mathematics inside and outside the classroom lee peng yee 28 november 2014
TRANSCRIPT
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Mathematics inside and outside the classroom
Lee Peng Yee28 November 2014
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Mathematics has changed
• Mathematics was a scholarly pursuit in the west / a trade in the east
• Today mathematics is learned in schools mainly for counting and computation
• Mathematics inside and outside the classroom differ greatly
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There are more questions to ask than to answer
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Mathematics in the classroom
• Arithmetic / shapes / patterns … in elementary schools
• Algebra / trigonometry / statistics … in high schools
• Calculus and more at universities
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In and out of the classroom
• Euclidean geometry• Tessellation / linear programming• Ellipse in polar coordinates / parametric
equations• Trigonometric identities … …
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Mathematics outside the classroom
• Wavelets as digital tools• Stochastic equations for financial mathematics• Big data to handle data of a great size and to
make quick decision
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Questions
• Do we introduce randomness in the elementary?
• Do we include coding as part of discrete mathematics in high schools?
• What changes do we make at the polytechnic level?
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University mathematics is another story
Milestones: astronomy, calculus, discrete mathematics (after WWII), …
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The use of mathematics has changed
• Easier to find applications for discrete mathematics
• Hard to find applications of high school mathematics as before
• Not everyone learns mathematics for the same reason
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Workplace
• We need more drivers than mechanic• More graduates work in the service industry• Students may not use it at work • When they do, they do not learn enough
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More people benefit from the use of mathematics
Fewer people work on it and apply it
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Is mathematics useful?
• Useful does not mean only in daily life• Schooling is more than training• Knowing mathematics is a sufficient condition
and not necessary• Definitely a good test for competency and
intelligence
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If students take learning seriously then they will learn and what they learn will be useful
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Teaching approach has changed
Some years after 1978• Emphasis on the process• Teaching in context• To teach is to facilitate --- a belief• e-learning
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Singapore syllabus 2013
• Learning experience --- make explicit the process
• Mathematical modelling --- within curriculum time
• Basics come first
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Latest trends
• Making sense and having fun may help• Apply multiple tactics in teaching• A quote: If you think you can catch the bus,
you will run for it
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e-learning
• It has not been tested• Even if tested, we still do not know• Learn fast and learn in pieces• Keep it as a question, not an answer
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Where we learn mathematics
• Mostly outside mathematics departments • Often different from those in mathematics
departments• Mathematics outside is also changing, e.g.
actuarial science
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What is mathematics?
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Redefining mathematics
• What mathematics do we teach?• How do we connect mathematics with
applications?• Is it our job to tell people what mathematics
is?
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In summary, what has changed?
• Mathematics• The use of mathematics• Teaching approach• Where we learn mathematics
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There is a big gap between mathematics inside the classroom and outside
Do we know? Are we willing to find out more about it?