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Doctor of Philosophy




Ansari, Daniel


How does the brain represent numerical symbols (e.g., Arabic digits)? Activity in left parietal regions correlates with symbolic number processing. Research with functional resonance imaging adaptation (fMRI-A) indicates that the intraparietal sulcus (IPS) exhibits a rebound (increase in activation) effect when a repeatedly presented number is followed by a new number. Importantly, this rebound effect is modulated by numerical ratio as well as the difference between presented numbers (distance). This ratio-dependent rebound effect could reflect a link between symbolic numerical representation and an approximate number system (ANS). In this doctoral dissertation, fMRI-A is used to investigate mechanisms underlying symbolic number representation.

The first study investigates an alternative to the ANS hypothesis of symbolic number representation: could the positional relations between ordered symbols (e.g., letters, numbers) explain activity observed in the parietal cortex for number symbols? The predicted distance-dependent rebound effect is exhibited in bilateral IPS for number symbols. This effect is not found for letters (which, like numbers, can be represented using an ordered sequence – the alphabet). The contrast between numbers and letters reveals greater activity for numbers in the left inferior parietal lobule. The hypothesis that general ordinal mechanisms underpin neural parametric recovery in the IPS is not supported.

What does the development of symbolic number representation look like in the brain? In the second study, I replicate Vogel et al. (2015; n=19) with a larger sample (n=45) of 6-14-year-olds. While Vogel et al. found a correlation between age and the ratio-dependent rebound effect in the left IPS, my data suggest an age-invariant, ratio-dependent rebound effect in bilateral IPS. Therefore, findings from Vogel et al. were not replicated.

The final study asks: does handedness of participants play a role in the neural lateralization of symbolic number representation? Right-handers demonstrate the predicted left-lateralized rebound effect within the IPS. When left- and right-handed groups are compared, results do not suggest group differences in laterality. These findings do not support the hypothesis that handedness plays a role in neural lateralization of symbolic number processing.

Results from these studies are discussed in terms of theoretical implications for symbolic numerical representations in the brain.

Summary for Lay Audience

Representing numerical information symbolically (e.g., with Arabic digits) is integral to modern society. Learning to understand number symbols involves learning the digit ‘3’ means 3 items (e.g., ···). This understanding is a necessary step towards learning more complex math. The use of number symbols is too recent an invention for our brains to have been evolved for this function. So how does the human brain learn to represent numerical symbols?

Using functional magnetic resonance imaging (fMRI), we can measure brain activity while people look at numbers. Research using fMRI has found that part of the brain, the intraparietal sulcus (IPS), is of particular importance for representing numbers. However, there are many outstanding questions surrounding the mechanisms underlying symbolic number representation. In this thesis, fMRI was used to address some of these outstanding questions.

In the first study, we examined whether brain activity looked similar for number symbols and letters. We found that letters and numbers did not display the same patterns of activity in the brain. However, a follow-up study where participants completed computer tasks outside of the MRI indicated that letters and numbers did show similar patterns in response time data.

The second study examined how children develop an understanding of number symbols. Children ages 6-to-14 looked at symbolic numbers using fMRI. We found that children demonstrated a similar pattern of activity in the IPS across the entire age group. This response was similar to that observed in previous studies with adults.

In the last study, we were interested in whether, through practicing to write numbers, the handedness of people may be related to how numbers are represented in the brain. Typically, in neuroimaging research, left-handed people are excluded from participating in order to reduce the noisiness of the data. We compared brain activity in response to number symbols in a group of left-handed participants to right-handed participants. Handedness of participants was not found to be related to brain activity for number symbols.

This research helps us to better understand how, over the course of learning and development the brain comes to be able to understand number symbols.

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Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.