"How am I supposed to be inspired by that?"

A few days ago, Jan Visser of the Learning Development Institute (LDI) posted this on LDI 's Facebook page

Attached is a link to Paul Lockhart's "A Mathematician’s Lament." A brilliant plea, in my view, to refocus education on such things as beauty and to acquire one's knowledge of disciplines like math and science within the context of relevant current issues that can be seen, also, within a historical perspective. Not an entirely new viewpoint, of course, but it's very well formulated. Enjoy! JV

Jan's right, it's a great paper on why our teaching of mathematics puts kids off instead of showing them what's fascinating and beautiful about it. Although it's several years old now (first published in 2002) it remains relevant - unfortunately. Here are a couple of tasters...

A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer.

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.

As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules: “Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key." ... educators soon realize that even very young children can be given this kind of musical instruction. In fact it is considered quite shameful if one’s third-grader hasn’t completely memorized his circle of fifths. ...

In the higher grades the pressure is really on. ...Students must take courses in Scales and Modes, Meter, Harmony, and Counterpoint. “It’s a lot for them to learn, but later in college when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high school.” Of course, not many students actually go on to concentrate in music, so only a few will ever get to hear the sounds that the black dots represent. ... “To tell you the truth, most students just aren’t very good at music. They are bored in class, their skills are terrible, and their homework is barely legible. ... I guess there are just music people and non-music people. I had this one kid, though, man was she sensational! Her sheets were impeccable— every note in the right place, perfect calligraphy, sharps, flats, just beautiful. She’s going to make one hell of a musician someday.”

...Sadly, our present system of mathematics education is precisely this kind of nightmare. In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul- crushing ideas that constitute contemporary mathematics education.

... By removing the process and leaving only the results of that process, you virtually guarantee that no one will have any real engagement with the subject. It's like saying that Michaelangelo created a beautiful sculpture without letting me see it. How am I supposed to be inspired by that?

Check out the full paper on the Mathematical Association of America (MAA) website.

BTW - the BEST mathematics book I have ever read is The Number Devil by Hans Magnus Enzensberger.

Reflection: How did I get here?

My mother was a secondary teacher, so one of the things I always promised myself growing up was that I'd never be one myself... which is a shame, because I L-O-V-E teaching, I just couldn't stand be a school teacher (!) I love learning new stuff, finding things out I didn't know before, testing my understanding and my thoughts against what other people know, and I love helping other people to discover the thrill of doing that.

Somehow though, that's not what school-teaching is all about. ECE, postgrad, workplace, anywhere else is fine - but schools and undergraduate university study are generally not. *sigh.*

When I left university with an Honours degree in economics I had had enough of formal study & promised myself I wouldn't ever go back. (It was a mediocre degree, university didn't engage or challenge me any more than school had. I've always regarded it as a double major - in Economics and Nightclubbing. As a consequence, the result didn't do me or the university in question much credit really. )

The thing that drove me back to education was having kids. In New Zealand we have a wonderful co-operative Early Childhood organisation called Playcentre (one word) where parents train to work as ECE 'teachers' learning child development, observation skills the ECE curriculum etc alongside their children. You get a very different perspective learning ECE pedagogy to support your own child and your friends' and neighbours' children from what you might otherwise. It can't help but be learner-centred. (Besides which, working in ECE settings is like herding cats - first of all you have to figure out where they want to go, then you work with that.... otherwise you're sunk!)

Once my kids had both gone to school I worked for about 5 years doing project management of course materials in a distance education institution, and as part of my PD there I began studying online in the University of Southern Queensland's M.Ed programme.

Postgrad rocks! You're allowed to have an opinion again - and to question and challenge and THINK FOR YOURSELF! I don't think it was just that I had learned by then to work to my own satisfaction, rather than anyone else's (although that was part of it), a big part of it I am sure was a difference in attitude on the part of the course leaders from what I had experienced in formal education anywhere before.  I loved it! Haven't finished my M.Ed yet, but I will (one day)...

The feral learning idea grew out of an assignment I did for a paper in Instructional Design. I once heard Marc Prensky quote his game designers as saying "You give an idea to an instructional designer and they'll suck all the fun out of it..." Frankly, I think they have a point - and not just instructional designers, professional educators across the board tend to fall into the same trap. And you know, none of those andragogy, pedagog or other-gogies actually describe how I learn, although Jack Mezirow's transformative learning is close (although he doesn't understand kids), and so is Linda Silverman's visual-spatial model. Why on earth not?

I was very fortunate to find myself participating in a group at CABWEB with Jan Visser of the Learning Development Institute (LDI), who was editing a book, "Learners in a Changing Learning Environment". Jan invited me to submit a chapter on feral learning (which I'd been holding forth on at some length) - so the ideas got formalised and incorporated into the book... which I'm very proud of.

