Montessori

Puddle Maths 2

WorkBooks

Over the last year we have been working on Maths in a variety of ways. Fran quite likes workbooks in moderation so we have used them intermittently. Her favourite has been the Early Bird Singapore set which are a realy nice collection of books. They don’t dwell too long on any subject but they are well thought out and it is easy to boost the topics with other work. She has also used Schofield & Sims books and likes them but she has been a very reluctant writer, so I tend to fill in answers for her to avoid it becoming a chore. it would be fair to say we use them rarely though, there are better ways to spend our days! However recently we have started to use Miquon Maths in a gentle fashion which she really seems to enjoy now.

Puzzle Sums

Most recently a spark has been lit by a game by DK called Puzzle Sums – it is a set of jigsaws made up of an adding or subtracting sum on one side and = whatever on the other – only the right answers fit as a control of error. Fran learnt to use these (properly, not by just fitting the jigsaws) in 30 minutes and is now competently doing addition and subtraction using numbers 0-10. We have used our maths rods and an abacus to work on the counting involved, both of which she really enjoyed.

Lolly Sticks

This was a fantastic moment and it came up out of nowhere. We had some plain and coloured lolly sticks hanging about and out of nowhere a conversation came up about zero. I cut up some bits of paper with 0-20 written on them and asked her to count out the number of sticks for each one – she got it right, as I expected she would, including zero. The I showed her how to use a coloured one to represent 10 as our lolly stick supply was becoming limited. The breakthrough came when we got to 20 and she figured out how to use 2 coloured sticks to represent the two sets of 10 involved.

100 Square and Base 10

The photo at the top of the page shows you our most recent game. I made laminated cards of 0-100 and we have been laying them out with a number square to help, practising the names of the 10’s as well – Fran still tends to say “twenty ten” not “thirty”. Its a good fun game right now. We have a wooden base ten set and have spent some time looking at how units become tens and hundreds – its fun!

Puddle Maths 1

Below is a resume of 2002

Maths has been my greatest fear for HE because it was such a terror to me as a child. I still panic now if faced with maths to be done at speed and I find it hard to cope with “3D” maths – ie maths in the wild where I need to apply intelligent logical thought to a practical problem! I supoose I have been slightly bolstered by the fact that my husband is incredibly mathematically able and I felt initially that he would be able to help if I got stuck.

In reality, so far at least, maths has been a relearning journey for me and good fun to do with Fran. of course so far she is very young but I think its what we do now that will make the biggest difference, I am keen to make sure she enjoys maths so I carefully watch her mood and how we go about things. I think it was my anxieties about maths which made me investigate Montessori so thoroughly and I am incredibly glad I did… we use Montessori materials or methods a good bit but it has also given me the courage to make my own materials as I feel they will be useful. So far I have got it right!

Last year…

Before we had the bubba it was easier to do floor work – since she got mobile we have to pick our times. But we spent lots of time using manipulatives, both sensorial and mathematical. A big success, and one we still use were the counters and numerals. Excuse the blackout – my children always seem to do maths half clad!

Wooden Numerals and Counters bought from Opitec

Completed, it looked like this:-

We also spent lots of time using the Montessori(bought) knobless cylinders which my then two year old loved. There is so much to do with these – I really must do it!

In addition we have made Red Rods – although they tend (ahem!) to get used a bit violently so are under lock and key! Fran learned her number predominantly from an ELC number jigsaw of the peg board type (also learnt her letters this way).

Montessori Quotes

Quotes from written and spoken word of this great advocate of positive education bringing world peace. With thanks to Tula for collating and researching them.

Quotes on Peace

Averting war is the work of politicians; establishing peace is the work of education.

It is the child who makes the man, and no man exists who was not made by the child he once was.

Grown ups and children must join their forces. In order to become great, the grown up must be humble & learn from the child.

It is not the child as a physical but as a psychic being that can provide a strong impetus to the betterment of mankind.

If salvation and help are to come, it is from the child, for the child is the constructor of man and so of society. The child is endowed with an inner power which can guide us to a more enlightened future.

Not in the service of any political or social creed should the teacher work, but in the service of the complete human being, able to exercise in freedom a self-disciplined will and judgement, unperverted by prejudice and undistorted by fear.

