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Socialist Mathematics Education

October 22, 2015 1 comment

Earlier this week I was in the Brotherton Library at the University of Leeds doing some reading for my dissertation. I saw this book and couldn’t help but pick it up:

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Socialist Mathematics Education edited by Frank J Swetz.

This wasn’t particularly relevant to my dissertation focus, but being a socialist and mathematics educator I was intrigued..what makes mathematics education socialist?

I embarked on a a mission to find out, but it turns out it wasn’t actually the mathematics education itself that was socialist. It was a study into the mathematics education that was happening within “socialist” states. I use the inverted commas as it seems the authors have a blurred definition of Socialism that seems to encompass Socialism, Communism and those regimes that are set up I  their name that don’t hold true to the ideology at all.

The book was released in 1978 and the countries it looks at are: USSR, East Germany, China, Yugoslavia, Sweden, Hungary and Tanzania.

There are detailed chapters on each state and the mathematics education within it, and the final chapter looks at themes and differences. It’s a very interesting read, if you are into that sort of thing.

One commonality that occured within these states was the heavy government debate on Maths Education, to a level where they were discussing the benefits of different approaches to each topic. One example cited was a debate on whether the vector approach to geometry was the best method. The authors pick out the positive of this as increased buy in from Economists, Labour leaders and other areas as they have a say and it increases the profile and visibility of education reforms. I agree with them that this is a positive, and feel that Gove’s greatest feat, whether you love him or hate him, was bringing Education  back to the forefront of political debate.  He made it a topic discussed around breakfast tables across the country and that can only be a good thing. The flip side is that this could de-skill teachers and remove from them some of the independence that is require in their classrooms. So educational debate on this level is good, but we need to be wary of producing something over prescriptive.

Other benefits of this approach to a collaborative approach to maths education from all sectors suggested involved the curriculum itself. The schools were trying to produce people to work in the government factories and industries and as such there was a strong focus on maths and science for all. There was also good links built between the education sector and the employers.

These societys all showed a heavy focus on mathematics, believing that mathematical advancement is paramount to the advancement of society. This lead to a hollistic approach to maths education with the aim of ensuring all young people had a strong foundation in the subject. This is an ideal I believe we should all be striving towards.

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The Code Book – A Book Review

March 4, 2015 Leave a comment

It may not surprise you to discover that Simon Singh (@SLSingh) is one of my favourite authors. I have previously reviewed “The Simpsons and Their Mathematical Secrets“, and “Fermat’s Last Theorem“, the latter of which is still my favourite ever book.

The Code Book” came out quite a while ago, but I’ve only just read it, and as with Simon’s other books I was hooked pretty much straight away. The narrative Simon weaves throughout the ages is amazing. Seamlessly switching between the hardcore maths of the subject and the historic events that drove the discoveries. What did Mary Queen of Scots use codes for? What about Julius Caeser? How brilliant was Alan Turing?

I was lost I’m a world of espionage, war strategies and amazement at how cryptographers (code makers) and cryptanalysists (code breakers) managed to keep in out doing each other, whether the driver was military power or purely academic.

The book covers some heavy maths, but it is broken down into terms that anyone with a high school education should be able to follow. At times I felt it was broken down a bit too much, but I realise I gave quite a strong mathematical background, and the subject of codes may appeal to people who don’t.

This book is a great read, a must read for anyone with the slightest interest in codes, which is probably a growing number in tge wake of the imitation game! I think if I’d read it as a teenager I may have ended up in cryptanalysis! There is also a version of the book aimed  at young adults.

From Here to Infinity, Ian Stewart – A Book Review

September 16, 2014 2 comments

I finished this book a while ago, but haven’t got round to reviewing it yet, so thought I would jot down my thoughts belatedly.

