To be more precise, what does “digital technology” mean and, precisely as possible, how is Digital Technology X used in Year Y of schooling?

It is now impossible, of course, to write a document on education without genuflecting to the God of Technology. The repetitious chanting of “technology”, like a wired Tibetan monk, is the way people with no sense of the past or the present indicate how hip they are with the future. But, what do they mean? What technology are they talking about? It is a serious question, of which we only vaguely know the answer. We want help.

Of course by “technology”, the Education Experts are never intending to refer to something like blackboards and chalk. They would not even recognise such primitive devices as products of technology, although of course they are. No, what the EE mean by “technology” is electronic devices, mostly computers and computer programs, and preferably devices that are internetted. So, calculators and electronic whiteboards and Mathletics and Reading Eggs and iPads, and so forth.

The question is, precisely how are these devices used in specific classrooms? For example, are calculators used in Year 5 to perform arithmetic calculations, or to check calculations that have been done by hand? Is Mathletics used in Year 7 to teach ideas or to test knowledge and/or skills?

The same question applies to all subjects. Are word processors used in Year 6 to check and/or teach spelling and grammar? Are iPads used in Year 8 to check the definitions of words?

We want to know as much as possible, and as specifically as possible, what electronic gizmos are being used, and with whom and how.

At the most basic, philosophical level, I would make the argument that science is the study of *causes* whereas technology is the study of *uses*, but the more common usage of “technology” seems to be the objects, not their study.

So – I use a computer, a phone, a television. On the computer I use multiple pieces of software written to aid mathematical calculations.

I use said technology for many purposes, but, I would argue (and here is perhaps the big difference) that I do it *by choice* and for the purposes of playing around with a function/graph/graphic/document rather than trying to answer an exam question.

In my opinion (which I will accept is likely very much in the minority), the issue with technology in schools is that it really takes away choice rather than adds to it. Give a student a particular brand of calculator and they will, in many cases, assume that this is the only tool at their disposal.

Those who take an almost polar opposite view to me (and I have worked with a few of them) sometimes argue that the calculator is a genuine tool because it “allows students to see correct answers from the outset” and “allows them greater scope to explore ideas”. Perhaps. I can’t recall ever really seeing it being used in this way, but whatever.

Although a completely contrived and unrealistic example – I would not give a woodworking student a band-saw and nail-gun during their school years.

RF, I agree that it is very weird to use “technology” to refer to the device, rather than the underlying ideas that make the device possible. But i’m less interested in the philosophy and the semantics than the specifics.

Of course. Just like the company is less interested in the teaching philosophy and more interested in how many sales they can make each year…?

Builders have complained to me that apprentices don’t know how to hammer in a nail.

For sure. I am still amazed at my father’s (who was a university lecturer) carpentry skills that he simply “learned while growing up” and my mother’s ability with a sewing machine because “we made our own clothes”.

Globalization has perhaps done many strange things to education (both within and outside of schools)

And we also use Numerical Acumen with our Year 7 students.

How? Do you instruct students to do this challenge at that level on this day? Is it used in the classroom? Do you teach mental tricks beforehand or during? Or, is it just around for students to use as they want?

I can only speak for my own class (but I kind of assume others follow my lead on this):

In the first 4 weeks of the year, we give nothing but NA as homework and ask students to do a minimum of an hour of it a week in sessions no more than 15 minutes at a time. I tell students to play around with the levels, do any challenge except fractions (until a bit later in the year) and show them that I can track what they have been doing.

While this is happening, I am teaching problem solving techniques in the classroom.

When we get to a topic such as algebra, I have some students who are simply not ready for this as they don’t know times tables nor in some cases how to add two digit numbers together. So, I prescribe them more NA as homework instead of what other students may be working on.

I also insist (with a small amount of push-back occasionally, but normally from outside the faculty) that students HAND WRITE their homework even though the Cambridge books will now allow students to do their working directly into the interactive book on their devices.

During lockdown, I had an advanced class sign up for Mathematica Online trials and had them explore some analytic geometry this way for two weeks. Would I have done this if students were physically in the classroom? I’m not sure, but I’m not planning on repeating it this year, even though they thought it was a success, I’m not convinced it added anything to the learning experience.

Is there any evidence that any students do anything other than “play around” with NA? Is there any evidence that NA as homework has done any good? What makes you think other teachers are following your lead?

To be clear, I’m a fan of NA. But it is not clear to me how it might be helping in your context.

“evidence” means different things to different people. Even though all my students take a “numeracy test” upon enrolment, I do not trust the results that much, so I will not claim there is any meaningful evidence that it helps.

