As a high school teacher focusing
on grades 10 – 12, this article is motivated by my observation of too many senior
learners making basic mistakes and thereby losing unnecessary marks. This lack
of basic understanding unfortunately emanates from the lower grades and
although it is not my intention to criticise primary and junior secondary maths
teachers, I believe that this issue is important enough to warrant some serious
discussion.
Primary school and grades 8 and 9
are where a solid foundation needs to be laid for mathematics. Given the
abstract nature of the subject, it is essential that one does not teach too much too soon. Learners need to be
given enough time to absorb and get a feel for mathematical concepts.
For
example, grade 4 and 5 CAPS states that learners should add and subtract
fractions with the same denominators. It is only in grade 6 that you are meant
to introduce different denominators, but not any denominators, one needs to be
a multiple of the other. If you are a teacher who feels that this is too simple
and goes beyond what is required, please be aware that this will very likely
lead to problems later on. If learners are not mature enough to grasp the
concept, they will end up following rote methods that have no meaning for them.
This will then result in them losing confidence and therefore the guts it
requires to succeed in mathematics. And because of the hierarchical nature of
maths, gaps start to develop in that all important foundation.
When learners graduate to grade
10, the demands of the curriculum are such that there is little time for going
back to plug gaps. They mostly stay gaps . . . and sadly often become bigger
gaps!
I would like to mention three
typical problems which have their roots in the lower grades.
1. Fractions, especially adding
and subtracting them. Just mentioning the word “fraction” rattles a lot of
learners and if they can’t add (a) imagine the problems they will have later with something like (b)! As I mentioned
earlier, if learners are not given enough time to absorb a concept, they resort
to memorising methods which they do not understand.
2. Negative numbers, and in
particular, adding and subtracting them. I have noticed that learners are quick
to grab their calculators to find the answer to – 2 – 3. A senior learner
should have no problem doing this in their head if they have a feel for the
concept of negative numbers.
3. Solving equations. Learners
get so tangled up in the methods that they completely lose sight of what they
are busy with. I had a learner the other day who could not understand why x = 5 in the equation 1 = (c).
And another who did the
following: (d) because the method he was taught is “take the 9 to the other
side and change the sign”.
As teachers, our job is to
motivate and inspire learners, especially when teaching mathematics. By laying
a solid foundation in the early years, learners will have a much better chance
of success with their mathematics . . . something we desperately need in this
country!
Written by: Peter Prentice
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