CMNetwork E-bulletin: June 2012

    © Copyright M. Worthington & E. Carruthers 2012

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New! 2012 - 2013: Masters Module in Early Childhood Mathematics: Bath Spa University and Redcliffe Children's Centre, Bristol

The following examples are taken from chapter 9 of our second book Understanding Children’s Mathematical Graphics: Beginnings in Play

Biscuits for bears

Luke and Zainab (both 4-5 years)

The children were having a ‘teddy bears’ picnic’ and there were some surplus biscuits. Their teacher Sara asked the children how they might share the biscuits equally between the six children.

The mathematics: counting, division by sharing, fractions

At first Zainab (whose example is on the left) decided to share the six biscuits between four children. She wrote numbers 1 to 6 and then drew four circles to represent biscuits. She drew a line from each number to a biscuit and had two left over. Zainab was unsure what to do with the remaining two biscuits and decided to divide them into quarters, adding the numerals ‘5’ and ‘6’ (to represent the two remaining children) and drawing four lines beneath each, to represent the four quarters of each biscuit. Although Zainab did not completely solve the problem, her graphics show how she was thinking about fractions. Zainab had reframed the original question, perhaps thinking that sharing four biscuits between six children was too difficult, and that adjusting the question would reduce its complexity.

Luke (whose example is on the right) drew one person to represent the six children, and then drew four biscuits. He decided he would divide the biscuits in half (so that each child could have an equal piece) but then discovered that there would be one biscuit remaining. Drawing a circle round this remaining biscuit, his solution was to put it in his back pocket (a potentially real life and meaningful solution)!

It is really important to look closely at the processes involved in young children’s thinking rather than focusing too closely on correct answers. By valuing the children’s own methods and really listening, teachers can uncover what the children know.

Taxonomy:

Written number and quantities: representing quantities that are counted, numerals as labels
Calculations – children’s own methods: counting continuously; separating sets

Gallery 5: Beginnings in Play

Resources

New! Gallery 3: Redcliffe Children’s Centre and maintained nursery

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