It’s world book day today, and despite dressing up as Rudy Baylor from “The Rainmaker” (you know, suit, shirt, tie etc) my pupils didn’t believe I was dressed up! I have been working on a pupil facing site, and wanted to include a page on suggested further reading, so far I have:
You all have textbooks to help with your course, and revision guides. If you want any further books/websites to specifically help with your course, try the revision page.
This page is a selection of books that are about maths, but not specifically related to the course. The maths in them should be accessible to A level maths students and they will help deepen your knowledge of maths.
For those of you considering further study they may be particularly helpful in shaping the direction you go in, and may provide excellent fodder for UCAS statements and university interview discussions.
These books are available from all good bookshops, we are looking at getting some into the library, and Mr Cavadino has a few of them which I’m sure he’ll lend you if you ask nicely.
Fermat’s Last Theorem – Simon Singh
This is Mr Cavadino’s favourite book. It is based around an enigma known as Fermat’s Last Theorem. Fermat was an amateur mathematician, but a brilliant one. He did Maths for the live of it and he came up with, proved and solved many great mathematical theorems and puzzles. When he died he left a number of theorems unproven. Slowly as the years progressed mathematicians proved them all, except one. His last theorem. One he posed with a note “I have a truly marvellous proof that this margin is too narrow to contain”. In the book, Simon Singh looks at the evolution of maths, and how this amazing theorem drove so many people to make so many amazing discoveries. If you only read one maths book in your life, make it this one.
The Simpsons and Their Mathematical Secrets – Simon Singh
Have you ever watched an episode of The Simpsons, or its sister show Futurama, and noticed a maths reference? Well so did the author. It turns out it’s not just a coincidence, but that the writing team are all mathematicians! For years they’ve been sneaking mathematics into the world’s most popular cartoon. The book looks at the maths they’ve included, why they’ve included it and how it relates to the episodes it’s in. If you like maths, and the Simpsons, then this book is for you.
The Code Book – Simon Singh
Another classic from the pen of Simon Singh. This one looks at the evolution of cryptography and cryptanalysis over the millennia and includes some fascinating accounts of where codes and encryption have been used throughout history. If you feel you may be interested at pursuing this as a career, or just have a passing interest in it, then make sure you read the book!
From Here to Infinity – Ian Stewart
Ian Stewart is a Professor of Mathematics and has written many fantastic maths books. This one is a particularly good one for learners who are interested in picking Maths at university. The book tracks the evolution of mathematics and gives a great introduction to many of the mathematical topics that will be covered on the course. The maths in this one does get quite heavy, and there may be a coupe of points where you can’t follow it. This shouldn’t matter as you should all be able to follow the majority of it and if you do read it and want to discuss any of it then mention it to your teacher. The variation of topics included in the books gives a good start point to future mathematicians who are unsure which areas of maths they would like to study.
Music of the Primes – Marcus Du Sautoy
Marcus Du Sautoy is a another Professor of Mathematics and he has also written many great maths books. This one is based around unsolved problems in Maths. He says the reason he wrote it was that when Fermat’s Last Theorem was getting a lot of press the non-maths world seemed to be of the feeling that when it was solved that was it, we had “done” maths. This is obviously not the case, as maths is infinite, and he uses this book to explore some of the big unsolved problems of the subject.
I am also going to include more books by Marcus Du Sautoy, some Rob Eastaway ones and Tony Crilly’s “How big is infinity”, then add books as I read them, but I’d love feedback on it and I’d love suggestions on what other books to include.
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.
A lot has been said recently on textbooks, the benefits they have and the bad press they get. This has had me thinking a lot about them, and their use in lessons. I rarely use them, certainly not the way they were used in my own schooling, but this doesn’t mean that I don’t think they have their uses.
Why do they have such a bad press?
I think they bad press comes from bad use of textbooks. I remember when I was at school lugging a ridiculously heavy bag around all day every day because there was a huge textbook for each lessons. I remember many lessons which began “Turn to page 6, Stephen (or whoever) can you begin reading.” then after the page was read the class would attempt the exercise. I remember a biology teacher who read the book to us, she’d fire questions off if she thought you weren’t listening. I sat next to Liam, and we’d sussed that you could answer the questions if you had the textbook on the correct page. One time the lesson was on organs, and the question was thrown at Anthony, who sat on the next table along. Liam and I often gave him answers. This time the question was “what’s the largest organ in the body”, I whispered “pipe organ”, which he then shouted out. It was hilarious.
