Communicating About Number: Fostering Young Children’s Mathematical Orientation in the World

Future citizens need a basic proficiency in mathematics, usually referred to as mathematical literacy. This article argues that mathematical literacy can be fostered from an early age by helping children with exploring their actual play situations from the perspective of number, and with translating number related problems into thinking objects that are accessible for mathematical refinement (i.e. mathematising). Through observational studies of young children’s play it is found that this mathematising can meaningfully take place in the context of young children’s play, and is strongly related children’s learning to communicate about number in a coherent way, rather than by training them on number operations. The article presents evidence from case studies that support the claim that early mathematising in young children involves at least three dimensions: involving children in mathematising activities, helping them to invent symbolic means for referring to number aspects of reality (communicating with number), and guided examination of properties of number (communicating about number). Its is concluded that young children’s mathematical orientation in the world can be fostered in the context of children’s play under the guidance of a teacher who helps children with improving their way of communicating about number.

[1]  Harrie van Oers Narratives of childhood , 2003 .

[2]  Mike Thomas,et al.  Grounded blends and mathematical gesture spaces: developing mathematical understandings via gestures , 2011 .

[3]  Dirk Jan Struik,et al.  The Mechanization of the World Picture: Pythagoras to Newton , 1986 .

[4]  B. V. Oers,et al.  Schematising activities as a means for encouraging young children to think abstractly , 2007 .

[5]  Bert van Oers,et al.  Emergent mathematical thinking in the context of play , 2010 .

[6]  Mary Kay Stein,et al.  Instructional explanations in the disciplines , 2010 .

[7]  Kelly S. Mix,et al.  Multiple cues for quantification in infancy: is number one of them? , 2002, Psychological bulletin.

[8]  Paul Cobb,et al.  Symbolizing and communicating in mathematics classrooms : perspectives on discourse, tools, and instructional design , 2000 .

[9]  A. Karmiloff-Smith Précis of Beyond modularity: A developmental perspective on cognitive science , 1994, Behavioral and Brain Sciences.

[10]  Martin Hughes,et al.  Numeracy and Beyond: Applying Mathematics in the Primary School , 2000 .

[11]  Iliada Elia,et al.  The role of pictures in picture books on children's cognitive engagement with mathematics , 2010 .

[12]  M. O’Connor Talking Mathematics in School: Language Socialization in the Mathematics Classroom: Discourse Practices and Mathematical Thinking , 1998 .

[13]  Bert van Oers,et al.  Educational forms of initiation in mathematical culture , 2001 .

[14]  B. Oers Learning and learning theory from a cultural-historical point of view. , 2008 .

[15]  Geoffrey B. Saxe,et al.  Children's mathematics , 1988 .

[16]  G Geeke Bruin-Muurling,et al.  The development of proficiency in the fraction domain : affordances and constraints in the curriculum , 2006 .

[17]  Harrie van Oers The Mathematization of Young Children’s Language , 2002 .

[18]  Leone Burton,et al.  Children's mathematical narratives as learning stories , 2002 .

[19]  J. Lave Cognition in Practice: Outdoors: a social anthropology of cognition in practice , 1988 .

[20]  J. Lave Cognition in practice , 1988 .

[21]  J. Piaget The Child's Conception of Number , 1953 .

[22]  Raymond Bjuland,et al.  The Interplay Between Gesture and Discourse as Mediating Devices in Collaborative Mathematical Reasoning:A Multimodal Approach , 2008 .

[23]  Chris Donlan,et al.  The Development of Mathematical Skills , 2021 .

[24]  J. Terwel,et al.  Schematising activities in early childhood education , 2009 .

[25]  Richard Lehrer,et al.  Symbolizing Space into Being , 2002 .

[26]  H. Freudenthal Mathematics as an Educational Task , 1972 .

[27]  B. van Oers,et al.  Meaningful Cultural Learning by Imitative Participation: The Case of Abstract Thinking in Primary School , 2012 .

[28]  Ricardo Nemirovsky,et al.  Everyday Matters in Science and Mathematics: Studies of Complex Classroom Events. , 2005 .

[29]  B. Oers Developmental education for young children : Concept, practice and implementation , 2012 .

[30]  C. Gallistel,et al.  The Child's Understanding of Number , 1979 .

[31]  Harrie van Oers The dynamics of school learning , 1996 .

[32]  Are you sure? Stimulating mathematical thinking during young children's play , 1996 .

[33]  Angeliki Kolovou,et al.  Mathematical problem solving in primary school , 2011 .

[34]  B. V. Oers,et al.  The transformation of learning : advances in cultural-historical activity theory , 2008 .

[35]  K.P.E. Gravemeijer,et al.  Developing realistic mathematics education , 1994 .

[36]  Elizabeth Carruthers,et al.  Children's Mathematics: Making Marks, Making Meaning , 2006 .

[37]  Jaan Valsiner,et al.  The Structure of Learning Processes , 1996 .

[38]  P. Cobb,et al.  Discourse, mathematical thinking, and classroom practice. , 1993 .

[39]  Jürgen Maaß,et al.  New mathematics education research and practice , 2006 .

[40]  D. Pimm,et al.  Speaking Mathematically: Communication in Mathematics Classrooms , 1987 .

[41]  Martin Hughes,et al.  Children and Number: Difficulties in Learning Mathematics , 1986 .

[42]  Catherine M. Sandhofer,et al.  Number words and number concepts: the interplay of verbal and nonverbal quantification in early childhood. , 2005, Advances in child development and behavior.

[43]  R. Stevens,et al.  Talking Mathematics in School: Disciplined Perception: Learning to See in Technoscience , 1998 .

[44]  N. Minick,et al.  Contexts for learning , 1997 .

[45]  Tanja Vehkakoski,et al.  To correct or not correct the erroneous utterances of children: teacher‐initiated organisation of repair in the L2 pre‐primary education classroom , 2010 .

[46]  B. Oers Semiotic activity of young children in play: The construction and use of schematic representations , 1994 .

[47]  Richard Lehrer,et al.  What Kind of Explanation is a Model , 2010 .

[48]  Niko Fijma Learning to Communicate About Number , 2012 .

[49]  B. van Oers,et al.  An activity theory approach to the formation of mathematical cognition: developing topics through predication in a mathematical community , 2006 .