Cognitive styles and solution strategies in arithmetic

The present project aims to investigate the influence of an individual`s cognitive style on problem solving. Most problems in daily life are complex and can often be solved in more than one way. However, as individuals differ with regard to their potentials, habits and preferences, efforts to make problem solving more efficient will have to take interindividual differences into account. In the last decade, our knowledge about the function of the brain has advanced greatly, but most research has, so far, focused mainly on the commonalities in information processing, rather than on the causes and consequences of individual differences. We propose a series of brain imaging (fMRI/EEG) studies to shed light on the neural basis of individual`s cognitive styles and preferred solution strategies. Arithmetic is an ideal domain to investigate complex problem solving, because it allows the systematic creation of comparatively homogeneous problems with different levels of difficulty. Arithmetic problems can often be solved correctly in more than one way. For example, when asked to calculate 9 x 37, one might add the results of the intermediate products 9 x 30 and 9 x 7 or solve this problem by first putting a `0` after 37 (multiplying with 10) and then subtracting 37 from the result. Although skilled adults are usually aware of both solution strategies, they differ with regard to how much they habitually make use of them. Furthermore, individuals might also differ with regard to the degree to which they employ different cognitive domains in solving a complex problem. For example, in mental addition, some individuals (visualizers) report visualizing the numbers that are to be added, while others (verbalizers) claim to solve the problem purely verbally without visualizing anything. In the present project, we have two general aims. Our first aim is to investigate the neurobiological basis of interindividual differences in cognitive styles and solution strategies while solving complex problems in arithmetic. Our second aim is to investigate whether and how different ways to solve a problem engange different brain areas to understand the neural basis of how cognitive style might lead to certain problem-solving preferences and strategies. We also hope to exploit the investigation of interindividual differences to investigate the domain- specificity of the brain areas subserving number processing and arithmetic. For example, it is unclear, whether brain areas with an assumed affinity to the verbal domain, such as the left angular gyrus, will show a systematic modulation depending on the degree of verbalization involved in a particular solution strategy or being due to a verbal cognitive style. If no such systematic modulation is observed, it could be concluded that the brain areas involved in arithmetic processing are domain-general rather than domain-specific.

The vanishing of unskilled labour in modern society demands ever more sophisticated problem solving skills from the individual. The ability to solve complex problems determines ever more individual welfare and career possibilities. Often, however, there are different ways to arrive at the solution of a complex problem. The present project investigated the influence of cognitive style (visual vs. verbal cognitive style) and different solution strategies in arithmetic problem solving. Arithmetic allows the systematic creation of homogeneous problems at different degrees of difficulties and is thus well suited to investigate complex problem solving. Individuals differ in complex problem solving for example in their degree of using the visual or verbal sensory modality. When asked to add two numbers in their head, some individuals (visualizers) will imagine the numbers as written on a sheet of paper whereas others deny visual imagination and claim to solve the problem verbally (verbalizers). Furthermore, often there are more than one way to arrive at the solution of a complex problem. For example, 37 x 9 can be solved by adding the simpler problems 30 x 9 and 7 x 9. Another possibilty is to multiply 37 by 10 and then subtract 37. We used brain imaging techniques such as electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) to identify brain areas involved in different cognitive styles and arithmetic solution strategies. We found that individuals with a verbal cognitive style activated brain areas relevant for language whereas individual with a visual cognitive style activated brain areas involved in visual processing. However, these differences are relatively small. Furthermore, we could detect no influence of cognitive style on strategy selection and solution behavior. These results suggest that there are different cognitive styles in problems solving, but also that they are of little practical consequence. It is therefore probably not necessary to particularly address an individual student's cognitive style in teaching.