There is not much point in posting further on ACARA’s appalling mathematics curriculum. At this stage a person either already understands that the thing is appalling or they will likely never understand. We received a from-nowhere email, however, flagging some Year 4 nonsense that seemed worthy of special mention.
Below is a content-elaboration combo from Year 4 of the (ugh!) Space stream:
represent and approximate composite shapes and objects in the environment, using combinations of familiar shapes and objects (AC9M4SP01)
physically or virtually using cubes to make three-dimensional models that approximate real objects; for example, building a virtual environment by using a computer software program to construct objects out of cubes
Geez, ACARA. If your idea of kids getting into the maths is for them to play some video games then save us all some time and simply write, “play some video games”.
Ah, Minecraft. I’ve lost count of the number of times I’ve seen it used in junior secondary science to entertain – I mean, educate, sorry – kids e.g. build a sustainable energy efficient home in Minecraft. Guess what percentage of that class played games while the ‘progressive’ teacher was smug about their behaviour management. Answer: 90%. The other two students were chatting for the whole period. Hey, at least nobody got physically hurt.
I have written a couple of papers with an enthusiastic Minecrafter about mathematics and Minecraft. I am not saying that Minecraft should be used to teach students about mathematics. However, Minecraft does lead to some interesting questions that are relevant to school mathematics.
The elaboration is idiotic.
I do not like video games anywhere, but I did enjoy showing my students with cubes why the volume of a rectangular block is the product of its height by the area of its base. Showing concretely the connection between the height and the number of layers of unit cubes. The connection between the amount of unit cubes in the bottom ot top layer and the number of unit squares in the rectangle of the base. Representations again. The high achieving Asian teachers do that too. Some of these representations are even in the books of mathematics history.
One cannot “show” the volume of a box is Base x Height.
That’s because it is defined as such.
Exactly. It is true because BISS.
Well, it depends.
You can define (1) the volume of a unit box is one, (2) the volume of a disjoint union of objects is the sum of their volumes, and (3) congruent objects have the same volume.
With this definition, you can proof that the volume of a generic box is aΒ·bΒ·c.
I think this is how it should be done in school (with the language adapted to the age of the students) if your intention is for the students to get some idea of what mathematics is about.
Who really does it that way?
I remember some time in 2013-2015 a kid in the year above me creating a calculator in Minecraft using redstone.
I understand that Minecraft is a whole (virtual) world, and that kids can do soem remarkable stuff within it. The elaboration is idiotic.
A while back someone made a working hard drive in Minecraft the same way, capable of storing 1Mb of data, IIRC.
Maybe it is sarcasm again! It is too hard to understand sarcasm in a non-native language. Sorry! Please explain your meaning of the word “show”. Sarcasm has been used in scientific debates to impose a wrong ideology, according to De Wall. Besides I am not even your opponent. I am very fond of direct teaching.
“I have seen it happen often. The English speaker rises from the audience, articulates a penetrating question, sometimes with a joke mixed in, and barely takes the time to listen to the clumsily phrased reply of his opponent. Since English speakers dominate all discussions, they form a class of great minds strutting around in the secure knowledge that no one will dare challenge them.”
Extracted from:
https://www.emory.edu/LIVING_LINKS/OurInnerApe/pdfs/WithoutWalls.html
Here I will be using my meaning of “show”: “to teach/illustrate/represent/communicate, etc.”.
I have taught the volume formula with cubes many times. I know it is hard work learning how “show” ideas with mathematics representations. I also find it much easier to write a lot of words complaining about the ideas and the teaching of mathematicians and educators. Yet students are strugling, at this very moment, to understand mathematics at primary schools. I did write a lot complaining about stupid teaching ideas, both from mathematicians and educators.
But there are hard working educators who are very much against stupid reforms. I consider myself one of them. Besides, I consider myself also a mathematician, as I had very high marks in mathematics subjects both at school and at university level.
When I started teaching I did try to learn many ways to “show” the concepts and “whys” (connections) involved in the teaching of students in the age range of 4-12 year olds. I can even “show” some (initial) trigonometry and calcullus concepts. Yes, there are much less ways to “show” concepts in harder algebra, calcullus and analysis. Yet I have attended classes with mathematicians and physicists (both in my country and in England) who tried to “show” in their classes a few concepts with diagrams which are one of the five main ways to “show” mathematics concepts (Lesh et al).
In the primary school curriculum it is so easy to “show” things such as 5 real bananas or a picture of 5 bananas. Parents do that at home, according to Yvete Solomon. Textbooks are full of them too. It is not hard.
Do you wish to see a video of one of my classes about volume? π π π
I made such videos more than once!
Thanks, Solange. I’m not being sarcastic, but I’m being a little cryptic, while trying to indicate an important point.
hjm above has a (very) slightly different point of view, but my take is that the area of a rectangle is defined to be L x W. That’s what we mean by area, that’s where we begin, and the then area of anything us done by cutting and combing and scaling and approximating and whatever.
Of course when you cut a (integer sided) rectangle into little 1 x 1 squares, you’re “showing” (your word) something. But I don’t think you’re showing why the area of a rectangle is L x W. I think what you are showing is why we define area in the manner we do. It is motivating a definition, not proving a formula.
All that, about, area is done before volume. By the way, I copied my volume (direct) teaching sequence from the book below, but I start the sequence by constructing rectangular blocks with real unit centimeter (students’ cubes) and decimeter cubes (teachers’ cubes). First the teacher shows (with direct teaching) the whole classe how to construct blocks with decimeter cubes. They were DIY with matress foam. Later the students are asked to construct some rectangular blocks (including bigger cubic blocks) with centimeter unit cubes made with wood or rubber. These small centimeter unit cubes are well known internationally as “Dienes blocks” and are sold as didactic materials in special shops.
The same holds true for volume. The volume of a box is defined to be L x W x H. You cannot show that it is true, you can only show why we choose to define it that way.
Holy God, that is one awful elaboration. You’re right: why not just write “use Minecraft…” (Education Edition (TM) of course, so it’s educational and not a game).
Basically from the same evil pot as “Using a CAS calculator…”
That is another version of formula which follows later as B = L x W. Stop being nasty! π π π
You know very well that both versions are right. But to “show” children with relational undestanding, H x B is the first to be presented. Then H x L x W follows.
I give up! Go and read about the “materia medica” and “Pedagogical Content Kowledge by Lee Shulman. Teaching should be a serious profession with its own “Materia Medica” (Shulman). Not a profession to be afflicted by stupid ideas from both mathematicians and educators. Use a “SS” formula/approach and we will perform well:
SS = Selection and Salary.
Select and pay teachers well and leave us alone. We will learn all we need from good textbooks as I did so.
No, the volume of a box naturally precedes the volume of a general cylinder/prism thing.
I am not being nasty; I am being blunt. If you do not appreciate my message or my style, you are free to leave at any time.
Paul Britten Book 4 (not book 3 as posted before):
Page 61-62, book 4