Why should I learn Multiplication Tables ?

In the usual way of teaching multiplication tables to class 1^st or 2^nd grade students, it is told that table means multiplication of a given number or repeated addition. And then various ways of how to memorize – like in rhyming ways, family of a number, drawing some pictures or doing some exercise of repeated counting. While all these methods lead to a better way of memorizing, however, they do not help to make the child understand why memorize the Multiplication Table? What if table was not there? Why is it necessary to learn table? Can’t I do maths without learning tables? When the dialogue is taken to this level of conceptual understanding, the child can naturally appreciate the advantage of learning table and will feel interested in learning it. Moreover, the concept thus registered will last longer and build a thought process, which first provokes the thought of “why” in the quest of knowledge and then demonstrates the way of how to do it.

So, let us come back to the questions asked above and begin the journey from there… Why Multiplication Table? What if table was not there? Why is it necessary to learn table? Can’t I do maths without learning tables?

I chose this situation, which my son Tanmay (2^nd grade) can relate to and also feels attached because it is about his birthday celebration. In our residential colony, we have 10 cross roads named as 1^st cross to 10^th cross. A basic table comprises of multiples up to 10 times, so this example fitted into the context. Next was to use this example to build a situation to stimulate the thought process.

So, I said… it is Tanmay’s birthday, and he invited his friends from all the crosses in the layout. As a starter, he will offer 2 smileys to each friend, when he comes home for the birthday party. First comes one friend from 1^st cross, so how many smileys will he give? And the prompt answer was: 2 smileys. Okiee! Now, 2 friends come from 2^nd cross, so how many smiley will he get from mummy to give them? He counted and said 4 smileys. Bingo J And then 3 friends from 3^rd cross come. He jumped to counting again and said 6 smileys. Cool !!! And then we continued in the same fashion. The answers kept pouring as 8, 10, 12, 14, 16, 18, 20. Though, with each iteration, it was taking longer time to get the answer as the counting increased.

So, I teased him… for the later friends in larger numbers, you are taking such a long time to calculate and then get the smileys. If you do like this, your friends who came earlier will make fun of you and may be some of them who came in just now will feel bad that they are not being given smileys on time. This question registered deeply with him and he was really wondering what he should do. This was the real powerful moment to stimulate the real need for doing something more than just knowing the addition, because it takes time to do this calculation every time, and it can affect the prestige among the friends who have gathered at his birthday party. So, he was receptive to the idea to do something better to handle this situation.

That’s it… the ground was set to realize the value of learning table and to use it. So, now I stepped in to put all the previous calculations in perspective to naturally lead him forward. Again, I was cautious enough not to jump into teaching tables which would break the continuum and will be forced to memorize. I wanted him to feel that tables have naturally originated based on the need. So, here is how I put the things in perspective. I said, let’s recall all that you did every time friends arrived at the birthday party.

2 smileys for 1 friend (of 1^st cross) è get 2 smileys from mummy

2 smileys for 2 friends (of 2^nd cross) è get 4 smileys from mummy

2 smileys for 3 friends (of 3^rd cross) è get 6 smileys from mummy ...

.

.

.

2 smileys for 10 friends (of 10^th cross) è get 20 smileys from mummy

And he nodded yes in agreement. Then, I repeated the same thing in a little more simplified manner as follows:

2 smileys for 1 friend è 2 smileys

2 smileys for 2 friends è 4 smileys

2 smileys for 3 friends è 6 smileys ...

.

.

.

2 smileys for 10 friends è 20 smileys

And he again nodded in agreement with the above arrangement. Now, it was the time to transform this arrangement into the way that he can memorize, and it was like this:

2              ones       are          2

2              twos      are          4

2              threes    are          6 ...

.

.

.

2              tens        are          20

And he realized that this is the same table he was taught earlier, and found it easy to associate with and also to memorize. Now every time he repeats this table, he has the birthday party example deeply registered with him (remember… the prestige among the friends!) and stimulates the learning in the background.

To make it further exciting, I said that now consider that it is Tanisha’s birthday (she is his elder sister). So, to each of her friend arriving, she will offer 4 smileys (since they are older friends). So, now counting has to be repeated for 4-4 smileys. Now, without much time taken, we could naturally lead to the table of 4.

4              ones       are          4

4              twos      are          8

4              threes    are          12 ...

.

.

.

4              tens        are          40

Through both the above examples, he realized that if he learns the tables, then such repeated counting can be done quickly with ease and make him confident to handle the real life situations. Clearly, it also conveyed, how tables can be applied to use.

The proof of pudding is in eating it. This whole engagement with my son had happened about a year back (in year 2015), and that is when I had captured these thoughts. Today, with an intention to publish this note, I just asked Tanmay about what he recalls of interaction of learning tables one year back: the example, and its benefit and so on. Much to my astonishment, he recalled majority of the things and also told that he enjoyed in the beginning for why to learn tables. He said, “Later, with practice, we memorize and do not need to worry about the why part because we have understood it.”

This feedback from my son reinforced my belief in this article and here you are reading it J

Maths as a life skill and not merely as a course subject

Among various life skills that a child learns through the initial years, the attention paid to Maths is much lesser than what it ought to be. Indeed, Maths as a subject is taught at a very tender age during kindergarten, though not as a life skill. Maths has probably not been given the stature of life skill during schooling, which is where the gap exists.

