Zachary Hawes

Zachary Hawes
University of Toronto | U of T · Department of Applied Psychology and Human Development

PhD

About

57
Publications
64,862
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1,620
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Introduction
Zachary Hawes is an Assistant Professor at the University of Toronto's Department of Applied Psychology & Human Development. Zachary does research in Developmental Psychology, Cognitive Science and Mathematics Education.
Additional affiliations
September 2011 - August 2016
University of Toronto
Position
  • Research Officer

Publications

Publications (57)
Chapter
Full-text available
Spatial thinking plays a critical role in the learning, doing, and communication of mathematics. Yet, spatial thinking remains an under-valued, under-recognized, and under-instructed feature of mathematics education. In this chapter, we argue that the teaching and learning of mathematics can be improved through 'spatializing' the curriculum-that is...
Article
Full-text available
Prior research has revealed robust and consistent relations between spatial and mathematical skills. Yet, establishing a causal relation has been met with mixed effects. To better understand whether, to what extent, and under what conditions mathematics performance can be improved through spatial training, we conducted a systematic meta-analysis of...
Article
Full-text available
There is an emerging consensus that spatial thinking plays a fundamental role in how people conceive, express, and perform mathematics. However, the underlying nature of this relationship remains elusive. Questions remain as to how, why, and under what conditions spatial skills and mathematics are linked. This review paper addresses this gap. Throu...
Article
Full-text available
Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation. We used Activation Likelihood Estimation (ALE) to construct quantitative meta-analytic maps synt...
Article
Full-text available
Background: Research into numerical cognition has contributed to a large body of knowledge on how children learn and perform mathematics. This knowledge has the potential to inform mathematics education. Unfortunately, numerical cognition research and mathematics education remain disconnected from one another, lacking the proper infrastructure to...
Preprint
Full-text available
Executive functions (EF) are crucial to regulating learning and are predictors of emerging mathematics. However, interventions that integrate to improve mathematics remain poorly understood. 193 four-year-olds (mean age = 3 years:11 months pre-intervention; 111 female, 69% White) were assessed 5 months apart, with 103 children randomized to an inte...
Chapter
Beyond 1, 2, 3 is a comprehensive collection providing an overview of important topics within the field of early childhood mathematics education in Canada. Chapters include a mix of theory and practice, a set of learning objectives, key terms, and discussion questions. In this chapter, the learning objectives are to: Engage in spatial reasoning as...
Article
Full-text available
There is an emerging consensus that numerical, executive function (EF), and spatial skills are foundational to children's mathematical learning and development. Moreover, each skill has been theorized to relate to mathematics for different reasons. Thus, it is possible that each cognitive construct is related to mathematics through distinct pathway...
Article
Full-text available
A vast body of work highlights executive functions (EFs) as robust correlates of mathematics achievement over the primary and preschool years. Yet, despite such correlational evidence, there is limited evidence that EF interventions yield improvements in early years mathematics. As intervention studies are a powerful tool to move beyond correlation...
Article
Full-text available
Studies show that spatial interventions lead to improvements in mathematics. However, outcomes vary based on whether physical manipulatives (embodied action) are used during training. This study compares the effects of embodied and non-embodied spatial interventions on spatial and mathematics outcomes. The study has a randomized, controlled, pre-po...
Article
Full-text available
Fractions remain a challenging area of school mathematics at every stage of education, with impacts that extend far beyond the school years. For this study, researchers engaged in classroom-based design research over a 6-year period to investigate effective strategies for teaching fractions with Canadian students. Participants included 86 teachers...
Preprint
The current study focused on the collaboration between cognitive scientists and educators to co-develop and progressively refine the Orchestrating Numeracy and The Executive (“The ONE”) Programme, an evidence-based integrated Executive Functions and Mathematics intervention composed of professional development and play-based activities. This iterat...
Preprint
Studies show that spatial interventions lead to improvements in mathematics. However, outcomes vary based on whether physical manipulatives (embodied action) are used during training. This study compares the effects of embodied and non-embodied spatial interventions on spatial and mathematics outcomes. The study has a randomised, controlled, pre-po...
Article
Full-text available
It is well established that spatial thinking is central to discovery, learning, and communication in mathematics, as indicated by convincing evidence that those with strong spatial skills also demonstrate advantages for Science, Technology, Engineering and Mathematics (STEM) performance. Yet, spatial thinking—the ability recall, generate, manipulat...
Article
Full-text available
Mental arithmetic is a complex skill of great importance for later academic and life success. Many neuroimaging studies and several meta-analyses have aimed to identify the neural correlates of mental arithmetic. Previous meta-analyses of arithmetic grouped all problem types into a single meta-analytic map, despite evidence suggesting that differen...
Article
Full-text available
