1. Mathematics inside and outside the classroom Lee Peng Yee 28 November 2014

2. 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

3. There are more questions to ask than to answer

4. Mathematics in the classroom Arithmetic / shapes / patterns … in elementary schools Algebra / trigonometry / statistics … in high schools Calculus and more at universities

5. In and out of the classroom Euclidean geometry Tessellation / linear programming Ellipse in polar coordinates / parametric equations Trigonometric identities … …

6. 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

7. 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?

8. University mathematics is another story Milestones: astronomy, calculus, discrete mathematics (after WWII), …

9. 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

10. 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

11. More people benefit from the use of mathematics Fewer people work on it and apply it

12. 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

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

14. Teaching approach has changed Some years after 1978 Emphasis on the process Teaching in context To teach is to facilitate --- a belief e-learning

15. Singapore syllabus 2013 Learning experience --- make explicit the process Mathematical modelling --- within curriculum time Basics come first

16. 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

17. 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

18. Where we learn mathematics Mostly outside mathematics departments Often different from those in mathematics departments Mathematics outside is also changing, e.g. actuarial science

19. What is mathematics?

20. Redefining mathematics What mathematics do we teach? How do we connect mathematics with applications? Is it our job to tell people what mathematics is?

21. In summary, what has changed? Mathematics The use of mathematics Teaching approach Where we learn mathematics

22. There is a big gap between mathematics inside the classroom and outside Do we know? Are we willing to find out more about it?

23. END pengyee.lee@nie.edu.sg