learning in progress ….

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

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 no maths genius, but something about tinkering here was a positive thing for me ...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 my maths and programming were rightly judged as unexceptional at the time - what surprises me since then is its quite rare to see it attempted or used as a teaching approach

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

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.

The curriculum in 2042 is now mostly about how to get a girlfriend or boyfriend, dealing with skin problems, legal remedies against your parents, and how to dress like one of the characters in Star Wars (a series which now consists of 3471 movies, and is the principle component of Western culture).

There are few remaining traces of the curriculum structures of the 20th century, which is now referred to disparagingly as the Knowledge Age. By 2042, we have moved well beyond this relatively primitive conception of education. There was a massive curriculum reform program in the early years of the 21st century, which achieved what was then described as the ‘post-modernisation’ of the curriculum. This program focused on what are being called the New 3Rs: resilience, relevance and generic skills. Pedants have pointed out that generic skills doesn’t start with an ‘R’. Supporters of the New 3Rs have retorted that Writing and Arithmetic don’t either. This has proved a telling argument.

On the standardised literacy and numeracy assessments which are conducted annually by each of the states and territories, in the year 2042 we have reached a very positive position: all Australian students are now well above the benchmarks, and all students are also well above average. Indeed, every Australian student is performing in the top decile. In the ACT, every student is in the top 1%.

makes some interesting points after the humour

I am sure you are familiar with the line that education is working on an industrial model in the information age. I don’t feel completely comfortable with that kind of analysis, because I think many of the elements of the industrial model are important in schooling: high levels of administrative efficiency, clearly defined roles, responsibilities and accountabilities, a focus on results: these are all matters which suit the delivery of education. So I don’t share the view that we should do away with the old industrial model school as the focus of educational delivery.

But there is something to that analysis. What it suggests is doing away with some of the rigidities and inefficencies of the current model. Let me suggest two areas, just as examples, where radical reform might help:

Firstly school organisation: If the research I keep citing is correct, we have to acknowledge that deep learning requires sustained teaching of key concepts for an extended period of time, and that the amount of time will be different for different students. That means that age-grading and lockstep progression are blockages to progress. We need more flexible and learning-focused approaches to student grouping and progression. We have to get better at managing how students are grouped together for their learning, to ensure that each student’s individual progress towards deep learning is maximised.

That implies a move on class sizes: the current arrangements about class sizes are an excellent example of what is wrong with the industrial model. In respect of class sizes, we are at the same stage of development as the automobile when Henry Ford said you could have any color so long as it was black. Setting inflexible maximum class sizes eliminates one of the major potential opportunities for improving student learning. To make the point simply: under current staffing ratios, every class of 50 that you run lets you run one class of 5. If you run a lecture for 100 students, you can run four classes of 10. Why wouldn’t you? I predict that we will have much greater class size flexibility (which doesn’t mean fewer teachers or, on average, larger

from the last link from this conference proceedings. like the Melb declaration, that conference seemed full of nice ideas, 'we must remove inequity from the system' - less clear how its ever implemented.

i like the comment about overdoing the information age and factory schooling comparison, which i've probaby done myself. Some of the assumptions in school do work - clear roles etc - but some don't; notably forcing kids through standardised curriculum at same age level. No-one thinks its a good idea, as far as i can tell, but its hard to really do otherwise given the structure of secondary school and curriculum. Don't know about the ratios comment but there is a need to find better ways to customise learning.

(reading Disrupting Class at the moment, which sees smarter use of IT as a possible way of doing this - not just putting computers in classrooms -  a waste of money if thats all that is done - but using the possibilities for self directed learning, customised curriculum, instant feedback, that they open up.

Sees the growth in home schooling and virtual schooling as the place where these disruptive possibilities are likely to incubate for a while.) 

In less grand terms, we might imagine a cook who produces a book of recipes without any reference to Providence or Creation; and the recipes still work just fine without a pious preface that might have been customary in previous generations. The question is whether this omission is just a question of efficiency of communication - there is no need to mix theology with the instructions on slicing tomatoes - or whether the separation goes to the very core of things - are carrots and communication and commerce all ultimately the blind consequences of dancing atoms, which are themselves the consequences of some random properties of quantum flux - a universe that happened to pop into being - or is there another realm of explanation and integration underlying all this- which all draw on for meaning even while ruling it off as 'not science' ?

Short of positing God behind the Big Bang, the original event, this separation of technical detail from metaphysical perspective seems, to a scientific mind set, to be the most practical way to proceed, since science tends to wants only the minimum (and often reductionist) perspective it can work with. And indeed one does not really want an aircraft mechanic or brain surgeon saying – “and this bit is where God comes in”; the understanding needs to holds without predicating that sense of explicit intervention. This is now so well established as to seem unremarkable, vindicated by utility of technology, axiomatic. The only question is how complete is this account and approach... does the separation that makes sense in cookery or astronomy or physics, ultimately need to be reconciled with another frame of reference; indeed does it already presuppose one, however disregarded the assumptions are?