BUT… if I’m going to get students in a homework routine, I can think of a lot worse ways to do it than NA.

I am a fan of it, mostly because it does not over-shoot in the way some online “resources” do and (perhaps more importantly) it is not gimmicky.

I suspect other teachers are following my lead because:

1. I tell them to.

2. They want to know what to do in the first few weeks, so see point 1.

3. I know their teacher NA codes, so can check on their classes if I want.

I should also say that I find NA a really useful exercise to assign to students for 5 minutes at the start of a lesson if I need time to set up another activity. It all helps.

Hi, RF. I’m not trying to nitpick. Starting with NA is about as sensible a beginning to Year 7 as I imagine. I’m just wondering, if you’re not being very prescriptive, will it do much good. With all of these do-what-you-want programs, electronic or otherwise, it seems obvious that the kids who need the most practice will do the easiest and the least.

Sure. Being prescriptive takes time and in some cases it is not worth the effort (more with other teachers than with students, by the way!)

At the end of the day I know it is not doing any harm (rule 1 in the Mathematic Oath…)

Also, if a student is given NA as a substitute for homework their parents say they won’t cope with and then the student doesn’t do NA… whatever. There is a limit to some things.

well, I think it’s potentially great you’re using NA, but you haven’t convinced me that in practice it’s more than a game.

In VCE General Mathematics Unit 1, my students are allowed to use calculators for anything.

The other day one of my students was trying to draw a straight line and admitted that he did not have a ruler. I pointed to the cover of his calculator and said “You have a $200 ruler there.”

Thanks, Terry. I should have specified that I was interested in up to Year 10. VCE is obviously its own weird thing.

And Year 11 General is a particularly weird (yet in its own way quite interesting) thing.

Some of the concepts could be quite deep and meaningful if a student had 3 to 5 years to gain a proper understanding of it…

Plus, I find the financial stuff is actually really useful for life skills if nothing else.

General Mathematics and Further Mathematics are often described in terms of “life skills” whereas this phrase is not associated with Mathematical Methods or Specialist Mathematics. Do students in MM or SM not need “life skills”?

Maybe VCAA assumes the lives of MM/SM students will somehow be different?

Whenever a student in my Methods or Specialist classes says “When will we need to know this?” / “What relevance does this have to real life?” – there’s a million and one ways to answer this.

One of my gold nugget favourites is that studying this level of mathematics (putting aside the fact that VCAA have butchered the actual curriculum and university mathematics is probably a better place to study “mathematics”) is that it trains your brain in much the same way that going to the gym trains your muscles. You don’t magically get the results of a workout(s) without actually doing the workout. Furthermore, there is pristine beauty in mathematics that isn’t found elsewhere – it’s just really cool to learn. Having the courage to tackle hard maths problems sets you up to tackle hard problems in your career or life situations.

If that’s not good enough, well the student has already turned the other way long before.

I’d argue that we don’t need to teach these “life skills” in MM or SM – it’s assumed that the students here are already smart enough to learn these skills themselves out of their own volition. They don’t need a teacher telling them how to calculate compound interest on a mortgage for example.

And Further Maths being a house for real-life mathematics? Yeah let’s keep it that way and let the mathematically-inclined students steer clear of the crap that is FM. What an abomination of a subject, seriously.

FM *could* be a great subject and from what I can see, it once got close, back when it was first created.

Then students (and schools) decided to push students into the subject that were not the intended audience and… well, we know the rest.

As for “life skills” I always think “fish grabbing with the bare hands” from J Abner Peddiwell’s, “The Sabertooth Curriculum” (it is a satirical take on post WW2 USA education, but a lot of the observations remain very relevant Down Under)

The whole “life skills” thing is complete shit and everybody, with the possible exception of Terry, knows it.

My copy of STC just arrived, finally. Looking forward to it.

Enjoy the read. I’ll discuss with you over a tequila daisy after you’ve read it (and by the time you’ve read it you’ll know why I said tequila rather than vodka)

What is STC?

A book. “The Saber Tooth Curriculum”. Written by J Abner Peddiwell (a pseudonym, assumed to be Harold Benjamin but as far as I know never actually confirmed).

It tells the story of the first ever teacher: New Fist Hammer Maker (New Fist to his friends) and is a rather scathing commentary on the American education system post WW2.

A Marty acronym for the book ‘The Sabre-Tooth Curriculum’:

If we accept that Further Mathematics (soon to be General Mathematics) and Foundation Mathematics are to exist, and that students will be allowed to use calculators for anything and everything, it would be better to let them use Excel rather than a CAS calculator. Proficiency in Excel would be useful to many students in subsequent years, and, in my experience, secondary students are not proficient in using Excel.

