Learning in Progress

of learning and pedantry

Posted on March 3, 2011 by rob

Ages ago, i borrowed a little article, , not properly bound ...that i happened to run into the Melb Uni library. 5 pages ..informally bound ... a preprint of an article, from maybe 25 years earlier.

Now, re-enrolling in a course is held up because i’ve lost that little article ... so i’m doing whatever needs to be done ...declaring it lost, getting assessment of replacement costs, paying fines, etc.

I mention it was not exactly a book – more like a manila folder with a barcode ..printed in the uni;

Librarian 1 is reasonable -hmm, maybe you could see if you can approach the author and see if they can provide you with another copy ... .might save the issue. (i've never met the author but i recognize her name as an academic who still works there).

Sounds like a good idea ...and 15 minutes i have actually found the professor with prestigious background in physics, maths, IT education ..who had no idea that this little pre-print from a couple of decades ago even existed...’somebody must have put it there for reading one year’.
She can put her finger right on the published version of the article, and even offers to photocopy it for me .

As she walks out of her office to kindly copy an article for an unannounced visitor, she also places a thick book in my hands ...”have a little glance through that while i’m gone”. I expect its another compilation of articles ...but its the expanded version of the same article- her phd thesis in fact -...of which the missing 5 pager was a little summary.

I’m captivated by this work, there are beautiful drawings by children, of paintings nested within paintings ...

There are stories in a child's handwriting, nesting stories inside each other
Dear Diary, today i went to see a friend...
..had some tea, Then i wrote in my diary:
Dear Diary, today i went to see a friend...

There are little Logo scripts that play with similar ideas ...

She comes back and we talk about all this ...of children's understanding of recursion ..i’m obviously interested ...(i had borrowed the summary article after all - which she has just handed to me again as a fresh photocopy)

I mention the other book i’d borrowed at the same time is Papert’s Mindstorms : Children, computing and powerful ideas

Ah yes, thats the key one, she says.

She is broadly of similar ilk as Papert, worked at MIT; taught physics, (and a programmer for IBM, in the days when you learnt programming during a three week intensive, and if you scored 95% or more you made the grade ...less than that and you just handled the punch cards)
I ask about the children's work - turns out to be her own kids, in their early primary years ..(pre ethics committees!)

I’ve come to think in recent years recapturing some of the lost history of educational computing (Papert and Kay et al) – that we can do much more ...that we could let kids build, if we found the right tools ...but i've never seen it laid out in academic setting in such a naively arresting manner

She discusses other examples of recursion that are appropriate for children ...Dr Zuess’ ‘The Cat in the Hat comes back’ book as 26 level deep recursion – 26 cats uncovering smaller cats ... or the story ‘Too many bears’ – (Ahlberg's Ten in a bed ) a quirky adaption of nested fairy tales - once her children were keyed with the thought they could see it everywhere ...and could program up models with this.

after an hour of discussion i mention that rarely has a lost article been so serendipitous – especially one with such a chunky title: ‘Children, recursion and logo programming: An investigation of Papert's conjecture about the variability of Piagetian stages in computer rich cultures’ perhaps doesn't get the reading it deserves.

Yet the ideas here are rich ...the question of whether use of Logo, or other programming languages for that matter, could make abstract concepts concrete, and thus accessible to young children ...is surely a deep topic for anyone interested in what we should be doing with computers in school, and in maths learning in particular.

I've hacked those ideas around enough before : and the article's title spells out the ideas clearly enough ...Piaget's observation that kids develop in stages (also based from studying his own kids) ...concrete manipulation before formal & abstract reasoning etc ...and Papert, who worked with him, wanted to use computers to ‘concretize’ and explore certain maths concepts and so open them to young children : this thesis reported on the promising effect of that approach.

There is a certain synchronicity about all this – since earlier in the day i’d just been at a briefing for the new national (Australian) curriculum ...and heard that recursive methods will be in the advanced part of the year 12 course. I doubt recursion gets the mention and resonance it had for the children whose work i'm reading, in this new curriculum.

Its rather inexplicable that we have lost all this .....that the critical mass around such approaches is diminishing, rather than building, even as computers get more prevalent.

