This one is a companion to our problem-solving treasure hunt, and again amounts to a competition. We have written roughly ten million words on what is wrong with the draft mathematics curriculum. And plenty of people, including a number of big shots, have signed the open letter calling for the draft curriculum to be withdrawn. But where are the arguments for the draft curriculum? There is undoubtedly support for the draft curriculum. In particular, we are aware of a decent amount of snark directed towards the open letter and this blog. What we are unaware of is any substantive arguments in favour of the draft mathematics curriculum. The only articles of which we are aware, we posted on here and here. The first article came out before the draft curriculum and doesn’t amount to a substantive defense of anything. The second article was written in direct response to the open letter, and is so weak as to warrant no response beyond the comments already posted. And, apart from these two articles we are aware of nothing. No blog posts. No tweets. No anything. Just an arrogant and vacuous dismissal of the draft’s critics.* And now to the competition:
What is the strongest argument FOR the draft mathematics curriculum?
To be clear, what we’re asking for are very specific examples of good things within the draft curriculum, examples of content and/or elaborations that are genuine plusses. So, for example, claiming “the focus on mathematising” as a good won’t win a prize. First of all because the suggestion is really stupid, and secondly because such a generalist statement provides no specific evidence of how the mathematising is good. If you really want to argue that the mathematising is a plus then the argument must be based around very specific examples. Similar to our problem-solving competition, the intention here is not to imply or to prove that there is nothing of value in the draft curriculum. Rather, the competition is intended to imply and to prove that there is very little of value in the draft curriculum. Your job is to try to prove us wrong. Answer in the comments below. The provider of the most convincing evidence will win a signed copy of the number one best-selling** A Dingo Ate My Math Book.
*) If anyone is aware of any article/post/tweet/anything in support of the draft curriculum, which also contains at least a hint of evidence, please let us know and we will seek to address it.
**) In Polster and Ross households.
We’ve finally ended this. The winner is really nobody, but we’ve awarded it to John Friend. See here for details.
48 Replies to “What Are the Arguments FOR the Draft Mathematics Curriculum?”
Here is an argument (and if no one can offer a better one maybe I win by default…?)
A new curriculum means new textbooks which means secondhand books become worthless and the publishers of the new books make more money.
I didn’t say it was a *good* argument.
Yep , the argument sucks, but you’re winning.
1) I’ll modify RF’s argument:
A new curriculum means new textbooks which means an opportunity to improve, perhaps even improve, on what’s currently available. That could be a game changer it happens, and all thanks to the daft curriculum.
2) Another argument in favour:
A new curriculum might arouse teachers from their indifferent torpor and rally them to demand better. Sensing revolution in the air, and wanting to assert their relevance and not be the ones with their backs to the wall, this might in turn encourage “organisations such as [the MAV], AMSI and AMT and AAS and AustMS … [to] get off their fat asses” and start demanding better as well. This might lead to those organisations starting to hold ACARA, VCAA etc. to greater account and to far less unhealthy ‘cosiness’.
3) It might unwittingly bring an end to the ‘Math Wars’, in a good way.
4) It might lead to the replacement of incompetents with people who actually have a clue.
(Admittedly, all these are arguments for how even shit can nevertheless be of some good …)
Geez. This competition is gonna be like Dipper winning the Brownlow.
I’ll try to win with brevity. It’s a fantastic bad example.
Stan, you might win with crypticness. What is your fantastic bad example?
OK, genuine attempt to answer the question (plus a major rebuttal of my own argument):
The draft curriculum seeks to “identify essential content and refine content descriptions and achievement standards.” (direct quote from their website)
And in preparing this draft, ACARA “consulted with practising teachers, curriculum experts, key academics and professional associations.” (direct quote from same page).
Both of these are, at a first reading, good things for a curriculum review to do.
Rebuttal: I have a hard time believing either statement is the whole truth.
Nah. If you can point out a “refined” content description etc, then that would qualify. Just.
OK. I think I understand the rules of the game…
…and it is not going to be easy as most of the content descriptors in this draft are far from refined.
