Educational Research Review 5 (2010) 97–105

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Position paper

Cognitive neuroscience meets mathematics education Bert De Smedt a,∗ , Daniel Ansari b , Roland H. Grabner c , Minna M. Hannula d , Michael Schneider c , Lieven Verschaffel a a b c d

Department of Educational Sciences, Katholieke Universiteit Leuven, Belgium Department of Psychology, University of Western Ontario, Canada Institute for Behavioural Sciences, ETH Zurich, Switzerland Centre for Learning Research, University of Turku, Finland

1. Executive summary While there has been much theoretical debate concerning the relationship between neuroscience and education, researchers have started to collaborate across both disciplines, giving rise to the interdisciplinary research field of neuroscience and education. The present contribution tries to reflect on the challenges of this new field of empirical enquiry. Recently, an EARLI Advanced Study Colloquium (ASC) entitled Cognitive Neuroscience Meets Mathematics Education was held from 25 to 29 March, 2009 in Brugge (Belgium), in which teams of cognitive neuroscientists and educational researchers presented their collaborative work. This workshop thus focused on empirical research at the crossroads of educational research and cognitive neuroscience within the domains of numeracy and mathematics. Taking the ASC as the background of our discussion, we present research on mathematics learning from neuroscientific as well as behavioural and educational perspectives to highlight the issues that are currently being faced in the emerging field of neuroscience and education. We contend that this field should be conceived as a two-way street with multiple bi-directional and reciprocal interactions between educational research and cognitive neuroscience. On the one hand, cognitive neuroscience might influence research in mathematics education by (a) contributing to our understanding of atypical numerical and mathematical development, (b) paving the way for setting up behavioural experiments and (c) generating findings about learning and instruction that cannot be uncovered by behavioural research alone. On the other hand, educational research affects cognitive neuroscience research by (a) helping to define the variables of interest and (b) investigating the effects of instruction on the neural correlates of learning. This interdisciplinary endeavour will allow for a better understanding of how people learn. 2. Introduction There has been much ado about the relationship between neuroscience and education. This is highlighted by the recent publication of several special issues in Educational Research (Howard-Jones, 2008), Cortex (Della Sala, 2009) and Journal of Philosophy in Education (Cigman & Davis, 2008) with theoretical accounts of the relationship between both fields and with reflections on how both fields can or cannot be integrated (see also Ansari & Coch, 2006; Stern, 2005; Varma, McCandliss, & Swartz, 2008). In addition to these theoretical considerations, researchers have begun to collaborate across both disciplines and neuroscience and education is becoming an interdisciplinary research field. This development is also witnessed by the foundation of new research Centres of Educational Neuroscience at the universities of Cambridge and London, the formation of a new International Mind, Brain and Education Society (http://www.imbes.org/), as well as the Graduate Program in Mind, Brain and Education at the Graduate School of Education at Harvard University

∗ Corresponding author at: Vesaliusstraat 2, Box 3765, 3000 Leuven, Belgium. Tel.: +32 16 32 57 05; fax: +32 16 32 59 33. E-mail address: [email protected] (B. De Smedt). 1747-938X/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.edurev.2009.11.001