Are number symbols (e.g., 3) and numerically equivalent quantities (e.g., •••) processed similarly or distinctly? If symbols and quantities are processed similarly then processing one format should activate the processing of the other. To experimentally probe this prediction, we assessed the processing of symbols and quantities using a Stroop-like...
Article
Full-text available
Significance Using three large-scale international assessments of student achievement, the current study examined the antecedents of math anxiety and the relation between math anxiety and math achievement across the globe. Results suggest that individual math anxiety is negatively associated with math achievement across the globe. Importantly, we u...
Preprint
Are number symbols (e.g., 3) and numerically equivalent quantities (e.g., •••) processed similarly or distinctly? If symbols and quantities are processed similarly then processing one format should activate the processing of the other. To experimentally probe this prediction, we assessed the processing of symbols and quantities using a Stroop-like...
Article
Full-text available
How are different formats of magnitudes represented in the human brain? We used fMRI adaptation to isolate representations of symbols, quantities, and physical size in forty-five adults. Results indicate that the neural correlates supporting the passive processing of number symbols are largely dissociable from those supporting quantities and physic...
Article
Full-text available
Research in cognitive development has highlighted that early numeracy skills are associated with later math achievement, suggesting that these skills should be targeted in early math education. Here we tested whether tools used by researchers to assess mathematical thinking could be useful in the classroom. This paper describes a collaborative proj...
Article
Full-text available
Higher spatial skills are associated with increased interest, performance, and creativity in STEM fields (Science, Technology, Engineering, Mathematics). However, evidence for causal relations between spatial skills and STEM performance remains scarce. In this study, we test the extent to which mechanical problem solving, a spatially demanding STEM...
Article
Full-text available
The emerging discipline of educational neuroscience stands at a crossroads between those who see great promise in integrating neuroscience and education and those who see the disciplinary divide as insurmountable. However, such tension is at least partly due to the hitherto predominance of philosophy and theory over the establishment of concrete me...
Article
Full-text available
Knowledge mobilization is becoming increasingly important for research collaborations, but few methodologies support increased knowledge sharing. This study provides insights, using a reflective narrative, into a transdisciplinary knowledge-sharing investigation of the connectivity of educational research to that of other disciplines. As an exempla...
Thesis
Full-text available
The principal aims of this thesis were to (1) provide new insights into the cognitive and neural associations between spatial and mathematical abilities, and (2) translate and apply findings from the field of numerical cognition to the teaching and learning of early mathematics. Study 1 investigated the structure and interrelations amongst cognit...
Preprint
Full-text available
This study reports on the design, implementation, and effects of a 16-week (25-hour) mathematics Professional Development (PD) model for K-3 educators (N=45) and their students (N=180). A central goal of the PD was to better integrate numerical cognition research and mathematics education. The results of the first iteration (Year 1), indicated that...
Article
Full-text available
The purpose of the current pilot study was to examine the effects of a teacher-designed and teacher-led numerical board game intervention. Fifty-four 4-to 6-year-olds were randomly assigned to either the number board game intervention or an active control group. Relative to the control group, children who received the number game intervention demon...
Preprint
Full-text available
Humans have the unique ability to represent and manipulate symbols. It is widely believed that this ability is rooted in an evolutionarily ancient system used to process nonsymbolic quantities in the human brain. In the current study, we used an fMRI adaptation paradigm to isolate the representations of symbols, quantities, and physical size in for...
Preprint
Full-text available
Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation. We used Activation Likelihood Estimation (ALE) to construct quantitative meta-analytic maps synt...
Article
Current evidence suggests that numerical, spatial, and executive function (EF) skills each play critical and independent roles in the learning and performance of mathematics. However, these conclusions are largely based on isolated bodies of research and without measurement at the latent variable level. Thus, questions remain regarding the latent s...
Article
A large body of research has documented that females experience more math anxiety than males. Researchers have identified many factors that might explain the relation between sex and math anxiety. In the current study, we present a novel theoretical framework that highlights the importance of examining multiple aspects of processing across differen...
Article
Full-text available
Basic numerical skills provide an important foundation for the learning of mathematics. Thus, it is critical that researchers and educators have access to valid and reliable ways of assessing young children's numerical skills. The purpose of this study was to evaluate the concurrent, predictive, and incremental validity of a two-minute paper-and-pe...
Chapter
Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent research reveals that spatial ability is not innate, but that through experience, education, and intervention, people of all ages can improve their visualization skills—a key component of the engineering habits of mind. In this chapter, we examine the spatia...
