Tag: arithmetic

Signs of the TIMSS

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December 8, 2020

6:36 pm

10 Comments on Signs of the TIMSS

Uncategorized

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The 2019 TIMSS results are just about to be released, and the question is should we care? The answer is “Hell yes”.

TIMSS is an international maths and science test, given at the end of year 4 and year 8 (in October in the Southern Hemisphere). Unlike PISA, which, as we have noted, is a Pisa crap, TIMSS tests mathematics. TIMSS has some wordy scenario problems, but TIMSS also tests straight arithmetic and algebra, in a manner that PISA smugly and idiotically rejects.

The best guide to what TIMSS is testing, and to what Australian students don’t know and can’t do, are the released 2011 test items and country-by-country results, here and here. We’ll leave it for now for others to explore and to comment. Later, we’ll update the post with sample items, and once the 2019 results have appeared.

UPDATE (08/12/20)

The report is out, with the ACER summary here, and the full report can be downloaded from here. The suggestion is that Australia’s year 8 (but not year 4) maths results have improved significantly from the (appalling) results of 2015 and earlier. If so, that is good, and very surprising.

For now, we’ll take the results at face value. We’ll update if (an attempt at) reading the report sheds any light.

FURTHER UPDATE (08/12/20)

OK, it starts to become clear. Table 9.5 on page 19 of the Australian Highlights indicates that year 8 maths in NSW improved dramatically from 2015, while the rest of the country stood still. This is consistent with our view of NSW as an educational Switzerland, to which everyone should flee. We’re not sure why NSW improved, and there’s plenty to try to figure out, but the mystery of “Australia’s” dramatic improvement in year 8 maths appears to be solved.

UPDATE (09/12/20)

OK, no one is biting on the questions, so we’ll add a couple teasers. Here are the first two released mathematics questions from the 2011 year 8 TIMSS test:

1.   Ann and Jenny divide 560 zeds between them. If Jenny gets 3/8 of the money, how many zeds will Ann get?

2.   \color{blue}\boldsymbol{\frac{4}{100} + \frac{3}{1000} = }

(The second question is multiple choice, with options 0.043, 0.1043, 0.403 and 0.43.)

To see the percentage of finishing year 8 students from each country who got these questions correct, you’ll have to go the document (pp 1-3).

A Simple Message to Primary Schools About Multiplication Tables

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August 13, 2020

6:57 pm

54 Comments on A Simple Message to Primary Schools About Multiplication Tables

education

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Dear Primary Schools,

If your students are not learning their multiplication tables, up to 12, by heart, then you are fucking up.

If you think giving your students a grab-bag of tricks replaces multiplication tables, then you are fucking up.

If you think orchestrating play-based, student-centred theatricalities replaces multiplication tables, then you are fucking up.

If you think quoting the Australian Curriculum gives you license to not teach multiplication tables, then you are fucking up.

If you think quoting some education twat gives you license to not teach multiplication tables, then you are fucking up.

Thank you for your attention.

BODMAS v USBB

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May 30, 2019

1:07 pm

5 Comments on BODMAS v USBB

teaching

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Yesterday, I received an email from Stacey, a teacher and good friend and former student. Stacey was asking for my opinion of “order of operations”, having been encouraged to contact me by Dave, also a teacher and good friend and former student. Apparently, Dave had suggested that I had “strong opinions” on the matter. I dashed off a response which, in slightly tidied and toned form, follows. 

Strong opinions? Me? No, just gentle suggestions. I assume they’re the same as Dave’s, but this is it:

1) The general principle is that if mathematicians don’t worry about something then there is good reason to doubt that students or teachers should. It’s not an axiom, but it’s a very good principle.

2) Specifically, if I see something like
3 x 5 + 2 x -3
my response is

a) No mathematician would ever, ever write that.

b) I don’t know what the Hell the expression means. Honestly.

c) If I don’t know what it means, why should I expect anybody else to know?

3) The goal in writing mathematics is not to follow God-given rules, but to be clear. Of course clarity can require rules, but it also requires common sense. And in this case common sense dictates

USE 

SOME 

BLOODY 

BRACKETS

For Christ’s sake, why is this so hard for people to understand? Just write (3 x 5) + 2 or 3 x (5 + 2), or whatever. It is almost always trivial to deambiguousize something, so do so.

The fact that schools don’t instruct this first and foremost, that demonstrates that BODMAS or whatever has almost nothing to do with learning or understanding. It is overwhelmingly a meaningless ritual to see which students best follow mindless rules and instruction. It is not in any sense mathematics. In fact, I think this all suggests a very worthwhile and catchy reform: don’t teach BODMAS, teach USBB.

[Note: the original acronym, which is to be preferred, was USFB]

4) It is a little more complicated than that, because mathematicians also write arguably ambiguous expressions, such ab + c and ab2 and a/bc. BUT, the concatenation/proximity and fractioning is much, much less ambiguous in practice. (a/bc is not great, and I would always look to write that with a horizontal fraction line or as a/(bc).)

5) Extending that, brackets can also be overdone, if people jump to overinterpret every real or imagined ambiguousness. The notation sin(x), for example, is truly idiotic; in this case there is no ambiguity that requires clarification, and so the brackets do nothing but make the mathematics ugly and more difficult to read.

6) The issue is also more complicated because mathematicians seldom if ever use the signs ÷ or x. That’s partially because they’re dealing with algebra rather than arithmetic, and partially because “division” is eventually not its own thing, having been replaced by making the fraction directly, by dealing directly with the result of the division rather than the division.

So, this is a case where it is perfectly reasonable for schools to worry about something that mathematicians don’t. Arithmetic obviously requires a multiplication sign. And, primary students must learn what division means well before fractions, so of course it makes sense to have a sign for division.  I doubt, however, that one needs a division sign in secondary school.

7) So, it’s not that the order of operations issues don’t exist. But they don’t exist nearly as much as way too many prissy teachers imagine. It’s not enough of a thing to be a tested thing.

Signs of the Times

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May 5, 2019

4:02 pm

25 Comments on Signs of the Times

Numbers

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Our second sabbatical post concerns, well, the reader can decide what it concerns.

Last year, diagnostic quizzes were given to a large class of first year mathematics students at a Victorian tertiary institution. The majority of these students had completed Specialist Mathematics or an equivalent. On average, these would not have been the top Specialist students, nor would they have been the weakest. The results of these quizzes were, let’s say, interesting.

It was notable, for example, that around 2/5 of these students failed to simplify the likes of 81-3/4. And, around 2/3 of the students failed to solve an inequality such as 2 + 4x ≥ x2 + 5. And, around 3/5 of the students failed to correctly evaluate \boldsymbol {\int_0^{\pi} \sin 5x \,{\rm d}x}\, or similar. There were many such notable outcomes.

Most striking for us, however, were questions concerning lists of numbers, such as those displayed above. Students were asked to write the listed numbers in ascending order. And, though a majority of the students answered correctly, about 1/4 of the students did not.

What, then, does it tell us if a quarter of post-Specialist students cannot order a list of common numbers? Is this acceptable? If not, what or whom are we to blame? Will the outcome of the current VCAA review improve things, or will it make matters worse?

Tricky, tricky questions.