Dor Abrahamson (PhD, Learning Sciences, Northwestern University, 2004) is a design-based researcher of mathematical cognition and instruction at the Graduate School of Education, University of California Berkeley, where he runs the Embodied Design Research Laboratory. Abrahamson draws on constructivist–enactivist, sociocultural, and dynamical systems theories to inform the design and evaluation of interactive educational materials. In turn he analyzes empirical data from implementation studies to develop theoretical models of mathematics education and to refine his pedagogical framework, embodied design. In recent projects, Abrahamson has been developing a new form of technologically enabled mathematics learning activities, the Mathematics Imagery Trainer, to explore relations between the learning of movement and mathematics, as well as to evaluate the relevance of movement science to research on mathematics education. Abrahamson has published widely in the leading journals of his field and has received grants from the Spencer Foundation and the National Science Foundation. 

Recent developments in the theory and methods of cognitive science are enabling educational researchers to evaluate empirically the historical thesis that mathematical concepts are grounded in sensorimotor activity. My presentation will survey results from several recent design-research studies that have used eye-tracking techniques to capture the moment at which a student first sees the world in a new way. For the student, this spontaneous perceptual construction serves as a handy solution for coordinating the control of an interactive system. In turn, through cultural mediation this construction evolves into a new way of reasoning that becomes a mathematical concept. I will speculate on implications for educational technology. 

Assistant Professor, Department of Psychology, National Research University Higher School of Economics, Moscow, Russian Federation.
Adjunct Professor, Faculty of Graduate Studies, York University, Toronto, Canada

Arsalidou obtained her PhD at York University and completed her Post-doctoral training at the Department of Diagnostic Imaging at the Hospital for Sick Children in Toronto. Arsalidou directs the NeuropsyLab with students and collaborators at HSE in Moscow and York University in Toronto. Her research focuses on understanding brain-behaviour relations across development with a special interest in mathematical cognition and cognitive giftedness.

According to the world economic forum an estimated 65% of children who are now entering elementary school will graduate to work on completely new occupations that do not exist today (Chapter 1: The Future of Jobs and Skills, 2016). Although, our world is changing rabidly and future labor market requirements are not fully understood, researchers agree that future workforce will have a higher demand for Science, Technology, Engineering and Mathematics (STEM) majors (Fayer et al., 2017). Mathematics is essential for STEM majors and occupations that are progressively more on demand. Traditionally, mathematics has been a core subject in school curricula and research shows that success in math relies in part on the child’s age and their readiness to receive instruction (Agostino et al., 2010). Advances in mathematical performance coincide with the development of fundamental cognitive processes such as mental competence and the protracted development of brain structures such as the pre-frontal cortex (Pascual-Leone et al., 2010). This plenary will discuss brain correlates of mathematical problem solving in adults and children, and potential implications to education.
About twenty years ago, a neurofunctional model was proposed to explain the brain areas that support mental arithmetic, mainly focusing on the functions of the parietal cortex, in posterior parts of the brain (Dehaene & Cohen, 1997; Dehaene et al., 2003). Although this model is based mainly on lesion patient studies, it has stimulated a substantial body of functional magnetic resonance imaging (fMRI) research with healthy individuals. fMRI studies on mathematical cognition typically fall into two categories those that use number tasks (i.e., stimuli are numbers or quantities and participants are asked to make simple magnitude judgements) and those that use calculations tasks (i.e., formal mathematical operations such as addition, subtraction, and multiplication). In quantitative Activation Likelihood Estimation (ALE) meta-analyses we examined neurofunctional activity associated with number and calculation tasks in healthy individuals, children (Arsalidou et al., 2018) and adults (Arsalidou & Taylor, 2011). Data shows that a large overlap exists among brain regions implicated in number and calculation tasks, however the regions in which they differed were most notable, such as distinct areas in prefrontal cortices. Specifically, compared to number tasks, solving calculation tasks elicit more activity in prefrontal brain areas; a difference, which suggests that calculations implicate more core cognitive resources, such as working memory and mental-attention (Arsalidou et al., 2013). Moreover, addition, subtraction and multiplication differentially implicated brain regions in the parietal and prefrontal cortex in the left and right hemispheres. Similar to adults, children activate a varied set of brain areas in established parietal and frontal regions when solving problems with numbers and calculations (Arsalidou et al., 2018). Importantly, children implicate extensively the insular cortex when solving calculation tasks. The insular cortex has not been previously emphasized in its role in mathematical cognition; instead it has best known for its involvement in processes of emotion and motivation (Duerden et al., 2013).
Concluding, this presentation will highlight neuroscience evidence to underline potential implications for teacher’s professional development and students learning experiences, and discuss the importance of Developmental Cognitive Neuroscience in evidence-based education.

Professor Stephen Lerman was a schoolteacher of mathematics before completing a PhD and becoming a teacher educator and researcher in mathematics education. He joined London South Bank University in 1987 and was promoted to a Chair in 1998. He was Chair of British Society for Research into Learning Mathematics (BSRLM) from March 1994 to December 1996, and President of the International Group for the Psychology of Mathematics Education (PME) from July 1995 to July 1998. His research focus has been on sociocultural and sociological perspectives on the teaching and learning of mathematics. Amongst many minor grants for research he was Principal Investigator on an ESRC funded research project from 2001 to 2003 entitled “The Production and Use of Theories of Teaching and Learning Mathematics” and co-Principle Investigator on a European funded research project entitled “Big Ideas in the Teaching and Learning of Mathematics” from 2009 to 2011. He was recipient of the Svend Pederson Award from Stockholm University in 2010. He is Editor-in-Chief of the Encyclopedia of Mathematics Education, first edition published in 2014, second edition due in early 2019. He was appointed Emeritus Professor of Mathematics Education at London South Bank University on retirement in 2012 and is Visiting Professor at the University of the Witwatersrand in Johannesburg, South Africa.

Abstract: Vygotsky’s approach to child development has had, and continues to have, a major impact on teaching and learning and on research in education. In this talk I will show some of that work and its significance in the field of mathematics education, whilst pointing to misunderstandings circulating in the community. Vygotsky died young, aged just 37. It is evident, given how he developed and changed his ideas as he approached death, that he had so much more to say but did not have time to write enough nor elaborate fully his theory. Thus we continue to research him and his ideas, as well as work to apply his insights in our studies of teaching and learning. I will propose some future directions for research in mathematics education building on Vygotsky’s thought.