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(http://www.gse.harvard.edu/academics/masters/mbe/) and an undergraduate program in Education focused on Education and Neuroscience at Dartmouth College. The present contribution tries to reflect on the challenges facing this interdisciplinary research field. Our aim is not targeted at proposing direct applications for teaching and intervention. This is considered by many a bridge too far (Bruer, 1997; Goswami, 2006). Rather, we would like to take a research perspective and reflect on possible ways to build strong bridges between neuroscientific and educational research. In doing so, we narrow down the focus from neuroscience and education to cognitive neuroscience and mathematics education. On the one hand, we focus on cognitive neuroscience because this sub-field of neuroscience is closest to educational research, given its focus on the neural mechanisms underlying human behaviour and cognition. Indeed, the essential role of cognition as a bridge between neuroscience and education, or between brain and behaviour, has been stressed for a long time (e.g., Bruer, 1997; Howard-Jones, 2008). Cognitive neuroscience uses measures of brain activity, such as functional Magnetic Resonance Imaging (fMRI) (e.g., Huettel, Song, & McCarthy, 2004) or ElectroEncephaloGraphy (EEG) (e.g., Niedermeyer & Lopes da Silva, 2005) to understand cognitive function and interprets brain activity in the context of psychological theories of the mind (e.g., Cacioppo, Berntson, & Nusbaum, 2008). It is therefore close to research on learning and instruction, which is also often guided by psychological theories. On the other hand, we focus on mathematics education. During the last decades, there has been very productive research on numeracy and mathematics learning in the field of both educational and cognitive neuroscience research. Given the importance of being numerate to life success in modern societies coupled with the great need to improve mathematics education in many countries around the globe, the domain of mathematics learning is an ideal area in which to explore possibilities for the new interdisciplinary research field of neuroscience and education. Against this background, we recently organized an EARLI Advanced Study Colloquium (ASC) on Cognitive Neuroscience Meets Mathematics Education in Brugge, Belgium (De Smedt & Verschaffel, 2009). The research papers at this colloquium all represented genuine collaborations between educational researchers and neuroscientists. In addition, there were keynote lectures by Ansari (2009), Dehaene (2009) and Szücs (2009). Taking this ASC as an input, we present research on mathematics learning from an educational and neuroscientific perspective to highlight the issues that are being faced by the emergent field of neuroscience and education.1 3. A two-way street scenario How should the interdisciplinary field of neuroscience and education take shape? In a critical evaluation of the prospects for the interaction between neuroscience and education, Mayer (1998) offers an interesting metaphor to think about this issue, namely that of a two-way street scenario. In this scenario, cognitive neuroscience influences educational research while educational research also influences cognitive neuroscience. Such a scenario necessitates the existence of interdisciplinary researchers and experts (e.g., Ansari & Coch, 2006; Szücs & Goswami, 2007) who are able to navigate in traffic on a two-way street. This approach should be preferred over a one-way street scenario in which findings from cognitive neuroscience are applied to educational theory. Although this is one important way of how both research disciplines might meet, it certainly cannot be the only one. While neuroscience offers a series of tools and methodologies, it can only be productive when its use is guided by psychological and educational theories and when it is complemented by convergent sources of evidence (Cacioppo et al., 2008). This forges an interdisciplinary perspective on the design and implementation of empirical research as a key starting point. In the remainder of this contribution, we will discuss how the two-way street approach to empirical research in the field of neuroscience and education might take shape. First, we will focus on how cognitive neuroscience might influence educational research. Subsequently, we will discuss how educational research might affect cognitive neuroscience studies. 4. Cognitive neuroscience studies influence educational research One of the often-cited ways in which cognitive neuroscience can influence (mathematics) educational research is through the study of the neural basis of arithmetic learning. Such research is helping to isolate and dissociate specific sub-processes that are part of school-relevant arithmetical tasks. The neural correlates of basic number processing and arithmetic learning have been reviewed recently by Ansari (2008) and Zamarian et al. (2009). The integration of these findings with cognitive and educational theories may yield a better and deeper understanding of children’s learning. The challenge of this endeavour is in combining the specificity of neuroscientific findings with a wide variety of educationally relevant variables taking place in any learning situation. It is important to note that most of the available neuroimaging studies have been carried out with adult participants. The application of existing findings to children’s learning of mathematics needs to be exercised with caution. Indeed, the majority of these adult studies do not take into account how learning changes across development and how learning is influenced by different instructional conditions (see Ansari, in press). Interestingly, as witnessed at the ASC, the number of

1 Studies presented at the EARLI ASC are marked with an * in the reference list. The full program including the abstracts of all contributions can be downloaded at http://www.earli.org/conferences/asc/asc2009.