So here I am... in a bit of a hiatus at the moment because Real Life has taken over again for a while - and developing my own PLN through interesting sites like Change the Schools,  Edutopia,  AERO,  Shifting Thinking and the like.

I wonder what's around the next corner?

What's wrong with this picture?

There’s something profoundly ironic about the difficulty professional educators have in accepting the power of an individual’s capacity and desire to learn.  I’ve even been in a seminar recently where the presenter joyfully produced a photo of a sign over a school gate:

“If you’re not here, you can’t learn!”

The teachers in the room loved it.

So, what's wrong with that?
What's wrong with that is that the real question is not if we’re learning, or where we're learning, it’s what we’re learning.

Would we accept a doctor telling us that if we aren’t in hospital we can’t heal, or a lawyer telling us that if we don’t have a defence attorney we’re not safe? I don’t think so.

[Thought: Perhaps everybody who works in education (or wants to) should be handcuffed to a 14-year-old for a fortnight or so to remind them what we're really there for, how hard and complicated life is, and how much our kids need us to help them find the things that will make their lives feel like a gift not a penance...]

Learning is what children do.
They can't help it. They sure as heck don't need us to tell them how to do it. Babies and young children are natural learners, natural scientists. They spend their lives conducting experiments - testing the world around them in order to understand it. Everybody’s first five years are shaped by a series of "scientific" experiments - an ongoing series of situations where you interact with the world around you in a purposeful way in order to refine or expand your understanding of it…Taste… Observation… Manipulation... Interaction…. An ongoing and vitally important process of trial and error. It may lack the level of verbal sophistication you would use now, but it's a robust scientific process none the less.

New Zealand's ECE curriculum by the way is a marvellous document - well worth a look as a model of how a genuinely student-centred curriculum can be created that works at a national level. Our school sector is moving towards a similar model, with the "revised" New Zealand Curriculum. There's a separate and parallel document for Māori medium education (Māori are New Zealand's first people).

If you want to understand learning - watch a kid 
 Back in Playcentre, my working definition of a scientist was "someone who finds out the answers to questions"… Now, doesn't that sound suspiciously like a definition of learning? [And I do mean “me learning”, not “you trying to teach me” which is something different]

So it's no wonder that children love science. It has been their constant companion since before they could talk.

And then they go to school, and we tell them that they can’t learn unless we let them...
 

So, let me ask you again - what's WRONG with this picture?

From the archive: Transformative learning (1)

This is a post from my original Mary's M.Ed. Journal blog which I've since discontinued. Much of that blog is specifically related to my study at USQ, however some of the posts contain thoughts, links, and insights that are key to ideas I'm developing here. Rather than flick between the two, I've decided to re-post teh relevant ones here.

Shirley put me onto the concept of transformative learning in her feedback on my project proposal. Bloody brilliant!

Here's one take on it from the Wikipedia link above [accessed 2Sept04] that sums it up quite well:

Perhaps one of the best definitions of transformative learning was put forward by O'Sullivan (2003):
"Transformative learning involves experiencing a deep,structural shift in the basic premises of thought, feelings, and actions. It is a shift of consciousness that dramatically and irreversibly alters our way of being in the world. Such a shift involves our understanding of ourselves and our self-locations; our relationships with other humans and with the natural world; our understanding of relations of power in interlocking structures of class, race and gender; our body awarenesses, our visions of alternative approaches to living; and our sense of possibilities for social justice and peace and personal joy." [My emphasis.]

Great stuff, eh?

In other words, transformative learning gives us a model of learning as personal growth - which is what I believe true learning always is. So, what I want to know now is:

- WHY IS THIS ALWAYS REFERENCED TO ADULT EDUCATION?

Isn't this the very essence of childhood and adolescence - to learn in ways that transform us from child to the adult we choose to be?

Two answers come to mind, and both of them quite cynical.

1 - Preserving academic power structures.
Academia takes itself quite seriously. And, in the world of academia, it's academics who define what's worth knowing and doing. And, not surprisingly, academics historically have tended to be older, male, use reductionist frameworks, and fit the definition of 'specialists' as those who know more and more about less and less, until finally they know everything about nothing.
(As opposed to 'generalists' who know less and less about more and more, until they know nothing about everything.)

In other words, what's worth knowing is defined in terms of what those at the top of the heap think they already know. And because of the way academia has evolved, what those at the top of the heap think they already know is defined in terms of domain, discipline, reductionism, and precedent. (All of which is perfectly valid as far as it goes, but still only one way of knowing.)

And what people like this know best is people like them. Older. Who learn the way they learned. Because that's how the system is set up, so to succeed in it you have to work the way it works. What people like this know least is - children.

