WWeesstteerrnn UUnniivveerrssiittyy SScchhoollaarrsshhiipp@@WWeesstteerrnn Electronic Thesis and Dissertation Repository 8-23-2013 12:00 AM NNeeuurraall cciirrccuuiittss iinnvvoollvveedd iinn mmeennttaall aarriitthhmmeettiicc:: EEvviiddeennccee ffrroomm CCuussttoommiizzeedd AArriitthhmmeettiicc TTrraaiinniinngg Christian Battista, 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 Neuroscience © Christian Battista 2013 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Cognitive Neuroscience Commons RReeccoommmmeennddeedd CCiittaattiioonn Battista, Christian, "Neural circuits involved in mental arithmetic: Evidence from Customized Arithmetic Training" (2013). Electronic Thesis and Dissertation Repository. 1560. https://ir.lib.uwo.ca/etd/1560 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact [email protected]. NEURAL CIRCUITS INVOLVED IN MENTAL ARITHMETIC: EVIDENCE FROM CUSTOMIZED ARITHMETIC TRAINING (Thesis format: Integrated Article) by Christian Battista Graduate Program in Neuroscience A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy The School of Graduate and Postdoctoral Studies The University of Western Ontario London, Ontario, Canada © Christian Battista 2013 Abstract An arithmetic training study was conducted using a novel paradigm known as Customized Arithmetic Training (CAT). Using the CAT system, self-reports obtained from the participants were used to generate individually tailored problem sets. These problem sets balanced strategy use such that each participant started with an equal amount of problems solved by fact retrieval (e.g., 2 + 2 = 4) and an equal amount of problems solved by procedural calculation (e.g., 34 + 37). Following the training period, participants solved trained and untrained problems from their customized arithmetic sets while undergoing an fMRI scan, after which they again provided self-reported strategy. Through the use of the CAT paradigm, which tracks (for the first time) arithmetic strategy both pre- and post-training, the neural correlates of arithmetic learning were examined by separating calculated problems which became memorized through training from problems that were rehearsed but did not show a shift in strategy. This analysis produced results consistent with previous studies of arithmetic training, namely a shift from widespread fronto-parietal activation to focal activation of the angular gyrus. However, it also produced several novel findings relating to neural correlates of mental arithmetic, namely an association between right anterior hippocampus in fact retrieval as well as evidence of a temporal gradient which affected brain activity when comparing new vs old arithmetic facts. Furthermore, analysis of training effects on calculated problems (which did not become memorized) revealed a modulation of activity in the putamen, a structure commonly associated with the procedural memory system. Keywords Numerical Cognition, Episodic Memory, Procedural Memory, Training, Mental Arithmetic, fMRI, Neuroimaging, Cognitive Neuroscience ii Acknowledgments To me, good science means walking the very fine line between the trivial and the impossible. I’d like to thank my supervisors; Dr. Daniel Ansari and Dr. Bruce Morton for helping me maintain a balance between these two extremes. I’d also like to acknowledge the valuable input I received from the other members of advisory committee; Dr. Stefan Köhler and Dr. Brian Corneil, as well as my examination committee; Dr. Roy Eagleson, Dr. Mark Fenske, Dr. Paul Gribble, and Dr. Ken McRae. Lastly, I must tip my hat to Dr. Ian Lyons, who indulged me in many passionate discussions regarding the interpretation of my data set on what seems to have been countless Friday evenings at the Grad Club. None of this very interesting data would have been collected without the help of several hard-working research assistants who never ceased to impress me with their diligence and dedication; Jordan Lass, Jordan Rozario, Michelle Hurst, and Heather Carlson. I wish you all the best and will surely come looking for favors once you become accomplished scientists yourselves. There are many factors involved in the successful completion of one’s Doctorate, and some of these lie outside the walls of the academy, and so two other sources of inspiration in my life must also be acknowledged. Christopher Wallace, whose words throughout the dissertation process were a constant reminder of the importance of work/life balance - your insights helped me to remain focused during the more taxing moments of my data analysis. And finally, Anthony Ray, who inspired me from a young age to pursue what I was interested in and attracted to, rather than to do what was approved and expected by those around me, and above all, to be honest about it. iii Dedication To my parents, Richard and Andrea. Thanks for all the love and support all these years. iv Table of Contents Abstract ............................................................................................................................... ii Acknowledgments.............................................................................................................. iii Dedication .......................................................................................................................... iv Table of Contents ................................................................................................................ v List of Tables ...................................................................................................................... x List of Figures .................................................................................................................... xi List of Appendices ........................................................................................................... xiv Chapter 1 ............................................................................................................................. 1 1 Introduction to the study of mental arithmetic ............................................................... 1 1.1 Models of mental arithmetic ................................................................................... 2 1.2 Studies of arithmetic learning/training.................................................................... 5 1.3 Individual differences ............................................................................................. 6 1.4 Current project ...................................................................................................... 10 1.5 Chapter 2 outline ................................................................................................... 11 1.6 Chapter 3 outline ................................................................................................... 11 1.7 Chapter 4 outline ................................................................................................... 12 1.8 References ............................................................................................................. 13 Chapter 2 ........................................................................................................................... 17 2 The development of the Customized Arithmetic Training program ............................ 17 2.1 Introduction ........................................................................................................... 17 2.1.1 Strategies for solving arithmetic problems ............................................... 17 2.1.2 Assessing strategy ..................................................................................... 18 2.1.3 Heterogeneity of strategy use .................................................................... 18 2.1.4 Training and strategy ................................................................................ 19 v 2.1.5 Current study ............................................................................................. 20 2.2 Methods – Experiment 1 ....................................................................................... 21 2.2.1 Objective ................................................................................................... 21 2.2.2 Participants ................................................................................................ 22 2.2.3 Procedure .................................................................................................. 23 2.3 Results - Experiment 1 .......................................................................................... 27 2.3.1 Pre-training – Voice production task ........................................................ 27 2.3.2 Pre-training – Choice task ......................................................................... 