one last time concerning ‘tables’ with a little question at the end…

I can’t do any more of this ‘tables’ stuff, but I am asked about the issue so much…

Look, here’s a ‘tables’ square, slightly adjusted:

tablessquare1

I’ve removed the 1x and 10x sectors. 1x is trivial, 10x needs special treatment.

If you fully appreciate the flip rule you can forget the grey airbrushed section.

The square numbers in the blue-green squares are a special beautiful group, well worth studying. Many patterns and much al-jebr live here…

The rest are in 8 columns, from 1 to 8. Add up the numbers from 1 to 8 in your head and it’s 36. [I did 8×9 and halved it).

The orange numbers can be found by doubling from single digit numbers. (Conversely by halving from the products).

The blue by treblings from single digit numbers.

There are 4 spaces left, 5×6, 5×7, 6×7, 6×9.

double 15, the two primes, 5 and 7 make 35, double 21 and double 27.

Study George Cuisenaire’s original product wall chart:

Product-Wallchart

You can see all the doublings.  Look carefully.

These products, the numbers in black, form

MILESTONES in the unknown territory to 100

By studying them as numbers, as we have previously discussed, their inner structures will become apparent, thus lessening the awful stress on memory so prevalent in today’s schools.

In addition by briefly studying the Primes to 100 it will become apparent to the little yellow belts that many numbers are rich in factors and many are not. They will generate a ‘feel’ for the rich numbers, learn their inner structures by familiarity and learn, as an aside, the so called ‘tables’ relevant to that number.

This however takes

A CHANGE OF PROGRAMMING

even in the minds of  teachers, never mind the administrators

THIS IS PROBLEMATIC…

because even you and I dear reader

IMAGINE OURSELVES TO BE FREE

huatou: ‘Am I free?’

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48

 

 

48 6x8 2x3x2x2x2

 

The LHS shows 6×8

The RHS shows 2x3X2X2X2  dust ( the 8 is 2x2x2 and the 6 is 2×3 )

As far as the number 48  is concerned the order of rods in the tower is irrelevant, but this needs ‘proving’. Take my word for it at the moment.

48 6x8 2x2x2x2x3

 

So long as the tower is constructed using the rods on the right, the order is irrelevant.

So, as 2x2x2x2x3 is the dust, this means we combine these a pair at a time in any order:

try it yourself..that’s best…but

here’s my mind at work for example:

start with 2, double it double it double it, that’s 16, times 3 is 48 (2 4 8 16 48)

2 threes are six, double it, double it, double it, that’s 48  (6 12 24 48)

2 twos are 4, two fours are 8, three of them is 24, double it, 48

and so on…..

IF YOU HAVE THE TIME AND THE SPACE IN SCHOOL TO DO THIS TILL THE COWS COME HOME AND YOU ARE LITTLE, AND YOU START SLOWLY WITH THE NUMBERS UP TO 10 AT FIRST, STUDYING THE NUMBERS ONE BY ONE FOR A DAY OR TWO EACH FOR EXAMPLE WITHOUT STRESS, YOU WILL ‘GET A FEEL’ FOR THE NUMBER YOU ARE STUDYING WHICH WILL BE VERY POWERFUL IN YOUR FUTURE STUDIES OF THE NUMBER SYSTEM AND OPERATIONS YOU WILL NO DOUBT BE REQUESTED TO CARRY OUT…

(In general, the present school arrangements almost totally inhibit this…)

ps 6×8 is one piece of your ‘tables’, using the dust you see and get the ‘feel’ for 6×8, 8×6, 3×16, 16×3, 2×24, 24×2, 4×12, 12×4, never mind ‘half of 48 is 24’, ‘half of 12 is 6’, ‘half of 48 multiplied by 2 is 48’, ‘a quarter or fourth of 48 is 12’, ‘an eighth of 48 is a half of 12’…and so on till the cows come home…

yap yap yap…

TRY IT

 

 

 

 

against too much prescribed content whilst being definitely FOR interesting other content

Teachers have too much to do. Even if they wanted to do something else they felt was relevant and appropriate, they can’t. There’s no time and too much pressure. They are tired of all this interference.

Surprisingly enough teachers are actually human beings with their own lives and interests, they are not simplistic ignorant automata created to perform exactly the same acts at exactly the same times within institutions. They love the children in their care, they want to do what they can for them, they would like to help them BE in the world and be sensible, sensitive, caring, knowledgeable, useful, well- balanced people.

Why not let them get on with it?

If a person knows something really well, whatever it is, and then communicates their love of it to others, this generates enthusiasm for learning, takes people beyond what they thought was within their range and generally increases the ‘dimension’ of their world.

It’s like a good curry:

A good curry has lots of ‘dimension’ in the sauce due to many ingredients and flavours. It’s not thin, watery and tasteless.

