Here’s a question. We’ve been invited to give a presentation to maths teachers. So, what should we talk about? What might one say to maths teachers that will make any difference? And, harder, what might one say that maths teachers will come to hear and that will make any difference?

**UPDATE: **And here we go.

You made a point in one of the QEDcat articles that mathematics is about ideas (I think one of the NAPLAN articles). Give maths teachers ideas to think about and do stuff with.

Thanks, Potii. Isn’t the world already kind of full of that?

Talk about the importance of learning algorithms to do calculations despite the existence of calculators.

Where and when is this talk happening?

Hi Sabine. Do you mean the importance of the traditional methods for arithmetic? How would you convince doubting teachers to come hear that? How do I avoid just preaching to the converted (fun as it is).

I

thinkthe talk(s) (the Evil Mathologer and others will also be talking) will be on either the Tuesday or Wednesday before the MAV conference, at Monash, Clayton. So, 3/12 or 4/12. I’ll post with precise information once it’s all settled.You could talk about the weather. Everybody else does.

11,000 scientists just talked about the weather (well, the climate). It doesn’t do a bit of good with neanderthals like ScoMoFo in charge.

What about the role of fundamental mathematics in the age of big data and AI?

Thanks, APMA. Can you tell me what “big data” is? I’m not being facetious: I see the term flung around, but I’m never quite sure what it means. Also, whatever BD and AI mean to mathematics, what does it mean to school mathematics and, thus, to mathematics teachers?

Marti,

In my commercial roles ‘Big Data’ is a Sales Pitch term used by Consultants to sell their unstructured data base source software data collection and reduction tools. Eg SAP Hana , oracle BI and many more

The application of self learning algorithms has helped Ai programs to outperform humans on complex games like Chess,Shogi ,Go etc by repeated practice without prior knowledge of strategy

Eg https://arxiv.org/abs/1712.01815

Demis H was a child prodigy at chess before designing the algorithms behind AlphaZero

Steve R

Thanks, Steve. The Alpha thing is definitely incredible. I’m still not sure what either Ai or BD means for school mathematics, as a topic or otherwise.

Me neither ? But I imagine it will be fairly generic with reference to programs like those used by Alpha Zero. And It would help if the curriculum writer(s) has/have some experience in programming in any language

Historically the process of extracting useful information from several large data sets was referred to as data mining and analysis before the sales people arrived.

.eg using cubes of extracted data on excel spreadsheets with ‘slice and dice ‘ capabilities

Steve R

OK, I think I get the principle. I might call the talk Doing Maths with the Kardashians.

Hi,

If you want a non technical (with no algorithms) introduction to ‘Big Data’ ,AI ,recommendation engines, hidden use of PokemanGo etc then Brian Clegg (Physicist) writes quite well about science matters in general

https://www.goodreads.com/book/show/35998462-big-data

Steve R

Thanks, Steve.

I’d second Potii’s idea (pun not intended). The focus in teacher training seems to be on the process (calculators included) when ideas are what is needed.

Something like your “how to teach X if you have to” but brought back to year 9/10 level might work well.

And yes, where and when?

Thanks, RF. See my reply to Sabine’s comment for the (vague) where and when. Interesting thought. The difference is, my “How to Teach Methods if you Must” was aimed at helping teachers deal with an awful and cemented curriculum and an awful textbook. The difference in Year 9/10 is there a lot more flexibility to teach good stuff with good materials, and a lot less “must”. (At least if your head of maths and/or principal are not morons.)

And therein lies a challenge for some.

For others (early career teachers may find this the case), knowing where to look for resources in the sea of junk is always difficult).

True, but if a teacher doesn’t know how to evaluate resources, why would they choose to come hear my evaluation?

Well maybe that could be the subject of the talk? “How to spot a WiTCH” as it were.

As to why would they come? PD hours to satisfy VIT requirements for one. And yes, sarcasm was intended in that last bit.

