Mathematics Tuition - Teaching Philosophy

It might not surprise you to know that I could talk at length about the very complicated, but very fascinating process of teaching and learning. When I’ve been teaching teachers to teach over the last decade, I’ve been able to refer to my ‘joined up’ philosophy. All that this means is that I believe I am consistent, and that the things I talk about work together as a coherent whole.

First, I think the only thing we can ask students to do is to try. We all want them to do well, but we cannot insist that they are all mathematical geniuses. To this end we should celebrate and reward effort as much, if not more, than achievement.

I was a late entrant to the teaching profession. I had a career in the commercial world before qualifying to become a teacher. When I was writing an paper for my Degree, I referred to the Cockroft Report. It does not matter that it is now thirty years old, it still contains truths. The one which resonated and stuck with me, the one which I have always kept very high in my priorities, the one which I have tried to persuade teachers around the world to embrace, is “Give your students the opportunity to experience success”. A simple thought, which is almost an attitude as much as anything else. Experiencing success is the platform from which to push for higher achievement. First students must be given the chance to get something right! Then we have the start of something on which we can build.

I usually enjoy myself when I am with students. If I am not enjoying the process of teaching and learning that would very likely mean that the students are not enjoying themselves either. That would be a bad thing. That would be defeating our prime purpose. People are unlikely to learn effectively if they are not reasonably relaxed and happy. Our primary purpose is to have our students learn Mathematics, so by making everyone tense and unhappy, we are defeating ourselves.

My method of teaching is very likely to be different to what students have experienced previously. I am here to help, but that will certainly involve the students being asked lots of questions. I have found that it is amazing how much students can construct their own learning and I do whatever I can to draw that from them. Contrary to what many teachers seem to think, I find that the less talking I do, the more active the students are, the more likely it is that meaningful learning will take place. My job is not to TELL things to people, it is to facilitate learning.

In case you get the wrong idea, let me be clear that I will push, I will challenge, I will ask students to think. They need to understand what they are doing, and it will not always be totally comfortable. The Mathematical learning journey takes a very narrow path!

In the past students may well have been shown how to do something with one or two examples, then asked to work on lots of questions, then given a mark. This is NOT teaching. It is an approach which will work for some, but not for enough of the students to convince me that it is doing the job of teaching. I have enjoyed a great deal of success in the past by de-constructing the Mathematical topics, making links, taking small steps, working through a few parts together, checking for understanding … there are many steps and different routes we can take … but all the time we are seeking understanding, not just the learning of routines.

Sometimes students can be frustrated by this approach. It is not what they are used to, and they just want a quick answer. Understanding and succeeding with Mathematics just does not work like that. As I have said elsewhere, it IS difficult. All I can do is to make it as easy as possible. It does still require some determination to succeed. However, I have never seen anybody punch the air, whoop with delight, in other subject areas. The goal is to escape from the cycle of the student being frustrated and and not experiencing any success. Please note, sometimes this can actually result in the student becoming confused for a short while, due to them now being taught correct and reliable methodology.

For students who are very far behind their expected level in Mathematics, it will probably be helpful for us to find a point where they do have some understanding and then work forward with me through the curriculum material. Although this won't immediately help with their current classroom work, this process will deal with the students’ areas of misunderstanding and it is the nature of Mathematics that you cannot skip steps, you need to climb the ladder one rung at a time.

Students will also be encouraged to develop good skills with arithmetic, with ongoing practise of mental and paper calculations. This is an addition to other work. It is important to develop a sense of number. To put that in explicit terms, it is important to know that what your calculator is telling you is reasonable. Recent research has shown, as I’ve always innately believed, that a sense of number is an important foundation of making progress with Mathematics.

We might also do a little work on examination technique, but I am confident that the best foundation for examination success is actual understanding of the work.

I do very much believe in accentuating the positive. I very rarely, if ever, use some words which are common in too many teachers’ vocabulary. For example, you will probably never hear me say ‘wrong’. It might seem a small detail, but I do not use a red pen, I usually mark using a green pen, and students soon get used to the fact that I only tick the correct answers. In the same vein, and unlike a lot of Mathematics teachers, I do not make a big fuss about neatness, I do not insist that everything is lined up and answers underlined twice etc. I usually find that students’ work is much better presented once they understand what they are doing! And I am certain that it is the understanding of the Mathematics, which is really the important thing. And so on … there are lots of things like that which, quite honestly, have very limited importance and occupy too much valuable learning time with some teachers.

I may determine that it might help to give the student extra work to be done away from the tutoring session, that additional work has to be meaningful. It can be valuable and will be given if necessary, but it should not be a regular expectation. Any additional work will take as little as ten, probably twenty, but less than forty minutes.

When working in schools, I’m an advocate of educating the whole child, but still always maintain that the primary job is to teach the subject material first. With private tuition, the focus has to be on the subject. I will however, in subtle and more obvious ways, work on developing the students’ self-esteem, their standards of behaviour, self-discipline, self-motivation, responsibility, levels of courtesy and consideration. I am not a replacement parent, but I do very much believe in the legal requirement from my home country of the teacher being ‘in loco parentis’. That means that whilst your daughter, son or ward is with me, you can be confident their best interests are very much at my heart, and I will act in the place of a good parent.

Copyright 2014 - Richard Messenger

Copyright 2014 - Richard Messenger