Continuing the saga of Pure versus Applied

I want to start the discussion this time by posting an interesting problem –

It concerns the number of ODD and EVEN numbers which appear in Pascal’s triangle. The question is as the triangle gets larger, what is the proportion of even numbers appearing in the triangle? Does it converge to a limit?

row 1 :        1
row 2 :     1    1
row 3 :   1   2   1
row 4 : 1  3   3   1

So only 1/10 or 10% of the numbers are EVEN

I am putting it here in the same form as shared by an awesome mathematics teacher I was fortunate enough to work with in Tokyo. This is an example of pure mathematics-this problems will develop deep thinking and problem solving skills required  by all lifelong learners but then the problem on its own does not have much value outside of the classroom.

I have discussed the Pure versus Applied with several mathematics teacher and all emphasize that real world application should not be forced upon a concepts.

In the words of the Jennifer Wathall who is a promoter of concept based learning of mathematics and the Head of Mathematics at Island school, Hong Kong- “Maths does have real life applications but because of the beauty of this subject, mathematics learning also develops critical thinking and problem solving. Students may be given opportunities to think logically and pattern seek (an innate quality all human beings have)”.

I recently attended a talk by Professor of Mathematics Education and he made a very interesting point – that if we are going to teach mathematics only for its usefulness, than very little would suffice. Mathematics should be taught as a tool for communication.

As a teacher or a parent if one really wants to look at relevant real world problems then read Dan Meyer’s blog-



IB too is now branching into Pure and Applied Mathematics. Here are the link for the IB blog that mentions it

For those who want to solve the problem – do submit your solution!!!

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