N.J. is Noel Johnson. Noel and I both enjoy solving maths problems. His hobbies and approaches to learning, philosophies or "Main Vine" are similar to mine. Noel is a strong believer of learning maths by doing.
Here is an email he sent me, slightly edited to make it all easier to read. This email describes his passion about how and what to teach. Noel's Main Vine! [See Chapter 2 of my book]
The papers I sent him are Paper 1 and Paper 2.
Paper 1 is from Jo Boaler (youcubed.org) and Paper 2 is from researchers at Waikato University and concerns how to become a problem based teacher.
I think you could fairly say that the study Boaler et al (Paper 1 above) did was more about getting maths teachers to be more creative and interesting with the lessons dished out. When this wee country of ours comes to its senses and crowns me ‘king’ one of my first proclamations will be to ‘ban all text books’. I can recollect people I have worked with who methodically made their way through boring schemes that were built around some text book. And what’s more they compiled these colorful records of how their pupils progressed !
I must admit to having been also fortunate enough to come into contact with some very creative, clever and inspiring mathematics teachers. There will always be a place for a gifted mathematics teacher to take a selected group of pupils on to a special maths programme, just as a gifted sports kid can be slotted into a higher sports team early on – Brendon McCullan was wicket keeper for the King’s first eleven when he was in the third ( year 9 ) form, Chris Laidlaw left school ( King’s) and went into the Otago team then the All Blacks. There was a pupil at Waitaki boys about 15 years ago who was doing his masters in mathematics while in year 12.
There is genuine drawbacks associated with streaming, a look at its effect on Maori and Polynesian pupils will confirm that, it can be equally damaging and destructive towards European pupils also. The best part of that study was the emphasis and value it placed on expecting teachers to present work that is engaging, challenging and most of all interesting, kids thrive on it.
Have you checked out the results of all the effort that has been put into validating the ‘Collatz Conjecture ‘ https://www.quantamagazine.org/mathematician-terence-tao-and-the-collatz-conjecture-20191211/ , I have played a bit with it with the little ones I get at my local Primary but overall it is limited what I can take them down – hard to explain log-log graph to them, pointless in fact.
Mathematics is a rich body of knowledge produced by us over a long time, This should be incorporated into our lessons, My kids thrive on stories of Mathematicians and what they have done. They are like an open book and you can easily tell when you have turned the lights on in a lesson for them. For mathematics lessons it is ‘content’ and more ‘content’, especially material that makes them think that should be uppermost in all classrooms.
As soon as I can I plan to go across to Te Anau and kayak up the north arm to a hut I have longed to get to, The paddle is about 18km but the kayak moves along at around 6 knots, so around a 6 hour paddle, which is ok provided it is not too windy.
Enjoy your fishing, they look very appetizing.
1. https://www.quantamagazine.org/mathematician-terence-tao-and-the-collatz-conjecture-20191211/ This is mentioned above. Lothar Collatz likely posed the eponymous conjecture in the 1930s. The problem sounds like a party trick.
Pick a number, any number. If it’s odd, multiply it by 3 and add 1. If it’s even, divide it by 2. Now you have a new number. Apply the same rules to the new number. The conjecture is about what happens as you keep repeating the process.
2 to 5.
Here is an image of the results for a few numbers that track back to 1.
More to come!