Talking to Teachers about Maths

Last week, by chance, I met a couple I know. They are in their thirties and have two children 6 and 9. She is a housewife and he a packer for a logistics company. Last year, due to Covid, schools closed and parents took over teaching their children with mixed results. We went for a coffee and they told me their woes, particularly with teaching maths. Actually, just arithmetic. Now as it happens, the british newspaper The Sun had an article on Jan 28th about what level of difficulty children can expect in an arithmetic quiz, and gets some of it wrong. I've included a screenshot below.

For question 3 The Sun gave the answer as 1; I would contend it is either 0 remainder 2 or 0.66 recurring depending on whether/how the 6/7 year old has been taught division. Integer division or floating point numbers.
For question 4c, continuing the series 1 4 5 9, which could be interpreted as add 3, then 1, then 4, then 1 etc OR as add 3, then 1, then 4, then 2 etc The Sun gave one definitive answer 14, 23, 37 assuming you add the last two numbers to get the next; I contend multiple approaches are possible to continue "the" series.
For question 6, the answers could be 6, or 8 or 10, depending on whether said prism is supposed to be 2 dimensional, or 3 , or 3 but counting the inside and outside as extra "sides" ;-)
Question 12 doesn't even take spectators in wheelchairs into account. So much for teaching non-discrimination against the disabled :-(

No wonder the parents were confused and struggling. And that was just simple arithmetic, imagine what will happen when the children have to learn algebra or even calculus! Here's Billy Connolly on Algebra.

Even the maths goes "wrong" sometimes. Consider this : for every number there is exactly one which is twice as big (it is even). Never two or three or zero, always exactly ONE which is twice as big. OK? Therefore there are exactly as many EVEN numbers as there are numbers at all! Does that blow your mind or what?

On another occasion, years ago, I was talking to on old friend Udalrike who is/was an art teacher, now retired. She wanted her pupils to paint ∞ (infinity) without using that symbol. I suggested drawing the railway track across the Nullarbor Plain in Australia. The name comes from the Latin, meaning No Trees. The railway line has the longest straight section of railway in the world (478 km, 297 mi). So perspective has the rails getting closer together and meeting at infinity. But you know that cannot be true or the trains would fall off the tracks. Anyway the rails don't meet at infinity, but in perspective appear to do so when the angle subtended at the human eye is about 50 seconds of arc (in the daytime), the eye's resolution limit. We rejected this idea as the pupils hadn't learned about perspective yet.

So I told her about Koch's snowflake. Initially an equilateral triangle is inscribed within a circle. Then each straight line-segment is divided into three and the central third used as the base of a smaller equilateral triangle. This is reiterated forever giving the perimeter of the snowflake. Interestingly, the snowflake has a finite area, 8/5 of the first triangle, but the perimeter is infinitely long because it gets bigger by 4/3 at each iteration. So, infinity.

Udalrike liked this idea and painted the first few iterations of it herself, then sent me this painting, which I treasure to this day :-)

By the way, for those of you who thought the paragraph separator I used above was something numerical, it is not. It is in fact an old inscription, written in Ogham, and means "ale hath killed us" ;-) Somewhere I have a mug inscribed with the Ogham alphabet which I bought in Ireland many decades ago. And a beer mat with that 'paragraph separator' on it ;-)

Comments (15)
Pergelator wrote " Clever post. 2 divided by 3 is 2/3. It's not one, it's not .66 and it's certainly not zero. Remainders are for people who can't divide. And computers. A hexagonal prism is 3 dimensional. A hexagon is two dimensional. Counting the inside surfaces of a hexagonal prism would get you 16, except since surfaces have no thickness, you are counting them all twice. I followed the same logic as you on 4C. I agree there isn't enough information to conclude what the rule is. Might be a trick question to see if there are any free thinkers in the class. Although whoever proposed this question should probably keep their head down, anybody caught thinking freely is liable to be persecuted. Problem 8 has a typo. 1279 does not equal 1000+200. Question 12 could be better phrased by asking how many people will not have seats. Lastly, the train doesn't fall off the tracks because the farther away it gets, the smaller it gets until it vanishes when the rails eventually come together. I need more math problems to chew on. Problem is finding ones with the right difficulty. Too easy and I solve them at a glance, too difficult and I have to work at it, and/or go look stuff up, and unless there's a real reason to solve it, I am not going to do that." You are right on problem 8; The Sun should have used a second plus sign instead of a second equals sign.
Jack wrote " First off it is Math not Maths ,for Christ sakes!" That's your regional dialect speaking; nowadays in the Queen's English it has an S. Similarly, I write Christ's with an apostrophe S, because it is in the genitive.
Pergelator comes to Jack's defence with a link to Simon Whistler's video Why Do British People Say 'Maths' While Americans Say 'Math'? and asks "This video popped up on YouTube this morning. You don't suppose Google reads me email, do you?" Google most definitely does, I can get them to send pr0n by prompting them with this link brown cock, white chick ;-)
Dennis wrote " Modular arithmetic in number theory is all about remainders. They call them residues or some such. divide two numbers by p and if they have the same remainders they are equal modulo p. Seems trivial at first, but modular arithmetic lets you ask and answer questions about friggin huge numbers. I've been watching videos by Michael Penn, where he demonstrates how to solve lots of math tournament problems, often using modular arithmetic. Most of it is above my pay grade, but you can get a glimpse of how to make absurd sounding problems tractable." Agreed.
Jenny (Ibiza) asked "The aborigines could speak Latin?" I suspect the name Nullarbor would have been given by the captain or navigator of a ship sailing past the south coast, who is more likely to have known Latin.
Carol (UK) points out "The picture you used behind the link 'confusion' has also made its way into your left sidebar ;-)" Oops, I need to fix that. Thanks.
Billions of Versions... wrote " I’m late to the party. All I was going to mention was #8. But if the last line of #12 said, 'How many people are standing?' The answer would be 'All of them. It’s a concert.' " Different responses in different countries.
Carol (UK) later added "Neat painting in the triangular frame. Show us some of your other art too." OK, at the weekend.
m.pergiel (USA), looking at the section on the number of numbers, points out that "Zero is a number." Sure, and it also has exactly one double. Which is also zero.
Schorsch (D) asks "How do you get that symbol for infinity? Do you turn an 8 on its side? How?" It has a name in HTML. You write an ampersand, followed by the 5 letters i n f i n, and close the name off with a semicolon, getting ∞ :-)
Schorsch (D) then replied with this jpg :-

David (NY,NY) asks "In what order did you learn the various fields of math?" Well, I no longer have my notebooks, so I'm guessing. In primary school arithmetic and euclidian geometry. In secondary school : algebra, trigonometry, logarithms, statistics, booleans and calculus. Tertiary education : Matrices, tensors, group theory (especially Lie groups for use in quantum mechanics), later non-euclidian geometry. I can't remember all the details. Maybe student friend and blogreader John (UK) can help me out here?
Yellowdog Grannie tells me "no one likes a smartass Stu." Did I offend you?
Anne (UK) shows us the need to learn arithmetic :-
Piet (NL) shows us "This is what happens when people are totally math-ignorant." Oh dear!

Copyright ^© Ole Phat Stu on February 3, 2022 permalink Comments Email

---

Link to the previous month's blog.

---