We chat and agree that software as ‘complex thing that is done for you’ has won out over giving children suitable tools to build things themselves. Also discuss some counter example –i mention that two young girls (4 and 8 ) had just won an award for programming, using the old Squeak software, ...which is a nice modern parallel to her thesis – and Scratch is something of a re-invention of the art

Also jammed into this unlikely day, i happened to hear a Mathematica presentation; a full lecture theatre in the math department. Computers are doing more here than representing traditional maths for these people – for many they seem to be the tools of the trade.
But seems largely lost on k12 curriculum. "Don't think we'll find any new maths out there".

later, i read up on her work, and find the 1990 edition of ‘Computers in the Schools’ full of interesting articles ...

Research on Logo : A Decade of Progress
Designing Software for Learning Logo
Logo and Geometric Thinking
Student Autonomy and Teacher Intervention in Logo Environments
Having Success with Logo : Observations from the College Classroom

(Resnick's "Learning through computational modelling" is typical of the style).

Flicking forward to the current version of the same journal, there are much less interesting topics ...generic discussions about ICT usage and interactive whiteboards etc.

But back to this lost article! i take the replacement article back to the library,

Neither the author or myself had noticed, but its not exactly the same version that had gone missing – the electronic records show we’re replacing an interim preprint, with a published version of the same article.

Reasonable librarian 1 has to consult with ‘Chief Librarian’ – who declines to show a face, but rules that this will not do. Although i venture the fact that this is freshly provided by the author, who was surprised it had ever been in the library anyway, and saw this as an equivalent version, that is not the point ...library rules are library rules.

In contrast to the interesting discussion and learning preceding this, with the author, this seems a ridiculous use of computers; isolating a version difference that no human is ever going to care about.

So..off to the central uni library, with a form saying i have lost an item in one hand, and a slightly updated copy of the same article in the other. This new librarian sniffs dismissively at the story, and calls the lost books guy. Who is, also, fortunately, a reasonable person; can see that i have got as close to a replacement as we are going to ever get, and undoes the ruling of chief branch librarian, with a click.

The whole thing mirrors, in some ways, the issue with computers and learning. Will we use information systems to pedantically enforce archivists rules - or will we be part of genuine learning, messy and unpredictable as it is?

And similarly, when i try to access the full thesis that i had briefly explored in that fortunate conversation, i am stymied again. Its been archived on microfiche at Monash Uni so i try an an interlibrary loan to at least get it to Melb Uni; there are forms and phone calls and procedures for that; which some weeks later turn out to not apply to microfiche. So - i can pay 50c a sheet for 500 pages to have it printed out; or i can drive 3 hours to sit at their microfiche in 2 hour slots.

so that beautiful work is locked in a librarians dungeon ...microfiche was not a good technology; in contrast to the electronic riches that are now unleashed; almost like a 2nd internet in their depth - every copy of every journal available from home, including all back issues. There's been a huge effort to digitize just about all journals and there's a wealth of riches available.

i mention the difficulty i'm having getting a copy, to the original professor, who is clearly not impressed that her work is so restricted : and indeed photocopies her own copy for me; all 500 pages, and leaves it for me to pick up.

(Don't tell the librarians : no doubt its also illegal on some level to photocopy your own work and give it away)

i could go on : very similar stories with the local library; but think i've aired the point. IT as "information management" leads to librarian over-ruling the local professor about the version of an old preprint; and keeping her thesis in a cage where no-one can read it.

IT as 'make your own' is the corrective here. It goes deeper than the poor librarians though. We need another dose of that Papert / Kay vision of what computers are about.

(open source vs commercial is not exactly the corrective either; finding that sweet spot where construction is possible, is the issue).

(update : someone saw this as a bit anti-librarian. i hesitated to post it - and edited out a lot more subsequent story at the time, for that reason. But of the 4 librarians i dealt with - (a folio of librarians? a quartet?) - i mention two were helpful and reasonable. The contrast between how info systems are used, which way they lean - creativity or control, tying things down opening them up, is what i'm trying to get at.

At a larger level i've noticed that the librarian movement/association have been influential in defining 'information literacy' - as being able to search for and decide on credibility of relevant info. Certainly a useful skill but a much narrower thing to do with computers - a simple extension of research skills - than the kind of learning suggested here. wouldn't matter except the terms ('Info literacy', ICT in the curriculum) can be up for grabs as to what they actually mean - and what is left out. Are we just sifting through a sea of information? or creatively using the potential of new media to tackle new styles of exploration?

