The Neurocognitive Underpinnings of Arithmetic in Children and Adults

185 Pages·2017·5.54 MB·English

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Anna A. Matejko, The University of Western Ontario
Supervisor: Dr. Daniel Ansari, The University of Western Ontario
A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree
in Psychology
© Anna A. Matejko 2016
Follow this and additional works at: https://ir.lib.uwo.ca/etd
Part of the Developmental Psychology Commons
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Matejko, Anna A., "The Neurocognitive Underpinnings of Arithmetic in Children and Adults: Examining the
Roles of Domain General and Domain Specific Abilities" (2016). Electronic Thesis and Dissertation
Repository. 4162.
https://ir.lib.uwo.ca/etd/4162
This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted
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Abstract
What are the cognitive underpinnings of arithmetic and how do they contribute to
individual differences in children’s calculation abilities? Behavioural research has provided
insights into which domain general (e.g., working memory) and domain specific (e.g.,
symbol-quantity associations) competencies are important for the acquisition of arithmetic
skills. However, how domain general and domain specific skills are related to arithmetic at
the neural level remains unclear. This thesis investigates the interplay between arithmetic and
both domain general and specific competencies in the brain.
In Chapter 2 I examine how visuo-spatial working memory (VSWM) networks
overlap with those for arithmetic in children and adults. While both children and adults
recruited the intraparietal sulcus (IPS) for VSWM and arithmetic, children showed more
focal activation within the right IPS, whereas adults recruited the bilateral IPS. These
findings indicate that the regions underlying VSWM and arithmetic undergo age-related
changes and become more left-lateralized in adults.
Chapter 3 provides evidence that basic number processing networks overlap with
those for arithmetic in adults and children. Number processing and arithmetic elicited
conjoint activity in the IPS in children and adults. Their overlap was also related to arithmetic
problem size (i.e., how demanding the problems were of time-intensive procedural
strategies); both arithmetic and basic number processing recruited the IPS when the problems
relied on procedural strategies that likely involve the manipulation of numerical quantities.
In Chapter 4 I investigate how individual differences in domain general and domain
specific competencies relate to the recruitment of the IPS during arithmetic. Both VSWM
and symbolic number skills correlated with brain activity in the IPS, however, the
relationships depended on the index of brain activity used. VSWM was related to a neural
index of arithmetic complexity (neural problem size effect), whereas symbolic number skills
were related to overall arithmetic activity (small and large problems).
The present thesis provides the first empirical evidence that shows how domain
general and domain specific abilities are related to the neural basis of arithmetic in children
and adults. Moreover, this thesis suggests the IPS plays a multifaceted role during arithmetic
and cannot be attributed to one function.

