I just came across this wonderfully clear explanation of division by zero.
It also gives a nice introduction to the ideas of undefined (‘leads to a contradiction’) and indeterminate (‘is true for any value of x’).
Aside from being suddenly very much better at Mathematics (due to working with your friendly neighbour tutor 😉 )here are some cool questions which you can use to puzzle your teacher.
They sometimes look simple but are actually fiendishly difficult.
This is a beauty:
I really admire Steven Strogatz…someone who can undertake cutting-edge applied maths research and yet also explain the subject with respect for learners.
“In teaching, you should tell the truth and nothing but the truth -but not the whole truth.”
If you are struggling to remember your exact trignometric ratios, here is a useful aide memoire.
I found this nice article on the BBC website.
It’s no great surprise that medics fail this particular test, since the teaching they receive aimed at understanding probability is generally poor.
I’ve included a graphical explanation below:
If this doesn’t make sense, do get in touch (especially if you work as a doctor of medicine!)
It’s shameful that people in positions of responsibility can’t or won’t answer simple arithmetic questions.
As this article suggests, one’s times tables are considered optional by England’s ruling class.
The diagram is interesting though. Why are certain multiplications more difficult than others? Why are there asymmetries? Does this reflect something about the sound patterns or about our underlying brain structure?
This article on the BBC makes some sensible points about hiring tutors.
Parents need to think hard about what’s best for their individual child.
It’s not just about the exam grades…the best tutors explain things so that the student is equipped and motivated to dig into the subject on their own.
You tend to get what you pay for. If a tutor has been working for some time, then they are unlikely to be incompetent. If they have been charging a lot, then they are probably worth it.
Many folk who are well qualified in a given subject can’t teach it to save themselves.
There is no such thing as a hard exam…it’s a sign of deficient teaching and/or insufficient student workrate.
Here’s an interesting video in which professional mathematicians get blamed for the widespread dislike of mathematics.
I’ve always used movement and noises to teach myself…now it appears that gestures by teachers help students of maths to learn.
I’m sure it helps when a teacher says “x is on this side (moves left hand) and y is on this side of the equation (moves right hand)”. I’m not sure why, but it seems we store this information as some kind of body memory. Einstein said that he could tell if an equation was right by feeling a tingling in his little fingers.
Gestures really help to place emphasis. One of my difficulties with learning from lectures is that people who write on the board whilst talking, usually fail to emphasise the important bits. Maybe the lack of gestures is what makes it particularly hard.
Here is an article which talks about the fees charged by private tutors.
It seems that many rich folk think “getting into Oxbridge” is the aim of education. As a Cambridge graduate myself, I’d disagree. Undergraduates at even the best UK universities often find difficulty in getting access to senior-level experts -they will have supervisions with downtrodden postdocs who have no incentive and usually little ability in teaching.
Great teaching, which results in the ability to build robust, fundamental knowledge, is simply very rare these days. I can understand that taxpayers feel they have already paid…and all they got was a third rate school for their children. That makes me incandescent, mostly because children deserve access to excellence in schools (which also means excellence in subject knowledge).
I wonder if people really do value an education for their offspring which goes beyond the absolute basics…or are they really more concerned about social standing? Why is no-one rioting because little Johnny still dislikes fractions or optics after n years at school?
The current labour rate for tyre fitting in my local town is £48 per hour.