The math problems
that one would want a homeschooled student to
learn can never be haphazard. Just as math is
taught in conventional schools, it needs to be
taught in a well-defined sequence of concepts
while homeschooling too.
To think of it,
the reason that a child is taught math is not
only to develop a capability to handle numbers,
but also to develop logical thinking.
And with evolution
of logical thinking in the child, one would see
a positive impact in the child's capability to
understand the concepts of mathematics and to
approach problems for solution.
To crack mathematical
problems, a child also needs to understand the
basic theories that are leveraged to solve the
problem.
But if a home schooling
tutor approaches a student with long and hard
terms, it is simply going to drive the child further
away from the foundations of mathematical concepts
rather than attracting him or her. The teacher
needs to:
- Use simple
words and multiple examples rather than terminology
- this registers better within the child's brains.
- Use real world
examples rather then fictitious ones - the child
can better relate such examples and apply the
thoughts behind such examples to solve math
problems.
An example of what
to exemplify for a child to understand addition
would be to ask, "If you have 2 chocolates and
your father gives you 3 more, how many chocolates
would you have?" And an example of what not to
cater as an example could be anything as simple
as "what is 2 plus 3" or anything more abstract
such as "2 units and 3 units sum up to 5 units".
Both are harder for the child - s/he would find
both the examples to be easier to forget rather
than remember and understand.
Once a child understand
one basic theory and can solve the related problems,
one should move ahead to the next logical sequence
and select the next best theory to teach.
Again,
the next theory can base upon the current theory
or be a complementary theory to this one. An example
could be to teach subtraction after addition and
to teach division after multiplication. Another
example could be to teach decimals after fractions.
After
a child starts understanding basic numbers at
the level of arithmetic and the basic operations
permissible on such numbers, it is advisable to
start introducing the child to the concepts of
algebra. While in conventional schools most often
algebra is started to be taught to kids eleven
to twelve year old, at home schooling it is advisable
to make better use of the implicit flexibility
the system provides, and thus start inching towards
the basic concepts of algebra right when the child
is around nine years old. One does not need to
understand the formulae right at that age. As
long as one understands the notion of algebraic
symbols in a simplistic sense, it would be a commendable
beginning. For example, a child need not understand
(a+b)-whole-square but would be nice if s/he understands
"x+3=5". As the child grows and matures, more
and more concepts and formulae of algebra need
to be gradually introduced.
Apart
from numbers, the other important aspect of mathematics
is about understanding shapes. The children in
conventional schools are introduced to geometry
in early enough phases of their careers, and the
children doing home schooling too need to get
introduced to geometry at the right age. Typically
the right age for a given would be around 7 to
8 years, when they start learning how to define
and understand shapes. Understanding the difference
between a normal rectangle and a square is a good
example of the level of concept desired at this
stage in the child.
As
children grow up and reach the age of eleven to
twelve years, they ought to be in a position to
manipulate shapes and be able to derive shapes
from given specifications. At this stage, given
an angle and the length of two sides of a triangle
the child should be able to draw the triangle
with a good accuracy at this stage, for an example.
As the child moves into early teens, they should
be able to analyze the mathematical properties
of shapes, and understand the theorems involving
shapes and angles.
While
taking a child through the process of homeschooling,
one must be aware that the child must be guided
such that his/her level of knowledge and understanding
is similar to children in the 10th grade in a
conventional school at the same age. This is because
if the child wants to go for higher education
then the homeschooling must not become a barrier
in terms of knowledge acquired. This is even more
applicable for a subject like mathematics, which
involves a number of concepts deeper than many
other subjects involving science and humanities.
The problem gradation, as noted in the few paragraphs
above, must be designed sequentially and methodically
enough to achieve this objective.
The
teaching methodology, as illustrated earlier,
must be kept simple. Often an example-based approach
to teach theories words well in practice, rather
than teaching hard and dry theories on their own.
The teacher would want to keep his/her record
of progress, and an occasional quiz-based performance
evaluation on theories and problems of mathematics
would ensure that the child sustains the knowledge
acquired in the process and can apply the knowledge
under conditions of test and challenge. If needed,
the teacher may want to consider some of the state-of-the-art
homeschool
software packages for teaching mathematics
that have become available in today's market -
this equips the student with the best of support
in the process.
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