The new mathematics curriculum can be viewed here, and you can “understand this learning area” here. The various documents can be downloaded here (Word documents, because ACARA is run by idiots). Direct links are below.
We’ve had no time to look at the thing, and God knows when we will. But we will update the post with categorised thoughts, once we look and according to what people remark below.
Get to work.
DOCUMENTS (Word, idiots)
Understanding the Mathematics Learning Area
Mathematics: Curriculum Content F-6
Mathematics: Curriculum Content 7-10
Mathematics: Scope and Sequence F-10
Mathematics: Support resource – optional content for post–Year 10 Mathematics pathways
Mathematics: Comparative Information
Year 9 “Students apply Pythagoras’ theorem and use trigonometric ratios to solve problems involving right-angled triangles.”
Year 10 “Students apply Pythagoras’ theorem and trigonometry to solve practical problems involving right-angled triangles.”
Huh
If that’s the biggest oddity I’ll be greatly relieved. And astonished.
And no non-right angle trig before yr 11.
“Students design and conduct simulations involving conditional probability, using digital tools.” This sounds nice, if it means Monte Carlo simulation.
Why is that nice?
I haven’t looked far, but there’s a lot of use of the verb “recognise”, which always leaves me wondering what they mean – is it just used as an sign that only very shallow learning is intended? For example:
* recognise terminating and recurring decimals, using digital tools as appropriate
(Would digital tools ever be appropriate for determining that a number has a terminating or recurring decimal expansion?)
* recognise irrational numbers in applied contexts, including square roots and π
(In these applied contexts, does it really matter that they are irrational? Am I just too clueless to understand? Are they just meant to be able to point at and “recognise”
in a formula?)
Yes, wst. The problem all along has been your cluelessness.
My main issues with the above points about irrational numbers are that:
and 
say are irrational are not used in applications.
(1) students are rarely exposed to any proof that irrational numbers exist
(2) the facts that
A small effort to remedy the situation for my Year 9 students is attached.
assignment2
Thanks Terry. I have the same concerns. That’s a very nice assignment. How did your students find it?
Thanks for the feedback; the students did this in class over several lessons; they were allowed to work together and ask questions of me; I see assignments as a way to learn as well as a means of assessment; the biggest hurdle for many was to understand the difference between “prove” and “give an example”.
I’m surprised that year 9 students were able to do such an assignment, even with your help and over multiple lessons.
I’m willing to bet that quite a few math teachers would be unable to complete this assignment, especially questions 2, 4, 6, and 8, at least without help. Then again my friend said that his Further teacher outright admitted to not understanding the graph algorithms used in the subject, so my opinion of school math teachers might be a bit skewed.
Or, it might not be.
“between any two given rational numbers, there are infinitely many
rational numbers.” should be changed to “any two given distinct rational numbers”
Thanks for picking that up. I have fixed it for next year – if there is a next year for me.
These commanding terms should really be deleted and swapped with more concise ones: such as distinguish, identify, interpret or determine, etc.
They should compare their ACARA curriculum with the clarity of the defined glossary in IB maths curriculum – and see which is better written….
I can just imagine a student erroneously stating that 1/29 is an irrational number as the recurring sequence is too long to be properly determined using the CAS (likely the digital tool they speak of). And then teachers being told not to tell them that’s wrong as there’s “no right answer” in mathematics.
My issue with this document (or entire sequence/series of documents) is the use of imprecise language, phrases that don’t make logical (let alone Mathematical) sense and the idea that teachers are meant to be reading this to plan their lesson sequences…
If I cared less (and I do genuinely try) as a teacher, I would assume that {insert name of random publisher here} has read the document and so all I need to do is to pick a subset of their work and demonstrate it to students and then hope they are somehow prepared for VCE.
Is it really that hard to say “students need to learn how to add, subtract, multiply and divide integers up to length X by year Y”?
Apparently it is.
Specific examples, please.
AC9M7N07: “compare, order and solve problems involving addition and subtraction of integers.”
Compare and order problems? Perhaps that is one tiny example of what Red Five means by phrases that don’t make logical sense?
Also, AC9M7N09 is an example where they’ve taken very specific directives and combined them into a vague mess that just confuses me. I wouldn’t know what to teach from that.
An excellent example.
There are many more; I’m having trouble putting them in any sort of order for now.
In the ACARA glossary, a random variable is defined as “a function that assigns real numbers to random events”. Given that the glossary does have an entry on “sample space”, wherein it mentions “sample points”, it would have been fully within the scope of the glossary to make the former definition more correct by replacing the words “random events” by “sample points”.
Christian, Your suggestion would be correct for a *finite* sample space.
Not really related to the post, but I’ve always wondered why victorian textbooks prefer to use the term “rule” instead of “equation” e.g. Come up with a rule that describes x and y, The rule for x and y is given as [..]. Is this some kind of a religious law where they had to abide to?
Huh. At the risk of derailing my own post, that’s a very good question. The term always grates, but I honestly haven’t thought much about it.
I am basing this conclusion only on what I have seen in textbooks, specifically of the Methods variety.
At 7 to 10, which is what this post is about, it is possibly one of those bits of crap (such as
fractions which just remains for no good reason)
Actually funnily enough I was taught the opposite: that an equation includes a domain, and that the rule doesn’t. In fact they told me that the definition for a function includes two parts, the domain (and the codomain, which they neglected to explain), and the rule.
I have never known which definition VCAA uses or if they use a consistent definition, but to me an equation is the bit with the equals sign.
Codomain is pretty much always R in Methods, and only recently I’ve tried to give an explanation to my Methods Unit 1 class about how codomain and range are not the same thing etc…
But perhaps this is again evidence of the need for an IB style glossary of terms…
…which will never happen.
No mention of volume of spheres in the new Yr10 curriculum, not even in the “option” topics for year 10. Also volume of pyramids and cones has been deleted.
I found this line (Optional Content for Post Year 10) a bit worrying on a few levels:
“Showing that
is not equal to 
for 
”
Firstly, has is not already been established that
is non-real for 
and, secondly, is it not more appropriate to simply say 
?
Alright, they were also saying “Showing that
is not equal to 
for 
“, but still… doesn’t fill me with confidence in their understanding of the content being described.
I agree. My reflex when reading that, being the contrarian troublemaker I am, is to say “oh but what about
“. I suppose they have an endemic ambiguity issue with qualifiers and we may, in our infinite grace, generously assume that they meant to say “for *all*” and were certainly very concerned with the reader interpreting this as “for *some*” and then going ham.
Simple. Just make
the smaller value and the second number is 
.
So it would just be
for 
And
for 
I have some issues with the algorithm content descriptors for instance “AC9M9SP03: design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements”. From what i can see this just means draw a flowchart or write a program. Not sure of the maths involved. Why is this a content descriptor and not an elaboration?
Thanks, Vicky. I’ll look carefully once I begin compiling. But on its face, it is insane.