Support of mathematical thinking through embodied cognition: Nondigital and digital approaches

Research on mathematics education has shown that learners’ actions can influence how they think and vice versa. Much of this work has been rooted in the use of manipulatives, gestures, and body movements. Our article dissects the mechanisms that underscore the impact of embodied activities and applies this lens to explore how to harness the affordances of new technology to enhance mathematical thinking. This is especially crucial given the increasing accessibility of technology—such as digital touch devices, 3D printers, and location sensors—for constructing embodied experiences. Providing guidance for incorporating those tools, we focus on the role that embodied cognition can play in communicating mathematical concepts as well as in allowing learners to experiment and evolve their ideas. To inspire future integration of theory in the development of technologically enhanced embodied mathematics experiences, we provide examples of how this can be done. Finally, we outline future directions in the areas of design, implementation, and assessment of embodied learning of mathematics.

[1]  Daniel L. Schwartz,et al.  Physically Distributed Learning: Adapting and Reinterpreting Physical Environments in the Development of Fraction Concepts , 2005, Cogn. Sci..

[2]  Michael A. McDaniel,et al.  The generation effect: A meta-analytic review , 2007, Memory & cognition.

[3]  Nicole M. McNeil,et al.  Should you show me the money? Concrete objects both hurt and help performance on mathematics problems , 2009 .

[4]  Geetha B. Ramani,et al.  Domain-Specific and Domain-General Training to Improve Kindergarten Children's Mathematics , 2017, J. Numer. Cogn..

[5]  Maria Montessori,et al.  The Absorbent Mind , 1949 .

[6]  J. Deloache,et al.  Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics , 1997 .

[7]  L. Richland.  Linking Gestures: Cross-Cultural Variation During Instructional Analogies , 2015 .

[8]  Frank Domahs,et al.  Mind the gap between both hands: Evidence for internal finger-based number representations in children's mental calculation , 2008, Cortex.

[9]  Gaea Leinhardt,et al.  Functions, Graphs, and Graphing: Tasks, Learning, and Teaching , 1990 .

[10]  R. Klatzky,et al.  Teachers’ gestures facilitate students’ learning: A lesson in symmetry , 2003 .

[11]  M. Alibali,et al.  The function of gesture in learning to count: more than keeping track * , 1999 .

[12]  K. Jellinger.  Cortex and Mind. Unifying Cognition , 2003 .

[13]  Susan M. Wagner,et al.  How our hands help us learn , 2005, Trends in Cognitive Sciences.

[14]  G. Duncan,et al.  School readiness and later achievement. , 2007, Developmental psychology.

[15]  Geetha B. Ramani,et al.  Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games. , 2008, Child development.

[16]  Chaitanya Ramineni,et al.  Development of number combination skill in the early school years: when do fingers help? , 2008, Developmental science.

[17]  David Birchfield,et al.  Collaborative Embodied Learning in Mixed Reality Motion-Capture Environments: Two Science Studies , 2014 .

[18]  B. Hommel.  Action control according to TEC (theory of event coding) , 2009, Psychological research.

[19]  M. Luz,et al.  Development and Application of a New Learning Object for Teaching Operative Dentistry Using Augmented Reality. , 2015, Journal of dental education.

[20]  Martin H. Fischer,et al.  When Digits Help Digits: Spatial–Numerical Associations Point to Finger Counting as Prime Example of Embodied Cognition , 2011, Front. Psychology.

[21]  Susan Goldin-Meadow,et al.  Gestures, but not meaningless movements, lighten working memory load when explaining math , 2012, Language and cognitive processes.

[22]  Richard E. Clark,et al.  Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching , 2006 .

[23]  A. Segal,et al.  Do Gestural Interfaces Promote Thinking? Embodied Interaction: Congruent Gestures and Direct Touch Promote Performance in Math , 2011 .

[24]  S. Dehaene,et al.  The mental representation of parity and number magnitude. , 1993 .

[25]  Korbinian Moeller,et al.  Walk the number line – An embodied training of numerical concepts , 2013, Trends in Neuroscience and Education.

