Multiplication Tables

Tables & Math Phobia

One of the age-old traditions of Mathematics in schools is the memorisation of the Multiplication Table. The controversy of whether multiplication tables needs to be memorized has been debated for many decades. My contention is that the multiplication table is very rich in patterns and memorizing them hides these patterns from students.

The tragedy is that, children are expected to memorise the table before they understand it. For example, many children may be able to say that 7X8 is 56 but not able to tell the different interpretations of 7 X 8.

Memorising multiplication tables like a song, becomes a language-related exercise which hides the hidden patterns in the multiplication facts. Since many numbers reappear in different forms, they also become difficult to memorise and recall. It is universally accepted that one of the most important reasons of anxiety & phobia towards mathematics is the memorization of the tables!

Justifications for Memorising Tables

Many teachers & schools have reasons to justify memorisation, which do not stand logical scrutiny.

Many say that children will not be able to answer questions on the examinations if they do not memorise tables. But they also accept that it is they who set these examination papers which require this skill! So, they become both the judge & the jury!

Many teachers also insist on memorising tables up to 16. The Place Value System and the multiplication procedure which has evolved from it, helps us to break any multiplication by a 2-digit number by the 2 one digit numbers which make up the 2 digit number. Hence, logically there is no need-to-know multiplication tables more than 9. Sixteen tables were considered necessary several decades back when One Rupee was equal to 16 annas! They have no relevance now.

Many others do not have any independent opinion on this issue. They accept it since it has always been like this in schools!

Multiplication facts are inter-related and have a logical structure

Multiplication facts of 1, 2 and 5 are very easy to remember. Facts of 9 can easily be got using fingers. Hence, we need to remember tables of only 5 numbers (3, 4, 6, 7, 8). Multiplication facts also occur in pairs. 4 X 9 is same as 9 X 4. Hence, we really need to remember only 15 facts! (3 X 3, 3 X 4, 3 X 6, 3 X 7, 3 X 8, 4 X 4, 4 X 6, 4 X 7, 4 X 8, 6 X 6, 6 X 7, 6 X 8, 7 X 7, 7 X 8 & 8 X 8). And the 7 table contains 5 of them!

Understanding the logical structure & patterns in the table would be valuable to students.

Multiplication Table Can Be Constructed

Schools have also created the wrong impression in the minds of students that multiplication tables come “printed” in the math textbooks. Further, each table is printed separately giving the impression that each table is “stand alone”. This makes students feel that the amount of memorisation is huge.

One of the best ways to make the students realise the logical structure of the table is to make them build their own table in a “one page” format. This format will also enable them to identify the interesting patterns in the multiplication table. It would also reduce their fear of the table and increase their confidence.

In the next chapter, we will deal with the construction of the “one page” table & strategies to remember the multiplication facts.