Finger Representation 1

< 5.4 Representing Numbers 1-9 using real life examples | Topic Index | 5.6 Simple Counting >

In the previous chapter we saw the various ways in which numbers from 1 to 9 can be represented and learnt through matching activities. In this chapter we will see representation of these numbers on our fingers.

Banning Use of Fingers in Math Class is Wrong

Finger representation is being dealt with separately since there are many misunderstandings in schools & among teachers regarding the use of fingers for understanding and doing mathematics. Many schools proudly proclaim that the use of fingers is "prohibited" in their classrooms.

This misconception arises due to a perspective that since mathematics is an abstract subject, it should only be done "mentally". Hence memorization is also encouraged. There is very little understanding of the developmental stage of the primary school student and the way the brain forms & stores abstract ideas.

Mental math is not doing math "in the mind". It is doing math "with the mind".

Neuroscience Research of Using Fingers

Educators & philosophers always recognized the importance of hands/fingers in human cognition. Aristotle called the hand the “tool of tools”; Immanuel Kant, “the visible part of the brain”.

Recent neuroscience research has revealed the important part played by fingers in concept formation at all stages in school life.

Please refer to article "SEEING AS UNDERSTANDING: The Importance of Visual Mathematics for our Brain and Learning" by Jo Boler, Professor of Mathematics Education, Stanford University.

The main conclusion of the paper is for teachers to encourage and celebrate students' "visual approaches, focus on finger discrimination and encourage finger use". Fingers are also available to all of us 24X7. There is never going to be a time when fingers may not be available to us for computations!

Some Finger Representation Activities

We give below some suggestions for representing numbers up to 9 with fingers.




 * 1) Numbers less than 5
 * 2) With one hand - Children are normally asked to show a number with fingers in only one hand. It is only for numbers greater than 5 that they are asked to use both hands.
 * 3) With both hands - However, children should also be asked to represent numbers less than 5 also using fingers from both hands. They should be able to show 4 in combinations of 1 & 3, 2 & 2 and 3 & 1 fingers. This has many advantages.
 * 4) One is that automatically some addition facts are being observed & internalised by them as patterns viz 4 = 3+1 = 2 +2 = 1+3 etc
 * 5) Second is that it avoids a misconception, created inadvertently by some teachers that One & Two make Twelve.
 * 6) Children should also be encouraged to use fingers which may not be next to each other. Such representations emphasize the fact that they are only "representations" which can be interpreted as per "rules" made by us.
 * 7) Numbers greater than 5 (up to 9)
 * 8) Children can represent numbers up to 9 with fingers of both hands.
 * 9) They should also be encouraged to represent the numbers with various combinations of fingers. For example, 7 can be represented as 2 (LH) &amp; 5(RH) or 3 (LH) &amp; 4(RH) & so on.
 * 10) These would again reinforce simple addition facts.

Finger representations should be practiced in various ways such that the numbers represented can be "seen" perceptually as designs rather than by "counting"

Fingers are Versatile Manipulatives

Up to now, we have mostly been talking about numbers up to 9. If we have talked about numbers more than 9, it has been only in the spoken form.

There are strategies even for representing numbers greater than 9 and for getting multiplication facts up to 9, using fingers. However, before we can learn these strategies, we need to understand the idea of a Number System & the concept of Place Value System.

< 5.4 Representing Numbers 1-9 using real life examples | Topic Index | 5.6 Simple Counting >