I could go on, but I’m sure you all had your share of uninspiring textbook lessons. I’ve seen them as a professional. I witnessed an A Level lesson where the teacher sat at the front and read the textbook to the class verbatim. It struck me as rather pointless, as they all could have read it themselves. I’ve seen a KS4 teacher, when I was an Nqt, hand out textbooks with the instruction “look at the example on page ten, then attempt the questions”.
All these examples are uninspiring, and not conducive to good learning. But I think it’s unfair to lay the blame on the textbooks themselves.
How can textbooks be used then?
During lessons, there will be a point when you want the students to do some work. Practicing a skill or solving a problem. Using textbook exercises isn’t necessarily worse than a worksheet or questions on the board. In fact, it could be argued it’s better. It’s a greener and cheaper long term alternative to a ton of printed worksheets. The right textbooks have extension work built in, or offer a selection of exercises of differing difficulties. They also usually have plenty of examples, so learners can use them if they’re struggling, then can request help if they still need it.
My favourites of the ones I have are probably these for KS3/4:
And these for KS5:
Within all these books there are some great things, but none of them are what I would call ideal. Each has plenty of flaws. I find that having access to all these, and many more, textbooks allows me to use ideas, examples and exercises from them as and when required. I sometimes think I should write one, it would be great!
So you think the right textbook would be fine?
Not on their own, no. The recent Sutton Trust report showed that a teacher with strong pedagogical subject knowledge is extremely important to the learning of a class. The right textbooks could aid these teachers, not become a band aid to cover for poor teaching or teachers with shallow subject knowledge. I also wouldn’t like to see them used in isolation. There are many other activities that can aid learning. Things that are quick and easy to check pupils have correct without the need to check each bit, resources such as Mathsloops and Tarzia or activities on mini-whiteboards. All these have a place in lessons, and all would be complimentary to the perfect textbook, which would aid, not replace, good teaching. Examples would be additional to the lesson and offer help learners who are still struggling.
Here is the BBC report into the comments by Education Minister Nick Gibb on textbooks.
Here is a nice article from the inside classroom project entitled “Why textbooks matter”.
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”
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.
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.
Today I read this phenomenal post by Tom Sherrington (@headguruteacher) about books he has read over the course of his life. He mentioned in his post he hoped others would follow. I then read this incredibly moving piece by Chris Waugh (@edutronic_net) who spoke about the literature that had a massive influence on him over his life. This made me think about reading, and the things I’ve read. I love reading, both fiction and non-fiction, but I don’t find as much time as I would like to engage in it.
When I was very small I apparently used to insist that “the three billy goats gruff” was read to me every night, I reckon I still know it by heart! At primary school I read Asterix books, and very little else. The teachers I had at primary school didn’t appreciate the genius of Goscincy and Underzo so made me read other things. Most of which I’ve forgotten, but I do recall a series of factual books I loved. It included the story of Edward Jenner and James Phipps, and the story of tightrope walker Paul Bondin. These two stories stuck with me more than any other from my primary school days. Thinking on it now, I don’t think my reading repertoire actually was that limited, and that was thanks to my mum. She took us on regular trips to the local library to take books out, and bought us a veritable library of our own. I remember loving the Railway Cat series by Phylis Arkle, the Professor Brainstorm books by Norman Hunter and the complete works of Betsy Byars (The only one of hers I didn’t like was “The Animal, The Vegetable and John D Jones” which bored me), Ruth Thomas and Nina Bawden (Carrie’s war is amazing). Blimey, that’s actually quite a lot! There were many more too, so clearly my earlier claim was clear nonsense.
When I reached high school I had lost the buzz for children’s stories, and for a time read nothing but autobiographies. Musicians, Sports stars and actors. I remember reading Eric Cantona’s in its entirety in one sitting on Christmas day. Then one day my friend Matthew handed me a book and told me: “You need to read this, it’s phenomenal.” The book in question was “The carpet people” by Terry Pratchett and it was, indeed, phenomenal. This was the first of two books Matthew did this with. This one was when we were in Y7. The next would be two years later. After reading the carpet people I was hooked on the writing of Terry Pratchett, and I spent the next couple of years reading his back catalogue and nothing else. The only none Pratchett book I remember reading during this period was “The Cuckoo Sister”, which we studied at school. I quite enjoyed it, but it didn’t leave a lasting impression. I assume we read other stuff during this time, but I don’t remember it!
