Tag Archives: Mathematics

Coding is not the answer (for every question)

23 Nov

There is a movement gathering steam at the moment with the aim of proliferating coding education, in itself a fine idea. Computers are everywhere, they are harder to detect than before and people need to know when people are using computers to game them – understanding a little bit of computer science is somewhere between very helpful to essential for these things – Defense Against the Dark Arts for the contemporary developed world.

Somewhere out of this movement has emerged a second movement proclaiming that teaching coding will teach people to think – seemingly an insufficient number of people were thinking until programmers started banding together to enlighten us.

Yes, part of my objection is to the slightly condescending way these people relate to the rest of us rather than their actual arguments, but there I still have objections to the content of their argument as well.They mainly stem from the fact that they’re arguing for programming as a way of teaching thinking as though other ways of learning to think were not available. In point of fact, the notion of teaching is at least as old as Socratic philosophy, and exists in a wide variety of forms, from Western and non-Western perspectives.

Sometimes coding proponents go as far as to suggest that coding is an ideal to learn maths or logic. Maybe they have a point about logic – formal logic studies maybe too esoteric for a lot of tastes.

On the other to recommend programming as a way of learning maths is kind of odd. You can only learn maths by learning maths. Natural aptitude for maths is highly correlated with natural aptitude for programming – it’s hard to imagine those weak at maths will have an easy time in programming.The strong ones will learn whichever they spend time on – either way time away from maths coding is just time away from maths.

This last is the crux of it – the proponents of coding in schools discuss the idea as though they are several hours per week of fallow time up for grabs. There are not. Something else has to go to make room for time spent coding. My personal guess is that most of the proponents of the coding in school idea are thinking of something in the humanities rather than a science or maths subject (although at least one self-identified software developer commenting on another blog wanted to reduce arithmetic teaching in schools – as if our society wasn’t innumerate enough!). I’ve read a number of data scientist cvs  – if I could change the education of that group of people, I’d be taking coding out and putting English lit in.

MOOCs and Mathematics Self-Learning

21 Oct

Over time, this blog has morphed from being about actuarial self-learning to being more about mathematics and statistics self learning, reflecting my personal career peregrinations. I kind of hope that such readers as there are not too turned off – to me it seems there is a lot of crossover. It also seems, at least from reading forums for actuarial learners (weak evidence, so feel free to provide your own counterpoint), that insufficient mathematics is at the root of a lot of difficulties that actuarial students discover along the way.

I intend to soon write a blog piece about my attempts to learn linear algebra and group theory via the slightly indirect route of learning about symmetry groups in crystallography, but today I just want to make a quick observation – the MOOC revolution isn’t coming, at least not yet, at least for mathematics.

2013 appeared to be the year of the MOOC. There were new MOOCs springing up all the time, in an ever wider array of subjects. Today it seems like the revolution has stalled – looking at Class Central, the MOOC aggregator, there are only six entries under the heading ‘Mathematics and Statistics’ (Recently Started or Starting Soon – there were also 17 courses in progress, of which 5 were non english, and two were kind of maths meta-courses a la ‘How to learn maths’), of which three are in Languages other than English. At one stage, MathBabe forecast that MOOC offers in the maths subjects most associated with non-mathematicians – single and multivariable calculus, elementary linear algebra mostly, probably also intro stats for non-statisticians, would put tertiary maths departments out of a job.

To me, unless there is growth in the courses offered – including at least a selection of the standard undergrad maths major subjects (so far, no English language abstract algebra or number theory), MOOCs, for better or worse, just aren’t going to take over the world of teaching, or even be a supplement for students beyond first year.

Self Learning Mathematics

9 Sep

The theme of this  blog has always been self learning – we started at self learning actuarial studies, have dabbled in self learning predictive modelling and now we are looking at self (re) learning mathematics, in order for a deeper push into predictive modelling and statistics.

I was reminded of the self-learning angle the other day when I stumbled across this blog:

http://latinandgreekselftaught.blogspot.com.au/2011/05/teaching-yourself-latin-and-greek.html

which charts the adventures of a gentleman self-re-learning the Latin and Ancient Greek he learnt up to the point he left tertiary education now that his time in the workforce has ended.

We have in common that there is an element of dishonesty in calling this ‘self-learning’ – this blogger above left tertiary education with an enviable grasp of the languages, helped by lecturers at uni and probably his high school teachers. He wasn’t going to stumble because the ablative case was too weird to understand, or become disheartened by deponent verbs.

In my case, I am re-learning some material that I have seen before and some other material that I haven’t seen before, and next year hope to take Linear Algebra, Abstract Algebra and Number Theory courses as non-award subjects to make sure that I have learned that material correctly.

Compared to the blogger, at least I have the advantage that where I have seen the material, it is only four or five years rather than 35 or 40 years since I worked with it. At the same time, half the motivation is to study some branches of mathematics that I think I should have studied before taking somewhat more advanced studies – Linear Algebra especially, which is obviously a foundation of statistics and spectral analysis.

My current foray into re-learning linear algebra is being supported by Serge Lang’s Introduction to Undergraduate Linear Algebra, which seems to have a terrible reputation among Amazon reviewers and commenters on places like math stack exchange. I think the reason is that the pace is fairly brisk. 

For my own part, I find the brevity a little bit refreshing, even when I am looking at stuff I have never seen before (or at least have no memory of seeing before!) The best part, is the portability which allows me to put it in a coat pocket, and take wherever I am going (some not true of the calculus text I used, by Anton Bivens Davis). Despite its brevity, it also seems to get to material which is advanced enough for my purposes – just short of the lecture notes for the course I plan to do next year, without the distracting ‘matrix operation’ notation and covering just about all of the same topics within the subject.

I also mentioned before that I had taken some more advanced studies in statistics and spectral analysis than my command of Linear Algebra ought to have allowed – it is certainly pleasurable to have various puzzles and obstacles of past studies resolved, although frustrating in the sense that I could have done better at the time with just a smidgen more Linear Algebra knowledge at my fingertips.