Mathematics for the Future

CHENG Chun Chor Litwin

HKIEd

APEC Conference 2014Khon Kaen Thailand

Mathematics for the future(or mathematics content and approach for the clas

sroom)

CHENG Chun Chor LitwinThe Hong Kong Institute of Education

Introduction

Mathematics for the future(or mathematics content and approach for the classroom)

The two basic requirementsImagination and operation

Thinking and DoingConjecture, Reasoning, AbstractionProcedure, Schema, application

There are 4 levels of mathematics achievement

Mathematician (explore and invent new mathematics) Engineers (using higher mathematics, application)Intellectuals(Using mathematics to understand the physical world)Layman(Using mathematics for daily use)

Algebra

Elimination of variables in equation(imagination)Transformation of expressions

Connecting operations (computer)Solving equation of degree 3 by machine

Geometry

Not the result (four points circle, or nine points circle)

The important thing is the axiomatic approach (thinking, idea)

Multiplication (as example)

From the 2 digits time two digits to 3 digits times three digits(we left this to the calculator)

Multiplication grids (helping to perform the multiplication)log table (imagination) and calculator

Trends and Shifts in content

We have more tools in calculationCan we do multiplication of multiple digits without understanding, just as we do the fraction division?

Cross over of the mathematics (application in different areas)

Using more tools to simplify the operation (calculators and programs)

Thinking, Operation and Application(Secondary Schools)

Statistics (for less interest people)Modeling Probability Calculus (How to teach calculus and application)Differential equations

What have changed in the content of mathematics in University ?

Calculus (still a core)Linear/Modern Algebra (core)Real/Complex analysis (core)Numerical analysis (options)ODE / PDEDiscrete mathematics and Graph theory (Abstract)

Why so much calculations when we have powerful calculator

Explorations!Solve harder problems!Make connections!

Using Models to teach Mathematics (as example)

Growth ModelSelection ModelWar ModelWashing and Drug Residue Model

Thank you