Mathematics
I enjoy helping students fulfil their potential and achieve their best by building both confidence and enjoyment from the Mathematical challenges presented.
I love to teach and I especially enjoy it when I can see that the penny has dropped and that a student fully understands something which they first thought impossible.
I try and make Mathematics a fun lesson so that the children want to learn; I need to catch their interest. Whilst it is a generalization, I have found unfortunately, that within the UK it has almost become accepted that Mum or Dad or both are not good at Mathematics and so it doesn’t matter if their child is likewise less than enamoured with the subject, and that the child doesn’t need to try.
My teaching approach is to focus on what children normally find difficult and the common errors and misconceptions they consistently make; such as, when you multiply the answer is always bigger. Once these are explained a child is less likely to be caught out. I also make sure that I break down the concepts into a lot of smaller steps which need to be addressed as we make progress and they develop. I listen to the child as we go along and spend longer improving confidence if required or move along at a much faster pace if that is required.
Teaching Mathematics at any level but especially at GCSE I tend to have 2, 3 or even 4 examples of a question type until a child tells me they are confident enough to have a go on their own. I also change my explaining method if that is needed to understand the concept. I then have usually, 8 questions ready to do. We spend as much time on these as the child needs before moving onto the next component. Luckily when tutoring we can go at the pace of the child, move on more quickly if they are happy to or spend more time fully understanding the concept.
Teaching to younger children works in the same way; identify the common issues, explain them, and what to do. They may require more pictorial examples or other methods. Indeed, all children will have a method of learning which works best for them; merely listening, in written format, in pictures or diagrams and/or perhaps involving movement. These learning styles are also important when tutoring a person.
I have many textbooks, which I use, covering all the age ranges. I have found that published Mathematics books don’t do what I feel a child needs, so I write many of my own. Here I explain things in detail using questions but presented in slightly different ways. I develop the skills into smaller steps so the children can see the connections. Then I have my TO DO questions for when a child is confident and happy enough to have a go.
Politicians tend to get focused on education it’s decline etc. and feel they need to step in and address the issues as they see them. This led in the 1990’s to them thinking that teachers were not necessarily teaching what they thought should be taught. This led to the introduction of the National Curriculum in 1989.
This was fine for a few years but then they thought they should check what was taught, so they introduced S.A.T.’s. Children can be tested at the end of each Key Stage; Year 2 KS1, and Year 6 KS2. This has become very political in recent years and many schools have pulled out.
The reason many have pulled out is that this has really impacted on what children are taught in Primary Schools and their stress levels. Unfortunately, given that tests are now in only Mathematics and English, and that schools are then judged on these results, this has led to many children receiving only those subjects. Quite often in my tutoring I get children telling me in the summer term, after SATs, that they have had a week of art. When asked why the response is we haven’t done any yet during the year. This is the case for many untested subjects.
This political scrutiny continues, and we quite often get a new government who feel they need to put their stamp on education. I am sure it is good for them but unfortunately not for the poor children and teachers who get left to pick up the pieces quite often at very short notice. This at GCSE level particularly, has meant extra stress for those children and teachers involved.
I always start a session by checking that what was planned is still what they want to focus on. Sometimes they have an issue which has arisen and they would like to look at that instead. That is fine by me as it must be important otherwise they wouldn’t have brought it up.
Reviewing the the work previously. This encourages the student to demonstrate their understanding and boosts their confidence.
In the lesson I introduce a new step or concept and I explain how to use it by working through examples together. I check after each one whether they feel confident ‘ to have a go’
Exercises on different levels. The student practices the new concept on questions in the same format. However, the level of difficulty increases to ensure they really understand and are confident in its use.
In the past we had O Levels, meaning Ordinary, and A levels, meaning Advanced. A level still exists but O levels were replaced many years ago by GCSE’s. The reason being that we had two levels of schools; those which were deemed academic, the Grammar school, and those which were for people who were less academic, the Secondary Modern.
This led to two types of examinations:
GCE General Certificate of Education ( the O level ) from the Grammar Schools and
CSE Certificate of Secondary Education from the Secondary Modern schools.
These were then amalgamated into the GCSE or General Certificate of Secondary Education
However, they still split them into two levels: Higher and Foundation papers.
Traditionally GCSE Mathematics for many years was easier than the older O Level. The reason for this was that at O Level they gave you a Mathematics question. You then had to work out how to address the question, know the mathematics, and do it to get the answer. GCSE on the other hand led children through by doing a series of mini questions which led to the final answer. Equally at O Level people were expected to know all the formulae.; GCSE gave them a formulae sheet, so they didn’t have to learn them.
This is now beginning to change, we are seeing questions which are more like the older O level; here is the question, work out what to do and do it. Secondly, they are working to get the children to learn all the formulae. This has been a bit hit and miss with the onset of the corona virus; Covid. I have also seen them introduce areas within Mathematics that I didn’t come across until A Level.
So, GCSE is getting harder. This means that in comparison to say twenty years ago, let alone 1986 when they were introduced, children’s abilities are further developed.
Do you have any questions?
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