If I found that the current curriculum is worse in ONE of these key areas, would that qualify (some sort of proof by negation)?
Yes that would qualify. Eradicating bad stuff from the current curriculum is a good thing.
You’d wade through swamps and compare their muck?
Wading through swamp in search of a mythical brass ring is bad enough!
(But either way you still get covered in muck).
JF – I will call it “professional reading” and claim it as PD hours when the VIT next asks for proof that I have been developed professionally.
OK, change “when” to “if”.
What a good idea! Use one piece of crap to solve another …
My reading is that participating in the discussion on this blog counts as PD. Seriously.
Oh don’t worry – I plan to use this blog as evidence if VIT ever decides to audit my PD claims.
Seriously. Between this blog and morning tea at MAV sessions, these are the most professional discussions I manage to have.
Insightful too, thanks to the variety of commenters.
The draft curriculum is so appallingly bad that it will hopefully unite many of this country’s leading mathematics teachers in active opposition to it and thus provide an opportunity for a well-led and expertly coordinated effort to prevent its obviously preordained implementation at the state level.
Indeed, Sir H. An eloquent description of Friendly argument 2) above.
It occurs to me that someone might make money writing a Structured Handbook Instructing Teachers on Elaborations. For example, a structured approach for
“estimating the cost of materials needed to make shade sails based on a price per [square] metre”
I agree, this is my response also.
Sir Humphrey, a very good point, but invalid for the competition.
Ten good points about the draft F-10 Australian Curriculum: Mathematics
1. The Curriculum has been developed with the intention that *all* students will study mathematics in years F–10 (p. 1). This makes is clear that mathematics should be taught at all year levels up to year 10.
2. The Curriculum is designed to show connections between mathematics and many other disciplines (p. 2). Too often, mathematics is associated only with science whereas mathematics can contribute to almost any field of knowledge. Unfortunately, students tend to compartmentalise their learning and the draft curriculum strives to correct this tendency.
3. The strand on probability has been separated from statistics (p. 3). While an important application of probability is in statistics, it’s potential for application goes way beyond statistics. We see the language of probability being used in a wide variety of situations such as health care, gambling, weather prediction.
4. While I don’t like the word “mathematising”, I do like the idea of showing students that mathematics can help us to see the world differently. Mathematics can shape our world view. (p. 7)
5. I like the emphasis on raising ethical issues in the Curriculum (p. 10). Many people are surprised to learn that there are ethical issues in mathematics, especially statistics. (See Lenard C., McCarthy, S., & Mills, T. (2014). Ethics in statistics. Australian Senior Mathematics Journal, 28(1), 38–42.)
6. It is admirable that the Curriculum endeavours to create links between mathematics and Aboriginal and Torres Strait Islander Peoples’ histories and cultures (p. 10). I see this as a first step in this direction.
7. There is a considerable emphasis on computational skills, including the use of calculators (p. 11). Technology affects every aspect of our lives, including the experiences of teachers and students. Calculators enable new mathematical experiences just as “a child who learns to speak has a new facility and a new desire” (Dewey, J. (1938/1956). Experience and education. Macmillan, p. 37.) We should strive to *maximise* the value of the impact of calculators in learning about mathematics because this impact will surely increase.
8. The link between mathematics and the arts is interesting (p. 12). Making such links might well engage a student who has a strong interest in art but not so in mathematics. It gives those students an entry point into the world of mathematics. Similarly for making links with the humanities and social sciences. Let’s replace STEM by PAM (pure and applied mathematics)!
9. Emphasising investigations is a first step towards introducing open-ended assessment in the mathematics classroom (p. 14) and, I suspect that we will see this also in Year 11 and 12. This is common in many other areas (history, English, art). The F–10 Curriculum will get students used to this sort of activity in mathematics at an early age and it might change the way in which mathematics is perceived.
10. The fact that the ideas above are included in all year levels gives a certain consistency to the Curriculum. It will be a challenge for universities to prepare graduates who can shoulder the responsibility of implementing the new Curriculum and be well-prepared for further changes.
Where’s the beef?
I think we’ve just moved on from Dipper to Bobby Skilton.
