Enriching Mathematics Education
			Workshop for mathematics teachers of standards XI and XII
			    Monday and Tuesday,  26th and 27th  September 2016
 			         	IMSc, Chennai

				    	TIMETABLE

			Monday 26th September

			0900 am Registration

			0930am--1050am  S. Viswanath: Calculus

			1050am--1120am  Tea break (coffee, tea, snacks)
			
			1120am--1125am  Remarks by Prof. V. Arvind, Director, IMSc.
			
			1125am--1245pm  Balaji Sampath: Technology as a tool for learning.

					Abstract: Ananya is hooked to her mother's mobile.  She can spend even an hour playing games
					and seeing facebook and youtube videos.  But in class she gets bored within a few minutes. Even
					if a question gets her interested she loses interest if she cannot solve it in less than a minute.
					Teachers everywhere are faced with a new problem:  how to grab attention and use it for learning.
					In this age of information overload, the classroom as the space where learning happens and the class
					period as the time when it happens are both losing relevance rapidly.  The role of the teacher needs
					to change:  from the person doing all the 'teaching' to a person 'directing and guiding' the child
					on a learning path.

					Is it possible to turn the problem on its head and make technology itself a tool for learning?  This
					question cannot be answered by technology alone.  It needs deep research into how children learn. When
					does a child's curiosity to learn peak?  Often at these 'peak curiosity' moments children can spend hours
					learning.  How does one create many more of these moments?   As we go to higher classes, why do many students
					give up Math and Science?   Is the subject really more difficult? Isn't there a way to make the transition
					smoother? These are questions at the center of the learning research we do at AhaGuru.

			1250pm--0150pm	Lunch

			0150pm--0310pm  Anirban Mukhopadhyay: Looking at primes, probabilistically.

					Abstract: Primes are deterministic objects, as opposed to random objects. It was a
					surprise when in 1936 Harald Cramer came up with a random model of primes and managed
					to show an analog of prime number theorem. Using elementary probability theory, we
					would discuss some predictions of this model, some of which matches with known results
					while some others go far beyond our current state of knowledge.


			0310pm--0330pm  Tea break (coffee, tea)

			0330pm--0450pm  K.N. Raghavan: How many real roots does a real polynomial have?

					Abstract:    The fundamental theorem of algebra says that a non-zero polynomial has
					as many complex roots, counted with multiplicity, as its degree. But what about the
					number of real roots of a real polynomial? Circa 1830, following Fourier's ideas on
					this question,  Sturm discovered a simple and beautiful algorithm that produces this
					number as output.   It involves polynomials that appear as remainders in the Euclidean
					algorithm for finding the g.c.d. of the given polynomial and its derivative. In this talk,
					we will discuss Sturm's algorithm with proof and, time permitting, an application.

			0450pm  Snacks

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			Tuesday 27th September


			0930am--1050am  S. Viswanath: Vectors and Coordinate geometry


			1050am--1125am  Tea break (coffee, tea, snacks)
			
			1125am--1245pm  Shashidhar Jagadeeshan: Enjoying mathematics: only for the select few?

					Abstract: Clearly some of us enjoy doing and learning mathematics. This includes those who
					use it as a tool, teach or do research. Unfortunately, this is a only a small minority of
					human beings. A much larger number have had the misfortune to encounter mathematics as a source
					of fear, dread and low self-worth. Even if they had some mathematical inclinations, their
					'performance' might have been used to deny them access to certain opportunities. 


					In this talk we will explore what kills the joy of learning mathematics and dialogue about what can
					be done to change the experience of learning mathematics. We  will also examine the hypothesis that
					the only sustainable and holistic approach to addressing this problem is to create an environment where
					learners enjoy the world of numbers, patterns, spatial reasoning and logical thought.
 					


			1250pm--0150pm  Lunch

			0150pm--0310pm  R. Ramanujam: From solving problems to explorations

					Abstract: Consider the following problem: n is a positive integer between 1 and 20.
					Aruna adds up all the integers from  1 to n (both inclusive), while Babu adds up all
					the numbers from n+1 to 20 (both inclusive). Can they get the same sum ? If yes, for
					what value(s) of n is this possible ?

				  	This is an interesting problem in itself, but can we formulate another three or four
				  	problems, based on this one, to further explore whatever has been learnt ? We suggest
					that such explorations / investigations are crucial for doing mathematics in the classroom,
					rather than acquiring pre-determined mathematical knowledge.

			0310pm--0330pm  Tea break (coffee, tea)

			0330pm--0450pm  Parameswaran Sankaran: Discussion session.

			0450pm  Snacks


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