Ian Stewart is an author whom I first discovered through Terry Pratchett. Together (and with Jack Cohen) they penned the “Science of the Discworld” series of books which use stories based on the Discworld to explain the science of our own world an universe, if you haven’t read them, I would certainly advise you do! I enjoyed them, and so I thought I would enjoy this one too.

From here to eternity had me hooked from the opening salvo, a paragraph so powerful it made me stop and write this blog post. Here is an abridged version:

“One of the biggest problems of mathematics is to explain to everyone what it is all about. The technical trappings of the subject, it’s symbolism and formality, it’s baffling terminology, it’s apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were summed up as ‘a lot of tadpoles drawn on a row of lines.’….. The symbolism of maths is merely its coded form, not its substance…. Mathematics is not about symbols and calculations, these are tools of the trade….  Mathematics is about ideas…. It is about how ideas relate to each other….understanding why an answer is possible…. good mathematics has an air of economy and an element of surprise. But above all, it had significance.” (Ian Stewart)

I was nodding along from the get go and my mind was entirely hooked from the get go. Stewart uses humour and anecdotes to weave an engaging tale around some really heavy mathematics, and all the elements add up to a thoroughly enjoyable book.

While reading it I found my love of group theory, graph theory and knot theory rekindled. The booked took a surface view of the topics and I found these tasters made me yearn for more. There were also area’s I knew little about, such as non-euclidean geometry, which I now have the desire to research further.

The book is exciting, and informative and I would urge anyone with an interest in maths to give it a read. Especially those embarking on a degree in maths who don’t yet know the area’s they want to investigate, it will give them a great taster.

Categories: Maths Tags: , ,

Nix the Tricks – A Book Review

July 15, 2014 3 comments

A little while ago I wrote a piece around BIDMAS and the problems it can cause just teaching mnemonics without bothering to fully explain the underlying concepts. It was borne of the frustration of many conversations along the lines of

“Sir, you’ve got that wrong 9 – 3 + 2 is 4 because you do addition first.” 

“No, addition and subtraction are inverse operations, they are of the same order you we perform them left to right.”

“No, Mr so and so taught me that you always follow BIDMAS”

“AAAAAAAAARRRRRRRRGGGGGGGHHHHHHHHHHH”

Someone responded to my post with a tweet which linked to “Nix The Tricks“, which is freely available as an ebook, and I downloaded and read it.

The book itself is great, it is a collaborative effort by many maths teachers who share my frustration with the problems that teaching this sort of “trick”, rather than deeper understanding, can cause. The book has been put together by Tina Cardone (@crstn85). Tina and her collaborators go one step further that venting about the tricks and offer some brilliant alternative methods to help teachers who haven’t thought in detail about how to teach certain topics.

Its a fantastic book and I would advise any maths teacher to download a copy, especially those new to the profession.

 

20 Questions about C4 integration – A Book Review

July 15, 2014 Leave a comment

A while a go I got a copy of this fantastic little ebook authoured by Colin Beveridge
(@icecolbeveridge). The book is great and written in Beveridge’s usual style- accessible, witty and very informative.

The book covers integration. IT is based on the current Edexcel A Level spec and covers all the integration you need to know for that specification, not just the bits that are solely in that module. There are some handy mnemonics, some really clear and concise explanations and some very funny quips.

The book would work really well as revision guide, and is something students can dip in and out of if they are having trouble with a particular aspect of integration. I think the section on which integration to use is perhaps the most handy bit of the book.

I would wholeheartedly recommend this book as a companion to anyone studying integration, but it should be used as that, a companion. It is written in a way to review stuff already learned and add clarity to areas you are struggling on, rather than as a book for the original teaching of the subject.

I hope Colin is planning an update for the new syllabus, and I would also love to see print copies available.

