Mathematics for the Future CHENG Chun Chor Litwin HKIEd.

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Presentation transcript:

Mathematics for the Future CHENG Chun Chor Litwin HKIEd

APEC Conference 2014 Khon Kaen Thailand Mathematics for the future (or mathematics content and approach for the classroom) CHENG Chun Chor Litwin The Hong Kong Institute of Education

Introduction Mathematics for the future (or mathematics content and approach for the classroom) The two basic requirements Imagination and operation Thinking and Doing Conjecture, Reasoning, Abstraction Procedure, 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 calculation Can 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 / PDE Discrete 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 Model Selection Model War Model Washing and Drug Residue Model

Thank you