I recall that in my engineering college, Mathematics was a part of the Humanities department, and not any of the science or engineering department. Even in the lower strata of society, to earn minimum livelihood, one needs elementary knowledge of maths. And that's where Maths stands to be recognized as a life skill and not merely a subject. It is a sad affair that the way Maths courses are structured, they expose a child to many lessons in Maths, but very little to build this skill as a way of life.

Lets take an example...When a child learns walking, what s/he learns is how to walk and not what it takes to walk. That's because parents know that learning to walk is more important than knowing what does it take to walk at that stage. Moreover, the child is so naturally engaged in learning to walk that the parent does not face resistance in making child to walk. Now lets look at Maths education. During primary school, a child is taught LCM, HCF, perimeter of a rectangle, prime numbers and such. Is the child being taught to feel the size of objects around ? E.g. the size of different rooms in the house can be easily compared by counting the number of floor tiles, and all you need to know is counting and not the knowledge of calculating area. In fact, the child will be thrilled to observe things around and feel them. This also generates curiosity to further explore different shapes and sizes. The need to learn geometry gets seeded, rather than first teaching the subject and then giving the examples. This is just the same as how a child feels the need to walk rather than first gaining the knowledge of what does it take to walk. That's in my opinion, Maths as a way of life !

To extrapolate it further, learning mathematical skill should be visualized in the same league as learning walking, speaking & reading a language, playing a sport etc. In subsequent articles, I would share more thoughts on how to nurture Maths as a life skill.  It is grossly demeaning to say that Maths is a difficult subject compared to other course subjects. Instead, one should say that Maths is difficult like mastering a sport or another life skill. That's when Maths will get its due honor and value in life.

Assessing inquisitiveness in education

I often wonder about the incompleteness of the assessment methodology that exists in our current education system. Traditionally, the assessment has focused on evaluating the answers given by the student for a set of questions provided. This helps to judge one's ability on certain dimensions like analytical, comprehension, memory etc. We also have assessment through lab practicals, which helps to judge one's ability to experiment and produce results. With time, advanced ways have also been introduced to assess one's creativity, be it in the form of making certain models, art-work etc. However, I feel one critical gap in current education system is the absence of assessing one's inquisitiveness.

The question is - why should you assess inquisitiveness ? Is it not inherent in any learning process ? Yes, it is inherent, and that's where the challenge lies. How can one enhance this ability to inquire and explore ? This is where the role of assessing this skill plays a vital role. It is a well known fact in quality management parlance, "what you can't measure, you can't improve". The measurement can be in tangible or intangible terms. This applies to the quality of output from the education system as well. If you can't measure inquisitiveness, you can't be sure to improve this skill. There are always exceptions, and several examples of great leaders, who reached great heights without any such support from education system. At the same time, there are thousands and millions others, who do not develop and grow as much as they can due to the inherent weakness of the education they get. We are talking about this mass segment. Needless to say, being inquisitive is essential for one to accomplish leadership in one's own chosen path.

So, how can we assess one's inquisitiveness ? Fortunately, the answer is not too difficult. In simple terms, it can be assessed in the similar ways as other skills. What is important is to be conscious about it and give its due importance as a part of overall education. Let me take a simple example. In a language comprehension test, a passage is given and then few questions are asked to evaluate the student's ability to comprehend an unseen passage. On the similar lines, can we demand the student to frame questions from the given passage ? To provoke inquisitiveness, evaluation can be based on the quality of questions framed. A question whose answer can reveal key insights or the human feelings or implicit message etc. can possibly be rated high. This is just an illustration, however, there can be guidelines for assessing the quality of question framed. Ability to ask exploratory and open-ended questions need to promoted. Another example could be - provide a graph from a business news article and let the student ask questions from it.

Why should we reserve the right to ask question and limit the student to only answer during assessment? This is just in-sufficient. Promoting an individual's ability to inquire and thereby preparing one to find answers to own questions builds a stronger person to navigate through real-world challenges. The results can be stunning. 

To quote a personal experience, I was coaching my daughter studying in sixth standard about the concept of percentage. I adopted an unusual approach of first asking her to self-study the chapter, answer questions given in the exercise, and then ask me anything which she could not understand. To my great surprise, she answered all the questions except two. This was indeed a great performance at the face value. It did not take me much time to discover that the questions she could not solve were those, which were different than the examples explained in the chapter. So, why did she get stuck up with these questions ? Simply because, she could not associate the meaning of percentage in the context of these two questions. It made me to ask her what is percentage, and she could answer it well much to my pleasure once again. So, where is the problem then ? I asked the next one - why do we use percentage or how would the life be different if the notion of percentage did not exist in this world ? And this was the real tough one for which she struggled to put the thoughts in place. And this is where the root of the issue existed for why she could not answer those two questions. Subsequently, I explained how percentage makes a difference in life, and also guided her to answer those two questions. The point to ponder upon is - could she have raised this question while reading the chapter instead of just limiting to what was stated there ? If she had asked this question (instead of me), it would have made a sea-change in what she learnt and how she learnt. 

This incident illustrates the power of being inquisitive. To inculcate this habit, we need to embed this as a part of the assessment in our education system. As I have highlighted through couple of examples, it is not difficult and does not require a big systemic turnaround to happen. For sure, what is needed is to recognize that developing and assessing inquisitiveness skill is critical and consciously, we need to extend assessment format to include this. As always, baby steps lead to revolutionary results and so will be proven true by assessing inquisitive skill and building a holistic education system.