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School Math - Math in Home School Teaching
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The
growth in capability to understand and express, both academically
and practically, as a child grows, has been seen to be directly
correlated to the child's understanding of mathematics and
gasp on language.
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Hence, while home
schooling a child, math deserves to be one of the
key focus areas in which one would want the child
to shine.
There are some challenges
to overcome in the process of teaching a child math
at home. These challenges have majorly two aspects
- problem gradation and teaching methodology.
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.
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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.
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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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