Hmmm… points 3, 5 and 6 look interesting on some level. Many of the others have already been rebutted by other commenters.
There are however some major issues. Point 6 – yep, about 100 years too late and far too little, feels more tokenistic than anything else, I’m not convinced either way although very much willing to be persuaded.
Point 5 – Again interesting to someone who has the time and willingness to really explore the idea, but in this current sense it is a bit too tokenistic for my liking.
Point 3 – Statistics in many university courses tries to separate itself from Mathematics with mixed success. The “statistics” done in school (and especially so in F-10) is beyond tokenistic in my view and in my experience statistics in 7 to 10 is very often left as a fill-in-the-time topic at the end of a semester (or year) and rarely assessed in a meaningful way.
I’ll briefly mention that Point 2 is something the IB world has been doing since inception – IB schools reach some level of achievement on this, but not a lot, and they have 50 years of practice. I can’t see ACARA succeeding where the IBO could not… again, willing to be surprised.
Terry, in terms of the competition, and standard argument, it’s not enough to regurgitate ACARA’s claims of what the draft is doing. You gotta show it is doing it.
In brief response.
1) You’re kidding.
2) This is probably the worst aspect of the draft and, ironically, you can still win the book this way. The overwhelming emphasis on non-mathematical connections in the draft is simply appalling. Still, you can point to some specific instance fo such a connection, and that could be a reasonable (isolated) plus.
3) Again, you’d have to be specific. In general, going from three to six strands is an awful move.
4) Bleah. Again, come up with a decent example and thats’ fine. In sum, the mathematising is at the heart of the inquiry-based lunacy of the draft.
5) Small beer, and be specific.
6) The endeavour is admirable. The result is farcical. Once again, choose a good example.
7) Pull the other one.
8) Again give an example which is not awful. And, again, the general maniacal desire to make connections comes at the expense of presenting mathematics as a coherent discipline.
9) Jesus H. Christ. The incessant investigating/exploring/modelling is excruciating. Pick a good example, thats’ fine. Your general point is absurd.
10) I’ll grant you this one: the level of the above nonsense in the draft is astonishingly consistent.
There are plenty of valid reasons “for” it, not in the sense that it’s good, but to explain why it exists. You just have to be cynical about the motivations of the actors.
1. Since it is long and complex, it has made work for some people. (Some of these people might be genuinely manipulative but others just need a job.)
2. Politicians are more impressed by a longer document.
3. The people who appear to have written it are international grifters who have made careers out of developing close relationships with government and business. Having completed this grift, they will be able to move onto another, using this grift as evidence that they are good at grifting. This is a rent-seeking process which leads to the writers becoming rich and well-known (at least, more so than an average teacher or academic).
3a. If you are an up-and-coming figure in the education bureaucracy, supporting the writers of the curriculum helps you to develop useful connections for your future advancement.
3b. More technology required in the curriculum = more profit for sellers of technology.
4. It makes the government look like it is doing something about an issue which people care about, or at least it allows them to deflect questions about it.
5. It puts various publicity-hungry people into the spotlight.
[the above reasons could be applied to any curriculum document of this type, so here are a few which are more specific]
6. It (like the other ACARA drafts) is anti-academic; the knowledge of people who actually work in the relevant academic disciplines is not just ignored but consciously marginalised. The terminology in these curricula is often deliberately redefined so that the curriculum writers and the experts literally don’t speak the same language. This has a number of positive effects for the people who write the curriculum: it paints the actual experts as out of touch nerds in ivory towers (Australian politicians think the general public likes this), while the curriculum writers get to control the discourse, it allows any kind of complaint about the content (big or small) to seem like carping, and most importantly it protects the writers from criticism during the process of writing, as this might harm the success of their grift.