[26]  M. Aster,et al.  Vom Fingergefühl zum Rechnen: Bedeutung der Fingergnosie für die Vorhersage numerisch-arithmetischer Fertigkeiten , 2015 .

[27]  L. Nyberg,et al.  Learning mathematics without a suggested solution method: Durable effects on performance and brain activity , 2015, Trends in Neuroscience and Education.

[28]  Mitchell J. Nathan,et al.  Embodiment in Mathematics Teaching and Learning: Evidence From Learners' and Teachers' Gestures , 2012 .

[29]  Michael P. Kaschak,et al.  Activity and Imagined Activity Can Enhance Young Children's Reading Comprehension. , 2004 .

[30]  Ulrike Cress,et al.  Learning and development of embodied numerosity , 2012, Cognitive Processing.

[31]  Johnna J. Bolyard,et al.  What Are Virtual Manipulatives , 2002 .

[32]  Sharlene D. Newman,et al.  Does finger sense predict addition performance? , 2016, Cognitive Processing.

[33]  Garry Falloon,et al.  What's the difference? Learning collaboratively using iPads in conventional classrooms , 2015, Comput. Educ..

[34]  Julie L. Booth,et al.  Numerical magnitude representations influence arithmetic learning. , 2008, Child development.

[35]  R. Passingham,et al.  Action observation and acquired motor skills: an FMRI study with expert dancers. , 2005, Cerebral cortex.

[36]  Martin H. Fischer,et al.  Finger counting habits modulate spatial-numerical associations , 2008, Cortex.

[37]  J. Deloache,et al.  Dual Representation and the Linking of Concrete and Symbolic Representations , 2009 .

[38]  Ulrike Cress,et al.  Full-body Movement in Numerical Trainings: A Pilot Study with an Interactive Whiteboard , 2015, Int. J. Serious Games.

[39]  Autumn B. Hostetter,et al.  Visible embodiment: Gestures as simulated action , 2008, Psychonomic bulletin & review.

[40]  Julie L. Booth,et al.  Development of numerical estimation in young children. , 2004, Child development.

[41]  Naomi J. Aldrich,et al.  Does Discovery-Based Instruction Enhance Learning?. , 2011 .

[42]  Ulrike Cress,et al.  Sensori-motor spatial training of number magnitude representation , 2011, Psychonomic bulletin & review.

[43]  Susan Goldin-Meadow,et al.  From children's hands to adults' ears: gesture's role in the learning process. , 2003, Developmental psychology.

[44]  Stuart J. Ritchie,et al.  Enduring Links From Childhood Mathematics and Reading Achievement to Adult Socioeconomic Status , 2013, Psychology Science.

[45]  S. Goldin-Meadow,et al.  Gesturing Gives Children New Ideas About Math , 2009, Psychological science.

[46]  Susan M. Wagner,et al.  Explaining Math: Gesturing Lightens the Load , 2001, Psychological science.

[47]  S. Goldin-Meadow,et al.  Making children gesture brings out implicit knowledge and leads to learning. , 2007, Journal of experimental psychology. General.

[48]  G. Aschersleben,et al.  The Theory of Event Coding (TEC): a framework for perception and action planning. , 2001, The Behavioral and brain sciences.

[49]  Susan Goldin-Meadow,et al.  Transitional knowledge in the acquisition of concepts , 1988 .

[50]  Korbinian Moeller,et al.  Training the equidistant principle of number line spacing , 2016, Cognitive Processing.

[51]  John D. Bransford,et al.  Levels of processing versus transfer appropriate processing , 1977 .

[52]  T. Loetscher,et al.  Head turns bias the brain's internal random generator , 2008, Current Biology.

[53]  John Sweller,et al.  Cognitive Load During Problem Solving: Effects on Learning , 1988, Cogn. Sci..

[54]  N. J. Slamecka,et al.  The Generation Effect: Delineation of a Phenomenon , 1978 .

[55]  Seong-Sik Kim,et al.  The Effects of VR-based Wii Fit Yoga on Physical Function in Middle-aged Female LBP Patients , 2014, Journal of physical therapy science.