Posted in IT in education, Uncategorized, learning | 1 Comment

half baked : 2 tier education system

Posted on December 17, 2010 by rob

read an article on the ABC site ("As innovative as a chalkboard')

"Thom Woodroofe was the 2009 Young Victorian of the Year and founder of Left Right Think-Tank. He recently finished his undergraduate degree after graduating from a public high school."

he sets out what he thinks is wrong with schooling

i agree with some of the analysis : the issue of the the industrial heritage (lock step factory system etc : timetables and bells etc; the expensive and ineffectual attempts at 'education revolution' etc).

so far, couldn't agree more

but his ideas about how to fix that are very half baked : extend the private system

i commented as follows, lightly edited here (as fred)

the passion here should be taken as thrashing out the ideas : no doubt the Young Victorian of the Year had noble intentions, but i think his 'solution' is barking up the wrong tree.

starts the analysis ok with the industrial era heritage of schooling.

but veers to a completely bizarre solution : promote private schooling as competition for the public system

might make some sense if there was any variation from that approach in private schools : but they're as wedded to timetables and graded year classes as anyone

there are a few variations from that in both systems

its also immoral, in my view, as a teacher who has taught in both systems, and worked hard at reconceptualising the model, to promote private schooling for those who can afford it, and leave those who can't with something inferior.

extracting the students with nice middle class families and richer cultural background into one system, inevitably impoverishes the learning culture of those who are left; and who most need an enriched culture : the usual skewed results show that the effect is very real. extending the middle class model with loans still leaves an underclass

the figures he quotes are also not accurate. the state system i worked in received $5500 per student

its also off target to bag teachers for resisting innovation : the unit of change has to be larger, or it will never be sustainable and systemic

a historical paper that looks at school reform : 'grammar of schooling [Why has Change been so hard?]" by Tyack and Tobin gives some deeper grasp of the issue

the reference to i/pads/phones and google's creative offices is also shallow.

i work with these things and tools : indeed develop interactives to be used on these devices, but there is zero merit in just using them : there have to be deeper skill sets cultivated

no-one will get a job with google because you know how to drive an ipad; their entry level requirements are more advanced : they want the kids who win the algorithmic olympiad : and if that means they learnt some techniques off a chalkboard, well and good

i read an article recently in Zadok that has been going around in my head : how can church schools (Good News to the poor?) justify running enormously expensive schools. who do they think are serving by doing that? how did that happen?

a friend who was a principal (in a lower socio-economic state school) said to me that the issue he had with the two tier system is not that some can pay for good stuff (eg some can send their kids on ski trips in Europe, while others have never seen snow, or maybe get a day trip tobogganing) since that's an issue that's wider than the school system itself can fix, and we will have to accept that some can choose these goodies and some can't

but what's immoral about allowing money to determine which school you even go to, and thus which kids you mix with, is that filtering kids by demographic, further impoverishes the culture of those who can't pay, and further concentrates the number of students damaged by poverty : which 35% secondary kids are in private schools? what does that tend to do for the classrooms of the other 65%? - especially if you then sort by post code?

i taught in a lower middle class catholic school for 7 years : and liked the culture of the place; fees were not that high - but still, in retrospect there is no doubt that they still present a hurdle that tends to filter off certain levels of dysfunction. we had some troubled kids, but even in a low fee paying school, the levels and frequency were less. I don't think anyone's parents were in jail, dragged off campus by the police etc, or all the other things that happen if you have a truly mixed approach. (I also notice that since Catholic teachers do deal with some messy situations (and generally have a compassion about it), and since many of these schools are waiving fees for some kids, they underestimate the differences in frequency and intensity of the issues : i was certainly ignorant at the time of the challenges round the corner.

the other comments on the article round out the discussion : nearly all comment that flashy technology is not the silver bullet for schooling that he suggests or that private schools do any better in rethinking the industrial model (specialised subjects and age grading). They just work with a different demographic : i'd see that as the sole difference, really.

and i don't think students who benefit from this are at fault - i was one and don't feel particularly compromised by it - any more than being born in a land of plenty should generate guilt : though perhaps it should generate some reflection on goals and purpose etc

but i'd argue a think tank is barking up the wrong tree in backing private education as a prod of 'competition' for the state system. Teachers really do pretty much the same in both systems and its a hugely untested assumption that there is some wonderful practice in private schools that state schools could emulate, apart from concentrating certain levels of financial and cultural riches. I taught the daughter of the guy who wrote the physics textbook one year: when a piece of equipment broke, she turned up the next day with a geiger counter. Wonderful kid; easy to grade well etc; as a teacher thats a nice classroom - and class - environment to teach in. But really no transferable structures or practices that unlock education in general : in fact no reason to question the status quo too deeply when there : sometimes the more innovative approaches seem to come out of more difficult situations.