Chapter
This chapter focuses on the relations between spatial reasoning, drawing and mathematics learning. Based on the strong link that has been found in educational psychology between children’s finished drawings and their mathematical achievement, and the central importance of diagramming in mathematics thinking and learning, we wanted to study children...
Article
Full-text available
This paper finds its origins in a multidisciplinary research group’s efforts to assemble a review of research in order to better appreciate how “spatial reasoning” is understood and investigated across academic disciplines. We first collaborated to create a historical map of the development of spatial reasoning across key disciplines over the last...
Article
Full-text available
This study describes the implementation and effects of a 32-week teacher-led spatial reasoning intervention in K–2 classrooms. The intervention targeted spatial visualization skills as an integrated feature of regular mathematics instruction. Compared to an active control group, children in the spatial intervention demonstrated gains in spatial lan...
Poster
Summary: Results of Study 1 showed that students in the experimental group outperformed the control group on a comprehensive test of visual-spatial reasoning at post-test. Results also showed a medium within-group effect size (Cohen’s d) on the same measure from pre to post. Teachers in the study also reported deep learning about connections betwee...
Article
Spatial reasoning plays vital roles in choice of and success in STEM careers; yet the topic is scarce in grade-school curricula. We conjecture that this absence may be due to limited knowledge of how spatial reasoning is discussed and engaged across STEM professions. This study aimed to address that gap by asking 19 professionals to comment on a vi...
Book
Full-text available
In Taking Shape, spatial reasoning is greeted and treated as integral to and foundational of all mathematics understanding - present in every action, influenced by and influencing every movement through our structured world, and impacting the language used to make sense of experience. To that end, spatial reasoning is not presented as yet another c...
Book
In Taking Shape, spatial reasoning is greeted and treated as integral to and foundational of all mathematics understanding - present in every action, influenced by and influencing every movement through our structured world, and impacting the language used to make sense of experience. To that end, spatial reasoning is not presented as yet another c...
Article
Full-text available
Abstract Increased efforts are needed to meet the demand for high quality mathematics in early years classrooms. Despite the foundational role of geometry and spatial reason- ing for later mathematics success, the strand receives inad- equate instructional time and is limited to concepts of static geometry. Moreover, early years teachers typically...
Article
Full-text available
The ability to mentally rotate objects in space has been singled out by cognitive scientists as a central metric of spatial reasoning (see Jansen, Schmelter, Quaiser-Pohl, Neuburger, & Heil, 2013; Shepard & Metzler, 1971 for example). However, this is a particularly undeveloped area of current mathematics curricula, especially in North America. In...
Article
Full-text available
Increased efforts are needed to meet the demand for high quality mathematics in early years classrooms. Despite the foundational role of geometry and spatial reasoning for later mathematics success, the strand receives inadequate instructional time and is limited to concepts of static geometry. Moreover, early years teachers typically lack both con...
Article
Full-text available
There is an emerging consensus that spatial thinking is fundamental to later success in math and science. The goals of this study were to design and evaluate a novel test of three-dimensional (3D) mental rotation for 4- to 8-year-old children (N = 165) that uses tangible 3D objects. Results revealed that the measure was both valid and reliable and...
Book
Full-text available
Over the past several years, "spatial reasoning" has gained renewed prominence among mathematics educators, as spatial skills are proving to be not just essential to mathematical understanding but also strong predictors of future success beyond the classroom in fields such as science, technology, and engineering. By exploring both primary and emerg...
Article
Full-text available
The ability to mentally rotate objects in space has been singled out by cognitive scientists as a central metric of spatial reasoning (see Jansen, Schmelter, Quaiser-Pohl, Neuburger, & Heil, 2013; Shepard & Metzler, 1971 for example). However, this is a particularly undeveloped area of current mathematics curricula, especially in North America. In...
Conference Paper
Full-text available
This Research Forum proposal arises from a recent focus on spatial reasoning that began with a multi-year collaborative project amongst a diverse group of researchers (mathematicians, psychologists, mathematics educators) from Canada and the US, and continues to expand with the goal of: mapping out the terrain of established research on spatial rea...
Article
Full-text available
Young students dance their way through a multifaceted differentiated approach to early algebra instruction.

Questions

Question (1)
Question
My partner has suffered from severe migraines for 5 years due to a tannin (type of phenol) sensitivity. After much research she has recently discovered that Xylanase, taken as an oral enzyme with migraine inducing food, allows her to eat these foods without negative repercussions. This has led us to trying to figure out how she can build up xylan-degrading microbes in the gut, as she assumes this is where the problem stems from.
Some migraine inducing foods for her: All nuts, all beans, all seeds, all berries, most fruit, coffee, tea, chocolate, many spices, anything with additives.
Thank you for any insight you may be able to provide!

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