7. While it is long, the curriculum is ambiguous. This has several non-educational advantages:
a) It generates further bureaucracy after the curriculum has been written (to explain and respond to complaints), thus generating more work.
b) Textbook writers (and similar people) can make money from updating their work. Furthermore, since it is not really clear what anyone should know, it is impossible to write a “best” textbook, or to reuse cheap basic resources from the academic discipline, so quite a few people can have a go at trying to corner the market. This makes the writers money (at least, more so than an average teacher or academic).
c) If you are a bad or unmotivated teacher or administrator (people like to pretend there are no bad or immoral teachers, but every teacher is bad or immoral sometimes, and some are all the time), the vague curriculum protects you from scrutiny. First, it’s not always clear what anyone should know after you’ve covered a certain part of the curriculum, and it is very hard for a student, colleague, or parent to identify exactly what you have done wrong (based on the draft, you have to look up a 9-digit alphanumeric code, and even then it’s not really clear how you determine if it has actually been taught or not). Second, it’s hard to prove that anyone has actually taught anything wrongly, because supposedly open-ended or investigative processes, which by definition don’t have a set outcome, can’t really be right or wrong. The teacher can literally do anything in the class, as can the students; all they need to do is point to a box and claim it’s been ticked.
d) It reduces the need or demand for well-qualified teachers who know their discipline, and reduces the power of teachers who do know the discipline. In tandem it enhances the power of those teachers and administrators who like sucking up to authority figures. Both of these give administrators more power and less stress.
8. Bearing in mind that this current review is driven by the Liberal Party, there is an argument that they don’t mind if the curriculum fails. This is partly for the general reason that they are philistines and don’t really care about education. More specifically, the Liberals believe that they can gain popular support from advocating a “back to basics”, conservative style of education. Obviously this conflicts with the drafts, but if schools aren’t good enough, it can be advantageous for the Liberals. They can paint teachers as left-wing radicals and students as delinquents, reinforcing their argument that people should vote for them because they can control society better. Of course it makes no difference if they contributed to the problem themselves. Also, poorly educated people tend to vote Liberal. (Random observation: Alan Tudge’s daughter attends an extremely wealthy private school where she can do the IB if she chooses.)
In short, a lot of people stand to benefit from processes like these, and hence it is understandable that such the draft curriculum looks like it does. It’s not caused by deluded or naive people. Of course a lot more people would benefit from a better curriculum, but those people have relatively less political power.
[BTW thanks for all the discussion on this blog. I’m not a mathematics expert but have been writing comments on some of the other drafts, and it’s been very helpful. I think the way forward, if there is one, is to write your own alternative curricula, make them public, and invite schools to use them. Some schools are pretty powerful, and if Snob Grammar in your local capital city spurns the Australian Curriculum in favour of one it likes better, I would be amazed if the government would even try to put it out of business.]
Wow …! Wow!
Thankyou for this contribution, niowov. You have beautifully articulated several thoughts I’ve had but could not find the words to adequately express them.
I totally agree with your point 7). This is one of the great harms of the Daft curriculum. Even a good and motivated teacher is going to struggle to know what to do. And there is huge potential for it to turn teachers ‘sitting on the fence’ into bad and unmotivated teachers, leading to a further decline in teaching standards.
I liked your final observation that “It’s not caused by deluded or naive people.”
I think you are correct. The cause is people I’ll call ‘back-room people’. The ‘back-room people’ choose their tools – in this case, the curriculum writers – very carefully. It is the writers who are deluded and naive, with no awareness of how they’re being used and manipulated. These ‘grifters’ – egos stroked – are willing and oblivious tools. And there will always be an abundance of ‘grifters’ for the ‘back-room people’ to choose from.
(BTW I love your use of the word grifter. It’s exactly what these tools are, except that their swindling has large-scale consequences that harms entire populations). A tool for every occasion.
I don’t think getting “Snob Grammar in your local capital city [to spurn] the Australian Curriculum in favour of one it likes better” is viable – the ‘back-room people’ are alumni of these schools. I think the only solution is to generate public awareness leading to public dissatisfaction leading to sufficient pressure for change (and might get Snob Grammar on board along the way). A tall order, I know.
Re: Sludge. Of course she does!
Re: “… open-ended or investigative processes, which by definition don’t have a set outcome, can’t really be right or wrong.”