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developmental, most importantly longitudinal, neuroimaging studies is growing (e.g., Meyler, Keller, Cherkassky, Gabrieli, & Just, 2008), and the field of developmental cognitive neuroscience is emerging (e.g., Blakemore & Frith, 2005; Diamond & Amso, 2008; Munakata, Casey, & Diamond, 2004). However, neuroimaging studies that also consider relations between brain activity and instructional features are scarce (but see Lee et al., 2007), and this represents an important, challenging avenue for future research. In the remainder of this section, we will highlight some examples of the way in which cognitive neuroscience might influence research on mathematics education. These involve (a) understanding atypical development, (b) paving the way for behavioural experiments, (c) representing a level of description that cannot be elucidated by behavioural methods alone. 4.1. Atypical development Cognitive neuroscience aids to our understanding of the origins of atypical mathematical development and dyscalculia (e.g., Kaufmann, 2008; Wilson & Dehaene, 2007). This area of research is probably one of the examples of where cognitive neuroscience, perhaps for the first time, met educational research, and which continues to be an active area of interdisciplinary research (e.g., Brigstocke & Göbel, 2009; Kaufmann & Vogel, 2009; Kucian & Rotzer, 2009; Landerl, Kadja, & Kölle, 2009; Ram-Tsur, Mevarech, Sela, & Breznitz, 2009; Rubinsten, 2009). Cognitive neuroscience research on dyscalculia (a specific learning disorder in the domain of arithmetic in the presence of otherwise normal cognitive functioning) suggests a (detectable) neural correlate. For example, studies in children with dyscalculia have shown structural (Rotzer et al., 2008) and functional abnormalities (Kaufmann & Vogel, 2009; Kaufmann et al., 2009; Mussolin et al., in press; Price, Holloway, Rasanen, Vesterinen, & Ansari, 2007) in those areas of the brain that are dedicated to the processing of numerical magnitudes. Cognitive neuroscience research thus suggests that children’s difficulties with basic arithmetic may have their origins in an abnormal development of the brain circuitry that supports numerical magnitude processing. In the next research step, this knowledge should be elaborated by longitudinal investigations of the direction of the association between abnormal functioning of brain circuitry and specific mathematical skills at the behavioural level. This will allow us to determine whether abnormal brain activation predicts subsequent mathematical skills or whether it is a consequence of those poor mathematical skills. This knowledge may guide appropriate educational intervention. For example, remediation tools may then be focused on children’s acquiring of representations of numerical magnitudes, in particular on the mappings between number symbols and the quantities they represent. Recent evidence suggests that these types of interventions improve children’s numerical understanding, not only in children with dyscalculia (Wilson, Revkin, Cohen, Cohen, & Dehaene, 2006) but also in children from low income backgrounds (Griffin, 2004; Ramani & Siegler, 2008). Another potential of cognitive neuroscience in relation to atypical development deals with the issue of early identification of at-risk children (e.g., Diamond & Amso, 2008; Gabrieli, 2009). If these children can be identified before or at the very beginning of formal mathematics instruction, it might be possible to minimize or even eliminate their difficulties with mathematics by remediating the foundations upon which higher level-skills are built, such as numerical magnitude processing (e.g., Booth & Siegler, 2008; Ramani & Siegler, 2008). An analogous approach has been successfully applied in the far more developed field of dyslexia, where longitudinal studies have demonstrated that brain measures, i.e. event-related potentials, collected in infants and young children (i.e. in the absence of symptoms) predict future language and reading development (e.g., Molfese, 2000). Similar research in the domain of mathematics might be published in the coming years. Related to this, studies in the field of numerical skills have been investigating disorders of a known genetic origin that have a high prevalence of numerical impairments (see Dennis et al., 2009, for a review), such as 22q11 Deletion Syndrome (e.g., Brigstocke & Göbel, 2009; De Smedt, Swillen, Verschaffel, & Ghesquière, 2009). These disorders are easily detectable at an early age, long before children start with formal schooling. The study of infants and toddlers with such a genetic disorder who are at risk for numerical impairments will enable us to understand the early stages of how mathematical development goes awry over developmental time and how compensatory mechanisms emerge, which might be exploited in new teaching and remediation methods. 4.2. Cognitive neuroscience research paves the way for behavioural experiments Cognitive neuroscience data provide an important source of evidence on mathematical and related abilities, which provides a ground for setting up behavioural studies. Numerous neuroimaging studies have shown that the intraparietal sulcus, which is involved in the processing of numerical magnitudes in children (Ansari, Garcia, Lucas, Hamon, & Dhital, 2005; Kaufmann et al., 2008) and adults (Dehaene, Piazza, Pinel, & Cohen, 2003), appears to be consistently active during arithmetical tasks (Dehaene et al., 2003; Rivera, Reiss, Eckert, & Menon, 2005). This has inspired several researchers to examine the role of numerical magnitude processing in not only atypical but also typical mathematical development. For example, it has been shown that measures of numerical magnitude processing, such as tasks that require the comparison of magnitudes or that involve the placement of a number on a number line, predict individual differences in mathematics development (Landerl et al., 2009; Reeve & Humberstone, 2009; see also De Smedt, Verschaffel, & Ghesquière, 2009). Interestingly, Booth and Siegler (2008) demonstrated that this ability to represent numerical magnitudes, in the context of a number line estimation task, predicts children’s learning of answers to novel addition problems as well as the errors they make on these problems. Moreover, recently, De Smedt, Taylor, Archibald, and Ansari (in press) tried to investigate the precise locus of the frequently observed association between reading and arithmetic (and their associated disorders). Data from cognitive neu-