Its true to the history to note Laplace was evidently a theist and Christian. While he is known for viewing the universe as entirely mechanistic, he drives home the point by imagining a mighty intelligence able to stand apart from this and see all of history - and calculate the future - all from the deterministic path of the atoms. This imaginary intelligence is conceived as outside the system - variously described - by others - as a demon or God. This is hardly part of his science - since he disavows that hypothesis - yet his imagination still posits such an omniscient observer to illustrate the point. And while he certainly promoted a deterministic and mechanical view of nature, it is not clear he actually imagined every act of human will was predetermined by the blind and inevitable pathways of atoms. Indeed reconciling a mechanistic universe with any notion of self determination is an unresolved paradox for any single minded scientific view - since even those who are convinced the God hypothesis has been falsified and should be permanently dismissed, like to retain a sense of independent personal action and moral indignation, which hardly emerges from a view of that view of the universe).

Galileo, Descartes, Newton and most of the ‘scientists’ (a 20th century word) also embraced some version of faith... so whatever separation of science and religion we now see in their name, was not necessarily developed in them; that is, while they may have methodologically bracketed off theology from ‘natural philosophy’, it did not rule out general faith in Creator, or, for that matter, Saviour.

We tend not to bother with these aspects of their thinking; we’d rather pull Newton’s laws away from his theology; ignore his lengthy attempts to use his new understanding of the heavens to reconcile dates and appearances of comets with biblical prophecy; just as we leave behind his prolific experiments in alchemy. Poor Newton, genius that he was, evidently didn’t attend popular schooling 101 to see how his science should have ruled all these aspects out of court.

We also take a Cartesian ‘frame of reference’ as to mean a coordinate plane for geometry, or the logical frame of thinking that privileges cognition as a basis for identity- (I think therefore ....) Academics might deplore the divided personality and view of the world that tends to arise from this approach - logical categories and primary qualities (mass, extension) here as the main game, while emotion and secondary qualities takes a much less privileged role over here; but nevertheless assume we can rule off his references to a deity, or his own account of a personal vision.

So popular history – including the science text book version - simplifies and purifies these ‘scientists’, extracts and codifies their science, removes most of the context; removes whatever theism was involved, and often casts them, or at least their science, as the enemy of the ‘stories of religion’. (Just as it truncates the ‘scientific method’ etc.)

Above all we read Galileo’s dispute with the Catholic church as the paradigmatic example of how religion has opposed the ascent and reign of science - uninformed by any subtler grasp of the history. (Peter Slezak, who happens to be atheist, has a much more nuanced view, he notes Gaileo friendships with many of the cardinals, comments on his faith, and sees the real issue behind the issues is who had the right to interpret scripture – so while religion indeed 'got in the way’, both science and faith were politicised in a way that we forget and over simplify).

In any case it is worth distinguishing between methodological naturalism as practiced by many of these ‘scientists’ (‘my method will proceed without direct reference to God; does not need that hypothesis’) and naturalism in a broader more encompassing sense; there is no God. They are not one and the same. Indeed, its arguable that the materialistic scientist in the latter sense, is less common than many assume- - those who follow Newton et al and reconcile theism with scientific method seem more common historically; and while we might not so readily proclaim on nature as a ‘second book’ of revelation today, its notable that many still do not equate their science with atheism. (Claiming that the faith of historical scientists was just social conditioning of their day will hardly do to explain it; one might just as well see the explosion of western science as drawing on an underlying faith in a rationally structured universe, which itself derived from this heritage; i’m not the first to suggest that of course).

I’ve written various ponderous posts here over a few years, without broaching all this; but i’m feeling i need to write on that dimension.

My own faith, for the record, is more immediate than it may appear from these writings, and i have no intention of defending it with reference to history or philosophy; trying to make its seems suitably reflective, intellectual, academically respectable. I’m not really going to make much effort to quote Whitehead, and the deep and insightful commentaries he writes on science, religion and education, as much as i did draw from his insights in earlier days. Nor Plantinga on methodological naturalism, or even CS Lewis, for a clear exposition of the reasonableness of faith, or a recent reading of Latour, on how the crossed out God is part of the modern set of pacts with has left us with multiple omissions in how we see science, society and religion.

Instead of doing that, casting things in that respectable and somewhat academic light I’ve decided to start another blog, which starts with a faith commitment just assumed up front, taken as given, not as needing defence or justification. Simple observation and experiences of faith as conceived and worked out in life, with a reflective edge i guess.

..on the need to be more deeply predicated on ideas from history and philosophy of education

all compares badly with the ready dismissal of theory by many ("spare me the ivory tower unless you can deal with 8G on a friday afternoon") .... and the results that follow ...too open to fads, too inclined to surface forms of control, stifling of long term teacher growth...teaching as craft learnt by apprenticeship rather than formed as profession with sound principles*, divorce of what school says it aspires to (various noble goals) from what it really does ..

from "The Relation of Theory to Practice in Education" (here):

as every teacher knows, children have an inner and an outer attention. The inner attention is the giving of the mind without reserve or qualification to the subject in hand. It is the first-hand and personal play of mental powers. As such, it is a fundamental condition of mental growth. To be able to keep track of this mental play, to recognize the signs of its presence or absence, to know how it is initiated and maintained, how to test it by results attained, and to test apparent results by it, is the supreme mark and criterion of a teacher. It means insight into soul-action, ability to discriminate the genuine from the sham, and capacity to further one and discourage the other. External attention, on the other hand, is that given to the book or teacher as an independent object. It is manifested in certain conventional postures and physical attitudes rather than in the movement of thought. Children acquire great dexterity in exhibiting in conventional and expected ways this form of attention to school work, while reserving the inner play of their own thoughts, images, and emotions for subjects that are more important to them, but quite irrelevant.

