Vision for School Mathematics:
• Children learn to enjoy mathematics rather than
fear it.
• Children learn important mathematics:
Mathematics is more than for mulas and
mechanical procedures.
• Children see mathematics as something to talk
about, to communicate through, to discuss among
themselves, to work together on.
• Children pose and solve meaningful problems.
• Children use abstractions to perceive
relation-ships, to see structures, to reason out
things, to argue the truth or falsity of statements.
• Children understand the basic structure of
Mathematics: Arithmetic, algebra, geometry and
trigonometry, the basic content areas of school
Mathematics, all offer a methodology for
abstraction, structuration and generalisation.
• Teachers engage every child in class with the
conviction that everyone can learn mathematics.
Many general tactics of problem solving can be
taught progressively during the different stages of
school: abstraction, quantification, analogy, case analysis,
reduction to simpler situations, even guess-and-verify
exercises, are useful in many problem-solving contexts.
Moreover, when children learn a variety of approaches
(over time), their toolkit becomes richer, and they also
learn which approach is the best. Children also need
exposure to the use of heuristics, or rules of thumb,
rather than only believing that Mathematics is an 'exact
science'. The estimation of quantities and approximating
solutions is also essential skill. When a farmer estimates
the yield of a particular crop, he uses considerable skills
in estimation, approximation and optimisation. School
Mathematics can play a significant role in developing
such useful skills.
Visualisation and representation are skills that
Mathematics can help to develop. Modelling situations
using quantities, shapes and forms are the best use of
mathematics. Mathematical concepts can be represented in multiple ways, and these representations can serve a
variety of purposes in different contexts. All of this
adds to the power of Mathematics. For example, a
function may be represented in algebraic form or in
the form of a graph. The representation p/q can be
used to denote a fraction as a part of the whole, but
can also denote the quotient of two numbers, p and q.
Learning this about fractions is as important, if not
more, than learning the arithmetic of fractions.
There is also a need to make connections between
Mathematics and other subjects of study. When children
learn to draw graphs, they should also be encouraged
to think of functional relationships in the sciences,
including geology. Our children need to appreciate
the fact that Mathematics is an effective instrument in
the study of science.
The importance of systematic reasoning in
Mathematics cannot be overemphasised, and is
intimately tied to notions of aesthetics and elegance so
dear to mathematicians. Proof is important, but in
addition to deductive proof, children should also learn
when pictures and constructions provide proof. Proof
is a process that convinces a sceptical adversary; school
mathematics should encourage proof as a systematic
way of argumentation. The aim should be to develop
arguments, evaluate arguments, make and investigate
conjectures, and understand that there are various
methods of reasoning.
Mathematical communication is precise and
employs unambiguous use of language and rigour in
formulation, which are important characteristics of
mathematical treatment. The use of jargon in
Mathematics is deliberate, conscious and stylised.
Mathematicians discuss what is appropriate notation
since good notation is held in high esteem and believed
to aid thought. As children grow older, they should be
taught to appreciate the significance of such conventions
and their use. For instance, this means that setting up
of equations should get as much coverage as solving
them.
In discussing many of these skills and processes,
we have referred to a multiplicity of approaches and
procedures. These are all crucial for liberating school
Mathematics from the tyranny of applying them only
to those algorithms that are taught