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roimaging studies indicate that reading (Pugh et al., 2001) and arithmetic (Dehaene et al., 2003) show a neural overlap in the left temporo-parietal cortex. In reading, this area appears to be particularly active during phonological decoding or mapping graphemes onto phonemes. In arithmetic, this area is particularly related to arithmetic fact retrieval, a process that is assumed to rely on phonological codes. Thus, reading and arithmetic rely on the processing of the phonological code of language and, hence, the quality of phonological representations. This led De Smedt et al. (in press) to hypothesize a specific association between phonological awareness, a measure of the quality of phonological representations, and arithmetic fact retrieval. In a behavioural study in fourth and fifth graders, phonological awareness was uniquely correlated with arithmetic fact retrieval. De Smedt et al. concluded that the quality of children’s phonological representations mediates individual differences in arithmetic fact retrieval, suggesting that more distinct phonological representations of arithmetic facts are easier to retrieve. All these findings might have implications for future educational research, especially because research of reading and mathematics has been developing in relative isolation of each other. 4.3. A unique source of evidence Data on brain activity obtained with cognitive neuroscience techniques might generate findings that could not be anticipated by behavioural data alone. Stated differently, neuroimaging provides a level of measurement and analysis that cannot be accessed by behavioural studies alone, allowing educational researchers to add another level of explanation to their exploration of questions related to learning and instruction. For example, Stavy and Babai (2009) examined the nature of intuitive interference in geometry. They investigated brain activation while participants had to compare the perimeters of two geometrical shapes under two conditions: one that was in line with intuitive reasoning and one in which the correct answer was counterintuitive (see also Stavy, Goel, Critchley, & Dolan, 2006). Results revealed that the correct answers to counterintuitive items were accompanied by activations in those areas of brain that are important for inhibitory control, such as the prefrontal cortices (e.g., Stuss & Knight, 2002). Stavy and Babai (2009) concluded that this highlights the importance of control mechanisms in overcoming intuitive interferences. Another example is provided by Kaufmann et al. (2008) (see also Kaufmann & Vogel, 2009). In their study, children and adults did not differ in performing a number comparison task at the behavioural level. At the neural level, however, there were differences in brain activation. Children but not adults activated those areas of the brain, which are involved in grasping and finger movements (i.e., the right supramarginal gyrus and postcentral gyrus), suggesting that children might have relied on finger representations to compare numerical magnitudes. Neuroimaging studies might thus reveal issues related to strategy use, such as compensatory strategies. Such strategies may not be observable at the behavioural level, but can be hypothesized against the background of brain-imaging findings. In turn, the latter findings might generate new hypotheses for follow-up behavioural and neuroimaging studies, thereby creating a productive cycle of interdisciplinary, empirical research. Neuroimaging methods may also help to specify the stage of cognitive performance in which a certain cognitive process takes place. A series of behavioural studies by Hannula and colleagues (Hannula & Lehtinen, 2005; Hannula, Räsänen, Lehtinen, 2007) observed individual differences in children’s Spontaneous Focusing On Numerosity (SFON), i.e. focusing attention on the aspect of the exact number in the set of items or incidents and utilizing numerical information in one’s action. Behavioural SFON studies could not exhaustively answer the question whether these individual differences are due to the differences in the processing stage of perception and encoding of the stimuli. Recently, EEG-methods were used to further explore this issue (Hannula, Grabner & Lehtinen, 2009). These findings showed that the oscillatory EEG activity during encoding of photos of natural scenes of 12-year-old children was different in photos from which children recalled exact numbers when compared to photos with no recalled numbers. Thus, these EEG data revealed that the individual differences in SFON are particularly related to differences in encoding stimuli. This more detailed understanding of SFON aids us to investigate which kind of stimuli trigger focusing on numerosity more easily. 5. Educational research influences cognitive neuroscience studies The other pathway, albeit less elaborated but equally crucial for successful interdisciplinary research, is going from educational research to cognitive neuroscience. Diamond and Amso (2008) noted that the major contribution of neuroscience to theories of development involves the investigation of the role of experience in shaping the mind and brain. In other words, cognitive development cannot be studied in isolation from the learning context. It is therefore important that neuroscientific studies consider the educational histories of their participants as well as their physical and social environments as important variables of interest rather than nuisance variables that need to be controlled for. This all attributes a pivotal role to educational researchers, because they have a large knowledge base of learning sciences research at their disposal, which can be used in interdisciplinary research to (a) define the variables of interest and (b) investigate the effects of instruction on the neural correlates of learning. 5.1. Defining variables of interest Educational researchers can have an important input in the design of cognitive neuroscience studies. Drawing upon their understanding of educationally relevant factors, educational scientists can point to important variables that need

