PoSWW 18: Inestimable Worth

We’ve whacked Essential Assessment on a previous occasion. Our daughter, who is in Year 4, did some of this nonsense on the week-end. (Our general policy is to let our daughter’s school do its thing, give or take a staged frown and raised eyebrow, and the occasional nudge of the well-meaning and intelligent Principal, but to forbid techno-junk at home. But, with home schooling, and our daughter’s understandable desire to please the beleaguered teacher, we let it go this time.)

Our daughter completed what we presume amounted to a diagnostic test on “multiplication”. It went from skip counting to multiple-digit multiplication requiring the standard algorithm (or some junky alternative), with a couple index  and square root questions thrown in somewhat randomly. In general the test, or whatever it was, was poor, with ill-defined progression, poor wording and some straight out weird questions. The following question was, by far, the weirdest.

47 Replies to “PoSWW 18: Inestimable Worth”

  1. Not wanting to defend the author of the question (I can’t) – but I have see questions like this in Year 7 textbooks under the heading “leading digit approximation”

    So… I’m guessing the intention is to say you could estimate (badly) the two sides as 20×30 = 600 and 40×10 = 400 and then insert the > symbol and move on with your life.

    Again, not agreeing with the question or the method (I don’t) – but it might not be as uncommon as some people think.

  2. RF, to approximate with leading digits is fine. To attempt to compare two such approximations is ludicrous. Do you really have examples of that? In any case, I’m not at all convincing that this is what was intended. Plus, on a diagnostic test on multiplication for primary school???

  3. Home schooling is making me fucking sick. I’ll give this question to my son (stage 2 as well but he is in year 3, but but he is in a 3/4 class) and see what he does. I’m not confident.

          1. The greatest pity is that the Opposition are a rabble. She will be a very strong chance for re-election because of this. A semi-decent Opposition would smash her in the next election.

  4. “Using your estimation skills”… So 20 x 25 = 500, but 44 x 11 = 440 + 44 = 484, so first guess is LHS > RHS.

    But this is pretty close, and I’d want to consider how 18 x 27 compares to 20 x 25. But then I might as well just work it out exactly…. It is useful to have the second-order skill of knowing when an initial estimate suffices and when it should be refined, but that seems a distraction at this stage.

    (Maybe a particularly sharp and knowledgeable Year 4 student would quickly do 3^5 x 2 = 243 x 2 = 486, so no estimation required?)

  5. Yes, it’s a dopey question alright.

    I suspect the intended ‘estimations’ are
    LHS approx 20 x 25 = 500.
    RHS approx 45 x 10 = 450
    LHS > RHS

    But as a precise calculation shows, it’s a line call – moronic to compare estimates of numbers that are so close. I suspect the justification would be that the ‘reasonable’ estimate gives the correct comparison. The question then is what makes some estimates more reasonable than others … It’s just dumb to have the answers so close.

  6. Purenonsense…
    “First do not confuse ” should be the motto of teachers
    I would not wish but would understand the author committing harakiri

    If though, the line was – without ref to estimating –
    18×26 ? 44×11
    Then obviously mid primary students are fluent in reasoning and properties of numbers leading to:
    but 22×22>21×23>20×24>19×25>18×26

    Another thought, may be we are missing something that is obvious to 3 graders

    1. Thanks, Banacek. Yes, the question is better without the “estimation” suggestion, then being merely ridiculous rather than obscene.

      And, no, we’re not missing anything. The questions in Essential Assessment are typically wonky, with evidently little or no thought having been put into the details of the required solution or the message, desired or otherwise, conveyed. It’s just junk. I’d say well over half of the questions made me react “could have been better” or something way stronger. Just by the probability elements of this random construction, a few questions reached Everest heights of absurdity.

      All this techno stuff is shit. None of it is teaching. And no one in Maths Ed seems to be aware or to give a fuck.

      1. The problem with techno-shit is that it’s embraced by many teachers as a time-saver. I know of many teachers who set tests straight from the digital test bank of a publisher because it saves them a heap of time with writing the test, writing the solutions, marking the test and giving feedback.

        Techno-shit is the teacher’s ‘friend’, unfortunately. This will not change. But maybe there’s a market for ‘good’ authentic techno-shit …

        It wouldn’t be quite so bad if the teacher could edit the techno-shit, make a few tweaks to some of the questions … But then it wouldn’t be the teacher’s ‘friend’ any more because it would require time and effort from the teacher.

        This is why on-line multiple choice tests are so popular, particularly at universities. Unfortunately, teachers must make compromises – more and more in the few last decades – simply to survive. Techno-shit is one of those compromises that many teachers make.

