stoner

“He found his release and fulfilment in the classes in which he himself was a student. There he was able to recapture the sense of discovery he had felt that first day, when Archer Sloane had spoken to him in class and he had, in an instant, become someone other than who he had been. As his mind engaged itself with its subject, as it grappled with the power of the literature he studied and tried to understand its nature, he was aware of a constant change within himself; and as he was aware of that, he moved outward from himself into the world which contained him, so that he knew that the poem of Milton’s that he read or the essay of Bacon’s or the drama of Ben Jonson’s changed the world which was its subject, and changed it because of its dependence upon it.”

‘Stoner’ by John Williams

what drives exploration and investigation?

jo2-124

 

Surprisingly, it is not the intellect.

The intellect may well be utilised as a tool but it is not the driver.

How do you lay yourself open to inspiration?

There is a big difference between simile and metaphor: If you are asked to dance, quietly feel the difference between ‘dance like a bird’ and ‘you are a bird’. If your presence can be filled with images , thoughts and feelings of you as a bird, and you forget the other story of yourself, you will dance well. As soon as you become aware of dualities, for example between what you are being and what others think you are doing it will fail.

When you are the bird you feel your feet clutching the branches, the wind in your face, the hardness of your beak. When you slip out of this into dancing like a bird, the duality reappears and you become fragmented as usual.

This non dual deep belonging is not a mental visualisation. All activity is transformed. Spontaneity appears. The person you were, or you normally think you are is not present. That story has vanished.

There is no one left who dances, there is only the dance.

The actor does not act the part. Only when the actor as person is absent does the other temporarily emerge. The other is the creative mathematician, the scientist, the artist, the writer.

That’s all I can say about becoming an explorer.

The main problem is that people do not believe they can explore, they do not believe they are capable, they believe the story of themselves that is their normal story which has unfortunately been constructed over the years by inadequate experiences.So treat yourself how you would wish to become.

Do not fear the judgement of others.

Forget ‘can’t’, ‘don’t want to’, ‘don’t like’………….

Be imaginative, be explorers.

Find things that have never been seen by you before.

Begin.

Find out something you didn’t know before about a square

like learning a language…

Some methods, especially those that rely on memory and de-contextualised vocabulary and intense grammar are awful. They start with lists of words and complexities of grammar that generally mean something to those who have studied grammar in their own language but feel so fragmented and distant from speaking that one senses its going to be very hard going. The best (in my opinion) way of learning a language is through a live course using ‘The Silent Way’, which was created by Caleb Gattegno as he learnt how people learn. Some other methods however such as the Michel Thomas courses are very good for learning at home. I personally am learning arabic using this method and find in some ways it is like learning maths in the style of the subordination of teaching to learning. I could not find a course on arabic using ‘The Silent Way’.

One immediately feels useful learning is taking place and a certain hopefulness and confidence to continue takes over. It feels optimistic and fruitful. Arabic is a bit tricky because of the written language, the unfamiliar sounds and the unfamiliar words having in general no Latin roots. Most words are completely different to what an english speaker knows and the word order and other things are also unfamiliar.

OK so this sounds a bit like coming across mathematical ideas when you are little.

The knowing use of algebraic ideas in simple conversations and question and answer ‘sessions’ using the rods is similarly freeing and powerful. You can just see it so easily in the children’s eyes and actions. There must be no pressure at all. Certainly no pressure to write anything down, unless it comes from the children, and even then do not force them to ‘write it down correctly’. Do not ‘be a teacher’ in that sense. Bide your time.

Look at Caleb Gattegno’s  ‘Mathematics with Numbers in Colour’ Book 1, part II, ‘Qualitative Work with the Rods.’  ONLINE…

Don’t take it as a ‘course’, just read it through three times:

1. As if you were reading a newspaper

2. As if you were reading it out aloud to another person and

3. Try and fathom the general flow and gist of the chapter.

WARNING: DEFINITELY DO NOT USE IT RIGIDLY AS A ‘COURSE’

rod man’s nightmare…

I feel frustrated, I feel thick, I just can’t see, nothing’s clear, the dark night of the soul, there’s something I just don’t see, I don’t get it, waiting for a flash of insight, can’t quite hold it in my mind, I’ve forgotten what I’m doing, can’t see a way forward, feel like going back to the beginning, puff and blow, I’ll write down what I do know…again, maybe I’ll sleep on it…you get the picture…

THIS IS NORMAL WHEN YOU ARE EXPLORING UNKNOWN TERRITORY

UNLESS YOU’RE LUCKY

awareness of skimmed milk…

I’m trying to reduce my calorie intake whilst still having optimum nutrition, but I am still in the learning process of ascertaining just what various quantities of foods look like in terms of kcalories. One can easily underestimate what one eats in a day…By measuring, just once, how much skimmed milk I like in tea, I now know that everytime I have a large mug of tea I use about 50ml of skimmed milk. I don’t have sugar now, so each large mug

COSTS 16kcal, not bad. I didn’t guess, I used this table:

dairyproducts199

I have learnt something…hurray!!!

observing oneself…

splat-image

I wanted to do a ‘piece of research’ in which I attempted to ‘observe myself doing it.’ I have been interested in patterns in nature for many a year and thought I would drop ink droplets onto paper to see what patterns might emerge, if any. The following are 3 grabbed images of this research. I have used images here because it is necessary to maintain the complex formatting: read the first section, upper left. This shows how the original tape recording was transcribed and then thought about and re-thought about so to speak…

splat-1

a further piece some way in:

splat2

When I had finished the whole experiment I made a series of knowledge claims which were quite extensive. Here’s a small example:

splat-3

Well, that’s what I did…

challenge: observe yourself making a cup of tea

(or similar)

gattegno buddhism and critical theory..ah well…

Gattegno maintained there were 4 stages in learning:

