Children\'s Mathematics

Theory

Behaviourism

Constructivism

Social constructivism

Socio-culturalism

Theory based onwork of:

Thorndike and Skinner

Piaget

Vygotsky

Vygotsky & Bakhtin

View of childrenas learners

Children were seen as

‘empty

vessels’ for

the teacher to fill

with prescribed facts. Learningwas seen as passive ratherthan active and dynamic.

Children constructknowledge of the worldthrough active involvementwith meaningful problem-solving.

Children constructunderstanding throughinteractions with peersand adults who aremore knowledgeable.

Children are powerful meaning-makers who use,invent and adapt their own marks and symbols toexplore and represent their mathematicalthinking. Socio-cultural and cognitive developmentwork together. Language, symbolic and graphicalrepresentations assist this process.

Implications forteachingmathematics

Skills-based teaching withlearning programmed in aplanned sequence.The value oflanguage and discussion wasnot recognised.

Emphasis on autonomy andactive ‘learning by doing’.

Value of discussionwith peers and teacherto take the child’sunderstanding further.

‘Mathematics as a subject matter is really aboutproblem-solving activity with symbolic tools’ (vanOers, 2001a, p. 63).

Role of EarlyYears teachers

Direct teaching (stimulus)followed by praise (reward).

Hierarchical view ofmathematics led to

widespread use of

published schemas and‘pre-number’ activities.

Relate mathematicalactivities to children’sown experiences.

Value and build on children’s multi-modal meaningsin diverse contexts (Kress, 1997: see pp.91 and 135).Develop rich mathematical learning environments.Model a range of ways of representing mathematicalmeaning (including standard symbols) in differentcontexts and for various purposes and audiences(see pp.205–15). Support and extend children’s ownmarks (drawing, emergent writing and mathematical)through collaborative dialogue. Emphasise thinking,meaning and understanding.

Role of family andculture

There was no appreciation ofthe role of the child’s culturewithin the home andcommunity, or of thesignificance of the socialculture of the educationsetting.

There was little

appreciation

of the

role of the child’s

culture within the homeand community, or of thesignificance of the socialculture of the educationsetting.

Talk aboutmathematics used byand within the familyand society for real purposesencouraged.

Engage in dialogue with parents and families andtogether share and recognise the child’sunderstanding and development. Value themathematical practices of the family, communityand culture.

Table 2.1

Four views of learning mathematics

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