We still have no time for the deep analysis of this shallow nonsense. So, we’ll just continue with the fish.
Below are two content-elaborations combos, from Year 5 and Year 6 Number. As near as we can tell, that’s about the sum of the instruction on techniques of multiplication for F-6.
ACHIEVEMENT STANDARD (YEAR 5)
They apply knowledge of multiplication facts and efficient strategies to multiply large numbers by one-digit and two-digit numbers
CONTENT (YEAR 5)
choose efficient strategies to represent and solve problems involving multiplication of large numbers by one-digit or two-digit numbers using basic facts, place value, properties of operations and digital tools where appropriate, explaining the reasonableness of the answer
ELABORATIONS
interpreting and solving everyday division problems such as, ‘How many buses are needed if there are 436 passengers, and each bus carries 50 people?’, deciding whether to round up or down in order to accommodate the remainder
solving division problems mentally like 72 divided by 9, 72 ÷ 9, by thinking, ‘how many 9 makes 72’, ? x 9 = 72 or ‘share 72 equally 9 ways’
investigating the use of digital technologies to solve multiplicative situations managed by First Nations Ranger Groups and other groups to care for Country/Place including population growth of native and feral animals such as comparing rabbits or cane toads with platypus or koalas, or the monitoring of water volume usage in communities
LEVEL DESCRIPTION (YEAR 6)
use all four arithmetic operations with natural numbers of any size
ACHIEVEMENT STANDARD (YEAR 6)
Students apply knowledge of place value, multiplication and addition facts to operate with decimals.
CONTENT (YEAR 6)
apply knowledge of place value and multiplication facts to multiply and divide decimals by natural numbers using efficient strategies and appropriate digital tools. Use estimation and rounding to check the reasonableness of answers
ELABORATIONS
applying place value knowledge such as the value of numbers is 10 times smaller each time a place is moved to the right, and known multiplication facts, to multiply and divide a natural number by a decimal of at least tenths
applying and explaining estimation strategies to multiplicative (multiplication and division) situations involving a natural number that is multiplied or divided by a decimal to at least tenths before calculating answers or when the situation requires just an estimation
deciding to use a calculator in situations that explore multiplication and division of natural numbers being multiplied or divided by a decimal including beyond hundredths
explaining the effect of multiplying or dividing a decimal by 10, 100, 1000… in terms of place value and not the decimal point shifting
UPDATE (29/50/21)
we’ve just discovered some multiplication techniques tucked inside some division elaborations, as indicated in this companion Crash. The two Crashes should be considered together (and should have been just one Crash, dammit.)
I’m not sure I have the mental energy to look through this more thoroughly, but it seems to me that the elaborations of the Year 5 material don’t involve “choosing efficient strategies for multiplication of large numbers by one-digit or two-digit numbers”. The first two are about *division*, and the third appears to read as “using a calculator”.
Thanks, edder. Yes, the Year 5 “elaborations” are not in any sense of the word elaborations, and the content surely needs proper elaboration, since there is no indication how such multiplications are to be done, what “efficient strategies” might be.
It is only a guess, but I think what is going on here is the writers’ hostility to the traditional multiplication algorithm. Ignoring the irony that the writers also profess to love “algorithms” and “computational thinking”, the writers are in a bit of a bind. They either explicitly note the traditional algorithm or they don’t. If they don’t, but they explicitly refer to these boxy variants, or whatever, they’re really opening themselves up for criticism. Saying nothing allows the facade of agnosticism. And, having decided to say nothing, they have to come up with filler for the elaborations.
I like the term digital tools. It allows for anything from fingers to wolfram-alpha: a timeless wording. It would be even better if it said without using digital tools do these.
I wonder if simply listing a set of sample problems and answers wouldn’t be an easier way to describe a math curriculum. Some of them to be done mentally and some using the digits on the end of your hands and feet and some using paper and pencil or pen.
A list of problems would have the advantage of
– being very explicit as to what students should be able to do.
– provide exemplars of how answers should be expressed.
– it should avoid length descriptions of what the mathematics is (something that should be obvious or available in better resources than a curriculum description.)
Stan Blakey. On the Busses you go!
You’re making far too much sense.
Your suggestion is something I have pushed for with VCAA Mathematics Stupid Designs – repeatedly and including the latest draft. To no avail. Once upon a time this was actually done in official curriculum documents in Victoria, and it’s still done in South Australia.
I don’t know why VCAA, ACARA etc. refuse to do such a simple and sensible thing. The only explanations I can think of is arrogance, incompetence and exercising control over the schmucks who have to teach this stuff. I doubt the clowns at ACARA understand what they’re telling everyone else to do. Such people hide behind jargon, gibberish and vagueness. The Daft Curriculum is full of it.
By the way, did anyone attend the MAV facilitated Daft Curriculum forum? If so, can you give a brief summary of what happened and whether the ACARA Svengali, the puppet master, was revealed.
I’d be interested in a brief summary of the MAV forum – although I thought that it was going to run over several days.
There is a follow-up at some point. The main point of the Thursday thing was for ACARA to run through the structure etc of the draft curriculum. I have it from a reliable source that it was pointless, that the attendees were either enthusiastically on board with the draft or, if not, silent. No pointed questions were asked.
Damn it.
(I would have attended if I could have, but I couldn’t. So I can’t complain about the stupidity and apathy/(fear?) of the attendees).
Digital tools = fingers.
Best comment EVER! Well said!
Also, natural numbers of “any size”… hmmm… that could end badly if taken too literally.
Fibonacci wrote about the art of finger counting, as did the Venerable Bede.
I’m hoping to tell ACARA to go forth and multiply when the opportunity arises …