So, the most important and relevant models are models of how successful academics have been taught. The least important and relevant models are the ones that deal with how children and young people grow and assimilate learning to become useful functioning adults.

Pardon?

2 - Preserving adult power structures.
In our society - in New Zealand anyway, formal education is defined in terms of teaching activity, not learning activity. When we think of the "education" of children and young people it is as something that is imposed on them, compulsorily, for 30 hours a week, whether they like it (or value it, or benefit from it) or not.

Now, before you start with the hate mail, let me hasten to say that this is my perception of the social and institutional aspect of our "education" system, not necessarily of individual teachers within it. There are some schools, some teachers, and some students, who do very well at creating meaning and transforming students' lives, in spite of the way the system is set up. But the structure and financing of formal "education" in New Zealand is institutionalised and collective - about the greatest good for the greatest number, NOT, as the rhetoric would suggest, about individual achievement of potential, about identifying and meeting individual needs, about nurturing the individual, about achieving personal growth.

The exception is the early childhood sector, (which isn't really regarded as "formal" education anyway) where the curriculum document, Te Whariki is framed in terms of the value and transformative effect of the curriculum on the learner. As the introduction to the curriculum explains,

This curriculum ...is about the individual child. Its starting point is the learner and the knowledge, skills, and attitudes that the child brings to their experiences. ...
Each community to which a child belongs, whether it is a family home or an early childhood setting outside the home, provides opportunities for new learning to
be fostered: for children to reflect on alternative ways of doing things; make connections across time and place; establish different kinds of relationship;
and encounter different points of view. These experiences enrich children’s lives and provide them with the knowledge, skills, and dispositions they need to tackle
new challenges. ...
The learning environment in the early childhood years is different from that in the school sector. ...This curriculum emphasises the critical role of socially and culturally mediated learning and of reciprocal and responsive relationships for children with people, places, and things. Children learn through collaboration with adults and peers, through guided participation and observation of others, as well as through individual exploration and reflection.

Te Whariki, page 9

Gosh, it makes them sound almost human!

Then they enter the school sector, and we spend the next decade or so training them out of the responsibility for their own learning and way of being. The emphasis changes, from who they are and who they can be, to what they know, and whether they can prove it.

Children and young people intrinsically have all the qualities required for genuine, reflective, transfoirmative, constructive learning. We just train it out of them until they get to graduate level. And then we wonder why they're not mature enough learners to take responsibility for themselves and their own learning. How ironic! It's our socialisation that erodes these qualities in children as they grow up, not any intrinsic lack of them. So, if you want to understand the essential nature of learning and teaching, take a look at early childhood.

And for God's sake, let's put an end to this patronising nonsense about old and young learners being different - it's not the learners that are different, it's how we treat them. 

Thursday, September 02, 2004

Things that get in the way

It's been a pretty stressful week one way and  another.

Work's been busy, home's always busy - just getting everything done that needs to be done. Making ends meet is a constant counterpoint to whatever else is going on in my life at any given time.   I may or may not be coming down with something - and to top it all off, I spent yesterday taking my son to the hospital for emergency surgery on his hand.

In the midst of all this, I'm trying to find enough spare time (and enough spare synapses) to process - and document - the thinking I'm doing about things educational.

One of the things that's becoming obvious is that it's incredibly difficult to assimilate anything new when you're already stressed. Hardly a unique or original observation, but one that's been reinforced again recently.

Timing is as important as time.

A number of years ago now I started learning Te Reo Maori. I really enjoyed it, and I have made several attempts since then to refresh and improve my ability to speak and understand it. So far I haven't got very far.  I'm not sure if the reasons I can identify are genuine reasons or just rationalisations. I feel guilty, frustrated and resigned about it by turns. But the bottom line is, there's more I want to do than there are hours (or kilojoules) available to do them all, and much as I want to do it, the timing just hasn't been right  yet. Meaning it hasn't got to the top of my priority list yet. 

One of the lessons I've absorbed on my way through life (social conditioning) is that this really means I lack the dedication, the genuine desire to learn Te Reo, and the intellectual honesty to admit those failings. In other words, there must be someone at fault, and it must be me. However much my adult rational self may know that putting food on the table for my kids, and holding down a job, being available to my friends and family when they need my support ...you know, reality... are legitimate priorities, part of me is equally sure that the only reason for not doing something is lack of trying hard enough.

I suspect we are still teaching our kids those same unhelpful lessons.

The reality is that life does get in the way sometimes, and we do have to prioritise what we do. Sometimes all the pieces fall into place, and we can make huge strides. Not only is learning not linear, but it's not constant either. It happens in fits & starts (the 'clumpy universe' again). So why do we insist on designing learning environments and curricula for our children that behave as if they are?