Understanding children’s developing calculations 131Gesture,movementand speechEarlyexplorationswith marksThe development of written number and quantitiesRepresentingquantities that arecountedCountingcontinuouslyExploringsymbolsSeparatingsetsStandard symbolicoperations withsmall numbersCalculating withlarger numberssupported byjottingsStandardwrittenmathematics, 8years andbeyond‘Melting pot’ – at this stagechildren use a wide variety ofdifferent ways of representingtheir calculationsEarly operations:development ofchildren’s own writtenmethodsPersonal explorationswith:Representingquantities thatare not countedEarly writtennumeralsNumerals aslabelsMulti-modal explorationsFigure 7.13Taxonomy – tracing the development of children’s mathematical graphics, from birth to 8 years8657part 2.qxd 04/07/2006 17:21 Page 131