There is so much content in the world. The world is content if you like. Why be so minimal about it?

The stress should be on learning how to learn, becoming interested in many things, moving beyond prescribed limits, being imaginative and creative, climbing Everest because its there, spreading the word about crochet if that’s your game……there’s no end and its all interesting.

All this is not to say there might be somethings it’s definitely useful to know, but you get the picture…

We need creative citizens who are not afraid to dig and delve,

TO BOLDLY GO……

ps  That’s why I did the posts on logarithms, because if you can and it seems appropriate, then do it. I’ve done indices, coefficients of polynomials and logarithms with 6 year olds. We also weighed an ant and simulated the Klondike Gold Rush of 1898. Why not? They learnt a lot. They learnt a lot that is in any curriculum and an awful lot more that wasn’t. Also, they enjoyed it.

pps  God bless us and give us strength to fight on against all the drivel endlessly dished out by this Government and the deluded being in charge of the Department for Education.

against too much prescribed content and the learning of undesirable outcomes

National curriculae have strong tendencies. A National curriculum might have as one of its aims to improve the access of all children to what is seen as a desirable amount of knowledge. That is fine, BUT…

National curriculae are mostly generated by advice from specialists tempered by ideologies of the prevailing political system. The first ensures an immense amount of material to be covered, because specialists live within their created worlds and love them so they can think of lots to do and the second ensures that a) the lists sound similar to what they did at school and b) great emphasis is given to processes, procedures and organisations for ‘learning’ that these power-possessing beings have had experience of. So, kids have a curriculum that is 1000 miles wide and an inch deep (maybe a foot) fragmented by Victorian attitudes and organisations for learning. The Victorian attitudes include the fragmentation of the world into a few subject areas, the fragmentation of the child’s time into standard units such as hours, and the fragmentation of the people of the world into ghettos they call groups or streams. The children quickly learn from these ancient environments who is smart or dumb, who is destined to be a king or a pauper, who will live to serve and who will serve, etc.

UNSATISFACTORY

This is the DARK SIDE of WORLD CREATION

There are better ways…

the journey 1

If you engage with arithmetic, or anything else, and you really want to know, you will begin a journey. It will probably last a lifetime. Once you have become a black belt, seventh dan, you may choose once again to wear the white belt. If you are a consultant doctor, you become Mr.

One gains knowledge and wisdom but never reaches an end. There can be no end. If you think you have reached the end you are mistaken.

It is clearly the same with engaging in the Cui way.

It is, or should be, not a way that is prescribed. You have to make it your own. As such, your way will be different in many respects to others’ interpretations of the way. This is normal and proper. There is nothing unusual about it. Everyone must start somewhere. Do not compare yourself to anyone else. It is your journey.

There are so many inappropriately incomplete and partial journeys generated by the present education system.

I live in a city. Where is this city? It exists in every inhabitants mind. There are as many cities where I live as inhabitants of the city. Clearly it can be located on a map, but the knowledge and understanding of the city and all that it means is personal.

This is the difference between a prescribed content, as a list, and a full and robust ‘feel’ of the meaning. You have to work at this kind of learning. It is beyond facts. It engages your whole being. You have to create the meaning yourself, through wanting to. If you don’t want to, you won’t begin. No one can force you. At least, you can be forced in school up to a point through fear, guilt and external discipline, but this is an unnecessary crime.

 

So, just begin.

the content of every curriculum is relative and loaded

Awareness and attitude beat content. More later…

There are an infinite number of lists of content. Every curriculum that has ever existed or will ever exist or any that can be thought about in the future will have different sets of content. As now, when the government sees fit to allow those with no real knowledge or insight into education and learning to control what happens with content (and process), these lists will be enormous. What’s more they will be created by the prevailing mental structures of the beings involved.

A dog would create content relating to doggish items such as food, smell, territory etc.

Those who have been exposed to certain conditionings will often, though not necessarily, include aspects of these in their ‘curriculae’. George Monbiot recently wrote about this aspect. Check out his other writings on the reasons behind the present ‘revisions’…George Monbiot…’A Capitalist Command Economy’.

Gradgrind, from Dickens’ ‘Hard Times’ was keen on facts, facts, facts…

The half truth here is that of course everyone needs facts to operate in the world, but one needs much more than facts to be a creative, engaging, imaginative, happy productive human being.

The present ‘Revised National Curriculum’ for England and Wales is an example of ‘the Gradgrind Way’ created by those who do not understand but have the power to enforce. There are more sinister aspects to this however including the forcing or bribing of state schools to become so called academies by making them attempt to achieve the dull impossible. Then ultimately the profitable ones can be dealt out between the ‘unelected oligarchs’. This is truly a crime.

This revised curriculum is 1000 miles wide and 1 inch deep.

Every CURRICULUM contains CONTENT that is RELATIVE and LOADED.