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to be incorporated in the design of an interdisciplinary study. A similar (theoretical) approach has been taken by de Jong et al. (2009), who identified questions that are prominent in various fields of educational research that could be further elaborated by means of neuroscientific techniques. These questions dealt with learning principles (e.g., learning from multiple representations, cognitive load, implicit vs. explicit learning, the role of imitation for learning), the role of affective processes in learning, learning disorders, second language learning and mathematics. In the field of mathematics, two examples of ways in which educational research inspired cognitive neuroscience are noteworthy. A first example relates to the large amount of educational research that has focused on the different strategies that children use when performing arithmetic, such as solving a simple arithmetic problem by means of fact retrieval (knowing that 12 − 4 = 8), decomposition strategies (e.g., solving 12 − 4 = by doing 12 − 2 − 2 = 8) or counting strategies (e.g., solving 12 − 4 by counting down 12, 11, 10, 9, 8) (e.g., Baroody & Dowker, 2003; Siegler, 1996; Verschaffel, De Corte, & Greer, 2007). Educational research has characterized these different strategies and has shown that they differ across individuals and may even differ within an individual on a trial-by-trial basis (e.g., Siegler, 2007). Cognitive neuroscience studies typically collapse performance across trials, thereby disregarding the issue of strategic variability. The rich descriptions of different strategies provided by educational research may be called upon when explaining differences in brain activation between populations with different competence levels or different socio-cultural or instructional backgrounds. For example, it has been shown that the brain activation changes as a function of arithmetic learning (Zamarian et al., 2009, for a review), and these changes have been interpreted in terms of a shift in strategy use, going from a reliance on effortful procedural strategies towards more automatic retrieval of arithmetic facts. Recently, researchers have begun to address this interaction between strategy variability and brain activation more carefully, pointing to reliable differences in the neural correlates that underlie different arithmetic strategies in simple arithmetic (De Smedt, Grabner, & Studer, 2009; Grabner et al., 2009a,b,c). This may provide an interesting starting point for the development of neural indices of these strategies. Behavioural studies typically use verbal reports to determine strategy use, but the use of these reports has been criticized (e.g., Kirk & Ashcraft, 2001). The combination of neural data and verbal reports might give a fuller picture of people’s strategy use. This might then facilitate studies that examine the individual differences in strategies as a function of different instruction (e.g., a comparison of instruction that stimulates the use of different strategies vs. instruction that focuses on the mastery of one particular strategy). A second example deals with the fact that educational researchers typically have stressed the idea of individual differences in learning arithmetic (e.g., Dowker, 2005), an issue that has been often neglected in cognitive neuroscience research. Interestingly, Grabner et al. (2009a) (see also Grabner et al., 2009b,c) examined at the neural level the interplay between individual differences in mathematical competence and arithmetic training. More specifically, they compared brain activation of individuals with high and low mathematical competence after a short period of arithmetic training. Findings revealed that after the training, competence-related differences in brain activation (in the left angular gyrus) disappeared, which suggests that these competence-related differences can be attenuated through acquiring a high level of expertise in a particular set of (arithmetic) problems. These data indicate that it is of crucial importance to take into account individual differences between learners and their interaction with training and instruction, as these differences may attenuate not only behavioural but also neural outcomes. 5.2. Effects of instruction Educational researchers play a crucial role in the investigation of the differential effects of instruction or remedial interventions on the neural correlates of learning. There is a large knowledge base of learning sciences research which is crucial for designing the instruction under investigation. Without this knowledge of instruction, cognitive neuroscientists are at risk for running naïve experiments with little or no relevance to educational theory and practice. Studies in the domain of mathematics that have examined the effects of instruction on brain activation are currently scarce. Delazer et al. (2005) compared an instructional approach based on drilling and rote fact memorization to another one that emphasized the understanding of basic principles and arithmetic relations. Results revealed that the brain activation patterns greatly differed between both instructional approaches, even though behavioural data indicated that in both instructional approaches the posttest problems were solved equally fast. Lee et al. (2007) examined the neural correlates of solving algebraic problems by two methods that are taught in schools in Singapore, i.e. the diagrammatic method (where students have to draw a diagram of the relationships represented in the word problem) and the symbolic method (where students have to transform the word problem into a symbolic equation). Findings revealed that while behavioural performance in both conditions was equivalent, the use of the symbolic method showed more activation in the superior parietal lobules and the precuneus, indicating that the symbol method perhaps requires more attentional demands. This illustrates that neuroimaging may be used to further understand the different neurocognitive processes elicited by different types of instruction. It is crucial to note that both Delazer et al. (2005) and Lee et al. (2007) demonstrated that equivalent behavioural performance does not necessarily indicate similar underlying neuronal processes (see also Sohn et al., 2004). This provides a powerful illustration of the utility of neuroimaging tools to provide another level of analysis, which complements and extends the knowledge that can be gleaned by the use of behavioural methodologies. Therefore, we expect this to become a priority on the agenda of future interdisciplinary research in neuroscience and education. It is also important to study the brain changes as an effect of remedial intervention in children with learning disorders. Such approach has been successful in the field of dyslexia (Schlaggar & McCandliss, 2007, for a review), where studies have