20 Questions about C1 – A book review

February 12, 2014 Leave a comment

20 questions about C1 is an Ebook from Flying colours maths’s own “Colin Beveridge”. The book is a revision/help guide for pupils studying Edexcel A Level Maths C1. It is written in a way which takes students logically through the sticking points of C1 and gives plenty of help on the understanding of the topic, and plenty of little tricks and mnemonics to help them remember stuff in the exam. The book explains things brilliantly, and in a way that is humorous and engaging. I don’t think I’ve ever laughed out loud at a revision guide before!

My only slight criticisms of the book are that on a few occasions, i.e. transforming graphs and dividing fractions, the help is constrained to the “how” of it, with not the why. And that Colin dismisses completing the square as pointless, but I feel that it is great for explaining the quadratic formula, is useful for seeing if a graph has real solutions and has its uses for higher level polynomials for those who go past A Level.

Colin and I differ on our opinions on the best way to complete the square, but his explanation of the equating co-efficients method is superb.

If you, or someone you know, is struggling with any of the topics involved in C1 then I would certainly advise buying a copy for your kindle. It is far better than any of the other C1 revision guides I have come across, and would be worth the money for the jokes, or the story of “bad guy x”, alone!

You can buy the book here.

A Book Review: Fermat’s Last Theorem – Simon Singh

January 12, 2014 3 comments

Recently I’ve notice that there are a lot of signposts online to great maths books that are available. Flying Colours Maths, Wrong but useful and the maths book club (Which i hope to get involved with soon) are but three examples of places where you can find mention of good maths books. As a maths teacher I have found an array of purposes for reading them. Firstly, I love maths so I find them interesting. Secondly, they give me a deeper working knowledge of the subject and improving your deeper subject knowledge should be a key priority for all teachers. And thirdly, I have found many lesson ideas in these books.

I figured that this blog would be a good place to review some maths books as and when I finish them. I did think about going back and writing reviews of all the ones I’ve read, but I don’t think my memory will allow it. Although I have decided to review one I finished at the end of 2013 which is still fresh in my mind.

Fermat’s last theorem – Simon Singh

When I started in the sixth form my pure maths teacher, Mr Armitage, had a poster up which intrigued me (as the problem had Wiles, decades before). It was based around Fermat’s last theorem. It contained the theorem, Fermat’s cryptic note about a proof but the margin being too small and a timeline of near misses up to Wiles’ achievement. I asked Mr Armitage if he could show me Wiles proof, as I was intrigued. He response was, “I’m sorry, I can’t. The proof runs to over 300 pages and some of the maths involved is beyond my own comprehension.” I was a little disappointed but understood, and decided that one day I would like to be in a position to understand the proof (Not there yet… I’m still struggling a bit with Modular forms…).

Anyway, since then I have always meant to read this book, but I hadn’t got round to it until 2013. And boy was it worth the wait.

The book is fantastically written and takes the reader on a whirlwind rollercoaster ride through mathematics history, from Diophantus to Wiles. There is a real suspense thriller feel to it in parts, and even though I knew the outcome I found myself entirely absorbed in the story and needing to find out what happened next, at points even questioning what I thought I knew.

Simon has kept the writing in the main text to a level where top GCSE level knowledge would be enough to follow, introducing new concepts in a way that is easily digestible. He also uses the appendices well to explore some of the deeper issues. This is a good way to appeal to those of us with a deeper thirst for maths without eliminating any of his potential readership.

There were a few occasions I thought I would like more information on certain things, but the further reading section has signposted me to places to look.

All in all, I think this was the best book (that’s any book, not just maths book) I’ve ever read. It isn’t just limited to Wiles’ battle with Fermat, but rather an amazing look at the world of maths, and mathematicians, through history that keeps you guessing and leaves you wanting more.

If you have even the slightest interest in maths, you MUST read this book.

You can see Simon on Numberphile discussing the maths involved in the book, and his more recent title “The Simpsons and there mathematical secrets” here

You can buy his books here.

You can follow Simon on twitter @slsingh

And as I’m currently reading “The Simpsons and there mathematical secrets”, you can watch this space for a further review.

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