Participants were then given an open-ended chemistry-based problem to solve. The problem did not provide students with all the necessary data, or lead students to a single correct answer. Students were expected to develop a strategy, make estimations, use judgement, and be able to justify their answers. No access to calculators or the Internet was allowed. There was no single correct solution to the problem and several different problem solving strategies were possible. The students’ solutions to the problems were scored on a 0–10 scale as described previously (Overton and Potter, 2011). Participants were then asked to supply their A level chemistry grade (these were not available for a small number of students from outside the UK who had alternative entry qualifications for the degree course). Algorithmic problem solving scores were then extracted from a relevant exam paper. The algorithmic problems involved were based on volumetric analysis and simple physical chemistry calculations that are typically found in the early stages of any chemistry degree.

Results

The means and standard deviations for each task are shown in Table 1. For the digit recall, block recall, and counting recall tasks the mean scores were equivalent to a memory span of between 6 and 7 items, and for the backwards digit recall task the mean scores were slightly lower, equivalent to just under 6 items. The correlations between scores on each task are shown in Table 2. Scores on each task assessing working memory (digit recall, block recall, counting recall, and backwards digit recall) were all significantly correlated to each other. Scores on the figural intersection test were significantly related to scores on the block recall task, but not to scores on the complex working memory tasks tapping the central executive (counting recall or backwards digit recall). Of particular interest to the current study, only scores on the counting recall task were significantly related to algorithmic problems solving and A level chemistry grades. In contrast, scores on the figural intersection test and backwards digit recall were significantly correlated with open-ended problem solving.
Table 1 Means and standard deviations for each task
  Mean Standard deviation
Digit recall (max = 81) 68.85 10.43
Block recall (max = 81) 64.83 10.85
Counting recall (max = 81) 64.93 10.92
Backwards digit recall (max = 81) 58.47 11.47
Figural intersection test (max = 36) 24.71 4.42
Algorithmic problem solving (max = 100) 64.29 14.07
Open-ended problem solving (max = 9) 3.65 2.87

Table 2 Correlations between scores on each task
  1 2 3 4 5 6 7 8
a p < .05. b p < .01.
1. Digit recall —              
2. Block recall .26a —            
3. Counting recall .55b .44b —          
4. Backwards digit recall .42b .42b .50b —        
5. Figural intersection test .15 .33b .18 .20 —      
6. Algorithmic problem solving .00 .20 .27a .17 .06 —    
7. Open-ended problem solving .05 .15 .16 .27a .24a .14 —  
8. A level grade .19 .07 .33 .14 .14 .24a .14 —

Further analyses were then conducted to examine the shared and unique variance of mental capacity and working memory in predicting problem solving and attainment. Due to the debate surrounding the cognitive resources underlying backwards digit recall (e.g.St Clair-Thompson, 2010), here analyses focused on the counting recall task as a complex measure of working memory. In one set of analyses the partial correlations between scores on the figural intersection test and problem solving were computed whilst statistically controlling for scores on the counting recall task. In a second set the correlations between scores on the counting recall task and problem solving were examined whilst partialling out scores on the figural intersection test. The results are shown in Table 3. Whilst controlling for counting recall scores on the figural intersection test did not predict any unique variance in algorithmic problem solving, open-ended problem solving or attainment. However, whilst controlling for scores on the figural intersection test counting recall still predicted variance in algorithmic problem solving and A level chemistry grades.

Table 3 Partial correlations
Partialled out: Figural intersection test Counting recall
Counting recall Figural intersection test
a p < .05. b p < .01.
Algorithmic problem solving .03 .24a
Open-ended problem solving .12 .13
A level chemistry .11 .34b

Discussion

The first aim of the current study was to examine relationships between measures of the central executive, phonological loop, and visuo-spatial sketchpad components of working memory and problem solving in chemistry. The results revealed that scores on counting recall, a complex working memory task assumed to tap the central executive component of working memory, were the best predictor of algorithmic problem solving and previous A level chemistry grades. Furthermore, counting recall was still significantly related to algorithmic problem solving and attainment whilst statistically controlling for scores on the figural intersection test assessing mental capacity. This is consistent with the findings of Roth (1990a) and further suggests that if the purpose of considering students’ mental capacity or working memory is to predict their problem solving and attainment, then researchers should use tasks involving both the processing and storage of information. Many such tasks have been developed within the context of the multiple-component model of working memory (Baddeley, 2000; Baddeley and Hitch, 1974).