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demonstrated that the brain activation patterns in children with dyslexia normalize as a function of intervention, with this effect being maintained one year after remediation (Meyler et al., 2008). Intervention studies in the domain of mathematics are currently lacking, although recent efforts in this respect have been started (Kucian & Rotzer, 2009). 6. Future challenges Future interdisciplinary research in the field of neuroscience and education should adopt a multi-method perspective, as nicely illustrated by the different contributions at the ASC. This should involve the use of a variety of neuroimaging techniques, such as fMRI, EEG, MagnetoEncephaloGraphy (MEG) (e.g., Simos et al., 2008), Transcranial Magnetic Stimulation (TMS) (e.g., Pascual-Leone, Walsh, & Rothwell, 2000; Sandrini & Rusconi, 2009), transcranial Direct Current Stimulation (tDCS) (e.g., Nitsche et al., 2008), Near InfraRed Spectroscopy (NIRS) (e.g., Dresler et al., 2009), and a diversity of methodological approaches, such as longitudinal and experimental designs, pharmacological approaches, training studies, and studies of atypical development. While most studies in the field of cognitive neuroscience and mathematics education have focused on the representation of numbers and on arithmetic, only few attempts have been made to study more complex and higher order mathematical skills. Several contributions at the ASC showed that researchers are starting to address this issue more systematically. For example, studies are beginning to examine the neural correlates of word problem solving (Dresler et al., 2009; Lee et al., 2007; Reiss et al., 2009; Sohn et al., 2004), geometrical reasoning (Stavy & Babai, 2009; Stavy et al., 2006; Preusse et al., 2009) and the representation of mathematical functions (Thomas, Wilson, Lim, Yoon, & Corballis, 2009). A particular challenge of this research is that it requires educational and psychological theories, which specify cognitive processes that are detailed enough to be examined by neuroimaging. This will be of crucial importance not only for interdisciplinary research in neuroscience and education, but also for educational research in itself in order to fully understand complex mathematical skills. Another challenge of the field deals with the external validity of the findings obtained in neuroscientific studies (see Ansari & Coch, 2006 for a discussion). Typically, the latter studies collect data in individual sessions and with a limited set of dependent variables. This is different from learning in the classroom, which involves interactions with other learners and which is affected by a wide range of (environmental) variables. There is clearly a need for studies that examine how and to what degree data obtained in neurocognitive studies relate to (or even predict) classroom learning. For these endeavours it is crucial that cognitive neuroscientists and educational researchers work together closely. The complexity of the learning environment and the subtleties of the design of teaching and intervention programs must not be underestimated by cognitive neuroscientists. We end this section with a very important mechanism for making two-way research possible, which is the interdisciplinary training of researchers (e.g., Ansari & Coch, 2006; Coch & Ansari, 2009). This is witnessed by the current emergence of positions in Neuroscience and Education within Education and Psychology departments and by the creation of undergraduate and graduate programs at universities worldwide. Crucially, this will facilitate the generation of new interdisciplinary researchers fluent in the languages of educational and cognitive neuroscience research. The ASC in Brugge provides a promising example of how such interdisciplinary training might take shape. The meeting involved a small group of researchers who gathered for an in-depth discussion on research designs, analyses, results, future research questions, current developments in the field of neuroscience and education. Most contributions came from research teams that involved genuine collaborations between cognitive neuroscientists and educational researchers, and thus covered a wide field of expertise. Most interestingly, participating teams consisted of both junior and senior researchers, providing structural opportunities for training in the field. There is no doubt that the continuing discussions at workshops and conferences about the research field will add to this interdisciplinary training. Against this background, a special interest group (SIG) of Neuroscience and Education (SIG 22)2 was recently founded within EARLI, with Bert De Smedt (Department of Educational Sciences, University of Leuven, Belgium) and Daniel Ansari (Department of Psychology, University of Western Ontario, London, Canada) as the first SIG coordinators. The aim of this SIG is to build fundamental knowledge about the ways that children and adults learn and develop knowledge and skills in the domain of mathematics as well as in other cognitive domains, by employing a research strategy that combines neuroscientific and behavioural approaches. Research that deals with the effects of different instructional environments on the neural correlates of learning and relates the latter to outcomes in learning (and development) is among the priorities of the SIG. This SIG will provide a forum to address and discuss on the promises and pitfalls of this new interdisciplinary field. In this way, it also will contribute to the training of interdisciplinary researchers who are able to navigate in the two-way research street. 7. Conclusion In the present contribution, we have contended that the relation between cognitive neuroscience and (mathematics) educational research should be conceived as a two-way street with multiple bi-directional and reciprocal interactions between

