Teaching Arithmetic to School Children
While many schools begin nursery education at three and
include pre-primary grades such as lower KG and upper KG, the view of this
author as well as several educators around the world is that preschool
education must not begin under the age of four under any circumstances. A child
under four is best at home under the care of a loving parent or if that is not
possible in a care center but definitely not a school. However since commercial
greed would even encourage a year old toddler to enroll just as long as it can
collect fees, it is up to governments to impose suitable regulations so that
the future of its children and by extension the nation is not compromised. Children
at the age of three do begin to play with pen and pencils and learn the
difference between one, two and three. A parent may teach a three year old how
to write 1, 2 and 3 if the child is interested but such learning must take
place at home and not in a school.
Children between four and five may learn numbers up to
twelve (because of the clock) and this teaching can take place in a nursery
school provided one can be found that has caring teachers and is located near
the home and to which the child can be taken safely by a parent for two or
three hours at the most and then brought back similarly. This author entered
school for the first time at age five and then went to attain the highest
levels of education from the best of institutions as available in the world.
Starting earlier would not have helped. In fact a year later would have been
even better, because in university this author discovered that those who were a
year older grasped new knowledge with greater ease.
At age five, a child enters grade 1 in India and many
countries. In some countries it is six or seven. However, assuming that primary
school begins at age five starting with grade 1, the sort of arithmetic
teaching that may be included up to grade five needs careful deliberation. Tables
I and II list proposals for this.This curriculum nay be named the FET ( Frobel Education Trust) Arithmetic Curriculum for primary schools
Primary School Arithmetic Curriculum – Table I
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Grade
|
Minimum
Age, years
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Numbers
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Addition
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Subtraction
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Preschool
|
4
|
1-12
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Of two small single digit numbers
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Differences of two small single digit
numbers
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First
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5
|
1- 20
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Of two single digit numbers
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Of
two single digit numbers
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Second
|
6
|
1-100
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Of any two, two digit numbers not involving carry over of digits
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Of two, two digit numbers not involving borrowing of digits
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Third
|
7
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1- 1000
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Of any size two, three digit numbers
|
Of any two, three digit numbers
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Fourth
|
8
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1 – 10,000
|
Of four digit numbers
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Of four digit numbers
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Fifth
|
9
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Any size
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Of groups of numbers
|
Of any size numbers
|
Primary School Arithmetic Curriculum – Table II
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Grade
|
Minimum
Age, years
|
Numbers
|
Multiplication
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Division
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Preschool
|
4
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1-12
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None
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None
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First
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5
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1-20
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With 2
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None
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Second
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6
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1-100
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With 2 and 3
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With 2
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Third
|
7
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1 -1000
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With 0- 5
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With 0 -5
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Fourth
|
8
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1– 10,000
|
With 0 - 10
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With 1-10
(not involving decimal numbers *)
|
Fifth
|
9
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Any size
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With two digit numbers
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With two digit numbers
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Note: Decimal
numbers begin in grade six
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It may be noted that the suggested pace of teaching is slower than traditional schools in grad 1 and 2 so as to capture the interest of the child and to build a strong foundation. It is increased later as the child becomes older. Thus by end of grade five or age ten, a child would be
familiar with basic arithmetic operations. The next two years (grade 6 and7)
may teach decimal numbers and applications of arithmetic through geometry and
other examples. Simple algebra and more geometry may be added safely in grade
8. Further classes would teach a child trigonometry, co-ordinate geometry,
higher algebra etc. Calculus can wait until grade 12.
The proposals here are suggestions and there is a need to
organize combined conferences of educators from primary to university level to
deliberate on the issue. Once a reasonable finality is achieved in curriculum,
there would be a need to develop attractive and appropriate text books for each
level. This author has already begun the exercise with a book for preschoolers
entitled – New Preschool Arithmetic – that has been received well around the
world.
UPDATE March15, 2014: Some modification of the curriculum presented in tables was made upon review restricting grade 1 children to arithmetic operations with single digit numbers only
UPDATE March 20, 2014:
It may be noted that based on further deliberations the curriculum has been modified somewhat as regards multiplications and divisions from standard three onwards as reported in the first and second book of the series. Instead of tables up to ten the modification proposed tables up to five only for seven year old children. It was felt that if memorizing tables up to ten is imposed on a seven to eight year old, it would not be in the long term interest of the child towards the subject.The modification has been entered in the tables.
UPDATE March15, 2014: Some modification of the curriculum presented in tables was made upon review restricting grade 1 children to arithmetic operations with single digit numbers only
UPDATE March 20, 2014:
It may be noted that based on further deliberations the curriculum has been modified somewhat as regards multiplications and divisions from standard three onwards as reported in the first and second book of the series. Instead of tables up to ten the modification proposed tables up to five only for seven year old children. It was felt that if memorizing tables up to ten is imposed on a seven to eight year old, it would not be in the long term interest of the child towards the subject.The modification has been entered in the tables.
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