There are innovations and endless opportunities for learning in both systems, but its naive to think one system has worked it out, especially if you factor out the flying head start one gets from the clientele. There are measurable metrics of language acquisition etc that back that up; the typical vocabulary of kids in different demographics etc. So its exactly at the policy level that the tilting of the field could be addressed.

while none of this is deterministic - there are many individual stories that go against the trend - and a large pool in the middle - we should not set the tide against the least advantaged; nor should we shrink the size of the pool in the middle; those who don't feel obliged to send kids to most expensive school they can afford.

(another complicating factor : sometimes refugee kids sometimes seem easier to teach than aussie kids - can be more passionate about pursuing opportunity - 1st generation anyway - than others whose culture has atrophied in generational poverty. Nevertheless i think the sorting into 2 systems is not good, overall, for the whole group. I'd suggest something opposite to Thom : dissolving the two systems into one. Finland is often cited as the best in the world - both in terms of level of results AND equity - and it has something like that : as well as more qualified teachers across the board. i still haven't finished my masters : guess i wouldn't be able to teach there:) (So ignore everything i say!)

Posted in futures, level playing field | 1 Comment

secrets of SEO

Posted on May 8, 2010 by rob

this is mostly an education blog, but for all you web types : i have discovered the secret of search engine optimization

i'm tempted to sell it in an ebook, but i'll just tell you

(a) don't use meta-tags of any description
(b) keep your main content on a blog that only linked to the front page ... and let the front page go stale
(c) on said blog, write unfashionably long posts on topics that have only niche appeal
(d) don't update the blog for months at a time
(e) let the domain name expire so your site goes offline for a few days - and then repurchase it again in a hurry when you realise

on the day you do that, you will become the number one result on google for the most relevant phrase that relates to your site ...

True story : over the 5 years i've had this domain name i've occasionally typed 'thinking curriculum' into google out of curiosity - it was never, so far as i recall, on the first page of results

(my ideas of what the 'thinking curriculum' is have also shifted ... but i haven't updated the initial pages on the site)

but once i accidentally let the domain expire the other day, and the site went down, and i then rebought it and it came back online .. two hours later google thought it was the number one result

(its dropped a bit now .. no doubt because i'm paying more attention - breaking google's secret algorithm)

oh, if you want to comment on these wonderful secrets, ~~i've also disabled comments on the blog till i get time to update wordpress~~

but yep, you heard it here first - the secret algorithm that google uses is really based on metrics of neglect

don't send money .. i'm testing if wealth accumulation works the same way

Posted in ICT | Leave a comment

grannies wisdom and neuroscience

Posted on March 5, 2010 by rob

had the chance to hear Martin Westwell * yesterday -Professor of neuroscience at Flinders uni, who comments a lot on the relevance of neuroscience for education, and also on the impact of technology ("technology is rewiring kids brains" being a simplistic sound bite that people quote, but he's much more balanced than just pushing that sort of agenda)

Refreshing to hear someone who doesn't propose that education can or should derive its practices as a simple consequence of research ...

He handled that part of it really well - is quite opposed to people flogging products or practices that supposedly come out of 'the new neuroscience research'. He made the point that neuroscience is only just catching up with education; that what educators have found to be valid and helpful, usually is, and probably turns out to have some relevant brain science behind it. (For example, the ideas that practice matters, emotion matters, context matters, personal meaning matters (a lot), environment matters etc - are all now supported by neuroscience)

In that sense, like all the research that shows exactly how and why its good to eat your vegetables.

Also commented that teachers are in the best place to judge what is going to work for their kids; they know them and the context best.

So general 'research' based proscriptions for education are dubious, from his point of view in neuroscience.

