Helping children learn maths
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Associate Professors Mike Mitchelmore and Joanne Mulligan |
Researchers at the Centre for Research in Mathematics and Science Education (CRiMSE) at Macquarie University have led world-first research into how young children learn maths, and have used their findings to develop an innovative program.
Associate Professors Joanne Mulligan and Mike Mitchelmore have found vital evidence as to why up to 20 per cent of young children struggle to understand mathematics.
After a three-year Australian Research Council study of the importance of visualisation in early maths learning, and research into children's ideas of, and ability to recognise multiplication, they found that an understanding of pattern and structure lay at the heart of children's ability to do well across all areas of maths.
While this awareness of structure and pattern - whether it be in a series of alternately coloured blocks, a geometrical figure or an algebraic formula - seemed crucial to the children's understanding of maths, Mulligan and Mitchelmore knew that few teachers or parents focused on developing it.
"Most teachers will teach students to solve problems from the textbook," Mitchelmore says. "They'll fix on a particular type of problem and say 'This is how you solve this'. Our approach is rather to ask 'What are the patterns here? What's actually happening? What is similar, what is different?'"
The importance of this approach has been further emphasised by doctoral research being undertaken by Marina Papic of the Institute of Early Childhood. Her project is investigating awareness of pattern and structure among preschoolers transitioning to kindergarten. Papic monitored two groups of children, one that had an intervention on early patterning and one that didn't, and tested them a year later. The intervention children had, almost exclusively, better awareness and were able to identify a single variable repetition type pattern, while the other children couldn't.
"The closer we investigate the core process of acquiring concepts, the younger we're starting to look at where things perhaps don't fit for some children," explains Mulligan. "Many kids are not really grasping underlying mathematical relationships and patterns, and it could be something quite simple rather than something incredibly complex."
Mulligan and Mitchelmore therefore began developing the Pattern and Structure Mathematics Awareness Program (PASMAP), with teaching and learning tasks in written folders of material outlining how teachers can build pattern and structural awareness in the classroom. They will supplement this with ongoing research to gauge how effective it is.
"The first version of PASMAP that we're developing is specifically for students with difficulties who probably just haven't seen the point of what they're doing in the way that other students have," Mulligan explains.
Three further packages, for specific school-year groupings (Years K-2, 3-4 and 5-6) will follow. Each will include a summary of the program and the research that underpins it, an instrument for assessing children's awareness of mathematical pattern and structure, activities and resources directed at improving this awareness, and professional development opportunities for teachers.
For further information visit the Centre for Research in Mathematics and Science Education www.aces.mq.edu.au/aces_re_crimse.asp