The child passes little by little from the unconscious to the conscious, trading always in the paths of joy & love.

It is the spirit of the child that can determine the course of human progress and lead it perhaps even to a higher form of civilisation.

If help and salvation are to come, they can only come from the children, for the children are the makers of men.

We shall walk together on this path of life, for all things are part of the universe, and are connected with each other to form one whole unity.

Other Quotes

No one can be free unless he is independent.

An individual is disciplined when he is the master of himself.

It is the child who is active, and not the teacher.

To develop a language from nothing needs a different type of mentality. The child has this. His intelligence is not of the same kind as ours.

Character formation cannot be taught. It comes from experience and not from explanation.

The first duty of the educator, whether he is involved with the new-born infant or the older child, is to recognise the human personality of the young being and respect it.

The essential thing is for the task to arouse such an interest that it engages the child’s whole personality.

Inner forces affect his choice, and if someone usurps the function of this guide, the child is prevented from developing either his will or his concentration.

The training…..of the senses has the obvious advantage of enlarging the field of perception and offering an ever more solid foundation for intellectual growth.

The children must be free to express themselves and thus reveal those needs and attitudes which would otherwise remain hidden or repressed in an environment that did not permit them to act spontaneously.

The adult ought never to mould the child after himself, but should leave him alone and work always from the deepest comprehension of the child himself.

Character formation cannot be taught. It comes from experience and not from explanation.

The hands are the instruments of man’s intelligence.

The human hand allows the mind to reveal itself.

Do not erase the designs the child makes in the soft wax of his inner life.

Our goal is not so much the imparting of knowledge as the unveiling and developing of spiritual energy.

If men of the future are to be strong, they must be independent and free.

The child is much more spiritually elevated than is usually supposed. He often suffers, not from too much work, but from work that is unworthy of him.

A man is not what he is because of the teachers he has had, but because of what he has done.

Montessori Solar System

Space Links

All of this page comes directly from my very good friend, and MuddlePuddle member, Tula. She is Montessori trained and experienced and what follows is a fantastic space project she put together and would suit a range of ages. I hope you enjoy it all. Huge thanks to Tula for her time and effort and allowing me to publish it.

Maths
Counting backwards from 10 “10,9,8,7,6,5,4,3,2,1,BLAST OFF!”

Investigate Zero – Play the ‘Zero Game’….Ask the child to bring you a set number of objects, e.g. 3 cars, then ask again, e.g. 6 crayons. Eventually ask for zero objects…the child may laugh or be confused & you can play it up as much as you & the child like…the end result is that it is a ‘trick’ as zero means ‘nothing’! (Most children love this sort of joke game especially as they can play it back on you!)

Make dot to dot puzzles in the shape of simple constellations. Older children can map out the night sky, using constellations. Use of a ruler can be employed here, either for measuring or simply drawing a straight line.

Can you design a game together? Perhaps it is a race across the galaxy past all of the planets or a trip around your favourite stars…don’t forget to add little bits like ‘roll again’ and ‘miss a go’.

Discuss ‘circles’. Draw them, using plates of various sizes, compasses for older children. Examine size, in relation to others, ‘large’ ‘larger’ ‘the largest’. Older children introduce concept of diameter, circumference & radius.

Language

Way to remember the order of the planets in our Solar System: ‘My Very Easy Method Just Start Understanding Nine Planets’ with each capital letter representing ‘Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto’.

LOTS of new vocabulary to explore…not just the planet names but ‘galaxy’, ‘universe’, ‘milky way’, ‘constellation’, ‘asteroid belt’, etc,etc,etc!!

We made a book of the planets on black card with cut out pictures of the planets in order. All of the writing was in silver and gold pens, which the children loved. The effect was stunning. The younger child can perhaps write over pencil words, or dots, whilst the older ones can add more information as they discover it.