Now, the teacher who is plunged prematurely into the pressing and practical problem of keeping order in the schoolroom has almost of necessity to make supreme the matter of external attention. The teacher has not yet had the training which affords psychological insight — which enables him to judge promptly (and therefore almost automatically) the kind and mode of subject-matter which the pupil needs at a given moment to keep his attention moving forward effectively and healthfully. He does know, however, that he must maintain order ; that he must keep the attention of the pupils fixed upon his own questions, suggestions, instructions, and remarks, and upon their "lessons. " The inherent tendency of the situation therefore is for him to acquire his technique in relation to the outward rather than the inner mode of attention.

Along with this fixation of attention upon the secondary at the expense of the primary problem, there goes the formation of habits of work which have an empirical, rather than a scientific, sanction. The student adjusts his actual methods of teaching, not to the principles which he is acquiring, but to what he sees succeed and fail in an empirical way from moment to moment : to what he sees other teachers doing who are more experienced and successful in keeping order than he is; and to the injunctions and directions given him by others. In this way the controlling habits of the teacher finally get fixed with comparatively little reference to principles in the psychology, logic, and history of education. In theory, these latter are dominant; in practice, the moving forces are the devices and methods which are picked up through blind experimentation ; through examples which are not rationalized ; through precepts which are more or less arbitrary and mechanical ; through advice based upon the experience of others.

Here we have the explanation, in considerable part at least, of the dualism, the unconscious duplicity, which is one of the chief evils of the teaching profession. There is an enthusiastic devotion to certain principles of lofty theory in the abstract — principles of self-activity, self-control, intellectual and moral — and there is a school practice taking little heed of the official pedagogic creed. Theory and practice do not grow together out of and into the teacher's personal experience.

Ultimately there are two bases upon which the habits of a teacher as a teacher may be built up. They may be formed under the inspiration and constant criticism of intelligence, applying the best that is available. This is possible only where the would-be teacher has become fairly saturated with his subject-matter, and with his psychological and ethical philosophy of education. Only when such things have become incorporated in mental habit, have become part of the working tendencies of observation, insight, and reflection, will these principles work automatically, unconsciously, and hence promptly and effectively. And this means that practical work should be pursued primarily with reference to its reaction upon the professional pupil in making him a thoughtful and alert student of education, rather than to help him get immediate proficiency.

For immediate skill may be got at the cost of power to go on growing. The teacher who leaves the professional school with power in managing a class of children may appear to superior advantage the first day, the first week, the first month, or even the first year, as compared with some other teacher who has a much more vital command of the psychology, logic, and ethics of development. But later "progress" may with such consist only in perfecting and refining skill already possessed. Such persons seem to know how to teach, but they are not students of teaching. Even though they go on studying books of pedagogy, reading teachers' journals, attending teachers' institutes, etc., yet the root of the matter is not in them, unless they continue to be students of subject-matter, and students of mind-activity. Unless a teacher is such a student, he may continue to improve in the mechanics of school management, but he can not grow as a teacher, an inspirer and director of soul-life. How often do candid instructors in training schools for teachers acknowledge disappointment in the later career of even their more promising candidates! They seem to strike twelve at the start. There is an unexpected and seemingly unaccountable failure to maintain steady growth. Is this in some part due to the undue premature stress laid in early practice work upon securing immediate capability in teaching?

I might go on to mention other evils which seem to me to be more or less the effect of this same cause. Among them are the lack of intellectual independence among teachers, their tendency to intellectual subserviency. The "model lesson" of the teachers' institute and of the educational journal is a monument, on the one hand, of the eagerness of those in authority to secure immediate practical results at any cost; and, upon the other, of the willingness of our teaching corps to accept without inquiry or criticism any method or device which seems to promise good results. Teachers, actual and intending, flock to those persons who give them clear-cut and definite instructions as to just how to teach this or that.

The tendency of educational development to proceed by reaction from one thing to another, to adopt for one year, or for a term or seven years, this or that new study or method of teaching, and then as abruptly to swing over to some new educational gospel, is a result which would be impossible if teachers were adequately moved by their own independent intelligence. The willingness of teachers, especially of those occupying administrative positions, to become submerged in the routine detail of their callings, to expend the bulk of their energy upon forms and rules and regulations, and reports and percentages, is another evidence of the absence of intellectual vitality. If teachers were possessed by the spirit of an abiding student of education, this spirit would find some way of breaking through the mesh and coil of circumstance and would find expression for itself.