          1. I’m sure this has been discussed before, so I’ll assume the question is somewhat rhetorical but give a brief and nowhere near comprehensive answer:

            There is an over-crowded curriculum (and I don’t mean just the curriculum of a particular subject) and greater ‘paper-pushing’ and ‘data handling’ requirements.

            A very current example of the over-crowded curriculum: The addition of ‘Respectful Relationships’ teaching at all year levels. Things just keep getting added every year. Spate of divorces – add curriculum on marriage. Spate of drownings – add swimming. Spate of …. – add …. Stuff that should (and used to be) ‘taught’ at home is now outsourced to schools. And not to forget that for everything that gets added, there is the time and effort required to ’embed’ it, related internal PD etc., so it’s not just about the ‘delivery’.

            Data handling examples: Assessment data is often double and triple handled. It’s often required to be submitted to multiple platforms. And it’s not good enough to provide brief written feedback on assessments for students. Feedback also has to be reported on various platforms for all assessments and in some instances you have to have a brief meeting with each and every student to discuss the assessment and how s/he can improve … (25 students times 5 classes times 5-10 minutes meeting time per student = ? minutes per assessment – there’s a NAPLAN question you won’t see).

            ‘Paper pushing’: Reports have to be submitted for every assessment on students who have ‘failed’, mental health reports have sky-rocketed etc. etc.

            I think there was a recent report that teachers (I’m assuming primary school teachers), on average are working 16 hours a week extra in overtime to get everything done.

            And don’t get me started on fucking SACs of shit (or their CAT predecessors).

          2. JF is correct. Publishers provide many resources to support the teachers, especially tests and assignments. To prepare a test for your students now requires only a few clicks. These tests include diagrams that are nicer than a teacher could produce easily. Furthermore, the tests are marked by the computer when the questions are multiple choice questions.

            Saw an interesting MCQ test the other day – not a mathematics test by the way. Candidates were told that there would be only one correct answer for each question. One or two questions went like this.

            Which of the following statements is correct? A B C D E=all of the above are correct. And E was deemed to be the correct answer!

            1. Are teachers aware and do they care when the tests are shit? It is one thing to have electronic add-ons to a text, which I assume are generally poor but basically functional. But all-electric materials such as Essential Assessment and Mathletics and Maths Pathways seem to be junk and utterly poisonous junk. They’re not poor testing, they’re astonishingly poor teaching.

              Do teachers care? And I’m sorry, I understand that teachers now have a mountain of meaningless crap to do. But giving kids these programs is insane.

              1. There’s a sliding scale of ‘care’. The ‘care factor’ for assessing in this way is relative to the ‘care factor’ for other priorities.

                My personal opinion: I think many teachers ultimately rationalise doing it and then stop caring. In fact, I think some teachers even rationalise it to the point where they think it’s a good thing.

                The other thing to remember is that assessment is not as ‘visible’ as other priorities. It’s the visible priorities that I think teachers will attach the most importance to if they have to make a choice in how to use their time.

      2. I think there’s also a large political / ideological component, with these maths software packages being marketed as “adaptive”, this is a way for maths education to portray itself as delivering “individualised” instruction for every child (because they’re all unique with their unique learning styles etc. etc.)

  7. To do with improper fraction.
    Perhaps these things should be fixed first. The text is Y7 essential Oz syllabus (Vic has the same)
    I could be confused. About 1.
    Pls correct if i am wrong.

    1. Hi, Banacek. Not sure I see the problem. (It’s hard to see anything, but I’ll redo your image, and maybe do a separate post, if there’s something to be hammered.)

  8. Is 4/4 an improper fraction? 2=8/4 seems to be in the category of improper, 8>4.
    Numerator greater than? or: greater than or equal?
    Did I miss this something in my schooling?

    1. OK, yes. I would think improper includes n/n, and the text appears to be wrong. Is there an issue with Exercise 1?

      1. I suppose Banacek is pointing out that the text distinguishes “whole number” from “improper fraction”. Of course, something like 3/3 is both.

        1. Sorry, maybe I’m punch drunk from the homeschooling (thanks, Gladys, you fuckbrain), but I still don’t see the issue.

          All I can see that the text says about “improper fraction” is that for m/n the text requires m > n rather than merely m ≥ n. I agree that this is weird, probably to the extent of being wrong, but is there anything else? I don’t see any incorrect suggestion that an improper fraction cannot be an integer (except for needlessly ruling out 1).

          1. First: yes, I’d say not treating 1 as an improper fraction is wrong.

            Other than that, it’s the text directly underneath the title “Exercise 2” that I’m objecting to. What would they do with 8/4? The text implies it should either be an improper fraction, or a whole number. It is confusing, but granted not worth a song and dance.