When a student asks “What’s the use of this?”, often the student does not want an answer. It’s likely to be a sign of frustration that he or she is not getting anywhere.

Very good point. Which means that one should more often be addressing a student’s frustration, rather than answering badly a bad question.

Except, in my experience, it is not so much the student who has the frustration but one or more parents who “never understood” the subject themselves.

It seems to me that SM, MM, FM are attempts at streaming students according to their mathematical ability.

A school near me last year was proud of the fact that one of its students got a score of 50 in FM. I wondered about this achievement.

Maybe SM, MM, FM, like gymnastics, should be described in terms of degree of difficulty; high, medium, low. A marketing consultant could develop better descriptors especially with a 4th subject on the horizon.

And yet the IB has managed four Mathematics subjects of varying difficulty for decades with no such issues… OK, very few take Advanced Mathematics HL since it means they cannot do two science subjects, but still they manage with no scaling between subjects (also not entirely true, but a darn sight more transparent than the VCE)

New answer (getting back to your information-gathering quest):

A lot of my colleagues are using One Note, pushing files out to students (I have no idea how this works and really don’t have a lot of desire to find out) on a regular basis. A few of the senior managers also seem keen on One Note, which possibly makes me less inclined to find out how it works.

There is a push since a new principal started to use Google Drive. A few people are a bit nervous about bowing to such a monopolistic technology deity, given how quickly they could just cancel everyone’s access should they wish to make a point (perhaps they feel this way because of the Facebook news saga).

Some teachers really like interactive whiteboards. I’m yet to be convinced.

Even though I’m no fan of Hattie – apparently a data projector is the most powerful tool you can give a teacher…

I have used One Note during the Master of Teaching (Secondary) at Deakin when we were doing group work. It was useful – but I doubt that it is particularly helpful in sharing mathematical ideas. Symbols are the problem again.

I have noticed a tendency to give students access to more and more resources. Yet I feel that, in mathematics at least, they have everything they need in the textbook, even with its imperfections. Students would be better served by learning the material in the textbook.

Terry, I agree, except for the fact that the texts are awful. But the point stands: choose one best source, and that’ll do.

The use/greater use of OneNote and its ilk is probably a consequence of the remote teaching in 2020. One big advantage is that it allows class notes to be shared and archived. However, I’m no fan of a teacher sitting at their desk and delivering their class via OneNote. I much prefer an electronic whiteboard – you can use it as a whiteboard and also as a data-projector (using an app like Vivi) and you can save the ‘slides’ to a pdf file at the end of each lesson (and hence archive class notes on a shared drive).

@Terry: I just saw your post. Symbols are not a problem. You can write in One Note using a stylus just like you would on a board using chalk or marker. Also, I hate textbooks. I prefer that students use them only for the questions. I much prefer giving students my own notes and thoughts.

Re: Google Drive etc. I don’t have a problem with efficient storage of and access to files. I think it’s essential. But only a fool would store files in the ‘cloud’ and not have those files backed up on hard drives, multiple USB sticks etc. My school is a big user of Google Drive – I tell my students to download the files they require onto their own devices, and in some cases (Topic outlines, solutions to assessments, summaries etc.) to print out hard copies for easy reference.

My unease with a new Principal and Google Drive would be if the new Principal is using uploads to Google Drive as a (nice simple) quantitative measure of ‘good’ teaching … And maybe some teachers consider that “using One Note, pushing files out to students” will be seen (by the new Principal?) as a sign of being a good teacher … My gut warns me that “A few of the senior managers also seem keen on One Note” supports this view. It wouldn’t be the first time that management mistakes quantity for quality. I have known teachers who deleted files from Share Drives and then uploaded them again simply so it looked like they were ones who did the work …

Yes, because what the students are really lacking is sufficient resources.

Keith Devlin calls the Spreadsheet, the “modern implementation of Algebra”. I am amazed that CAS Calculators, with their huge cost, difficulty of use and little application outside of school, have taken the place of a Spreadsheet, with their no cost, ease of use and ubiquitous applications World Wide. There are also significant conflicts of interest regarding the mandating & revenue CAS generates from the VCE &HSC since about 1997. There has been little to no protest from teachers & Unions. The domino effect of CAS in Y11&12 has reached junior years, where most schools also introduce CAS to Y7 students. So Spreadsheets are effectively removed from the Curriculum ( I realise CAS has limited spreadsheet functionality but for the cost this is piss weak). I’d be interested to hear if this has also reached primary schools. I’m trying to promote the use of Spreadsheets in Schools and have developed this series of lesson on Sports Ranking, if anyone wants to help out let me know – https://sportranking.blogspot.com

Any principal or maths head who mandates CAS for year 7 is a fucking moron and should not be allowed anywhere near children, or sharp implements. As for Keith Devlin, he can be a real twat when he puts his mind to it, and I think this is such an occasion. George, I cannot agree: I think the data-ization of school education is appalling.

