Online tuition
More and more tutors are providing online tuition these days. I use a digital pen and an interactive whiteboard. Notes that I write are displayed on a shared screen and the student can also interact via this learning space. Documents in jpeg or pdf format may easily be uploaded. All that is needed is a stable internet connection at both ends. There are so many resources on the internet to enhance any lesson. I give about 50% of my lessons online and it is very convenient. Lesson notes may be retrieved at any time.
One factor in choosing online tuition is the lack of availability of good local tutors, if the student lives in a remote area or if you simply want convenience.
I currently tutor students regularly in the UK and overseas. I believe that it is going to be the future of learning. There are even schemes to introduce online teaching to poorer families by teaching several students at once. The cost is then shared equally, allowing parents who could never afford private tuition to be able to do so. Just imagine if a scheme could be rolled out like this in the developing world. Five or so poor kids from a South African township meet up at their local church or community centre and log on to computers or even just mobile devices. They have an interactive learning experience with a teacher in the UK and it costs them almost nothing because the relatively low cost per student is subsidised by the organisation they are meeting at.
How to motivate your teen in Maths and Physics
We all know that teenagers can lack focus during the important years that they are studying for GCSEs or A-levels. What with demands from friends to socialise and attention spans shortening by the minute (with mobile phones winning first place), parents can be tempted to try to do everything for their children at this time, including making detailed revision plans and checking whether they have completed homework. But doing too much in this way can result in a loss of a sense of responsibility and ownership of the results of their decisions. I recommend a softer approach where you encourage them to reflect on the subjects that need revision and how they need to spend their revision time most effectively. As a tutor, I tend not to set specific homework for students of this age group. I prefer to guide them to relevant resources and tell them what areas they need to be looking at in more detail. In this way, they feel that they are making the decision to revise or do homework rather than having it imposed on them. I think it is only the weakest of students or possibly those with specific learning difficulties who need their study time to be monitored in fine detail. You don’t need to be an expert in each subject they are studying but knowing how the curriculum is broken down can help you be informed. To find this out, you need to download the specification from the examination board’s website. In the case of the IB Diploma, this is called the Guide – for example, Physics HL Guide. These are lengthy documents but they contain information on the material covered as well as the structure of the assessment. Especially during their study for A-levels, the students themselves are the best ones to know which areas they need to work on most. They are surprisingly good at this.
In the event that you feel that your child is not working well, I recommend that instead of making your enquiries about how their revision is going sound too intrusive, you could ask them encouraging questions such as ‘did you find that maths website useful’ or ‘is your school hosting extra revision sessions this term’.
To maintain interest in mathematics, at least at GCSE level, an appreciation of the applications of mathematics in everyday life can be very motivating. There are so many great documentaries available to watch on demand. There is the very impressive BBC documentary ‘The Story of Mathematics’ by Marcus du Sautoy. This can be found on the web. To stimulate interest in physics, there is ‘The Sky at Night’ and the great Physics Footnotes website that offers gifs and video clips demonstrating principles in physics. If you want to see how a golf ball deforms when hit by a golf club in slow motion, this is for you. News aggregate websites collate great science news clips for the general public. For example, the Apple news app allows you to choose to have relevant news items pop up in your feed.
An interest in computing can be exploited to develop their logic skills. After all, mathematics is basically the application of logic and the process of deduction. The Raspberry Pi is a tiny computer available for only about £34 that is very versatile. People learn to code with them. There are many websites that offer ideas for projects using the Raspberry Pi as the core. It has become very popular and a host of sensors and accessories are available for it. People have built their own digital radios and mobile phones with the Raspberry Pi but to start with, a less demanding project would be advisable.
The jump from A-level to university is very large so it’s best to encourage them to be self-motivators as soon as possible. I speak from experience having taken a physics degree, which is of course heavy in mathematics too. Students do have a wealth of material available on the internet now, which is a great help, so it is a good idea to encourage them to be discerning users of this wealth of information. I also think that there is subject-specific advise to give for the study of mathematics as a whole. GCSE and especially A-level students neglect the importance of good arithmetic skills. Though there is no longer a non-calculator paper in the new A-level maths syllabus, being able to check sums by estimation and work quickly and efficiently without recourse to a calculator at every step is essential for success.
Biographies of physicists worth reading
I recently read the book by Graham Farmelo about the British physicist Paul Dirac. It is called The Strangest Man. It is a well-written and touching look at the life and personality of the man who was at the heart of the development of Quantum Theory. He grew up with a dominant father who set oppressive rules for hm and his young brother to follow. The young Paul found ways to rebel silently. He won a place at a prestigious grammar school in Bristol, a city in the west of England.
” When you ask what are electrons and protons I ought to answer that this question is not a profitable one to ask and does not really have a meaning. The important thing about electrons and protons is not what they are but how they behave, how they move. I can describe the situation by comparing it to the game of chess. In chess, we have various chessmen, kings, knights, pawns and so on. If you ask what chessman is, the answer would be that it is a piece of wood, or a piece of ivory, or perhaps just a sign written on paper, or anything whatever. It does not matter. Each chessman has a characteristic way of moving and this is all that matters about it. The whole game os chess follows from this way of moving the various chessmen.”
Paul Dirac
In the background of this engaging narrative is the unfolding of the greatest human achievement of the twentieth century. At the same time, it is a very human story of a man overcoming a domineering and bullying father to become perhaps the second greatest physicist of all time.
