PISA Triangles

Tony Gardiner did some hunting and found a document containing PISA’s released mathematics items for 2022. In a comment on our PISA non-post, Tony made some remarks about a triple of triangle questions contained in the document. The questions, each with the same triangle picture prompt, are below. The questions are followed by PISA’s discussion. The detailed marking rubric can also be found in the items document (pp 9-14). Note that PISA is a test for 15-year olds; as with all such tests, the questions are intended to range from easy to difficult.

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Tony Gardiner: What is Mathematical Literacy?

A couple days ago, I non-responded to the release of the 2023 PISA results (because, this). In a comment on that post, Tony Gardiner referred to a paper he had written for ICME10, held in 2004. In that paper, Tony claims, he “worked really hard … and totally failed” to make sense of “mathematical literacy”, one of the core nonsenses of PISA. Failure or otherwise, I think it’s a great paper, and Tony has kindly given permission to reproduce it here (and the PDF is here).

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We Are the Robots

First, enjoy some great Kraftwerk, because, and just because:

Regular readers may recall Australian reporter Natasha Bita. Natasha did some really excellent stenographic work for ACARA. Natasha also played right along with AMSI’s most recent Chicken Little crusade. It turns out that Natasha is an excellent stenographer even when there’s nothing to stenograph. Continue reading “We Are the Robots”

PoSWW 28: The Intersection of Feminism With PISA

A few days ago Greg Ashman handballed an article to us, suggesting we might enjoy it, although clearly he meant “enjoy” it. The (paywalled) article, just published in the journal Research in Mathematics Education, is titled

Intersectional feminism to reenvision mathematical literacies & precarity

Yeah, you don’t have to read the article. We did.

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Signs of the TIMSS

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).

PoSWW 12: They is Bach

There’s much we could write about Matthew Bach, who recently gave up teaching and deputying to become a full-time Liberal clown. But, with great restraint, we’ll keep to ourselves the colourful opinions of Bach’s former school colleagues; we’ll ignore Bach’s sophomoric sense of class and his cartoon-American cry for “freedom”; we’ll just let sit there Bach’s memory of “the sense of optimism in Maggie Thatcher’s Britain”.

Yesterday, Bach had an op-ed in the official organ of the Liberal Party (paywalled, thank God). Titled We must raise our grades on teacher quality, Bach’s piece was the predictable mix of obvious truth and poisonous nonsense, promoting the testing of “numeracy” and so forth. One line, however, stood out as a beacon of Bachism:

“But, as in any profession, a small number of teachers is not up to the mark.”

We is thinking that is very, very true.

A Question from a Teacher

A few days ago we received an email from Aaron, a primary school teacher in South Australia. Apparently motivated by some of our posts, and our recent thumping of PISA in particular, Aaron wrote on his confusion on what type of mathematics teaching was valuable and asked for our opinion. Though we are less familiar with primary teaching, of course we intend to respond to Aaron. (As readers of this blog should know by now, we’re happy to give our opinion on any topic, at any time, whether or not there has been a request to do so, and whether or not we have a clue about the topic. We’re generous that way.) It seemed to us, however, that some of the commenters on this blog may be better placed to respond, and also that any resulting discussion may be of general interest.

With Aaron’s permission, we have reprinted his email, below, and readers are invited to comment. Note that Aaron’s query is on primary school teaching, and commenters may wish to keep that in mind, but the issues are clearly broader and all relevant discussion is welcome.

 

Good afternoon, my name is Aaron and I am a primary teacher based in South Australia. I have both suffered at the hands of terrible maths teachers in my life and had to line manage awful maths teachers in the past. I have returned to the classroom and am now responsible for turning students who loathe maths and have big challenges with it, into stimulated, curious and adventure seeking mathematicians.

Upon commencing following your blog some time ago I have become increasingly concerned I may not know what it is students need to do in maths after all!

I am a believer that desperately seeking to make maths “contextual and relevant” is a waste, and that learning maths for the sake of advancing intellectual curiosity and a capacity to analyse and solve problems should be reason enough to do maths. I had not recognised the dumbing-down affect of renaming maths as numeracy, and its attendant repurposing of school as a job-skills training ground (similarly with STEM!) until I started reading your work. Your recent post on PISA crap highlighting how the questions were only testing low level mathematics but disguising that with lots of words was also really important in terms of helping me assess my readiness to teach. I have to admit I thought having students uncover the maths in word problems was important and have done a lot of work around that in the past.

I would like to know what practices you believe constitutes great practice for teaching in the primary classroom. I get the sense it involves not much word-problem work, but rather operating from the gradual release of responsibility (I do – we do – you do) explicit teaching model.

I would really value your thoughts around this.

Warm regards,
Aaron

Two PISA Crap

Below are two “units” (scenarios) used in the PISA 2012 testing of mathematics. The units appeared in this collection of test questions and sample questions, and appear to be the most recent questions publicly available. Our intention is for the units to be read in conjunction with this post, and see also here, but of course readers are free to comment here as well. The two units below are, in our estimation, the most difficult or conceptually involved of the PISA 2012 units publicly available; most questions in most other units are significantly more straight-forward.

SAILING SHIPS

 

REVOLVING DOORS