Keywords

Arithmetic, domain general, domain specific, visuo-spatial working memory, number
processing, fMRI, individual differences, children
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Co-Authorship Statement
The work presented in this doctoral thesis was designed and written in collaboration
with my advisor, Dr. Daniel Ansari. For each of the studies within this thesis Dr. Ansari
contributed to the design, analysis, and interpretation of the findings. Though this thesis is
my own work, it should be acknowledged that Dr. Ansari contributed to the revising and
editing of each of the chapters.
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Acknowledgments
First and foremost, I would like to express how grateful I am for the mentorship and
guidance of Dr. Daniel Ansari. Thank you for your generosity, infectious enthusiasm for
research, and tireless support. I cannot imagine a more supportive and encouraging
supervisor. I am grateful to have a mentor who is so devoted to the success and well being of
his students. Thank you for challenging me to be a better scientist, for always being there
when I feel lost, and for being a life-long role model.
I would also like to express my gratitude to my examining committee, Dr. Bert De
Smedt, Dr. Marc Joanisse, Dr. J. Bruce Morton, and Dr. Derek Mitchell as well as Dr. Lisa
Archibald who served on my advisory committee.
I am also very grateful to the current and former members of the Numerical Cognition
Lab, as well as the inhabitants of Room 215: Bea Goffin, Ian Holloway, Stephanie Bugden,
Stephan Vogel, Nadia Nosworthy, Christian Battista, Ian Lyons, Rebecca Merkley, Tali
Leibovich, Celia Goffin, Moriah Sokolowski, Zachary Hawes, and Niki Kamkar. Thank you
for being my support system and for giving me the gift of laughter in the happiest and most
difficult moments. Your smiles and words of encouragement propel me forward and always
brighten my day. It is a pleasure working with such brilliant, positive, and inspiring people.
A special thank you to Jane Hutchison who spent many hours helping me collect,
analyze, and score data for this dissertation. I feel fortunate to have worked with such a
talented student and research assistant.
I am also indebted to the Mathematical and Cognitive Development lab at the
University of Alberta: Dr. Jeffrey Bisanz, Dr. Rebecca Kong, and Dr. Carley Piatt. Without
the mentorship of Dr. Jeffrey Bisanz I would not be where I am today. I will be forever
grateful for your continued guidance, for challenging me to think deeply about child
development, and for encouraging me to continue pursuing my interests outside of research.
To my first role-model, Dr. Rebecca Kong, thank you for being patient with me when I was
beginning, and for sharing your implicit and explicit knowledge about graduate school. To
Dr. Carley Piatt, I gain strength from your enthusiasm for learning, and am so grateful for
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your guidance and friendship. Thank you for teaching me to ask questions, stay positive, and
to savor the joys in life.
To the D-Eazies, Karen Zhang and Kyleigh Schraeder: thank you for being my
cheerleaders, for holding me accountable to my writing goals, and for providing unending
support and words of encouragement. Every day I spent working on my dissertation with you
was a joy.
It is impossible to express enough gratitude to my parents, my sister, and Geoff.
Thank you for helping me find a path when I feel lost, for celebrating my successes and
cushioning my failures. To my parents, thank you for teaching me to be curious about the
world and for imparting me with the skills to tackle the most difficult problems. Also, thank
you for always answering my panicked phone calls, no matter what time of day or night. To
my wonderful sister Emily, thank you for keeping me laughing and reminding me about the
most important things in life. I always look forward to the moment when you call and I can
leave my desk to talk to you. To Geoff, thank you for always seeing my strengths, even when
I do not see them. I am so grateful for your hugs, patience, delicious dinners, and endless
words of encouragement. I would not have been able to complete this dissertation without
your love and support.

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Table of Contents
Abstract ................................................................................................................................. i

Co-Authorship Statement .................................................................................................. iii

Acknowledgments .............................................................................................................. iv

Table of Contents ............................................................................................................... vi

List of Tables ....................................................................................................................... x

List of Figures ..................................................................................................................... xi

List of Appendices ............................................................................................................ xiv

Chapter 1 ............................................................................................................................. 1

1
  General Introduction ....................................................................................................... 1

1.1
  Behavioural Predictors of Arithmetic Skills ............................................................ 2

1.1.1
  Domain Specific Predictors of Arithmetic .................................................. 3

1.1.2
  Domain General Predictors of Arithmetic ................................................... 5

1.1.3
  Combining Domain Specific and Domain General Predictors of
Arithmetic. ................................................................................................... 7

1.2
  Neural Basis of Arithmetic ...................................................................................... 8

1.2.1
  Developmental Changes in the Arithmetic Network ................................. 10

1.2.2
  How Strategies Impact the Calculating Brain ........................................... 11

1.2.3
  The Role of Domain General and Domain Specific Abilities in the
Arithmetic Network ................................................................................... 12

1.3
  Summary, Outstanding Questions, and Overview of the Current Thesis .............. 18

1.4
  References ............................................................................................................. 21

Chapter 2 ........................................................................................................................... 31

2
  Age-related changes in the neural processing of visuo-spatial working memory and
arithmetic ...................................................................................................................... 31

2.1
  Introduction ........................................................................................................... 31

2.2
  Method ................................................................................................................... 35

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2.2.1
  Participants ................................................................................................ 35

