Teaching Arithmetic to School Children

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A trend has been noted in arithmetic education of children across many countries around the world. It has been noted that while several fifth and six graders are unable to carry out simple addition and subtraction exercises, leave alone multiplication and divisions, there is a tendency to rush children even as young as three with too much learning by their respective school boards or private managements The need of the day is to slow down the pace at which education is thrust upon children while ensuring that whatever is taught is done so firmly. It goes without saying that the process of learning must be made enjoyable to engage a child.

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
Grade
Minimum
Age, years
Numbers
Addition
Subtraction
Preschool
4
1-12
Of two small single digit numbers
Differences of two small single digit numbers
First
5
1- 20
Of two single digit numbers
Of  two single digit numbers
Second
6
1-100
Of any two, two digit numbers not involving carry over of digits
Of  two, two digit numbers not involving borrowing of digits
Third
7
1- 1000
Of any size two, three digit numbers
Of any two, three digit numbers
Fourth
8
1 – 10,000
Of four digit numbers
Of four digit numbers
Fifth
9
Any size
Of groups of numbers
Of any size numbers



 



Primary School Arithmetic Curriculum – Table II
Grade
Minimum
Age, years
Numbers
Multiplication
Division
Preschool
4
1-12
None
None
First
5
1-20
With 2
None
Second
6
1-100
With 2 and 3
With 2
Third
7
1 -1000
With 0- 5
With 0 -5
Fourth
8
1– 10,000
With 0 - 10
With 1-10
(not involving decimal numbers *)
Fifth
9
Any size
With two digit numbers
With two digit numbers
Note: Decimal numbers begin in grade six


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.

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