            It does strike a nerve though. I’ve been through the irritating experience of explaining to a school teacher that whole numbers are also fractions twice in my life (thr second time, they asked for an example of a fraction, my son wrote “Graham’s Number/Graham’s Number” (annoying, yes) and he was marked wrong because “1 is not a fraction”).

            Anyway, not a huge deal, but I don’t like it. And I’m extra easy to annoy right now because of home schooling.

            1. I don’t think the text implies that 8/4 is an integer [exclusive] or improper fraction. But, I think the stupidity of exercise suggests this more strongly.

              Of much more concern is your other example, the common misunderstanding of inclusive definitions.

      2. Had to check text ‘s answers . The ones equal to 1
        (d and j) appear to not be improper fractions.
        Integers greater than 1 are classified as both.

        1. OK, now I get: by “1”, you mean Exercise 2.

          Then, given what you’ve said about the text’s answers, Exercise 2 is not wrong, other than for the m/m not improper thing. Nonetheless, Exercise 2 is pretty damn stupid.

        2. That’s really dumb!
          The book gives a clear definition which (appears to) rejects any fraction that’s equal to a whole number as being an improper fraction.

          So there’s three issues:

          1. Whether the book’s definition is right or wrong. (It’s wrong).

          2. Whether the book is incorrectly applying its own definition. (It is, but see below).

          3. Does the book define “whole” as the the natural number 1? If so, then the answers are consistent with the definition and the definition was written by a moron.

          1. Jesus, I really don’t want to defend this shitty text, but I still don’t see it. How does the book suggest that a whole number cannot also be an improper fraction?

            We agree that:

            a) The text stupidly thinks 10/10 is not an improper fraction.

            b) Exercise 2 is stupid.

            But is there anything else? I don’t see it.

            1. The first part of the definition says it all: “An improper fraction is greater than a whole …”

              I’ve just realised how fucked that really is.

              Student A: 9/3 is not greater than a whole, namely 3 (or 4 or 5 … take your pick) therefore it’s not an improper fraction.

              Student B: I must respectfully disagree. 9/3 IS greater than a whole, namely 2 (or 1) therefore it IS an improper fraction.

              Student C – excitedly: Maybe it’s both! Like a cat! A cat is a feline AND a mammal.

              Student D: My brain hurts. May I be excused?

              So what’s the meaning of “whole” in the definition. The definition was written by an asswhole. It should simply state:

              An improper fraction is a fraction whose numerator (the top number) is greater than or equal to its denominator (the bottom number).

              Is such a simple definition really so hard to write?

              1. The meaning of “whole” is 1. They are comparing an improper fraction to 8/8, the whole pizza.

                I’m not saying it’s not crappy writing. But I can see no actual error other than the exclusion of 8/8 etc as improper.

                1. OK. Then it’s even stupider than I thought. Calling “1” a “whole” is beyond stupid. It’s beyond crappy writing. I wonder what they define a “whole number” to be …
                  (Student E: How can 2 be a whole number when 1 is a whole?

                  Student F: Who da whole? One da whole!)

                  1. Yes. I think it is really really stupid. But not wrong, except for the strictness in the definition of improper.

                    1. I don’t see the point in even talking about “proper” and “improper” fractions.

                    2. Well, there’s a small point, but not much. Worse is the common instruction that mixed fractions are the preferred form.

                    3. Mixed fractions (mixed numbers) are blight on the arithmetic (and algebraic) landscape.

  9. “Mixed mathematics” was a common term in days bygone. One might be a Professor of Mathematics – Pure , Applied, and Mixed.

      1. Re: “what happened to vulgar fractions”

        I guess they were too common …

        But seriously, do we need a word to distinguish between fractions such as 2.69/3 and 2/3 …?
        The only time I’d use this term (if it was in common use) would be when I’m explaining to Maths Methods students that VCAA do not accept answers that are fractions whose numerator and/or denominator is not a whole number. If the term ‘vulgar fraction’ was in common use, I could say VCAA only accept vulgar fractions, as is befitting of its vulgar spirit.

  10. hi,

    I think the question meant you to compare 10% less than (30*18) with 10% more than 44*10

    stupid nevertheless unless you are into mental arithmetic

    steve r

    1. I’m probably about to take the ball again … but I remember, vividly, my classes in mental arithmetic in grade 3. We would open our books on mental arithmetic and hold the pages in place by placing our hands on the top corners of two facing pages. Then we would go through all the questions on the two pages answering the questions that the teacher fired at us. We were not allowed to move our hands. At the end of the lesson, my hands were quite stiff from being fixed in the same position for 30 minutes or so.

      1. Well, you kicked the ball, but this time to everyone’s benefit.

        Without advocating giving kids’ arthritis, the notion of expecting and demanding primary kids pay attention for that long, to even sit still for that long, is two standard deviations of sanity away from what we have now.

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