2.2.2
  Procedure ................................................................................................... 36

2.2.3
  Experimental Tasks & Design ................................................................... 36

2.2.4
  MRI data acquisition ................................................................................. 39

2.2.5
  Analyses .................................................................................................... 40

2.3
  Results ................................................................................................................... 41

2.3.1
  Behavioural Performance .......................................................................... 41

2.3.2
  Brain Imaging ............................................................................................ 43

2.4
  Discussion .............................................................................................................. 51

2.4.1
  Age-related Changes in the Parietal Cortex for VSWM and Arithmetic .. 52

2.4.2
  Relationships Between Visuo-spatial Processing and Arithmetic ............. 55

2.4.3
  Limitations ................................................................................................. 57

2.4.4
  Conclusions ............................................................................................... 58

2.5
  References ............................................................................................................. 59

Chapter 3 ........................................................................................................................... 66

3
  Investigating the shared neural circuits for arithmetic and basic number processing in
children and adults ........................................................................................................ 66

3.1
  Introduction ........................................................................................................... 66

3.1.1
  Shared Networks for Number Processing and Arithmetic ........................ 67

3.1.2
  How Strategies Influence the Relationship Between Arithmetic and
Number Processing .................................................................................... 69

3.1.3
  The Present Study ...................................................................................... 70

3.2
  Method ................................................................................................................... 71

3.2.1
  Participants ................................................................................................ 71

3.2.2
  Procedure ................................................................................................... 71

3.2.3
  Experimental Tasks & Design ................................................................... 72

3.2.4
  MRI Data Acquisition ............................................................................... 75

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3.2.5
  Analyses .................................................................................................... 75

3.3
  Results ................................................................................................................... 77

3.3.1
  Behavioural Performance .......................................................................... 77

3.3.2
  Brain Imaging ............................................................................................ 81

3.4
  Discussion .............................................................................................................. 90

3.4.1
  Limitations ................................................................................................. 93

3.4.2
  Conclusions ............................................................................................... 94

3.5
  References ............................................................................................................. 95

Chapter 4 ......................................................................................................................... 100

4
  Individual differences in children’s domain specific and domain general abilities relate
to brain activity within the intraparietal sulcus during arithmetic .............................. 100

4.1
  Introduction ......................................................................................................... 100

4.2
  Method ................................................................................................................. 105

4.2.1
  Participants .............................................................................................. 105

4.2.2
  Procedure ................................................................................................. 105

4.2.3
  Experimental Tasks & Design ................................................................. 106

4.2.4
  MRI Data Acquisition ............................................................................. 110

4.2.5
  Analyses .................................................................................................. 111

4.3
  Results ................................................................................................................. 113

4.3.1
  Behavioural Assessment: Domain General and Domain Specific Predictors
of Math Achievement .............................................................................. 113

4.3.2
  Brain Imaging .......................................................................................... 116

4.4
  Discussion ............................................................................................................ 120

4.4.1
  Limitations & Future Directions ............................................................. 125

4.4.2
  Conclusions ............................................................................................. 126

4.5
  References ........................................................................................................... 127

Chapter 5 ......................................................................................................................... 135

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5
  General Discussion ..................................................................................................... 135

5.1
  Integration of Findings ........................................................................................ 135

5.1.1
  Summary of Thesis and Common Themes ............................................. 136

5.2
  Domain General and Domain Specific Contributions to the IPS During Arithmetic
138

5.2.1
  Domain Specific Contributions ............................................................... 138

5.2.2
  Domain General Contributions ................................................................ 140

5.2.3
  Implications for Developmental Dyscalculia .......................................... 141

5.3
  Age-related Changes and Similarities ................................................................. 142

5.3.1
  Lateralization of Function ....................................................................... 143

5.3.2
  Cognitive Similarities Across Age .......................................................... 144

5.4
  Limitations and Future Directions ....................................................................... 146

5.5
  Final Remarks ...................................................................................................... 148

5.6
  References ........................................................................................................... 149

Appendices ...................................................................................................................... 157

Curriculum Vitae ............................................................................................................. 164

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