Mathematics inside and outside the classroom

Lee Peng Yee28 November 2014

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

There are more questions to ask than to answer

Mathematics in the classroom

• Arithmetic / shapes / patterns … in elementary schools

• Algebra / trigonometry / statistics … in high schools

• Calculus and more at universities

In and out of the classroom

• Euclidean geometry• Tessellation / linear programming• Ellipse in polar coordinates / parametric

equations• Trigonometric identities … …

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

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?

University mathematics is another story

Milestones: astronomy, calculus, discrete mathematics (after WWII), …

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

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

More people benefit from the use of mathematics

Fewer people work on it and apply it

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

If students take learning seriously then they will learn and what they learn will be useful

Teaching approach has changed

Some years after 1978• Emphasis on the process• Teaching in context• To teach is to facilitate --- a belief• e-learning

Singapore syllabus 2013

• Learning experience --- make explicit the process

• Mathematical modelling --- within curriculum time

• Basics come first

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

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

Where we learn mathematics

• Mostly outside mathematics departments • Often different from those in mathematics

departments• Mathematics outside is also changing, e.g.

actuarial science

What is mathematics?

Redefining mathematics

• What mathematics do we teach?• How do we connect mathematics with

applications?• Is it our job to tell people what mathematics

is?

In summary, what has changed?

• Mathematics• The use of mathematics• Teaching approach• Where we learn mathematics

There is a big gap between mathematics inside the classroom and outside

Do we know? Are we willing to find out more about it?

END

pengyee.lee@nie.edu.sg