Sinduja Ragunathan

One of my recent late night past time activities has been sitting with the good old R.D. Sharma textbook. Solving CBSE math questions isn’t exactly to be described as a past time activity, but as a PGCE student, I could be forgiven. Little would I have imagined back in the early 2000s that these books would find a place again in my shelf. Perhaps in my flustered moments preparing for the CBSE Board Exam, I had muttered something on the likes of… “I wish I had another shot to get this all right…” Sometimes we need to be careful what we wish for.

In any case, the guide, along with the NCERT textbooks, have been extremely crucial components in my PGCE preparation. This is one thing I do wish were present here in the UK – a standardized textbook that one can refer to. Although there are many books from companies like CGP and Pearson, they somehow seem more like practice books rather than a text to comprehend the key concepts, organized and presented systematically.

A video is sometimes a great way to break this streak of working out, and TED-Ed has some fantastic videos on math. Take this one, for example. Titled One is one…or is it?, it gets you to pause for a few seconds and ask, ‘Wait…what exactly is 1?’ It’s easy to take language and the concepts it evokes for granted. But more importantly, from a math education perspective, whole and parts are foundational to a lot of ideas a student will come across, and to stay with this theme and play around with it is perhaps crucial.

The video puts across the idea that 1 is an entity, and this entity is sometimes a composite made of sub-entities, which in turn could be complete or further breakable into components. This is nothing new, of course. But it’s a crucial shift of perspective that sometimes isn’t automatic. When we see 10 eggs, we see 10 ‘separate’ eggs, but rarely unify them in our mind and think, oh here’s ‘one’ bunch of eggs. On the flip side, when we see an egg, we think, ‘Here’s 1 egg,’ but seldom think, ‘Oh, here’s 4 1/4th parts of an egg’.

But why bother, really? What difference would it make, other than add an extra layer of processing or complexity in our daily life? I guess it’s more a philosophical muse on what composes a whole, separate unit. If the idea of 1 is just the boundary of what our visual system is able to distinguish as separate and concrete, and considering our visual processing system isn’t universal or immutable, is there a ‘1’ at all? Consider this comment on the video, for example:

“I know that this video seems like an exercise in stating the blindingly obvious, but actually it throws up a very interesting philosophical problem. This is: if no intelligent beings existed would 1 + 1 = 2? The common answer is to say, “Well yes, of course it would and we have simply discovered a truth about the universe”. But actually it is not as simple as that. The number ‘1’ (or any means of expressing quantity) is meaningless without the existence of certain ideas that can only derive from an intelligent mind. These ideas are those of identity, category, similarity, function, composition and so on… Two rocks hurtling through a completely mindless universe are only “two rocks” (i.e. 1 rock plus 1 rock) if the category of ‘rock’ or ‘rockiness’ has already been formulated, so these two objects can be identified as existing in the same set. Without these prior ideas “two rocks” is meaningless.“

Working out problems in an R.D. Sharma text isn’t exactly supposed to lead one to question what ‘s ‘1’, but sometimes that’s the interesting path the mind can take, and mathematics leads us to many such paths. If not exactly a GCSE brownie point, it will at least makes you a more interesting person on your first date.