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A Mathematics Teaching & Learning Resource.

This is a revision/self-teaching site for Mathematics. I envision that it will deal with the entire UK GCSE and 'A' Level syllabi eventually but I am starting off with the basics of fraction arithmetic and the basic algebraic techniques. The next topic to go live will be a series on percentages, which includes a lot of wordy questions (Everyone's favourite!).

I am fairly forthright in my views here, largely because I can. This is not a commercial site and I am not employed in any educational capacity any more, so if you don't like it, ignore it and move on. Nobody has to use it so you can keep your complaints and whining to yourself. Some people reading some of the articles and essays on this site, which are all my fault by the way, will inevitably take offense, particularly when I talk (all too frequently, I am afraid) about Mount Stupid from the excellent Dunning-Kruger research.

Now let me give you a rider to the above paragraph: I am, like most people, prone to errors. I don't like being wrong about stuff, so if you spot something which I have said which is factually incorrect, or inevitable grammar and spelling mistakes, please do leave a message using the contact page to let me know about it. The errors are my fault. Please tell me about them. If on the other hand you simply disagree with my stated viewpoints, like that the soon to be ex-POTUS is a crazed loon and the UK PM is just about as bad, well you should consider what the wonderful and late-lamented Kurt Vonnegut suggested, regarding doughnuts!

The site is not very pretty as I am not a graphic designer. Currently it works okay in a desk/laptop browser or a tablet. It is not great on small mobile devices at the moment, though I am working on a small screen style-sheet and navigation system for it, which will go live just as soon as it works properly, though most of my time, at present, is taken up with adding educational resources, which are my top priority. If anyone with the multifarious skills I lack is interested in helping out with the design/graphics, please do get in touch. However, please do not fill my inbox with commercial offers, as I have precisely no money to spend on this at all. Covid19 has destroyed my income like so many others and this is an attempt to give teachers, parents, carers and students who are also struggling financially and/or mathematically, a free resource to help out with their Covid19-messed-up educations. There is no shortage of fancy resources available to buy, but very little of quality in the public domain. Anyone interested in the philosophy behind this, please have a read of 'Mutual Aid: A factor in evolution' by Pyotr (Peter) Kropotkin. This book and the philosophy it lays out has, quite literally, changed my take on modern life. I think, for the better. Many disagree, though mostly in bad faith and/or ignorance.

Anyone is free to use the site and I do not intend for it to end up behind any kind of paywall. Nor will it be loaded down with advertising. Let me stress again that this is not a money making venture. If, however, in the future, people do find it useful and wish to contribute to its continued development, I will (with gratitude) set up a way of doing that.

Every topic on the site contains one or more of the following:

  1. An introduction, giving some basic information or history pertaining to the topic.
  2. A set of worked examples which are used to talk about the underlying principles.
  3. A set of exercises for self-assessment.
  4. Some puzzles, which relate to the topic. (These are currently in short supply due to time constraints, but they are going to happen, so long as I don't drop dead any time soon.)

For this educational methodology to work, you need to change your thinking from "What is my mark on this exercise?" and adjust it to "Where did I go wrong and why?". I have intentionally not written into this system a method of scoring because I am not interested in helping people toward a "satisfactory or better mark", but rather towards an understanding of why an error occurred, and how to put it right so that you do not make the same error next time. To this end, I have included an answer at the bottom right of the question. It is hidden initially by an eye. Clicking on the eye will reveal the answer, (though not in the instance on this page; you can click away to your hearts content and no answer will appear. However, in the exercises, clicking the eye will furnish you with the answer.).Eye

My expectation is that students will check their answer after each and every question they attempt. This is something which many students of all ages are pretty bad at, as it takes additional time. This is true, but I would argue that the advantages outweigh the disadvantages. The method which most students (and even some teachers) adopt is to do an exercise and then mark it, which in my opinion is worse than pointless, as all it achieves is that the student practises their errors until they become second nature. Just as when playing music, practising your mistakes makes you good at your mistakes. This is not a desired outcome. Now the authoritarians out there will be tearing their hair and bellowing about cheating and such. The only cheating that I know about is the pretense that you understand something which you do not. Do not practise your mistakes. Please! Check your answers every time. That way, you don't need to waste time doing questions which you have already mastered and can move on to the fun stuff later on. It is important to note at this point that mathematics gets more fun as you progress.

I am going to try to look at each basic mathematical concept, initially from the perspective of school level mathematics, but most importantly, trying to place it in its historical and practical context. I hope that it will grow to involve more academic essays and sections which hopefully will help people to start loving mathematics, logic and their applications to life. On this site, I am more concerned with building a mental structure to place your understanding of mathematics into, rather than just endless drills, though there is always a place for exercises with feedback as they can give us immediate feedback about what we can and cannot do. This does not mean that younger readers/learners are excluded, but many may require adult guidance much of the time. I will try throughout, to define difficult terms as I use them. What I hope to achieve with this site is to create a set of resources so that parents and/or teachers can have access to the sorts of connections and isomorphisms which generally, only Mathematics teachers know well. I will almost certainly borrow liberally from the work of others: Richard Skemp (author of "The Psychology of Learning Mathematics") and Georg Polya (author of "How to Solve It") are likely to be referred to often, by their work, if not by name and Bertrand Russell pops up a lot for blatantly obvious reasons.

I have set up a Glossary of terms, available from the main menu (the green box on the left). The hope is that this, also, will grow over time.

Currently, there are limited resources and only in the Number & Algebra sections, but more will be coming along as they are written/transferred from the digital resources I accumulated over the years.

© Richard Sharpe 14/01/2021