Another seminar, another aftermath post.
Yet another season of ज्ञानवर्धक व्याख्यानमाला organized by Educational Resource Center, Jnana Prabodhini and I was again invited to give a talk related to mathematics. You can find report of previous talk here -> Playing with Numbers
Since I was not thrown out of the lecture hall by the kids despite cracking all sort of indirect jokes (like slide of Goku screaming Formulaaaaa!!) I was a little more confident this time around and chose to go with geometry. Thus the topic Curves.
Geometry is a very mistreated topic in schools. I don’t know about other parts of the world but in general geometry in schools is very simplified. (my opinion!) The toughest topic one gets around is circle. More than half of your stuff is solved by either Pythagoras theorem or Basic Proportionality Theorem. And no one bothers to ask some of the very basic doubts which should be asked. e.g. I believe in 8th standard or 9th standard Indian students learn about Irrational numbers. But till they reach Junior College (+1 or 11th) rarely they are exposed to questions which has an irrational number as the answer leave alone the difficulty level. Why? Also at the same time around they learn how to plot irrational numbers on number line. They always plot squareroots because it is easy when you correctly utilize Pythagoras. Fair enough. But why no one even bothers to ask the teacher why are we not plotting a single cuberoot? The answer that it is impossible to do so is acceptable but why not tell them that? Due to such ignorance about deeper understanding of geometry and dilution of syllabi students are satisfied with mugging up theorems.
So I thought what if I choose geometrical figures for which there are not many theorems and even if there are there will not be an iota of possibility of them having heard that. Thus I chose curves which they see everyday around but are not even exposed to their geometry unless they choose to graduate in Mathematics.
I discussed 3 curves Spiral, Cycloid and Cardioid. This time I faced some technical issues but they were mostly due to my old laptop, poor chap is nearly at the end of its lifetime unless I find dragon balls. The response was highly positive with more students opening up. I also discussed some scientific phenomena this time so they were very interested as they could try out experimenting at home. Lesson for me – teenagers are more likely to get interested in things they can do physically rather than something they need to do mentally. There were lot of followup queries with some students even starting to discuss the ‘stuff to do at home’ part in seminar hall itself. What else can make you happier than that lovely sight of a group of 4-5 boys of age barely 13/14 discussing properties and possible theorems of Cycloid 🙂 Or the sight of students discussing which curves are constructible by straightedge and compass alone and which are not 🙂
As usual thanks to ERC team for their help. The presentation is on slideshare -> Curves
Comments and suggestions are welcome. The presentation contains links to some unusable files. They and several of their alternatives are all freely available on internet. You should not have problem with that. Like previous time I would not recommend using this presentation as it is since it does not have many other demos and diagrams I drew on the blackboard while explaining things but it is recommended if you want to use it as a starting point for learning various curves.