Then Matthew handed me another book, “Of Mice and Men”, with a similar line. He gave me it on the bus home, I missed my stop because I had become engrossed in it. I thought it was brilliant, and have read it many times since. This sparked an interest in other books. My mum has a collection of classics which included “Grapes of wrath”, another fine book. I read “Tom Sawyer” (a great book) and “Huckleberry Finn” (a truly amazing book). My reading had widened but I was still reading Pratchett, Gaiman and the such and was enjoying the contrast.
There were also many texts to study at school, some I’ve forgotten entirely, but some stuck with me as I thought they were brilliant. I loved MacBeth, The importance of being Earnest, The Speckled Band, Examination Day and Lamb to the Slaughter. I loved the poetry of Healey, Armitage, Owen, Byron and Hughes.
About this time a modern day retelling if Great Expectations, starring Ethan Hawke, was released. I loved this film and so read the book and was totally blown away (not quite as blown away as my English teacher, Mr Gibbons, was when I appeared at his room to tell him I’d read it, loved it, wanted to discuss it and wanted his advice on which of Dickens work to read next!). I read A Christmas Carol, Bleak House and The Pickwick Papers and loved them all. I then read a tale of two cities, and was disappointed. I had heard it was his finest work, but I didn’t think it was a patch on the others I’d read.
These books helped me understand the world, and the people in it. As I grew up I read many books and plays from many genres. I had a classics phase, where I read Metamorphises, Aeneid, Illiad and Odyssey, truly living them all, but preferring Homer to Virgil and Ovid. I had a real Gothic phase, reading Daphne du Maurier and Mary Shelley, I read a lot of Marx, Swift, Orwell, Huxley, Miller and Foot. I continued to read Sci Fi and fantasy, really enjoying Douglas Adams and Hg Wells. Its not only classics and Sci Fi though, I also love thrillers, particularly the work of Dan Brown, Lee Child and Stephen Coonts.
I love to read science and maths books too. Simon Singh’s, Ian Steward’s, Stephen Hawking’s and Richard Dawkins’s especially. I thoroughly enjoy “The science of the discworld” series, where Pratchett weaves a novella around some real hard science from Ian Stewart and Jack Cohen, combining two of my favourite genres!
These days I also read a lot about education, blogs, articles and books, all of which I find interesting, fascinating and enjoyable.
I thought I’d end this post with a top 5. My favourite books:
At 5: The Carpet People, Terry Pratchett : A phenomenal and funny book that got me back into reading fiction and opened my eyes to a whole new world.
At 4: Of Mice and Men, John Steinbeck: A phenomenal book that entertained and moved me. I have often said this is my favourite book, but in writing this post I have realised there are a few I prefer. Again, this book opened my eyes to q whole branch of fiction I was unaware of.
At 3: The Adventures of Huckleberry Finn, Mark Twain: This book is amazing. It is a dark satire on all that Twain viewed to be wrong with the world. It is hilarious, thought-provoking and entertaining. When I finished reading it, I read it again, straight away.
At 2: Great Expectations, Charles Dickens: this book is immense. It made me realise that even though the world has changed so much since then, the relationships and interactions still have relevance in our world. It made me thirst to know more about the time, and it made me seek out my English teacher to discuss it at a higher level. What more could you ask for in a book?!
At 1: Fermats Last Theorem, Simon Singh: Maths, that’s what! But seriously, this book is amazing. It isn’t just about the maths, it’s also about the mathematicians and the time. It follows the progress of mathematics from its inception and the stories the emanate around it are thrilling, funny entertaining and at times stranger than fiction. A truly brilliant book. (Read my fuller review here.)
While writing this list I’ve changed my mind numerous times, on the order and what should be included. I’ve settled on these because I think they are brilliant, and some of them led me to whole new genres. Some of the ones that nearly made it: Death of a Salesman, Hitchhikers Guide, Odyssey, Demons and Angels, Wages of Sin, Good Omens, Rebecca, MacBeth, The Time Machine, Henry V and there are many, many more.