I like that topic! I don’t think it would work for the coming talk, but definitely food for thought. As for the VIT comment, I think you meant “contempt” rather than “sarcasm”. But of course there are much more “useful” PD talks that teachers can choose to attend: “How to Draw a Dog with Desmos”, or whatever.

Yeah, I sat that one out.

Re: “How to Teach Methods if you Must”. To what is this referring – a talk / article? If so, where might one find it (assuming it is available)?

Hi, SRK. It was a talk I gave at the MAV conference a few years back. The slides in isolation may not make much sense (and perhaps the talk didn’t either), but I’ll see if I can dig them up.

Thanks Marty, I’d appreciate it if you could. I avoid the MAV conference, and find most mathematics education “professional development” excruciating.

I am a teacher and a challenge I see for primary years colleagues is they don’t feel confident with mathematics and don’t understand how to teach it. The focus is on process and content delivery with very little understanding of how to excite and engage students in mathematics. We want children to think like mathematicians. That is; express curiosity, hypothesise, experiment, test ideas, seek and use patterns, and cope with novelty. Talk about how to do that?

Thanks very much, Aaron. Lots of food for thought, which deserves at least a whole post, and probably a book, to address.

I can certainly appreciate that very few primary (or secondary) school teachers are confident with or engaged in mathematics. How could they be? I think this is a disaster, in fact THE disaster, for Australian mathematics education. The disaster is also two-pronged. First how do you get primary (and secondary) teachers confident and engaged? Then, how do teachers pass that on to students?

I don’t think it is obvious how to address either disaster, for various reasons. But, the most obvious is, I don’t think you can get more than a handful of primary (or secondary) teachers to voluntarily come listen to me or anyone talk about the nature of mathematics and what that means for students. And, whether or not it would do any good, I don’t see anyone with a whip ordering them to attend. How do you convince primary (or secondary) teachers, or anyone, that it is indeed a disaster?

I’ll just ask one question. Why do you want students, particularly primary students, to think like mathematicians? What does it mean for, say, a grade 2 student learning multiplication, and how does it help?

I’m studying to be a maths teacher now. I used to tutor at uni and found a lot of students were afraid to spend any decent amount of time on problems.

Now that I’ve done my first placement at school, I feel like maybe it is because that is what they are taught at school. There’s a lot of emphasis on speed because everyone is worried about preparing students for VCE exams, where being fast matters. So if students spend more than a few minutes trying to make sense of something, they think there must be something wrong.

And everyone is in a rush to get through the curriculum. So maybe it is not worth talking about and this is silly, because what can teachers do about it anyway?

But perhaps you could talk about how long mathematicians might sometimes spend on a problem?

Thanks, S-T, and a great comment. You are absolutely correct that the VCE maths exams are completely ludicrous speed tests. The exam system is insane and it is evil. It (and, eg, CAS) also obviously poisons the teaching of senior students and, as you indicate, it cascades down to the teaching of lower year levels.

Is it then “silly” to talk about something because there’s nothing we/teachers can do about it? Thanks! You just wrote off 15 years of my presentations as silly! But I humbly disagree: howling at the moon is at least cathartic. And, more seriously, I think teachers are often a lot less hamstrung than the idiot VCAA, and possibly their idiot principals, would like them to be, at least at pre-VCE levels.

As for the appropriate length/difficulty of maths problems and the appropriate time to think about them, that’s an excellent question that had never consciously occurred to me. Obviously research mathematicians can spend years on a problem. That “years” hides the fact that any such problem will be broken into many sub-problems, but still the time-frame can be pretty astonishing to an outsider (and even an insider). In school/undergrad, obviously some healthy mix is on order, but I think what constitutes “healthy” would be very context-dependent. Multiplication tables and exact trig values, for example, should be measured in tenths of a second.

But why should multiplication and exact trig values be measured in tenths of a second? It is nice to calculate in less than a second. But if you can’t, what is the harm in taking a bit more time?

For example, if I forgot what sin(π/3) is, I might think about it for a few minutes, and think well π/3 is the angle in an equilateral triangle, which I can split in half to get two right-angled triangles, and then calculate the ratio using Pythagoras’ theorem. So it might take a few minutes, but isn’t that better than thinking ‘I don’t know straight away so I give up?’