There are good open-ended tasks and not-so-good open ended tasks. I agree that the outcomes are not set, in the usual sense, but a well-written rubric guides the student and the teacher in what is expected. Such tasks allow students to explore ideas; they can be liberating. They are used routinely in the humanities and social sciences.
These activities help to dispel the myths that mathematics is right/wrong, the answers are all in the back of the book, or mathematical questions can be answered in less than half a page.
To be sure, they are not easy to design or mark, and they take us out of our comfort zones. But, in my experience, they are worthwhile.
This is a useful reference for primary schools: Sullivan, P., Lilburn, P. (2017). “Open-Ended Maths Activities”, OUP. I have used some of the ideas in secondary schools.
While I am suggesting that there is a place for open-ended tasks in the mathematics curriculum, I am not suggesting that all tasks should be open-ended. We should give students a taste of them.
OK… “open ended” tasks in schools are not always “open ended” and I worry a bit that with emphasis on technology there may be more of this, with minimal benefit.
For example, cutting the corners out of a rectangle to maximise the volume of the resulting box. Once calculus has been learned, the task ceases to be “open-ended” but I have often seen this activity used as an “open ended” task with spreadsheets in junior secondary mathematics (I vaguely remember doing it myself in Year 7/8 as a student).
As to why I am worried by this: sure there are some situations where there is no “perfect” right answer and having students learn how to argue that their solution is the best non-perfect solution to a genuinely open-ended problem *might* have some benefits.
Unfortunately, the majority of mathematics DOES rely on things being right or wrong and this is to me quite a key feature of the discipline. I’m not convinced that there is a need to shift the conversation away from mathematics being about right/wrong (leave that to the ethics teachers…) and a large part of me worries that to do so we would have to give up a lot.
In short: genuine open-ended tasks good, motivation for more of them questionable at best.
RF: I used to work in a hospital using mathematics to address problems of interest to the hospital. For example, in planning for a new cancer unit, I was asked to address the question, “How many chemotherapy chairs will we need 5 years from now?” I regard this as an open-ended question and this was typical of the questions that I dealt with every day. Often techniques based on quite advanced mathematics were used; sometimes a simple method did the job. Whether my answers were right or wrong would not be known for five years.
Recently I wrote a report that predicted the number of school aged children in Bendigo, by age group and year, for the next 20 years. We will not know whether my predictions are right or wrong for twenty years, but the trends are undeniable and provide a useful basis for planning for schools in Bendigo. (The baby-bonus had a major impact on this work.) One principal called me in to discuss the report after he read it in detail: so it was of interest to one key school principal.
Solving problems such as these involve advanced mathematics, and mathematicians – I venture to say only mathematicians – have the skills to address them. But the solutions do not lend themselves to a simple classification of right or wrong.
As for ethics, I served on the Human Research Ethics Committee at the hospital for several years. This too involves mathematics. A researcher might put up a proposal that would involve a sample of 100 patients. I would ask “Where did you get 100 from?” This is a mathematical question, often non-trivial. The sample size should be calculated – and there are formulae for doing so. To pluck a sample size out of the air is bad science, and hence unethical.
And if you go back to the book on open-ended tasks for F-6 students that I mentioned earlier, you will see the question “How much does it cost to keep a dog for a year?” This generates good discussion even in a secondary classroom although it involves only arithmetic.
For Year 12 students, one might ask “How much will it cost you to go to university?” Parents might be interested in this question!
When I finished high school, I applied for a scholarship with ABS to support me at university. I got into the final 10 in the state. We had two days of tests and interviews. I remember one assessment quite vividly. We sat around the table and the question was put to us “How would you count the number of people in the state on 30 June in the coming year?” Our task was to discuss this amongst ourselves – we probably had at least 30 minutes – and develop a proposal. ABS staff watched and listened.
And these are genuine open-ended questions.
They require some serious knowledge of mathematics (and statistics – which I will come back to soon) to even begin to know where to start.
School mathematics does not (in my opinion) lend itself to this type of analysis at all.
Statistics DOES lend itself to open-ended questions a lot. What I’m seeing in this curriculum draft is an attempt to force open-ended questions into parts of Mathematics which do not lend themselves to this style of question.
