Learning angles through movement: Critical actions for developing understanding in an embodied activity

Abstract Angle instruction often begins with familiar, real-world examples of angles, but the transition to more abstract ideas can be challenging. In this study, we examine 20 third and fourth grade students completing a body-based angle task in a motion-controlled learning environment using the Kinect for Windows. We present overall pre- and post-test results, showing that the task enhanced learners’ developing ideas about angles, and we describe two case studies of individual students, looking in detail at the role the body plays in the learning process. We found that the development of a strong connection between the body and the abstract representation of angle was instrumental to learning, as was exploring the space and making connections to personal experiences. The implications of these findings for developing body-based tasks are discussed.

[1]  Taylor Martin.  A Theory of Physically Distributed Learning: How External Environments and Internal States Interact in Mathematics Learning , 2009 .

[2]  Richard Lehrer,et al.  Longitudinal Study of Children's Reasoning About Space and Geometry , 2012 .

[3]  Anne Birgitte Fyhn,et al.  A climbing class’ reinvention of angles , 2008 .

[4]  G. Goldin.  A Scientific Perspective on Structured, Task-Based Interviews in Mathematics Education Research , 2000 .

[5]  Paul White,et al.  Development of angle concepts by progressive abstraction and generalisation , 2000 .

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

[7]  Julie Sarama,et al.  Development of turn and turn measurement concepts in a computer-based instructional unit , 1996 .

[8]  Dor Abrahamson,et al.  The mathematical imagery trainer: from embodied interaction to conceptual learning , 2011, CHI.

[9]  Paul White,et al.  Development of angle concepts: A framework for research , 1998 .

[10]  Douglas H. Clements,et al.  Learning of Geometric Concepts in a Logo Environment , 1989 .

[11]  Tracey Wright.  Karen in Motion. , 2001 .

[12]  Patricia S. Wilson,et al.  A Dynamic Way to Teach Angle and Angle Measure. , 1992 .

[13]  K. Krainer.  Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction , 1993 .

[14]  Valérie Munier,et al.  About the concept of angle in elementary school: Misconceptions and teaching sequences , 2013 .

[15]  Christine Browning,et al.  What's Your Angle on Angles? , 2007 .

[16]  Caro Williams-Pierce.  Being Mathematical Relations: Dynamic Gestures Support Mathematical Reasoning , 2014 .

[17]  G. Lakoff,et al.  Philosophy in the flesh : the embodied mind and its challenge to Western thought , 1999 .

[18]  A Physical Situation as a Way to Teach Angle. , 2008 .

[19]  Richard Noss,et al.  Children's Learning of Geometrical Concepts Through Logo. , 1987 .

[20]  H. Freudenthal.  Didactical Phenomenology of Mathematical Structures , 1983 .

[21]  R. Yin.  Case Study Research: Design and Methods , 1984 .

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

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

[24]  Kevin Moore.  Making sense by measuring arcs: a teaching experiment in angle measure , 2013 .

[25]  Luis M. Casas-García,et al.  The study of the pupil’s cognitive structure: the concept of angle , 2013 .

[26]  F. J. Langdon,et al.  The Child's Conception of Space , 1967 .

[27]  G. Rizzolatti,et al.  Listening to action-related sentences modulates the activity of the motor system: a combined TMS and behavioral study. , 2005, Brain research. Cognitive brain research.

[28]  V. Braun,et al.  Using thematic analysis in psychology , 2006 .

[29]  F. J. Langdon,et al.  The Child's Conception of Space , 1967 .

[30]  Douglas H. Clements,et al.  The Effects of LOGO on Children's Conceptualizations of Angle and Polygons , 1990 .

[31]  G. Rizzolatti,et al.  Premotor cortex and the recognition of motor actions. , 1996, Brain research. Cognitive brain research.

[32]  Douglas H. Clements,et al.  Geometry and spatial reasoning. , 1992 .

[33]  Keith M. Sturges,et al.  Mapping the Process: An Exemplar of Process and Challenge in Grounded Theory Analysis , 2005 .

[34]  I. Johnsrude,et al.  Somatotopic Representation of Action Words in Human Motor and Premotor Cortex , 2004, Neuron.

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

[36]  Doug French,et al.  Teaching and Learning Geometry , 2004 .

[37]  M. Alibali,et al.  Gesture-Speech Mismatch and Mechanisms of Learning: What the Hands Reveal about a Child′s State of Mind , 1993, Cognitive Psychology.

[38]  A. Glenberg,et al.  What memory is for: Creating meaning in the service of action , 1997, Behavioral and Brain Sciences.

[39]  Michael C. Mithcelmore.  Young Students' Concepts of Turning and Angle , 1998 .