Transcript Mathematics for the Future

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