I have noticed that CAS calculators are not permitted in some 7-10 schools in Bendigo.

On the other hand, one parent pointed out to me that one item on the booklist for her daughter was a $15 ruler. When she asked about it, the teacher told her that the ruler has formulae on it that her daughter will find useful.

Excellent news. Let’s all move to Bendigo. As for a $15 ruler, that’s obviously insane.

Reminds me of those $15 rulers with tiny calculators and random gizmos on it…. A silly gimmick at best.

Mathomats could cost $15. I wonder if it’s that?

The way I use digital technology in my teaching is as an “addition” to the lesson.

For instance, I teach students how to simulate random events using excel. This is done after teaching students about probability, so they have all the fundamentals down.

It is a good lesson, especially when we talk about how a computer can generate random numbers.

There are also good discussion about assumptions and what is reasonable to assume.

I avoid using digital technology in a way that would remove mathematical thought, it should be used to give NEW opportunities in their learning.

As for calculator use in the classroom, I ban it in year 7 until around the end of term 2 – after we have done all the multiplication, fractions, etc. I tell them that it is faster to do arithmetic in your head than reach for a calculator.

(I teach in an academically selective school, maybe I would band calculators for longer in other schools). Once the year goes on, the kids have an expectation that they should use calculators and its too hard to keep saying no (e.g. when we do area, the arithmetic doesn’t seem as important to them as the techniques to find area).

Potii, I appreciate that using computers to provide demos is fundamentally different from a more intrinsic delivery of a lesson. Nonetheless, I’m highly sceptical. On occasion I’ve watched such tools/demos, and I don’t think I’ve ever been impressed. By its nature, I don’t see how watching a black box do things can be convincing of anything, and I’ve failed to be convinced of anything, other than that black boxes have no place in school education.

It’s interesting that you suggest you might ban calculators for longer in a weaker school. Of course, that is appropriate, but the forces against such a ban would be much stronger. Your final sentence is somewhat self-contradictory.

Yes it is contradictory and at times you just want to give a weaker student a calculator to make things quicker.

I doubt a lone teacher can do anything if the surrounding culture has other plans.

I don’t use technology for demos, I use it to model things with mathematics. Maybe it is still just black box magic but I try to get students to apply their mathematical knowledge and think (if technology is not needed in the modelling process I don’t use it).

Thanks, Potii. Yes, I misunderstood you slightly. I still think a black box is a black box.

My raw feeling is that the education debate never really started the right way and has continued off course ever since. Rather than asking “how can we improve students knowledge/understanding of Mathematics?” the starting point has been “how can we use technology in the classroom to…?”

Once the technology becomes such a heavy part of teacher education as I know it to be having worked recently for a university in their pre-service teacher education, it is a bit of a one-way street!

Undoubtedly modern maths education has completely lost the plot. Obviously in relation to “technology”, but in other ways as well. These people are poisonous.

Can this battle actually be won though or is it inevitable given the “technology allowed” exams are now everywhere and becoming more and more CASified?

RF, small but not insignificant battles can be won. But, as for the war, no fucking chance. All one can do is go down fighting and swearing.

As an example of a battle that can be won, there is absolutely no reason why calculators are needed at all in Year 7 (or earlier, or later), and there are compelling arguments against them. So if, for instance, one is a head of maths at a school, one can and should argue for this. Yes, it is quite likely that the Principal and her henchmen are idiots and will veto this. But they should forced to do so. A second and similar battle is CAS calculators before Year 11; they do nothing but cripple students.

If, lets say, I managed to get calculators off the booklist for Year 7 and the science department just put them back on… what next? Ban them from my classroom? Easy. What about all the other classrooms?

Unfortunately, as you know from working in universities (schools are not quite as bad in many ways!) there are those who exercise their powers of veto with no explanation.

Good point, although note that this point does not apply to CAS calculators. Yes, you ban them from the maths classroom. You can also make clear homework is meant to be completed without a calculator. Of course that is unenforceable, but most Year 7 students want to do the right thing, and consider a teacher an authority to be respected.

