Estonia’s government has commissioned Mr Wolfram’s consultancy in Oxfordshire to modernise maths courses for secondary-school pupils. Starting this month, it will pilot lessons built around open-ended problems which have no single solution. One example: “What’s the best algorithm for picking a romantic date?” (Possible answer: go on more dates with a lower quality threshold to maximise the chance of success.) Another: “Am I drunk?”, which leads into quantitative analysis involving body masses, rates of alcohol absorption and other variables.
Time for a Ceasefire | Feb 1st 2014 | SHANGHAI AND TEL AVIV
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Sunday, February 9, 2014
Onward and upward
In The Economist:
John Mighton's article on JUMP Math in AMS Notices
John Mighton, the Canadian mathematician (and playwright) who created JUMP Math, has an article worth reading in the current issue of AMS Notices.
He provides probably the only description I've seen that really gives meaning to the word "balanced approach":
"H. Wu has warned against drawing false dichotomies in math education (for instance, between concepts and deep understanding versus procedures and algorithms). One dichotomy is particularly damaging to students: the false opposition between “explicit” or “direct instruction” versus “discovery” or “student-centered” instruction. Current research in cognitive science suggests that effective lessons should combine elements of both approaches. In 2011 A. Alfieri et al. conducted a meta-analysis of 164 studies of discovery-based learning and concluded that “unassisted discovery does not benefit learners,” whereas discovery combined with “feedback, worked examples, scaffolding and elicited explanations do[es].”
"An effective lesson can be student-centered but still led by the teacher. Research in cognitive science suggests that, while it is important to teach to the strengths of the brain (by allowing students to explore and discover concepts on their own), it is also important to take account of the weaknesses of the brain. Our brains are easily overwhelmed by too much new information, we have limited working memories, we need practice to consolidate skills and concepts, and we learn bigger concepts by first mastering smaller component concepts and skills."
So when a school administrator tells you "We use a balanced approach", the chances are fairly good that they are not doing what Mighton is writing about above.
He provides probably the only description I've seen that really gives meaning to the word "balanced approach":
"H. Wu has warned against drawing false dichotomies in math education (for instance, between concepts and deep understanding versus procedures and algorithms). One dichotomy is particularly damaging to students: the false opposition between “explicit” or “direct instruction” versus “discovery” or “student-centered” instruction. Current research in cognitive science suggests that effective lessons should combine elements of both approaches. In 2011 A. Alfieri et al. conducted a meta-analysis of 164 studies of discovery-based learning and concluded that “unassisted discovery does not benefit learners,” whereas discovery combined with “feedback, worked examples, scaffolding and elicited explanations do[es].”
"An effective lesson can be student-centered but still led by the teacher. Research in cognitive science suggests that, while it is important to teach to the strengths of the brain (by allowing students to explore and discover concepts on their own), it is also important to take account of the weaknesses of the brain. Our brains are easily overwhelmed by too much new information, we have limited working memories, we need practice to consolidate skills and concepts, and we learn bigger concepts by first mastering smaller component concepts and skills."
So when a school administrator tells you "We use a balanced approach", the chances are fairly good that they are not doing what Mighton is writing about above.