In the latest international PISA tests, some 500,000 students applied their skills to common tests in order to track their relative academic abilities. Asian countries have topped scorers in maths and science and, in 2015, Singapore became the first nation to top in all three subjects. The three nations that have fallen furthest since Pisa began are all Anglo-Saxon: in order, Britain, Australia and New Zealand. The almost identical tracks of Australia and NZ suggest that there may be common factors driving them both down.The biggest gains, among those who have been in Pisa since it started, have all been in Europe: Luxembourg, Portugal, Poland and Germany. Concerns about the dumbing down of education in places like Australia and New Zealand have recently hit the headlines – as in this article. Some have suggested that the reason for lowered performance from New Zealand is the result of classes being streamed, as in this link. However, some of New Zealand’s most successful academic schools have rigid streaming, so this may not be a major factor? Read more on the PISA results here.
As the new year approaches, you may be (or not be) interested to learn that the largest known prime number is 274,207,281– 1.
This number is an incredible 22 million digits long and 5 million digits longer than the second largest prime number. Hang on to your primes you might ask, “Why are prime numbers important? Are they of any practical use in real life?
What this means is that the time required to factorize integers into their prime factors grows (roughly) exponentially with the number of bits in the integer. So if the encryption uses very large integers, it would take an unrealistic amount of time to “crack” it.
If (or when) quantum computers become a reality, they would have the potential to make all of these algorithms obsolete, since there are quantum algorithms (in particular) that can factor arbitrarily large integers much faster than any known classical algorithm. This has led to the very important field of .”
The following question was one that appeared during interviews for potential employees at Apple. How would you answer it?
“There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?”
[Answer shortly in Post Support]
“You have to have talent, and you have to be willing to work hard!” This sums up the high scores achieved recently by students in their state-wide math exams.
A recent article highlights the underlying secret to high scores in senior school Mathematics, in the southern state of Victoria, Australia: “In Melbourne’s eastern suburbs, Vermont Secondary College has been celebrating some impressive further maths results. A record three students at the state high school achieved a perfect study score of 50 in the most popular maths subject – and they were all in year 11.
Overall, 18 students at the state school achieved a 40-plus score in further maths.
Director of numeracy Mary Zervos attributed this success to the school’s team of young and experienced maths teachers. She said students worked tirelessly, completed many practice exams and asked questions. “You have to have talent, and you have to be willing to work hard,” she said.
“We are a community school that works with all the students in the neighbourhood to achieve the best we can for them.”
Westall Secondary College was another government school that produced some sharp further maths minds unlikely to be fazed by curly exam questions about 50 cent coins. The relatively small school in Clayton South has just over 50 year 12 students, but managed eight scores of 40 or above in the subject.
Principal Tristan Lanarus said the school had a strong maths culture, and one of its students last year represented Australia at the International Maths Olympiad.”
[Ed: “Culture” features widely in some recent innovative Mathematics programs. For example, the difference between Western and Asian math scores was discussed at length here on cnbc and in this paper from Massey University – developing-mathematical-inquiry]
This just in from my newsfeed,
“WASHINGTON (AP) American students have a math problem.
The latest global snapshot of student performance shows declining math scores in the U.S. and stagnant performance in science and reading.
Education Secretary John B. King Jr. says this country is losing ground and he finds that to be a troubling reality when, in today’s economy, ‘the best jobs can go anywhere in the world.'”
Well, hello hello, the same news story has come out of Australia and New Zealand recently too. In fact, Math scores are falling in most western nations (see: http://www.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=11757118). The politicians are placing the blame at the feet of teachers (see: http://www.nzherald.co.nz/opinion/news/article.cfm?c_id=466&objectid=11759955) and teachers are placing the blame at the feet of math-deficient parents and parents who never could do Math are blaming anyone who will listen. It turns out that Australian 15 year olds are now two years behind their international peers (see: http://www.smh.com.au/national/education/australian-school-students-two-years-behind-worlds-best-performing-systems-20161206-gt4w8p.html); and 15 year old math students in the ACT (Australian Capital Territory) are 18 months behind their overseas peers in Mathematics. So, who is to blame – the media, business, test scores themselves, or perhaps…no, it can’t be…the students themselves??! Oh, this debate will rage as long as Mathematics is being taught or, perhaps, trying to be taught? (Note: students themselves hardly ever get blamed for this decline).
Since this…(for fun)
In the new film “Arrival,” alien visitors appear all around Earth and humankind scrambles to understand their purpose in visiting. Perhaps they have come to improve their math?
Anyway, the movie’s creators approached Wolfram Research (creators of Mathematica, the online problem-solver Wolfram Alpha, etc.) to produce some charts for use in the movie. CEO Stephen Wolfram, helped out and his son, Christopher, generated visualizations for use in the movie.
“Wolfram told Space.com, “Who’s to know? Maybe something that I invented for science fiction will turn into some real physics.” [8 Modern Astronomy Mysteries Scientists Still Can’t Explain]
Space.com talked with Wolfram about the way science fits into movies, how aliens are like artificial intelligences and whether math is invented or discovered — and what that would mean for alien mathematics and alien thought.
Space.com: How were you approached to work on the project?
Stephen Wolfram: Because a lot of scientists use our software systems and we produce a lot of interesting graphics, we have a pretty regular stream of requests from movie makers of various kinds saying, “Can we show this graphic in our movie.” This one was kind of amusing, because it was like — we’re about to start shooting this fairly big-budget movie, and we need these screens that should look realistic and can you help us do this?”
Q: Imagine a ladder leaning against a vertical wall with its feet on the ground. The middle rung of the ladder has been painted a different colour on the side, so that we can see it when we look at the ladder from the side on. What shape does that middle rung trace out as the ladder falls to the floor?
(see answer in post support)