30 2.3.3 Post-training – Voice production task....................................................... 31 2.4 Methods - Experiment 2........................................................................................ 33 2.4.1 Objective ................................................................................................... 33 2.4.2 Participants ................................................................................................ 34 2.4.3 Procedure .................................................................................................. 34 2.5 Results - Experiment 2 .......................................................................................... 35 2.5.1 Pre-training choice task............................................................................. 35 2.5.2 Post-training – Choice task ....................................................................... 37 2.6 Discussion ............................................................................................................. 39 2.6.1 Limitations and improvements to the paradigm ....................................... 40 2.7 References ............................................................................................................. 42 Chapter 3 ........................................................................................................................... 44 3 Neural correlates of arithmetic fact retrieval ............................................................... 44 3.1 Introduction ........................................................................................................... 44 3.1.1 The influence of training ........................................................................... 44 3.1.2 The influence of strategy (retrieval vs. calculation) ................................. 45 3.1.3 Temporal gradients affecting semantic memories .................................... 46 vi 3.1.4 Current Study ............................................................................................ 47 3.1.5 Hypotheses ................................................................................................ 47 3.2 Methods................................................................................................................. 48 3.2.1 Participants ................................................................................................ 48 3.2.2 Experimental procedure ............................................................................ 49 3.2.3 Stimuli ....................................................................................................... 52 3.2.4 fMRI data acquisition ............................................................................... 52 3.2.5 fMRI data preprocessing ........................................................................... 53 3.2.6 Thresholding ............................................................................................. 53 3.3 Results - Behavioral .............................................................................................. 53 3.3.1 Calibration................................................................................................. 53 3.3.2 Post training fMRI .................................................................................... 55 3.4 Results - fMRI....................................................................................................... 56 3.4.1 Strategy (no training) ................................................................................ 57 3.4.2 Training effects ......................................................................................... 59 3.4.3 Temporal gradients ................................................................................... 60 3.4.4 Difficulty effects ....................................................................................... 63 3.5 Discussion ............................................................................................................. 67 3.5.1 Strategy effects (fact retrieval vs. calculation) ......................................... 68 3.5.2 Training effects ......................................................................................... 68 3.5.3 Temporal gradients ................................................................................... 69 3.5.4 Interpreting the MTL activation................................................................ 69 3.5.5 How arithmetic facts are stored ................................................................ 70 3.5.6 Limitations ................................................................................................ 72 3.5.7 Future directions ....................................................................................... 72 vii 3.6 References ............................................................................................................. 74 Chapter 4 ........................................................................................................................... 78 4 Strategy-specific training effects.................................................................................. 78 4.1 Introduction ........................................................................................................... 78 4.1.1 Training ..................................................................................................... 78 4.2 Current Study ........................................................................................................ 79 4.3 Hypotheses ............................................................................................................ 79 4.4 Methods................................................................................................................. 80 4.5 Results - Behavioral .............................................................................................. 81 4.5.1 Main effect of Strategy ............................................................................. 81 4.5.2 Main effect of Training ............................................................................. 81 4.5.3 Training x Strategy interaction ................................................................. 81 4.6 Results – Post training fMRI................................................................................. 82 4.6.1 Main effect of strategy .............................................................................. 82 4.7 Discussion ............................................................................................................. 89 4.7.1 Main effects of strategy and training ........................................................ 90 4.7.2 Interactions ................................................................................................ 91 4.7.3 Limitations and future directions .............................................................. 94 4.7.4 Conclusion ................................................................................................ 94 4.8 References ............................................................................................................. 96 Chapter 5 ........................................................................................................................... 98 5 Conclusion ................................................................................................................... 98 5.1 Fact Retrieval ...................................................................................................... 101 5.2 Calculation .......................................................................................................... 103 5.3 Future Directions ................................................................................................ 103 viii 5.3.1 Developmental differences ..................................................................... 103 5.3.2 Dynamic systems .................................................................................... 104 5.3.3 Structural correlates of arithmetic learning ............................................. 105 5.4 Summary ............................................................................................................. 107 5.5 References ........................................................................................................... 108 Appendices ...................................................................................................................... 111 Curriculum Vitae ............................................................................................................ 113 ix