Nevertheless, there are useful perspectives - things its useful to know, even if its not obvious what you do with them. So what you do with the complexities of a situation is always a judgement call based on imperfect information, neuroscience can provide a background layer of understanding.

For example, most boys may be more competitive and task orientated, and most girls may be more co-operative and process orientated - but there are good quarter to a third of each who show the opposite trend.

one example he gave - if you decide, this year, the boys and girls in this year level just aren't getting on in class, so lets run separate classes - just be aware that that a good chunk would prefer the mode of operation that may be more on offer in the other class. You still have to make a judgement call, based on various constraints etc (socially who wants to be the boy in the girls class etc) - but it helps to be aware of it.

Similarly, whatever grouping one uses, needs to have a clear purpose behind it - and then it will probably have good result, rather than inflexible streaming (tracking) that just sits there for ever and day and becomes a self fulfilling prophecy of student performance

Other things - quoted some research showing that walking up a hill with a positive friend, and then being asked to indicate the angle of steepness - there is a measurable reduction in how steep people perceived it to be, compared to those who walked it alone. Again neuroscience or psychology catching up with popular instinct.

Also research showing that asking African-American kids to indicate their racial grouping along with their name, on the front of an IQ test, measurably impairs performance, compared to asking the same demographic to just write their name on the front - being reminded of their societal 'boxing' just before starting the test detracts from performance.

similarly promotional materials (eg 'girls in engineering' posters - showing a female lecturer or engineer etc) can backfire - it can function to hilight role of gender, rather than ability

i also liked his stuff on executive function vs automaticity

That is, executive function is the (frontal lobe based) processes of integrating diverse information, deciding what to do with it etc - effortful, conscious thought

Where automaticity - skills that have been developed by practice (whats 5 x 3 ? (can you stop yourself from saying 15? )

in short, the interplay of both is whats needed

What i took from that is we should hive off as much as possible to automaticity

and need to also develop capacity for decision making (executive function) etc (through more self directed learning and taking responsibility etc)

traditional education might have majored more on 'automating' skills of numeracy and literacy

where progressive education espouses the value of personal meaning and decision making

the balance is needed

- one doesn't want to be effortfully doing things that should be automated (manually wrestling your way through 5x3 in high school) - free that up for higher tasks

(conversely, learning too many things by rote limits one to 'right answers' - 'sculpts' the thinking into limited answers. For example, how many senses do we all have? We probably know the 'answer' is 5 - but why? where is the sense of balance? of heat? of pain? Aristotle apparently said we had 5 ... and thus we repeat that for ever and a day.

there is a balance here - an interplay ....

he uses the example of riding an elephant

the rider is the executive function; the limbic system is more like the elephant

symbiosis needed to get anywhere

teenagers are in the process of mastering this -the elephant might get the better of them as the frontal lobes (reasoning, executive function of the rider) are 'under reconstruction'

balance of training and piloting

he mentioned that where people had assumed that teenagers simply don't understand the consequences of risky behaviour - say speeding or premarital sex - some research indicates that they actually tend to over estimate the risks - but still get caught up in the moment; the elephant stampedes; the rider (executive brain function) is not yet strong enough to take control

[i was an interloper with a group of catholic principals who were hearing him for a morning as part of their professional learning; appreciated the chance to attend]

Posted in learning, neuroscience | Leave a comment

tv to text

Posted on January 28, 2010 by rob

i'm not normally much for handy little hints, but we upgraded our analogue tv with a 'set-top' box to pick up digital TV.
didn't expect too much, but there are some nice features

one, thats good having young kids, is the option of subtitles / captions on all the kids programs

so suddenly TV watching can be more closely linked to text learning - reading along with the dialogue etc ...

my son is a pretty fair reader and he likes it; turns captions on himself - can't tell how often he reads them, but it can't hurt; and does open up a lot more potential reading time

so - the idea of turning on the captions for primary age kids, is my first handy hint

(digital jazz radio, and multiple ABC channels for kids, program guides, are the other good bits)

Continue reading →

Posted in ICT, hints | Leave a comment

pedagogy of poverty

Posted on December 28, 2009 by rob

not sure what i think of this Pedagogy of Poverty article yet. might overdo the case but some parts resonate

The teaching acts that constitute the core functions of urban teaching are:
* giving information,
* asking questions,
* giving directions,
* making assignments,
* monitoring seatwork,
* reviewing assignments,
* giving tests,
* reviewing tests,
* assigning homework,
* reviewing homework,
* settling disputes,
* punishing noncompliance,
* marking papers, and
* giving grades.