It is, however, important to note that scores on tasks assessing the phonological loop and visuo-spatial sketchpad were not significantly related to either algorithmic or open-ended problem solving, or attainment. The results are therefore consistent with previous findings that scores on working memory tasks are typically more closely associated with measures of attainment than scores on short-term memory tasks (e.g.Daneman and Carpenter, 1980; Engle et al., 1999). Therefore if researchers and practitioners are considering working memory, for example how to reduce working memory demands in learning activities (e.g.St Clair-Thompson et al., 2010), they need to focus on requirements to simultaneously process and store information, rather than just considering the overall amount of material to be remembered in working memory. It is, however, worthy of note that performance on these short-term memory tasks is influenced by strategies such as chunking, and thus further research may benefit from exploring the influence of strategies on relationships between short-term memory and problem solving.

The second aim of the current study was to examine whether the same cognitive resources underlie performance on algorithmic and open-ended problem solving. Although scores on counting recall were the best predictor of algorithmic problem solving and attainment, a different pattern of findings emerged for open-ended problem solving. Scores on the figural intersection test and backwards digit recall were significant predictors of open-ended problem solving. These results are consistent with previous findings (e.g.Overton and Potter, 2011; Tsaparlis, 2005). However, scores on the figural intersection test were no longer related to problem solving when statistically controlling for counting recall. This suggests that the relationships with problem solving arose as a result of the shared variance between counting recall and the figural intersection test, and that the figural intersection test is no better at predicting performance on open-ended problem solving than complex working memory tasks such as counting recall.

These results suggest some dissociation between algorithmic and open-ended problem solving. In addition, scores on these two types of problem solving were not significantly correlated to each other (see also Overton and Potter, 2011). This is consistent with previous studies which have found some dissociation between measures of lower-order and higher-order cognitive skills (e.g.Zoller, 2002; Zoller and Tsaparlis, 1997). It appears that open-ended problem solving may rely, in part, upon mental capacity or working memory capacity. However, it is important to note there was still a large amount of variance in performance that was unaccounted for. Further research would therefore benefit from exploring other cognitive constructs which may be important for solving open-ended problems and carrying out other higher level cognitive skills. One possible construct is field independence (e.g.Overton and Potter, 2011; Tsaparlis, 2005). Given the current trend in science education, to encourage teachers to employ methods which develop students’ higher-order cognitive skills (e.g.Zoller, 2012; Zoller and Tsaparlis, 1997), such research could have important implications.

The results also suggest some dissociation between the cognitive resources underlying performance on tests of mental capacity and working memory. In addition to having different associations with problem solving and attainment, scores on the figural intersection test and the counting recall test were not significantly related. It is possible that this is a result of the storage requirements of the two tasks. Although the counting recall task involves the simultaneous storage and processing of information, the figural intersection task has been described as assessing perceptual resources and imposing no storage requirements (see Niaz and Logie, 1993; St Clair-Thompson and Botton, 2009). Performance on the figural intersection test was significantly related to performance on the test assessing the visuo-spatial sketchpad. However, this may be a result of domain-specific visual relationships rather than storage requirements (e.g.Jarvis and Gathercole, 2003). It is also worth of note that the figural intersection test was administered with restricted time. Some participants may have tried a trial and error approach, being successful but using a lot of time for each problem. The other cognitive tasks administered did not impose time constraints. Future research would therefore benefit from a larger scale investigation of relationships between measures of mental capacity and working memory, for example using latent variable modelling, and may benefit from exploring participants’ strategies and also the influences of speed of processing on figural intersection task performance.

Conclusion

Tasks assessing the central executive component of the Baddeley and Hitch (1974) model of working memory are better predictors of algorithmic problem solving and A level grades in chemistry than tasks assessing mental capacity. Further research is needed to explore the shared and unique variance of mental capacity and working memory for predicting other types of problem solving. There is also a dissociation between algorithmic and open-ended problem solving, which may well reflect the distinction between lower-order and higher-order cognitive skills. The findings could have important implications for teaching chemistry. For example, designing assignments and examinations that require higher level cognitive skills, such as open-ended problem solving, may minimise the chance of students failing to achieve as a result of a poor working memory.

Acknowledgements

This work was supported by Nuffield Foundation Social Sciences Small Grant 38972.

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