Some mathematicians I know would argue that statistics is not mathematics (and at least one statistician I know would agree).
So, I take your argument as valid from a statistics perspective, I’m not convinced that it can be applied to the whole of school mathematics. Not yet anyway.
Without getting into the distinction between mathematics and statistics – that’s another issue – I agree that open-ended questions are not always appropriate. My point is only that there is a place for open-ended questions in the school mathematics curriculum, and yes, statistics lends itself to this sort of questioning. The study of graphs and networks might also lend itself to open-ended questions.
BTW, a university in Denmark has based all its degree programs on multidisciplinary problem solving. The university is here:
OK. You are clearly a skilled and experienced proponent of both Mathematics and Statistics, and if you can design an open ended task for use in your own classes – all credit to you. I will openly admit attempting it myself with mixed success thanks to the requirement for SAC questions to be “open ended” (another story entirely).
What I dispute is the underlying tone I find in this documentation that open-ended tasks should be the main goal, rather than the icing on a well constructed cake.
Again, time may convince me otherwise and I’m prepared to wait and see what the experience is more widely.
RF, I do not believe Terry is talking about the draft curriculum. He just took our ball (again).
Thanks, Terry. If ABS is still listening to you, can you politely ask them to stop screwing up the Australian curriculum?
Terry, your last is the most important paragraph, and should have come first.
Also, it is not a “myth” that mathematics is right or wrong, and it is a red herring from niowov’s point. I understand your point, although you’ve tried hard to make yourself incomprehensible, but you’re overplaying it. In particular, and you clearly recognise this, even open-ended tasks must have some possibility for evaluating the answers. Whether one calls such answers “right” and “wrong” is a distraction.
Which raises the main point. This is a competition to find the arguments *for* the draft curriculum. Your repeated stating that there is good to be had in well-designed investigative tasks has probably been noted by everybody. So what?
Hi, ionowov, thanks for the great comment, and I’m sorry to be slow to respond. Your points are directed generally at educational authorities and their fellow travellers, and I’d bet they are generally valid. I’ll respond to your comments in the context of ACARA and the draft mathematics curriculum.
2. In general, yes, but, for whatever reason, it is not at all clear that Alan Tudge is thrilled with ACARA or, in particular, with the draft mathematics curriculum. Tudge has noted AMSI’s opposition to the draft, and he is signalling ACARA should not dismiss it in the manner ACARA is attempting.
3. It is not entirely clear what the role has been of the Center for Curriculum Redesign. I suspect you are correct, that these clowns for hire are a major part of the screw-up, but some clarity would be welcome.
4. The idea of a periodic curriculum review is not unreasonable. This review was supposed to be a modest “refining” and “decluttering”. It is ACARA, not the government, that has gone all revolutionary.
5. I don’t know if there’s been much spotlighting here, and I genuinely feel sorry for the unfortunate person who has been the face of the draft mathematics curriculum. De Carvalho seems to like the spotlight, but he’s been ducking the mathematics spotlight of late.
6. This is a painfully excellent point.
7. Also a painfully excellent point.
8. This point, I think, is confused and contentious, and I will leave it for another time. In brief, I am a traditional Lefty, and I would gladly line all the Liberals and their business and media goon-mates up against the wall if I could, but I am also in favour of a “conservative” (I would use “reactionary”) style of education.
I will have a go:
The best thing that one can honestly say about the “new curriculum” is that it is.
It implies that the current/previous ones are not suitable/appropriate/good enough – though most people here would say that it does not fix the problem.
I hope it is enough for the prize.
I also have a comment and a question about “open ended” tasks.
I do not think they are suitable( too often )for minors. They need a precise answer, even psychologically.
One does not have them on call for every occasion. They may come up from time to time in the course of teaching and then good, use them, skillfully.
Now the question: how is/are fuzzy logic / fuzzy sets doing these days?
Hi, Banacek. A very good, and valid, point. But nope, it doesn’t qualify.
