JOIN USSpice up learning with creativity
Veena Prasad shows you how a fundamental algebraic formula can be taught with the use of some simple tools. This kind of teaching, she assures you, can spark the wonder in a child’s mind.
This is the first of a series of articles focussing on the importance of nurturing creativity and making learning as well as teaching an enjoyable experience with far reaching effects. Practical tips on achieving this are also provided. The first part demonstrates how a fundamental algebraic formula can be brought to life using simple tools on hand. Later parts discuss ways of bringing adventure into certain subjects that may be perceived as dull or boring or just plain difficult. The idea behind this approach is to kindle an interest in children, motivate them to nurture a passion for the subject, and learn for the sake of learning — and not just for scoring top grades, which although important, is never an end in itself. A learning born out of passion cannot help but lead to top grades, whereas a learning driven by marks alone cannot hope to sustain the passion.
Teaching algebraic concepts geometrically
Our formative years in school contribute in no small measure to how our personalities shape up as adults. We gain so much experience, information and skills that we forget that we quite possibly lose something as well. A recent incident at a school trip aptly illustrates what it is that we may lose, if we are not careful. A group of students were taken on an educational tour of a bird sanctuary. At the end of the trip, they were asked to depict the number and types of birds they saw in the form of a picture. There were thirty-four students on the trip and what emerged was thirty-four different ways of seeing the same data. It was a marvellous collection — ranging from a pie chart to a scenic drawing of different birds perched in different areas.
In contrast, every single adult drew a bar graph.
This speaks volumes about how we let creativity take a backseat to what we perceive as “the done thing”. As students get older they progress (almost without realising) from writing what they want to express to writing what is expected of them. They ask the kind of questions that they are supposed to ask, and not those that they want to know the answer to. The reasons for this could be many — ranging from a fear of being ridiculed for asking “silly questions” — to simply not having a question in mind, as a result of years of being conditioned to learn what is in the text book and accept that that is all there is.
This approach works to a certain extent, indeed, it has been working for many years, but in a rapidly changing world, is it enough? Clearly not, if we want to create the next generation of leader and innovators — which is a crucial need for our country at this stage. And the best place to start doing this is in the classroom. The following sections talk about a few small steps a teacher can take towards making learning creative, enjoyable and more effectively retainable.
Most schools in Bangalore have an integrated pre-school. And most pre-schools come equipped with Montessori material, even if they do not completely follow the Montessori methodology. The reason is apparent to anyone who has seen or handled this material — the colourful and child friendly objects make you want to jump right in and find out what it is all about. The surprising thing is that they need not be confined solely to pre-school, they can be very effectively used in teaching primary and even high school mathematics. The solid shapes are a great way of introducing three-dimensional shapes in primary classes. When a child can touch and feel the objects, the learning is deeper.
But most effectively, algebraic formulae can be taught geometrically — completely transforming a young mind’s perception of the subject. For example, consider the following formula:
(a+b)2 = a2 + 2ab + b2
The conventional way of teaching this is to write it down on the board for the children to copy and remember. A few problems are solved using this, and some children may try verifying the formula using different numbers. A test paper is set, most children get it right, and it’s time to move on to the next formula.
Now consider a slightly different approach. The teacher draws a line segment on the board measuring 5 cm. She calls this ‘a’. She draws another line segment measuring 3 cm and calls it ‘b’. She then shows the class a red wooden square of sides measuring 5 cm.
“What is this, children?” She asks them. They (hopefully) chorus “a-squared!”
She shows them another square whose sides measure 3 cm. Children chorus, “b-squared!”
Next two rectangles measuring 5 cm x 3 cm are produced. The teacher labels these ‘ab’.
She then proceeds to arrange the pieces as shown below, and voila — you have a square whose sides measure (a+b) cm. In other words, (a+b)2.
Following this, the children make notes, remember the formula and tackle exam questions based on this. The only difference is — six months later, they will clearly remember the concept behind the formula, and if they get confused they will draw squares and figure it out, rather than blindly relying on memory.
At this point, many readers may point out that the same can be achieved without the use of expensive Montessori material. That is absolutely right. A few pieces of cardboard will suffice, as will simply drawing it on the board. The reason for building the example around this is that the very idea was sparked by Montessori material.
Additionally, most schools have access to this equipment anyway, and once the teachers understand the usage, there is no limit to the number of ways they can be put to use.
Explaining a concept by writing it down is enhanced by drawing it, and this is further enhanced by showing it. In fact, one can go a step further by getting the children to make the squares and rectangles using cardboard, and perhaps they will come up with the formula all by themselves!
Practically speaking, this may seem like too many additional hours spent teaching one simple formula. However, this time should be seen as an investment, as it will undoubtedly save hours of repetition and revision in the coming months. As a bonus, we would have sparked wonder in a child’s mind, when she or he sees how beautifully everything falls into place in that enigmatic subject called mathematics. They may even be inspired to ask questions no one has asked before. This after all, is the first step towards discovery, and greatness.