There are so many great books available; especially recommended are any by Dorling Kindersley. The local library should have a good supply of Space books suitable for all ages. (Try not to underestimate what your child will like – my son was engrossed in the complex non-fiction books long before he could read & it is amazing how much he has retained due to interest)

Science

Raid the library for great ideas, as well as the sites listed at the end. We made balloon rockets out of tissue paper, decorated with shiny stickers. Take a long balloon & inflate & tie up. Wrap tissue paper around it & stick with celotape – DO NOT ATTACH TO BALLOON! Add other features as desired, e.g. a pointy front for the rocket (technical terms of course!!), windows,etc. Then POP the balloon. Add some torn tissue streamers to the rear of the rocket. Attach a drinking straw to one side of the rocket & thread with a long length of string. (We made ours long enough to go through the kitchen, dining room & into the living room!) Inflate another long balloon but do not tie up…insert this into the rear of the ‘rocket’ and countdown…54321 BLAST OFF! The air pushes the tissue paper rocket along the string – We had loads of fun with this & measured how far we could get it to go, how many puffs it needed to get to the end, etc,etc.

Banana Rockets – you need:Bowl, bananas, chocolate, lolly sticks, sugar strands or chocolate sprinkles, a freezer. Cut the bananas in half and push the lolly sticks into the end. Put into the freezer for 2 hours. Melt some chocolate in a bowl & dip the frozen bananas in at one end & then dip into the sprinkles………YUM!

Investigate gravity with some simple experiments (can be extended for older or more able children) E.g. Which will hit the ground first? A leaf or twig? A feather or chicken bone? A 50p or a £5? A flat or crumpled piece of paper? Can you guess before you try?

Make a rope plan of the Solar System: Mercury: a knot at 2 feet, Venus:knot at 3 ¾ feet, Earth: knot at 5 ¼ feet, Mars: knot at 8 feet, Jupiter: knot at 27 ½ feet, Saturn: knot at 50 ½ feet, Uranus: knot at 101 ¼ feet, Neptune: knot at 159 feet, Pluto : knot at 210 ¼ feet. (Yes I know it is a LOT of rope but beautifully clear & simple for a child to understand) If you have enough children this rope can be held on to at one end (the Sun) whilst the others make a circle around the outside – a child holding each planet. Younger children can use balls to represent the Earth’s rotation of the Sun & the Moon’s rotation of the Earth. Be creative!!

There are so many wondrous facts to learn about the Solar System These can be made into crosswords or word puzzles (use Internet sites e.g. puzzlemaker) How many moons does Earth have? Saturn? Mars? It’s amazing to think of seeing 2 or more moons in the sky!

Art

We made junk model rockets, covered them in pva glue & tissue, painted & decorated them. Use air drying clay or play doh to make ‘Moon Footprints’ in. (The footprints made by men walking on the moon will always remain as there is no wind or weather to blow them away). We trod on the clay in our boots and trainers, leaving beautiful prints, then painted them silver when they were hard.

Make a mobile of the planets in the solar system. Cross two sticks together & suspend the planets beneath. We painted numerous rockets/ spaceships/ planets etc, etc. Sainsbury’s sell space shaped pasta. We placed it onto black card and sprayed it with silver. When the pasta was removed it left eerie space shape stencils. These shapes can also be used as collage.

Music

Twinkle Twinkle (of course!)

The Planet Song

- (sung to the tune of The Farmer’s in the Dell)
  - >”The family of the sun,
  - The family of the sun
  - There are nine planets in the family of the sun.”
  - “Mercury is hot & Mercury is small
  - Mercury has no atmosphere
  - It’s just a rocky ball.”
  - “Venus has thick clouds
  - That hide what is below
  - The air is foul the ground is hot and it rotates very slow”
  - “We love the Earth our home,
  - It’s oceans & it’s trees
  - We eat its food we breathe it’s air, so no pollution please “
  - “Mars is very red,
  - It’s also dry & cold
  - Some day man might visit Mars if he is very bold”
  - “Great Jupiter is big,
  - We’ve studied it a lot
  - We’ve found that it has 16 moons and a big red spot!”
  - “Saturn has great rings,
  - We wondered what they were
  - Now we know they’re icy rocks, which we saw as a blur.”
  - “Uranus & Neptune,
  - We don’t know much about
  - Maybe you can study them & then we’ll all find out”
  - “Pluto’s last in line
  - It’s farthest from the Sun
  - It’s small and cold and icy too, to go there wouldn’t be fun.”
  - “The family of the Sun,
  - The family of the Sun
  - There are nine planets in the family of the Sun”
  - (N.B. NOT my lyrics!!)