As for higher-up idiots vetoing things without explanation, or with crap, of course. Nothing one can do, but it doesn’t change the fact that higher-up idiots should be forced to make the decisions.

CAS is a difficult beast to attack, especially when it is a non-Mathematics teacher who controls the booklist.

Exactly how TI “won” the battle over Casio and (I’ve never actually heard of a school that uses them) HP is one I would love to hear one day. I suspect those who know the truth are very few and unlikely to share.

As for non-CAS calculators – I think you will find in many schools that when students are “weaker than the median” or require some level of “assistance”, a lot of those teaching mathematics classes (not so often genuine Mathematics teachers) will assume that letting said student do their assessment with a calculator is somehow levelling the playing field (which is, of course, totally missing the aim of the exercise)

I don’t understand your first point. If the Head of maths doesn’t want CAS in the school’s Year 9 classes, why should some glorified secretary be able to overrule that? Just tell them to do their fucking job, at least until some higher up twat interferes.

Also, what “many schools” do, or why, is neither here nor there. We are talking about determining sane policy, for which the accepted practice of “many schools” is entirely irrelevant.

Because… (wait to RaTS) all changes to a booklist have to be approved by the curriculum committee.

Thankfully CAS is not on our booklist until Year 10.

It is quite hilarious (in a really sad way) that, for example, the Art department needs approval from the majority of other faculty heads to change their Year 9 electives and the mathematics department needs approval to add/remove scientific calculators from any year level.

Ironically, changing the rules would also require a majority vote, with the principal holding a power of veto, which in previous administrations was used quite a bit.

Re: “Exactly how TI “won” the battle over Casio and (I’ve never actually heard of a school that uses them) HP is one I would love to hear one day. I suspect those who know the truth are very few and unlikely to share.”

1) It helps when decision-makers in high places have friends, relatives etc. who work(ed) at TI …. I can’t explain how such conflicts of interest never got investigated.

2) I’ve recently heard that for a number of years a number of people have consistently been approached by some commercial organisations specifically to make TI presentations at maths conferences … I have a conspiracy theory on why this is occurring.

I’m sure there are other pieces to the puzzle, but I think the above are some of the largest pieces.

One of the many pseudo-arguments for CAS calculators before Year 11 is that students need the practice in order to be proficient in its use by the time they get to Units 3/4 maths. Yes, I know … But this is the entrenched mindset in the vast majority schools.

What makes it exponentially worse for mine is that the CAS-calculator is such a bogus piece of shitful ‘technology’. Say what you want about Mathematica (and Matlab, Maple etc.) but at least they are extensively used beyond secondary school … Unfortunately, the real agenda of VCAA’s Mathematica Pilot program was to get rid of paper exams, not to get rid of a bogus piece of shitful ‘technology’.

I just wish VCAA would stop lying and give its so-called mathematics subjects names that reflect its hidden agenda. If they called them CAS-Assisted Mathematical Methods (CASAMM!), CAS-Assisted Specialist Mathematics (CASASM!) and KABLAM! then at least the pretence that these are actually mathematics subjects could be dispensed with. As it is, we are all teaching the Emperor’s new clothes.

Thanks JF. Yes, that pseudo-argument is standard, and complete nonsense.

Any idea where the argument started? I have one name in mind from a particular university, but I would be interested to know if anyone was in one of those CAS-pilot schools and remembers the arguments first-hand.

RF, I think it’s natural stupidity. If you think Pre-VCE is nothing but training for VCE then you’ll easily think some pretty dumb thoughts.

There are some very well-known names who cultivated their ‘reputations’ from the CAS-Pilot and are consequently considered mathematical authorities. This is one of the greatest con-jobs in Victorian mathematics education, and was/is abetted by many teachers too naive to see through the charade. Those names are now very much entrenched in VCAA and its affiliates and are a cause of the many insidious problems of both. The lucrative CAS gravy train shows no sign of being derailed.

It is astounding that such a bogus piece of shit that is completely irrelevant and redundant outside of schools can be so entrenched. It is the tobacco industry of mathematics education.

Perhaps more sugar than tobacco, but otherwise completely agreed.

Yeah, well the sugar industry doesn’t say their product is good for you and you should consume as much as you can, although the do often disguise their product and then say the disguised product is good for you.

These ‘names’ keep telling us that their product is good for us. I’ll stick with my original analogy. It is a cancer on the educational landscape.

I just did a search on seek.com.

First, I searched for Excel and got > 16000 hits.

Then I searched for CAS – but that picked up “Casual”, e.g. FT/PT/CAS.

Finally I searched for “CAS calculator” – you can guess the result.