Fractions, decimals and percentages – rules vs relationships

This research paper, by Fosnot and Dolk explores how providing children with rich learning experiences that encourage inquiry and problem solving, rather than teaching rules and procedure, leads to creative thinking and a deep understanding of number.

Fosnot & Dolk 2002p148-153

It shows examples of children solving problems with fractions, decimals and percentages, where they are actively making sense of the relationships involved through group dialogue and problem solving tasks. The teacher acts as a facilitator through the discussion, constantly asking the children to explain why the rules they use work to reveal their understanding, or not! The genuine sense of curiosity and puzzlement that the children experience allows them to discover relationships for themselves and see maths as something creative and challenging as they make sense of their findings.

This approach relates so well to the concepts behind the Highland Numeracy Progression, and the context of fractions and decimals seems very relevant to the findings of the SSLN, which shows the huge difficulties many children experience with these concepts.

Education Scotland have produced this Professional Learning Resource to support teaching of fractions and decimals, which again promotes planning learning experiences which allow children the chance to explore, visualise and make connections with their learning. Discovering relationships and strategies for themselves will lead to deeper learning and flexibility in their thinking when faced with problems involving these types of numbers.

http://www.educationscotland.gov.uk/learningandteaching/assessment/ssln/resources/numeracysecond/secondfractions.asp

I love these quotes from Einstein and Piaget, cited in the paper,

“It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry…..”

“Disequilibrium is one of the mechanisms that spur genuine learning.”

This teaching approach is exemplified so well in the New Zealand approach – look at these links for ideas how to promote discovery and exploration in work with fractions and decimals:

http://www2.nzmaths.co.nz/frames/ONPD/M10/26.aspx

http://www2.nzmaths.co.nz/frames/ONPD/M10/27.aspx

http://www2.nzmaths.co.nz/frames/ONPD/M9/20.aspx

http://www2.nzmaths.co.nz/frames/ONPD/M11/27.aspx

http://www2.nzmaths.co.nz/frames/ONPD/M11/08.aspx

Lots more ideas are in the Teaching Book 7 and on the website – look on the NZ maths page for more information!

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