“Paradoxically, there are many situations where it is actually easier to solve a general problem than it is to solve a specific one.
I also think that this underscores the importance of being willing to learn outside the classroom.”
See this post for a glimpse into the mind of the young Feynman.
I found this video inspiring.
Using unsolved problems in mathematics to teach schoolchildren, if done well, is a great way to build confidence. Just telling young people ‘here is a problem which is simply stated, but which the greatest minds can’t solve’ really gets them interested -and using their natural creativity, rather than looking for some boring, half-remembered algorithm.
This video makes a good stab at mapping out the entire subject. Something like this would be a useful addition to all maths courses.
I’d really like to understand WHY we have selected some bits for inclusion in public exam curricula and left other bits out. My suspicion is that it’s based on the preferences of various senior academics. As usual, these political types don’t care much about whether this material will actually help young people -either in daily life or in higher study.
This contributes to the feeling that studying maths is about gathering a basketful of disconnected tools. It should be more integrated -and having in mind the big picture would greatly help.
I liked this introductory article about the historical usage of the mean vs the median value.
It shows that there is no representative value for a data set which is absolute. You need to understand the data distribution before making a choice of central measure.
Here is Albert Einstein’s small ad. for his services as a tutor in Mathematics and Physics.
Although never the world’s best mathematician, the number one Physicist of all time was uber-determined and a patient teacher. I’m sure that his students got good grades.
(I notice he offered a free trial lesson).
We knew this already, but here is some corroboration for the idea that one-to-one tutoring is highly effective.
Mind you, it depends on the tutor…and the tutee.
“…data from the 13 million students who took PISA tests showed that the lowest achieving students worldwide were those who used a memorization strategy – those who thought of math as a set of methods to remember and who approached math by trying to memorize steps. The highest achieving students were those who thought of math as a set of connected, big ideas.”
It really is important that maths teachers stop teaching handle-turning methods and equating speed of solution with ability. See more here.
I love this little tale about Albert Einstein who helped explain a little girl’s maths homework -almost daily, for four years.
What a decent thing to do.
There are some really clear explanatory videos on some challenging subjects in Mathematics here. These include probability, synchronisation, calculus… definitely worth a look.
Another useful source of background reading and explanation is Plus, an online maths magazine.
Ok, so this is a pretty contrived little problem, but it shows the mindset of mathematicians and offers a neat, generally applicable answer.