Listen to The Planet Suite by Gustav Holst (can be used for movement too!)

Also the theme to Space Oddity or Thunderbirds or Starwars.

Montessori Zero Lesson

Contributed by Tula, with huge thanks for all her time and effort.

Whilst a young child is exploring the concepts of number and their value, they will inevitably encounter the ‘zero’ and question what it is exactly. “What is ‘zero’?” they may ask. “Nothing,” you reply, “Nothing is zero!”
How does the Montessori Method approach this curious mathematical moment? By playing ‘The Zero Game’. (See ‘Discovery of the Child‘ Maria Montessori p.269-270)

The Zero Game

The adult asks a child to come towards her ‘zero’ times. The child unsure of his task will inevitably go to her and be puzzled.
“But I asked you to come ‘zero’ times…Zero is nothing… you must stay quite still and do nothing!” she states.
“How can I come to you ‘zero’ times?” asks the still puzzled child.
“You must not move. You must not come even once. ‘Zero’ means no times at all!”

When the child begins to understand, the adult asks him to blow ‘zero kisses’. This time the child may sit still. With humour in her voice the adult asks again, imploring the child to blow ‘zero kisses’. Still the child blows nothing.

Now the adult may play teasing games with the child; “Why are you sitting still? I asked for zero kisses!” The child laughs at the joke played upon the foolish adult: “I did! I did! Zero means nothing. I sent you no kisses!”
“Thank you”, the adult replies and smiles. “Ah, I see, zero is nothing at all!”

In my experience as a Montessori Directress, I feel it is important not to make the child feel silly or dumb. I believe it was Montessori’s intention to make herself look the fool to the child in trying to ask the child to do something irrational whilst at the same time make him come to his own realisations about the ‘nothingness’ of zero.

The Spindle Box

This concept was first developed alongside the Montessori Spindle Box, a wooden box with ten compartments. This may be a complete unit with numbers from 0-9 written on the back of the box, or divided into two separate boxes, 0-4 and 5-9. The divided box makes the presentation simpler as only the numbers 0-4 need be introduced initially. There are 45 wooden spindles with a separate basket or box to keep them in.

Note: Montessori suggested using all sorts of objects to count with at this stage, “sticks, tiny cubes, counters”. Acorns, small fir cones, pencils etc are also ideal for this purpose.

For an explanation of how to use the Spindle Box, please look at:
Shu-Chen Jenny

Montessori herself advocated not directly teaching zero in the Spindle Box. She wrote: “We wait for the child to ask, pointing at the compartment for zero: “And what should I put in there?” We then answer: “Nothing, a 0 is a nothing” (‘Discovery of the Child’ p.268)

In this way the child learns to feel the zero, this ‘nothingness’, by playing a game with the adult. It helps if other number games are familiar to the child, especially those that count back towards zero.

Suggestions for number games to explore ‘zero’

Five little speckled frogs
Sat on a speckled log
Eating some most delicious bugs (Yum! Yum!)
One fell into the pool
Where it was nice & cool
Now there are four green speckled frogs. (Glub! Glub!)
Etc., etc……

Ten fat sausages, sizzling in a pan…
One went “Pop!” and another went “Bang!”
Eight fat sausages, sizzling in a pan…..
One went “Pop!” and another went “Bang!”
Six fat sausages, sizzling in a pan…..
One went “Pop!” and another went “Bang!”
Etc., etc……..

Ten green bottles, hanging on a wall (x2)
And if one green bottle should accidentally fall……
There would be nine green bottles hanging on a wall.
Etc. etc…….

Five little ducks went out one day
Over the hills and far away.
Mother duck said “Quack, quack, quack, quack!”
But only four little ducks came back.
Etc., etc……

Ten in the bed and the little one said:
“Roll over! Roll over!”
So they all rolled over and one fell out…
There were nine in the bed and the little one said:
“Roll over! Roll over!”……
Etc., etc…….

Five currant buns in a Bakers shop
Big and round with a cherry on the top.
Along came (Alfie) with a penny one day….
He bought a currant bun and took it right away.
Four currant buns in a Bakers shop…….
Etc., etc….