So in the face of the shallow and lean soil that might accompany urban poverty there is temptation to just keep kids busy, and jettison nobler ideas of what education is, and just break down content and tasks to bite-size and do-able although disconnected bits, since the culture of learning seems to work against bigger themes or more challenging work.

And certainly its striking when some refugee kids can be much more highly motivated than many local kids in the lower end of the state system, who might be relatively affluent against that global scale, but are not deeply imbued with any love of learning and don't feel the privilege of education as opening up the future - skool sux etc

When he accepted the 1990 New York City Teacher of the Year Award, John Taylor Gatto stated that no school reform will work that does not provide children time to grow up or that simply forces them to deal with abstractions. Without blaming the victims, he described his students as lacking curiosity (having "evanescent attention"), being indifferent to the adult world, and having a poor sense of the future. He further characterized them as ahistorical, cruel and lacking in compassion,uneasy with intimacy and candor, materialistic, dependent, and passive -- although they frequently mask the last two traits with a surface bravado.
Anyone who would propose specific forms of teaching as alternatives to the pedagogy of poverty must recognize that Gatto's description of his students is only the starting point. These are the attributes that have been enhanced and elicited by an authoritarian pedagogy and do not represent students' true or ultimate natures. Young people can become more and different, but they must be taught how. This means to me that two conditions must pertain before there can be a serious alternative to the pedagogy of poverty: the whole school faculty and school community -- not the individual teacher -- must be the unit of change: and there must be patience and persistence of application, since students can be expected to resist changes to a system they can predict and know how to control. Having learned to navigate in urban schools based on the pedagogy of poverty, students will not readily abandon all their know-how to take on willy-nilly some new and uncertain system that they may not be able to control.

goes on to a series of statements of what good teaching might involve ... many of which seem easier to apply in humanities or english contexts ...

however i really like the idea that the whole school faculty and school community -- not the individual teacher -- must be the unit of change

seems a lot of research and policy assumes that the basic structure of school remains the same and the teacher must somehow re-invent themselves within this along more progressive lines, teach for deeper understanding etc ... and while there can be some merit here the unit of change really needs to be the school - or at least a group of teachers; the cultural context has a huge influence; students' general experience of school is harder to shift in one class trying something else; the lone teacher has a harder time rethinking school on the fly

Who is responsible for seeing that students derive meaning and apply what they have learned from this fragmented, highly specialized, overly directive schooling? It is not an accident that the present system encourages each constituency [he has referred to parents, administrators, teachers, school oversight, teachers, students] to blame another for the system's failure. My argument here is that reforms will take only if they are supported by a system of pedagogy that has never been tried in any widespread, systematic, long-term way. What prevents its implementation is the resistance of the constituencies involved -- constituencies that have a stake in maintaining their present roles, since they are, in effect, unaccountable for educating skilled, thoughtful citizens.

from here

i'd say its not just poverty that does this - or if this is an impoverished view its more widespread than just poorer schools .. and the challenge of escaping it and getting a more personalised version that connects more deeply, stretches across the whole system

wealth can sometimes disguise the fact that the 'good results' are often the result of high levels of spoon feeding which can still lead to passive reception and brittle or inert knowledge

Continue reading →

Posted in learning, level playing field | 1 Comment

maths wars : take 5

Posted on December 15, 2009 by rob

now, what cutting edge curriculum is this from?

and what would most teachers say - we don't have enough access? thats all very well for the laptop school down the road?

this from my 1985 year 12 text book, at a time when the computer ratio was perhaps 1:20 in the school

like most of my friends though, we tinkered a bit at home, typing in game code etc ...

