Koller, Justé Anca
(2012)
Mathematics Experience and Formatspecific Effects in
Numerical Cognition.
PhD thesis, National University of Ireland Maynooth.
Abstract
A persistent issue in numerical cognition research is how the format of
numerical information influences numerical processing. The formatindependent
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 formatspecific 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 eyetracking 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 onscreen. 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 formatspecific 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 eventrelated 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
formatspecific view of number processing by suggesting that in comparison with
digitformat, wordformat impeded the use of direct memory retrieval in
arithmetic, an effect that seemed to be more pronounced for individuals with low
mathematics experience. Eyetracking data also supported behavioural data as
well as selfreport 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
answerretrieval stages in digit and wordformat 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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