New Cur 14: Moving the Decimal Point, and Other Sins

The Year 6 Number stream of the new mathematics Curriculum contains a notable content descriptor:

multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers (AC9M6N06) 

Yep, we’re just like Singapore.

There’s not too much to say about such absurdity. At Year 6. We do want to comment upon, however, a companion elaboration:

explaining the effect of multiplying or dividing a decimal by 10, 100, 1000 … in terms of place value and not the decimal point shifting

Should students develop some proper understanding of place value, a sense of its meaning beyond the mechanics? Of course. But should students also be forbidden from “explaining” multiplying or dividing by ten in terms of “the decimal point shifting”? Life is way too short for such fusspottery.

Of course no one explains multiplication by ten in terms of moving the decimal point. Rather, the expression is used to describe the visual effect of that multiplication. It is a short, clear and useful description. Except for overlording pedagogical pedants.

The new Curriculum is bloated with such nonsense, where some justifiable concern for understanding is worried to death, where straight-forward description is forbidden, is shoved aside in order to engage in meaningless ritual. David Treeby’s term for this absurdity is Rote Learning, and it fits perfectly.

The foundation of mathematical understanding is solid practice of well-chosen exercises. With a good sense of how the mathematics works then, and only then, can students begin to seriously ponder and appreciate why the mathematics works the way it does. But the curriculum writers care nothing for practice. As long as the children don’t stray from The Path, as long as they chant the The Sacred Words, all is good.

23 Replies to “New Cur 14: Moving the Decimal Point, and Other Sins”

  1. In ancient Egypt they had a clever system. I can’t use hieroglyphs here, so I will improvise. X stands for 1, Y stands for 10, Z stands for 100, W stands for 1000. Thus ZZYXXXX stands for 214. To multiply by 10, replace X by Y, Y by Z, Z by W and get WWZYYYY.

      1. You jest, but the point is valid.

        0.x represents x “tenths” and so if we move the decimal point and write x we have x “ones”.

        The name of the place value implies what happens when the decimal point is moved.

        I really don’t see the issue ACARA has here.

        Maybe they meant to write “…and not just the decimal point shifting.”

        Or maybe not.

          1. OK. I’ll accept your superior (although I suspect not totally pleasant) experience as fact on what ACARA means by these statements.

            I am still at a loss to see how and/or why they could have an issue with naming a process that is defined inherently by how we describe place value.

            ACARA even refers to place value in the previous clause.

            Their conclusion seems logically flawed even if I accept their premises (which I do not)

            1. The really important point, as edu-clowns see it, is that there is a position for the ones, a position for the tens, and so on. These positions don’t change, and the numerals move from position to position: “the 5 is now in the tens position, and so means 5 tens”, and so on. If instead you “move the decimal point”, with the “5 in the same spot”, it is more difficult to see that “the 5 now means 5 tens”, etc. .

              There’s an ounce of sense in what they are pushing, and a ton of misdirected obsession.

              1. Perhaps there is an ounce of sense but I still feel they are trying to be way too abstract in their ideation. The result is a statement that teachers find difficult to interpret and so will quite possibly ignore.

                The “move the decimal point” idea may not be perfect but at least it does not violate the commandment “first, do no harm.”

                Can the same be said of ACARAs new statements? We may know in the future, but that assumes a decent number of teachers actually read and understand the document.

                1. You’re inviting me to defend ACARA? I’ll get back to you …

                  However, edu-clowns would indeed claim that the expression “move the decimal point” does harm.

                  1. Just as a side-track…

                    If you rearrange

                    A DECIMAL POINT

                    you get

                    IM A DOT IN PLACE.

                    Coincidence? Yes, but still amusing.

                    1. I cannot claim originality.

                      I learned it from a website INTERNET ANAGRAM SERVER which is itself an anagram of I REARRANGEMENT SERVANT

                      This particular gem was from their anagram “hall of fame”. The anagram of PRESIDENT CLINTON OF THE USA has to be seen to be believed.

  2. One hopes that students come to appreciate the beauty and importance of place value in our system of numerals. At least they might set out a column of numbers well.

    1. We live in constant hope… some do, some don’t. Some line up their decimal points when adding or subtracting as well… it is a thing of beauty!

    2. You’re both dreamers. Little attention is paid to writing neatly, in straight lines. The hope that the numbers will be in clearly defined columns is, well, hopeful.

      1. At my school this year, there was a focus on handwriting for about 6 weeks across the curriculum. It was quite well done. Another school where I was, hired a occupational therapist to work with students on their handwriting. Have you ever noticed how students hold a pen or pencil as if they are going to stab the page? So, in my short experience, schools are aware of the issues and trying to do something about them.

        I have a very good Year 9 students whose handwriting is terrible. I said to him the other day that, over the next couple of years, he should focus on his handwriting. He told me that his parents had bought 3 books on handwriting for him – at least his parents noticed and cared.

        Related to this is the way in which students write text message translates into their handwriting; e.g. “BC” for “because”.

          1. I did not claim that this was *the* solution. I offered it as an example of how one school was trying to address the problem of poor handwriting.

            1. I know, I know. But the fact that secondary schools need to address the problem in an ad hoc manner is insane. It’s *always* like this: the education system is a basket case, and some individual schools and teachers do their best to hammer some local sense. Just insane.

      2. I can still appreciate it when I see it…

        Yes, gone are the days where the mathematics exercise books were ruled in light-blue rectangles to force everything in columns. I remember in Grade 3 trying to fit one digit per rectangle without first sharpening one’s pencil (I was late getting my pen license)

        We are still allowed to hope, surely. Just as we are entitled to ask for change. Except from a vending machine or a Liberal government.

    1. Unless it can be done with PSEUDOCODE, there is probably no interest.

      Even then… I’m yet to be convinced VCAA or ACARA really understand what an operator actually is/does.

    2. A bit shift operator (acting on an unsigned int) does exactly what was dogmatically required, moving the numerals and not the decimal point.

      It’s the floating point representation of numbers that would break them!

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