(i learnt the DO and IF statement for example, on a Vic 20 that took 20 minutes to load 3k of memory from tape drive ... and it seemed unremarkable that the beautifully written manual would teach you how to write a binary search routine etc, or by plugging in a 16k system module, design your own characters using binary addition on an 8x8 grid .. and i was not the computer geek in the class, just a bit curious about these things

one page in to this maths 'option' :

anybody game to try even that introductory example with kids today? ( i know Bill grappled with that one .. but its unusual .. )

i was not a maths genius, but something about tinkering here was a positive thing for me, writing an algorithm for processes like this made the maths feel more creative ...it stayed with me over the years; and i found myself wanting to open that possibility to kids i taught

but i think few would disagree that this looks like it has faded from the curriculum ... even from the IT curriculum, and certainly from the maths

for example it seemed quite possible in my first year of teaching to ask the year 10 kids to find and plot every prime number up to 20,000 ... and when that proved a little ambitious, to show them how .. i'd seen a Ulam spiral somewhere and it looked quite do-able and interesting

So while this seemed normal at the time, what surprises me since then is its quite rare to see it attempted or used as a teaching approach - not that particular example, but any similar investigation that requires coding an algorithm

here's the rest of the module - its overly loaded with questions and content; not saying its the best way it should be done ... but at least it was done

it seems to me that the maths faculty should be leading edge of these technical skills... unless i'm missing something?

so repeating some diagrams ...

this omission and exclusion seems most striking in the maths faculty ...

i guess the questions that remain for me are

(a) in terms of my research - can i justify all these diagrams ... maybe i need some hard data to back up my impressions

(b) technology in maths can soak up some hackwork... but does this mean letting a black box of a program - one we would no longer presume to try to write - do the thinking for you?

(c) should technology change content as well as make some of the work more efficient... (should it open new ways of exploration - like the humble Ulam spiral example)

(anyone following this might notice the maths wars posts 3,4 have disappeared. I'm trying to hone in one a research topic, and trying out a few ideas by blogging them ... but decided there was little mileage in those mid posts)

Posted in IT in education | 1 Comment

math wars 2

Posted on December 14, 2009 by rob

the last post got a bit theoretical (though the discussion article that inspired it is less so) to recap - and to hone it down - for sorting out my masters topic if nothing else! - i made the not very remarkable comment that this sort of spectrum seems common in discussion and thinking about maths teaching and then proceeded to suggest that maybe its possible to see aspects of the left side as being contained within the right side:

on reflection, i don't think thats very radical. Everyone is going to agree that skills training should ultimately support problem solving - its just how and when - and what balance you aim for. Do you have to learn the skills before progressing to an application (working outwards); or formalise skills after tackling interesting problems (working inwards)

thats perhaps more contested

from a classroom angle, i think i ran over this a bit by accident some years ago. I gave a class of year 11 students an assignment - on applications of trigonometry - and then realised i hadn't taught them half of what they would need to complete it. But instead of this being a problem, i noticed that the girls - it was a girls school - were actively asking for the skills instruction as they got to those places, with more interest and motivation than in their 'usual' lessons where this would have been on offer - and this was by no means the advanced class - quite the opposite.

so rather than the needing to teach skills first, which then support a problem solving application, it was going the other way, at least as far as the timing and motivation was concerned. And so i stumbled upon this as one way to let the problem solving precede the skills teaching.

as it happened i was teaching year 11 IT at the same time, and found myself doing something similar there ... I had given an assignment which i knew they wouldn't be able to do, and would need explanation as we went. i'd done this because teaching the skills there in themselves was too boring - 'this is how you use a vlookup table' etc ... so i'd set up some sort of assignment that needed these skills, with the idea of teaching skills at key points. Of course the downside of whole class instruction like this is that very soon everyone is at a different stage of the assignment, and so don't tune in very well to instruction that is related to something two questions ahead.

in this case hyperlinking to skills sheets with lots of visual screen shots ended being the scaffold that was needed; and using some screen casts to show little movies of what it should look like also helped

so the skills were still needed on the 'inside' circle, but ICT (or a busy teacher) can deliver them at point of need - and using the context seemed to generate more motivation than suggesting skills would be needed 'in the future' - (whether the future was next year or next weeks assignment)

(personally a goal driven approach is often how i've learnt ICT as well - i have a goal - so now i need to go and get the skills - read the books or tutorials - that make that possible. Kids just need the scaffold to be closer and more aligned to start with)

anyway, no 'wars' on that i suspect

but i still think the frequency would possibly be contested :

how often should you focus on 'skills first'? - how often let a self paced approach through a problem context, drive the acquisition?

and for those who think maths is too skill and drill, is this really what problem solving is about, or just a better way to deliver the skills?

