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    Mathematics Experience and Format-specific Effects in Numerical Cognition


    Koller, Justé Anca (2012) Mathematics Experience and Format-specific Effects in Numerical Cognition. PhD thesis, National University of Ireland Maynooth.

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    Abstract

    A persistent issue in numerical cognition research is how the format of numerical information influences numerical processing. The format-independent view postulates that information from various formats (e.g. ‘3’ or ‘three’) is represented in a uniform numerical code and that format should thus have no influence on number manipulation. The format-specific view assumes separate representational pathways for arabic digits and number words, which come into play during number processing as well as manipulation. Five experiments were undertaken with methods ranging from behavioural measures of reaction time to more refined measures of cognitive processes such as eye-tracking and eventrelated potentials (ERPs). In each experiment, effects of format were investigated at different levels of mathematics experience, in order to examine how the processing of numbers might differ in this regard. The first three experiments focused on basic number processing and processing differences that can occur for arabic digits, number words and quantifier words. In Experiment 1, a modified counting Stroop task was employed to investigate cognitive interference of arabic digits and number words. Participants took longer to respond on incongruent trials (e.g. 4 4 4; how many numbers are present? Correct response: ‘3’) relative to neutral (e.g. * * *; Correct response: ‘3’) and congruent (e.g. 3 3 3; Correct response: ‘3’) trials. Individuals with high mathematics experience showed greater interference on digit trials, whereas no effect of mathematics experience was found for word trials (e.g. three three; respond ‘2’). This suggests that the influence of format on number processing can be regulated by mathematics experience. Experiment 2 investigated this effect further by considering numerical (e.g. 5 2; which number is higher?) and physical size (e.g. 5 2; which number is physically bigger?) comparisons of digit and word stimuli. For both formats, participants responded faster on trials with a large numerical distance (e.g. 2 7) compared to trials with a small numerical distance (e.g. 2 3) suggesting that specific number meanings are accessed spontaneously from digits and number words, however the size congruity effect only occurred for digit stimuli. Individuals with greater mathematics experience showed an overall advantage for numerical comparison, regardless of format. Based on the findings from Experiments 1 and 2, Experiment 3 modified the counting Stroop task (Experiment 1) to investigate if mathematics experience can be related to the processing of quantifier words (e.g. many, few, each). Stimuli were presented as either specific (e.g. both both; correct response ‘2’) or general (e.g. some some) quantifier words and participants were required to count the items on-screen. While the effects were minimal in comparison with Experiment 1, any effects related to the congruity of the stimuli only emerged for the highly mathematics experienced participants, suggesting the involvement of number experience in quantifier word processing, and in turn for extracting number meaning from language in general. As the first three experiments demonstrated format-specific effects in basic number processing, the second part of the thesis investigated these effects for more advanced numerical processing such as arithmetic. The second part of the thesis also employed more refined measures of cognitive processing (eyetracking and event-related potential [ERP] technology) to investigate effects that might not be evident from behavioural data alone. Experiment 4 employed eye tracking technology to compare effects of problem size, operation and format at different levels of mathematics experience. Fixation patterns supported the format-specific view of number processing by suggesting that in comparison with digit-format, word-format impeded the use of direct memory retrieval in arithmetic, an effect that seemed to be more pronounced for individuals with low mathematics experience. Eye-tracking data also supported behavioural data as well as self-report data that have been noted in reports on strategy use in arithmetic. From this, inferences were made regarding the degree to which surface format influences subsequent calculation processes and how this might be moderated by mathematics experience. Experiment 5 investigated the interaction between the encoding and answer-retrieval stages in digit- and word-format arithmetic by separating the presentation of the first operand and the rest of the equation in a true–false verification task (e.g. ‘3’ and ‘x 4 = 12’; correct response ‘true’). Before each test block, participants were told which operation was to follow (addition or multiplication). ERP findings suggested that operands presented in the same format were encoded in the same way, with effects of operation only emerging during the second part of the equation, after participants had seen the operation sign (‘+’ or ‘x’). Regardless of format, the High Maths group showed greater left anterior potentials for multiplication than addition, suggesting an advantage for arithmetic fact retrieval. In the final chapter of the thesis the findings are discussed in relation to existing theoretical accounts on the influence of format in numerical cognition, with specific focus on the benefit of considering mathematics experience in this regard.

    Item Type: Thesis (PhD)
    Keywords: Mathematics experience; format specific effects; numerical cognition;
    Academic Unit: Faculty of Science and Engineering > Psychology
    Item ID: 4759
    Depositing User: IR eTheses
    Date Deposited: 05 Feb 2014 14:46
    URI:

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