[56]  John B. Black,et al.  Direct-manipulation animation: incorporating the haptic channel in the learning process to support middle school students in science learning and mental model acquisition , 2006 .

[57]  R. Shepard,et al.  Mental Rotation of Three-Dimensional Objects , 1971, Science.

[58]  Frank Domahs,et al.  Embodied numerosity: Implicit hand-based representations influence symbolic number processing across cultures , 2010, Cognition.

[59]  S. Goldin-Meadow,et al.  Gesturing makes learning last , 2008, Cognition.

[60]  Susan Goldin-Meadow,et al.  Action’s Influence on Thought: The Case of Gesture , 2010, Perspectives on psychological science : a journal of the Association for Psychological Science.

[61]  Steve Benford,et al.  The role of physical representations in solving number problems: A comparison of young children's use of physical and virtual materials , 2010, Comput. Educ..

[62]  Robb Lindgren,et al.  Getting into the cue: Embracing technology-facilitated body movements as a starting point for learning , 2014 .

[63]  Victor R. Lee.  Learning technologies and the body : integration and implementation in formal and informal learning environments , 2015 .

[64]  M. Aster,et al.  Schwache Fingergnosie als Risikofaktor für zukünftiges Rechnen , 2015 .

[65]  Margaret Wilson,et al.  Six views of embodied cognition , 2002, Psychonomic bulletin & review.

[66]  James J. Gibson,et al.  The Ecological Approach to Visual Perception: Classic Edition , 2014 .

[67]  Geetha B. Ramani,et al.  Taking it to the classroom: Number board games as a small group learning activity , 2012 .

[68]  Michael P. Kaschak,et al.  Grounding language in action , 2002, Psychonomic bulletin & review.

[69]  Elizabeth O. Hayward,et al.  The impact of individual, competitive, and collaborative mathematics game play on learning, performance, and motivation , 2013 .

[70]  Kira J. Carbonneau,et al.  A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives , 2013 .

[71]  R. Mayer.  Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction. , 2004, The American psychologist.

[72]  Fred Paas,et al.  Watch Your Step Children! Learning Two-Digit Numbers Through Mirror-Based Observation of Self-Initiated Body Movements , 2015 .

[73]  L. Martignon,et al.  Finger gnosis predicts a unique but small part of variance in initial arithmetic performance. , 2016, Journal of experimental child psychology.

[74]  S. Kita,et al.  The nature of gestures ' beneficial role in spatial problem solving , 2013 .

[75]  Martin H. Fischer,et al.  Random walks on the mental number line , 2013, Experimental Brain Research.

[76]  J. Holt.  How Children Fail , 1964 .

[77]  M. Noël,et al.  Finger gnosia: a predictor of numerical abilities in children? , 2005, Child neuropsychology : a journal on normal and abnormal development in childhood and adolescence.

[78]  J. Bittner,et al.  Cognitive Research : Principles and Implications , 2017 .

[79]  J. Bisanz,et al.  The Foundations of Numeracy: Subitizing, Finger Gnosia, and Fine Motor Ability , 2007 .

[80]  Lawrence W. Barsalou,et al.  Perceptions of perceptual symbols , 1999, Behavioral and Brain Sciences.

[81]  F. Craik,et al.  Levels of Pro-cessing: A Framework for Memory Research , 1975 .

[82]  Pierre Barrouillet,et al.  Predicting arithmetical achievement from neuro-psychological performance: a longitudinal study , 1998, Cognition.

[83]  Katherine A. Rawson,et al.  Testing the retrieval effort hypothesis: Does greater difficulty correctly recalling information lead to higher levels of memory? , 2009 .

[84]  Bernhard Hommel,et al.  The theory of event coding (TEC) as embodied-cognition framework , 2015, Front. Psychol..

[85]  J. Piaget.  Play, dreams and imitation in childhood , 1951 .

[86]  Thomas W. Schubert,et al.  Embodiment as a unifying perspective for psychology , 2009 .

[87]  G. Lakoff,et al.  Where mathematics comes from : how the embodied mind brings mathematics into being , 2002 .