1. there is something to be explored

2. the exploration of this ‘field’

3. practice in this field leading to mastery

4. transfer of this knowledge to wider fields

The Four Noble Truths of Gotama Buddha, the cattari ariyasaccani are:

1. an unsatisfactory state exists

2. how this ‘suffering’ arises

3. how to end this ‘suffering’

4. the means by which this ‘suffering’ can be eliminated

In his book ‘The Idea of a Critical Theory’, Raymond Geuss describes a typical critical theory as being ‘ a transition from an initial state of bondage, delusion and frustration to a final state of freedom, knowledge and satisfaction.’ Further, he defines a typical critical theory as consisting of three parts:

1. the belief that a transition from the initial state to the final state is in fact possible

2. the demonstration that this is in fact necessary

3. this transition can come about if one follows the particular tenets of that critical theory.

Well, at least, Gattegno, the Buddha and Raymond Geuss have in common the idea that…

‘EMANCIPATION IS POSSIBLE’

but it is clearly not going to be a push-over

huatou: is it possible to change?

awareness 2 some examples in rod pre-number…

some algebra before arithmetic pre-number awarenesses

examples of free play awarenesses:

rods are good things to play with

we can make pictures

we can build models and buildings

we can play games

we can invent games

we can share our ideas

we can learn from each other

rod colours are in families

rods can be packed away in family colour order if we like

rods can be packed away in other ways

rods have a definite regular order of size

I can recognise rods by how they feel

rods can be named by colour and in other ways

directed informal awarenesses:

rods of same colour are same length

rods of same length are same colour

groups can be made of the same colour

groups can be made of the same lengths

language (word concept) awarenesses:

trains can be made in a variety of ways

rods can be swapped for others

 staircases can be made in a variety of ways

 mats can be made

mats can be made with rows of rods of the same colour

we can answer questions by making patterns of rods

awarenesses relating to adding and its inverse:

I can find one rod to fit two others

I can find two or more rods to fit one

I can find rods to fit long trains

I can find the difference between two rods in different ways

I can find the difference between two trains of any length

awarenesses relating to equivalence, multiplication and factors:

I can find one rod which fits two or more rods of the same colour

I can find rods of the same colour to fit some other longer rods

I can find rods of the same colour to fit some, but not all trains

assessment as it is…

I-reckon-he's-hooked

 The ultimate zen assessment:

You cannot know another you do not know yourself

…it is not possible. You cannot ‘know’ another in the fullest sense. I cannot know you. I ‘see’ your outer coverings, your skin, your body, your clothes. When I speak to you we discover more about each other. All the time we are making judgments and attempting to interpret each others’ responses and so on. Clearly we can get somewhere, but…

‘I’ can ‘know’ ‘you’, up to a point, but that is all. Ultimately I do not know myself, never mind you.

We are always assessing people in general though, through automatic responses, automatic generalisations. ‘I like the look of him.’ ‘People who have their trousers hanging low are stupid.’ ‘I hate people who smoke.’ and so on… These ‘automatisms’ are deeply ingrained. If we are unaware of them, well…what do you think?

As teachers we are required to assess others in more specific ways

For example if its my job to teach you addition it would be very useful for me to know what you already know. At least, that seems a reasonable supposition. How do I do it?

I can only attempt it by spending time and focusing attention on the specific areas I am interested in.

To start with I need to look at myself. Do I know what I am looking for? Do I actually know what I am talking about when I say ‘I want to teach addition?’ Most people don’t apply too much attention in these areas. It’s dark in here and the ground is hard for digging. Read this Sufi story.

Basically, if you know what you are doing and you look and listen openly whilst asking suitable probing questions that’s a start

You will have to spend time and effort and you should work on each child at a time

You may have noticed that this is very hard to achieve in a large class and when you are burdened with too many other demands

to create order, energy is required

in physics, to increase order is to decrease a measure known as entropy

(I like entropy that’s why I’ve put it in….it’s closely related to the most fundamental law of physics, the Second Law of Thermodynamics…)

Entropy tends to increase throughout the whole universe…

Your desk becomes dis-ordered in the course of a day

iron rusts

you age

if you wish to tidy (order) your desk you will have to expend energy

If you wish to assess another, to increase your ordered knowledge of them, you will have to

EXPEND ENERGY

to expend energy in this sense you will need TIME…

ps For those interested in our most accurate representation of matter: There is no unique universal relation in quantum theory that could stand on equal footing with the position-momentum uncertainty relation. The energy operator is called H the Hamiltonian. There is no dual relationship between H and T.

Not yet, anyhow…

see sister post

some important people…

Caleb Gattegno

Most of his works are available to read on line for free here:

calebgattegno.org

Roslyn Young – a modern exponent of Gattegno’s ideas

try this: On awareness and awarenesses

Read this book, co-authored with Piers Messum,

‘How We Learn and How We Should be Taught’,

Vol 1: Duo Flumina Ltd, 2011, ISBN 978 0 9568755 0 1

Caroline Ainsworth

An example of a ‘research process in all its complexity’

a case study of one teacher’s professional development journey

Madeleine Goutard

the wonderful exponent of STL*

Talks for Primary School Teachers

Educational Explorers Company, 1963

Mathematics and Children – a reappraisal of our attitude

Same series.

*The Subordination of Teaching to Learning – begin here