Hi, S-T. I’ll give other readers/commenters a chance to reply first. They may or may not agree with you. (There are plenty of maths ed lecturers who agree with you.)

For every level of mathematics there needs to be automatic recall of certain key knowledge. If students get bogged down recalling knowledge that helps them solve problems, then their working memory will be overloaded with trying to figure out what the knowledge is as well as how to use it to solve the problem. Working memory has a limited capacity and should be focused on the main problem – not searching for underlying knowledge. Searching for basic knowledge can also contribute to frustration for the student.

Also, if knowledge is learnt with meaning (e.g. deriving the key knowledge to remember or linking that knowledge to prior understanding) then it should have a good chance of being stored in long term memory. Forgetting such key knowledge may indicate the student does not understand it, so deriving it may not even be an option down the track.

This has been my experience (albeit short) as a teacher of secondary students. While deriving knowledge is obviously important, and should be done, capable students have recall of key knowledge that then supports them to solve more complex (and usually more interesting) problems – especially ones not encountered before.

Thanks, Potii.

Very nicely put, Potii. (Rote learning is not necessarily a dirty word, although many would have you think it is).

Thank you. That makes sense. I was thinking from the point of view of what would be valuable beyond the classroom. But now I understand having automatic recall increases how much students learn in the classroom, so it gives them access to more material, and that in turn is valuable beyond the classroom.

The cynic in me would love to see a discussion on the responsibility, if any, professional organisations such as the MAV has in the scrutiny of VCAA and in keeping it accountable. But I would not recommend talking about this – too much of a hot potato and I don’t think teachers want to come along to hear what they would probably consider was a political agenda.

Thanks, JF. Yes, obviously it’s too contentious. I would never, ever criticise the MAV or the VCAA in a public presentation. And the same for the VIT or ACARA or AMSI or AAMT or Maths 300 or the ABS or ACER or CSIRO. Just wouldn’t happen.

So, the Premier just called and put me in charge of all aspects of maths education in Victoria. Blank slate. Money. Access. A nice retainer. And this is what I’m gonna do.

(Alluding to https://m.youtube.com/watch?v=tyyoaBa7DaE) CAS calculators / Computer Based Maths in Classrooms? I say we take off and nuke the entire idea from orbit.

Canon of names/books/ideas/people maths teachers should know.

to English Teacher: “you heard of William Shakespeare?” “Of course!”

to Maths Teacher: “you heard of Martin Gardner?” “Sorry who?”

I never saw it, but I loved the report of you doing maths/science with calculators – dropping em, swinging em, flying em, breaking em, etc…

I too would like to attend talk.

I like the “Alien” sentiment! I also think the canon thing is a great idea, but maybe as a post. And thanks very much for reminding me of the Death to Calculators “talk” (More performance art than a talk). Ah, those were the days.

I know this is OBE, but…commenting forces me to think.

A big thing that is interesting is that you’ve seen a lot of different kids and from a lot of different teachers. Having a list of the biggest issues you see (and the “story” of how YOU fix them) would be interesting because teachers mostly just know themselves.

Don’t need to make it about “this is what a good/bad teacher is” like Umbridge checking on Hagrid, but more like “I’ve seen a lot of squeaky wheels and here’s how I dealt with it” Then let them think on it. Maybe a very gentle summary of thoughts/advice at the end (do more drill, break up lectures, use the unit circle to introduce trig, use the in/out machine to first describe functions…not ordered pairs for neophytes, don’t spend so much time on PEMDAS, or whatever you think.). And with the caveat that it’s just your thoughts from dealing with the kids that need/want tutoring.

I would skip the rant on bad exam questions and textbook pages. For truth in advertising, you could say that you have a lot of sarcastic opinions and they are on your blog. (So the little innocents aren’t shocked when they come across it later.) But for the lecture, you want to keep a theme of “lessons from tutoring”.