Genius: Richard Feynman and Modern Physics describes a character almost the complete opposite of Paul Dirac. Richard Feynman is an extrovert genius in the true sense of the word. Working in secret for years on the Manhattan Project as a young man must have been an amazing experience. Richard Feynman was relentless in his search for the truth and in debunking misconceptions. He revealed the cause of the Challenger disaster in 1986 in a public press conference using the simplest of demonstrations. He also wrote the famous Feynman Lectures, and was an advocate for physics education.
Resources for A-level maths revision
Here are some of my preferred A-level maths revision websites.
http://m4ths.com/teach-yourself-a-level-maths.html
This site is run by retired maths teacher Steve Blades and contains links to a great deal of instructional videos that offer a lot of detailed help on all areas of the syllabus.
https://www.savemyexams.co.uk/a-level/
Save My Exams offers help on maths and the three sciences in not just A-level but pre-U, GCSE and IGCSE exams and is syllabus specific.
https://www.physicsandmathstutor.com/maths-revision/
This site offers syllabus specific support and has solution banks and past papers.
https://www.biochemtuition.com/
Despite its name, this site has extensive support as well as copies of text books (copyright alert!)
https://www.examsolutions.net/
This website is highly rated by my students. It has instructional videos on examination past papers for mathematics A-level. It covers Edexcel, AQA, OCR and MEI syllabuses.
GCSE maths resources
Many students going back to school in year 10 and 11 quickly realise that they are not prepared for the demands of the course – especially in mathematics. It is a demanding subject and requires discipline and a lot of practice, practice and more practice. It is essential to get into good habits early. I have some resources to recommend as well as some tips.
Don’t neglect to work on your arithmetic, both mental and written. An inability to work quickly and carefully with the basic operations of arithmetic trip up many students. They get muddled and trip up before they even start. To help, I recommend doing online practice wit a website such as www.arithmetic.zetamac.com.
Review the fundamentals before starting to try examination questions. There is no point trying examination questions until you understand the fundamentals. You will find two kinds of questions in your text book and on websites. There are ‘consolidation’ or ‘confidence-building’ exercises and actual exam type questions. If you find that your school provided text book might lack exercises in some topics. In which case, you will need to supplement your revision with some good online resources. Three of my favourite resources are below.
Poor understanding of maths vocabulary can hinder learning. I recommend reviewing GCSE maths vocabulary as a part of revision.
Ti-nspire graphing calculator resources
I use the Texas Instrument Ti-nspire pictures, which is a computer algebra system graphing calculator. Some great resources for this calculator are listed below.
http://www.johnhanna.us/TI-nspire.htm
https://learnit.hoonuit.com/2410
Year 8 and year 9 physics resource
In 2009 and 2010, I created a Google Sites website for the Key Stage 3 students that I was teaching. I hadn’t looked at the site since 2010 but then yesterday, I took a look. You might find it useful as it links to many resources.
My favourite resources for tutoring maths and physics
Here are a few of my preferred resources.
Desmos Graphing Calculator is a web-based calculator. It is very versatile and can plot functions in Cartesian, polar and parametric form. It is very intuitive. You can switch simply between degrees and radians and it is web based so there is no need to download any software.
Mr Barton GCSE Maths Takaway is a GCSE site of course with a lot of resources arranged conveniently by topic. It is a free resource and very popular.
Exam Solutions offers video instruction (short video clips) which are tailored to specific syllabuses. For those students who really need to see it done in real time rather than learn from the book, this is excellent. Many of my students have said that they like this website.
I tutor the International Baccalaureate Diploma in maths and physics. An excellent WordPress site is IB Physics Notes. It is very detailed and offers detailed revision material on all parts of the syllabus broken down by topic.
I also recommend Hyperphysics because it offers a clickable concept map showing all topics within Physics. It’s great for revision too.
Also thoroughly recommended is the inspirational site Physics Footnotes. This offers a large range of explanatory video clips that bring to life the principles in Physics.
Fermat’s Last Theorem and Andrew Wiles
Any maths student will be familiar with the fact that there are pairs of integers whose squares add up to the square of another integer, for example 3^2 + 4^2 = 5^2.
Examples of these so-called Pythagorean Triples have been known for millenia.
Fermat’s LastTheorem posited that there are no integers for which a^n + b^n = c^n where n is an integer greater than or equal to three.
There is a fascinating documentary by Simon Singh about the proof by the English mathematician Andrew Wiles and his very lengthy proof in 1995.
It may be found here.
Pierre de Fermat was a famous mathematician who lived in the 17th Century in southern France. He is best known for Fermat’s principle that explains how light travels and Fermat’s Last Theorem in number theory, which he described in a note at the margin of a copy of his book Diophantus‘ Arithmetica.
Fermat’s Last Theorem is possibly the most well-known theorem in mathematics. It was suggested by Fermat, and indeed he said that he had a proof for it but this was never published. A theorem without a proof is a strange thing indeed – not a theorem but a conjecture – a mathematical law which has not been proven.
It took over three hundred years and seven years of work for a British mathematician, Andrew Wiles, based at Princeton University in the USA to solve the problem.
The idea of Fermat’s Last Theorem can easily be understood with a few examples and a calculator. Challenge students to find a case where n is greater than two. They may well not believe that such cases don’t exist.
The documentary lasts 50 minutes and first explains what Pythagoras Theorem is. It then extends the idea to any power to a whole number and explains the hint by Fermat that he had found a proof that there are no integer solutions to the equation
x^2 + y^2 = z^2 for n>2.
It then discusses quite clearly how a problem in one field of mathematics can be translated into a different problem in another area of mathematics. So it was that the original problem was translated into a different problem to which a solution needed to be found. Andrew Wiles, through a flash of inspiration, which he describes vividly, came to this solution.