(i'd be inclined to say 'no' and 'yes' to that double barreled question - the 'no' being that that the timing but not the content is inquiry driven in this structure - they're unlikely to come up with unexpected ways to solve these problems). But at least its a step away from the lock step classroom and retains some of the useful aspects of mastery learning and practice, without killing motivation.

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math wars

Posted on December 11, 2009 by rob

i wrote a post on the maths wars a few years ago ... coming out of observations of tensions in the local school system in how maths was viewed ...

I began to realise that was a typical expression of a bigger, and more widespread, debate about how school mathematics should be taught. This year, the debate came up again in another context so i had the opportunity to contribute to a broader discussion article that examined the issue in more detail, reviewing the issue ..

i notice this sort of discussion is current at the Research in Practice bloginteresting timing, since while i had come up with a continuum of sorts ...

and discussed the claims and counter claims under each 'side', i'm also trying to work out what to do with a masters ... and deciding which research methodology suits my style and interest has been tricky. One that appeals to me goes by the rather overblown name of 'phenomenography' - which basically looks at how people perceive things! It uses the idea that simpler views of something can often be considered to be contained within more complex ones

Chris Cope, introduced me to it ... and one his articles says

the research has found that the different ways of understanding a phenomenon are related in a hierarchy of depth of understanding based on logical inclusiveness. Deeper levels of understanding of a phenomenon are inclusive of shallower levels of understanding. An example to demonstrate these findings is a study of the different ways of understanding mathematics as a course area in ... first year undergraduate students ... A hierarchy of five different levels of understanding of mathematics was identified. The lowest level of understanding represented a fragmented view of mathematics as numbers, rules and formulae. The deeper levels described a more complex view of mathematics as a means of solving complex problems and developing new insights used for understanding the world.

The deeper understandings were found to be inclusive of the lower levels of understanding. Students who experienced mathematics as a means of solving complex problems were aware that numbers, rules and formulae were the tools used to solve problems. Students who only experienced the study of mathematics as learning rules and formulae had a view of mathematics that would limit them in terms of solving complex problems they had not experienced before.

the idea being that limited views can be contained within deeper and more encompassing ones, rather than being opposing points on a continuum, suggests this sort of thing to me:

so the view of maths as predominately skills and formulae etc is not necessarily opposed to a more open ended problem solving approach, but can be contained within it

don't know that fully resolves how its taught but it might suggest we don't just focus on skills for a purpose that is always defined as 'you'll need it later' (as in, years later)

i asked Alan Schoenfeld a similar question when writing that discussion article

Dear Alan,
Rereading your 1994 'What do we know about Mathematics Curricula' article

You mention at one point that

Things about which I am confident: (1) most mathematics can be taught in the style of my problem solving courses; (2) large amounts of mathematics can be learned as sensible answers to sensible questions - i.e., as part of
mathematical sense-making, rather than by "mastery" of bits and pieces of knowledge; (3) many basic skills can be picked up in the context of meaningful mathematical work. Things about which I am not confident: (1) how much mastery of some basics is required for competent, flexible performance on more demanding tasks; (2) what the best ways of mastering some of those basics might be; (3) how best to think about organizing a curriculum in a way that does justice to what is important in the traditional content, while engaging students meaningfully with the mathematics.

I wonder if you have since gained a fuller sense of 'how much mastery of some basics is required for competent, flexible performance on more demanding tasks' ? / or perhaps published on the topic, in relation to secondary, even elementary, curricula ?

his response is interesting:

The long answer is NCTM's Principles and Standards, which I helped write... I don't have a short answer in print, nor do I think it's a matter of percentages - one thing that can be done is to develop a lot of the mathematics in meaningful contexts, in a problem-oriented if not problem-based way. The trap one should avoid is to think that students have to "master" something before they can use it. Often pieces of something (or the whole thing) can be developed in interesting contexts, or via reasonable problems, at which point the math the kids have done can be codified cleanly. Some degree of automaticity is useful if not necessary - Arthur Rubenstein practiced scales, and nobody would say it harmed his piano playing - but he practiced them with purpose...

italics added - makes sense to me - i often think we learn by immersion into conversations and procedures we don't yet fully understand. The issue is that traditionally math curricula have not been structured like this (immersive problems from which skills and principles can be generalised) and so curriculum often seems to default to lists of content and skills, which perhaps build up to 'application'. Nothing wrong with that, but might be overdone as a pathway.

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