Thank you all for the comments so far, and I will try to keep more up to date with replying.*
Just to be clear, as far as I can tell, no one has even entered the competition for the book yet. Sure, it’s not a great book, but it’s free, and it’ll be signed by a Mathologer (and a ratbag). One good elaboration or the like is enough to enter.
*) Not gonna happen.
Here we go Marty, I’ll give it a serious attempt.
The draft curriculum contains often use of technology, supporting students in becoming digital natives. While the previous curriculum did involve the use of technology, it did not do so to the level that is in the draft, and this will have many flow-on benefits for the students.
You asked for specific examples of evidence to support an argument. For this one, you don’t need to look very far: technology use is explicitly dictated in many content descriptions from quite early in the curriculum, for example AC9M3A01, AC9M4A01, AC9M4ST01, etc etc.
Now excuse me while I go and be sick.
Glen, you’re joking, right? I mean, you’re winning, because you’re the only person so far who has mentioned anything specific in the draft. But you just made me throw up on my keyboard.
Yes, of course, it is a crazy “positive”. Importantly, the argument is NOT claiming that the use of technology helps them learn mathematics, just that the use of technology helps the students learn technology.
I’m trying to pretend I just linked it from someone else’s tweet or something, instead of having typed it myself.
To the readers: Please feel free to flame this argument. Please.
“…and this will have many flow-on benefits for the students.”
Yeah… and requiring all schools to be 3-story buildings will help with their physical fitness, but hey, let’s install lifts because technology is available and should be embraced…
I don’t know if it is your logic or your premise I have an issue with here, but I reject your conclusion (as you have already done, so nothing gained).
It is a bit like saying the draft curriculum is good because having a draft is better than not having a draft. An argument that is very difficult to argue against, so we need to attack the assumptions and fundamental premises on which it is all based.
This makes Marty’s contest more difficult though as it basically says nothing is good in the draft because the foundations are themselves rubbish.
So, I think I’ll retire from the contest now (I already have a copy of the book) and wish everyone else happy hunting!
The best feature of the draft curriculum is that it has generated a wide, public debate about how mathematics should be taught in our schools.
Has it really though?
“Wide” – a subjective qualifier at best.
“public” – in the sense that anyone can read this, yes. In other ways… not really.
“how” – also debatable, since most of this “debate” is about the “what”.
It is not an original opinion in that TGuttmann has mentioned it before me, here, on this blog.
So, the heart of the matter is: the ultimate evidence of proficiency in mathematics should be in the form of PROBLEM SOLVING.
I will expand on it in my own words.
In the past, not that long ago, final y12 state examinations were based on : problem solving. Just a few. Not 20 or 30 questions; derive this, antiderive that, tell what the amplitude is what the equation of the asymptote is – these facts and skills should be tested internally, in schools, on tests, perhaps.
On the examinations students should evince they are capable of applying their skills to : solving problems, in their entirety, with logical steps taken and (verbal) explanations of these steps provided as part of the solution – these should be required for full marks.
Why am I setting basically the same question for end of the year exam in say y10 as I did on their topic tests? To find if students still remember how to solve simult eqns? factorise quadr? Or similar routines.
The reality is that they usually have difficulty keeping up with them, yes.
Changing the format of exams to exclusively problem solving style could cost me a lot, troubles coming from students and their parents and subsequently school management.
So it better come from above, like acara.
The fact that they stab in the dark re. how to achieve the target of such an ultimate method of assessing seems to be the weakest link (plethora of weak links, should I say) of the curriculum.
But you asked for ONE good/positive thing in it.
Here it was.
Hi Banacek. As always, it depend what you mean by “problem-solving”. In terms of the competition, you would have to come up with your best explicit example within the draft, or at least some proper specificity within the draft, not just undefined motherhood twaddle, which the draft has by the ton. (It also then be a better entry for the other comp)
In terms of what a Year 12 exam should look like, again it depends upon the meaning of “problem-solving”. Victoria’s HSC used to have what I called elsewhere “hard exercises”. So, definitely a lot deeper than the microscopic trivia of VCE, and definitely there were questions where you had to think before plowing in. But still predominantly skill-based, with the exercises/problems reasonably constrained and requiring a reasonably constrained bag of techniques.