2 More information on the EARLI SIG Neuroscience and Education can be found at http://www.earli.org/special interest groups/22. Neuroscience and Education.

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educational research and cognitive neuroscience. This interdisciplinary endeavour will allow researchers to pose and answer new and often unforeseeable questions about the learning brain. A better understanding of these processes has the potential to result in new ways of teaching as well as in new diagnostic and remedial approaches to prevent learning difficulties. However, before such applications are possible, the framework for empirical research within the emerging field of neuroscience and education needs to be further established. We hope that the present paper will encourage more consideration of and action on how to construct empirical research at the intersection between cognitive neuroscience and educational research. Acknowledgements This work originates from the EARLI Advanced Study Colloquium on Cognitive Neuroscience and Mathematics Education held from 25 to 29 March, 2009 in Brugge, Belgium, organized by Bert De Smedt, Lieven Verschaffel, Daniel Ansari, Pol Ghesquière, Roland H. Grabner, Minna M. Hannula, Erno Lehtinen, Michael Schneider, Elsbeth Stern, Erik Lenaerts, and Goele Nickmans. We would like to thank all participants for their highly valued input and discussion and the EARLI Association for funding and supporting this ASC. Special thanks are due to Goele Nickmans for her careful proofreading of this contribution. Bert De Smedt is a Postdoctoral Research Fellow of the Research Foundation Flanders, Belgium. References Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9, 278–291. *Ansari, D. (2009). Numeracy and arithmetic in the brain: The role of development and individual differences. 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