Waldorf Math Gnomes
updated March 16, 2022
Recorded here is my own personal collection of articles, resources, favorite links, teaching ideas, and lesson plans. It encompasses many years, from the very beginning of my experience studying and learning about Waldorf to the present time. People from all around the world visit my site and recommend it to others. Welcome!
This site records my journey. I hope my honesty is encouraging and helps break down some barriers that may prevent people from trying Waldorf methods. Because this is an ongoing site documenting my curriculum planning and ideas, some materials are more Waldorf-y than others. Please feel free to take what you like and leave the rest.
This page has helpful links and LOADS of free resources to help you plan your first grade year. Enjoy!
Mission Statement - Consulting Services - Lending Library
The Math Gnomes
for Class 1
5-DAY ONLINE COURSE:
Waldorf Main Lesson Block Planning: Math Gnomes
Join a community of fellow homeschoolers planning this exact same main lesson block for plenty of help and support.
This course is aimed at homeschoolers who are already familiar with the Waldorf method, but
would appreciate extra feedback and encouragement in planning this block.
Make friends and ask specfic questions of
an experienced Waldorf homeschool teacher and consultant as you work through this inspiring, do-able, step by step course.
Making a Set of Waldorf Math Gnomes: Why & How
my detailed blog post
I do like Jamie York's work, and he has written a book for Elementary School Math, yet my favorite
resource for understanding the Four Processes block remains the excellent
Putting the Heart Back into Teaching: A Manual for Junior Primary Teachers by Stanford Maher and Yvonne Bleach.
Unfortunately the Maher and Bleach book is out of print and used copies are very expensive!
Making Math Meaningful: A Source Book for Teaching Math in Grades One Through Five
(a fairly good option)
Putting the Heart Back into Teaching: A Manual for Junior Primary Teachers
(the VERY BEST choice)
I found, out of all the enchanting Waldorf curriculum ideas I read about, that the hardest one for me to get concrete information on was the Math Gnome Stories.
It sounded so dreamy in the abstract, but it was confusing when I went to actually teach it. And, of course, I wanted to do it the right way!
WHO are the gnomes? What are their names? What color are they? Do the colors matter?
HOW are they introduced? What verses do you use? What stories?
AND THEN WHAT? What happens after the gnomes are introduced?
What kinds of math problems follow the introductions? What about manipulatives? Do you actually have to buy glass gems?
HOW exactly do these math gnome stories go? How do you write them successfully?
HOW do these characters interact? Are they paired up in the same math problem, one helping
where another has made a mistake? Does Plus bring too much and then Minus gives some away so that the gnome king gets the right amount in the end?
Is there always a story to go with every math problem you give your child?
And what about the main lesson book? What goes in it? How can you possibly fill up an entire big main lesson book with just four little gnomes and their king?
Even after the MLB is done and the block is done, do you still continue to do Math Gnome stories? Or just go back to the mental math and clapping and skip counting games in circle time?
And what about the squirrels? Don't some people do squirrels instead of gnomes? Do you make little squirrel finger puppets with the math symbols embroidered on them? Use piles of acorns?
Let me offer a few excerpts from the Maher & Bleach book that may help...
Understanding Children's Temperaments
The first thing to understand is that the four gnomes i.e. the four processes are aligned with the four temperaments.
This is crucial. I cannot stress this enough!
When you are ready
to introduce the characters and you need to be able to make your stories dramatic and lively (and for your children to be able to grab a silk
and act out a gnome's personality), you first need to understand the four temperaments thoroughly. This is also useful in Form Drawing, when
you have to choose specific forms aligned to your child's temperament.
I disagree with the notion of choosing squirrels to represent the math gnomes because squirrels by their nature are always sanguine. It is
difficult to imagine a melancholic squirrel (not to mention the problems inherent in dressing a squirrel in a tunic with holes in the pockets)
or a phlegmatic one. Therefore I think math gnomes or, as Maher & Bleach envision it, any set of advisors to a king.
Imagine that you have the four elements found in nature in your classroom -- fire, air, water and earth. Would it be exciting and helpful, or
just pandemonium? It might depend on whether each element was properly controlled. Fire in a fireplace is fine; fire in dry bush country is a disaster.
Water running freshly over a waterfall is a pleasure; water lying in a stagnant unmoving pool is not. It may surprise you to know that you
have both these possibilities -- and others -- in your classroom.
Every teacher has four basic types of child in her class: a Fire-Child, an Air-Child, a Water-Child and an Earth-Child -- as well as certain
mixtures of the four. The ancient Greeks knew them as the four temperaments -- they called them the choleric (fire), sanguine (air),
phlegmatic (water) and melancholic (earth). They believed they were related to the "four humours" in the body: blood, phlegm and two
kinds of bile. They thus recognised that a person's temperament is ingrained into the physical constitution and cannot be changed.
Rudolf Steiner brought a modern understanding of the temperaments which has proved very helpful to teachers, parents and therapists. On one occasion he
characterised them somewhat in this way:
Four children are walking, one after the other at some distance, along a path on their way to school. The first child finds her way blocked
by a pile of stones, sticks and bushes which make it difficult to go either through it or around it. This first child to arrive is tall and thin with
a sad face, lacklustre eyes and a drooping (one might even say tragic) mouth. She looks at the obstacle, her body sags and her eyes fill with tears.
Throwing out her arms she addresses the world: "Why does this always happen to me?" (Recognise her?)
The second child joins her suddenly. She is of normal build, slender, with a well-formed body. She has a distracted air and arrives
skipping merrily along the path.
"What's the matter?" she asks, hardly waiting for an answer.
The sad child points helplessly at the pile of rubble.
"Oh, is that all? Why don't you just jump over it?" And she proceeds to skip over the lowest part of the obstacle, tearing her skirt. She does
not notice that she has dropped her bag of school books and will arrive there without them.
The third child to arrive is a boy. He is well-built in a rounded way, even plump. His eyes are quiet and calm and he appears not to notice
the birds flying in front of him. He arrives at the obstacle and stands there looking at it. He wonders who will do something about
it so he can get to school. And he is prepared to wait quite a long time for someone to come.
Someone does come. The fourth child is a short, stocky boy with lots of energy who walks as if pressing his heels into the ground
at each step. He has a strong build and his short neck is pressed down into big shoulders. His eyes stare straight ahead of him, almost in a glare,
as if challenging anyone to get in his way.
"What's this?" he says irritably, looking at the pile of sticks and stones. He rushes at it and starts kicking. Soon the pile of branches
is strewn over the path and there is no longer an obstacle. He stalks on his way, feeling somehow satisfied and less irritable.
The third child, who has been watching, stand looking at the mess, then, realising that he doesn't have a problem any more, slowly
ambles on his way to school, munching a sandwich he had intended to keep for lunch.
This little story demonstrates the difference between the four types of children. The sad child is the melancholic or Earth-Child. (The names of the four temperaments --
phlegmatic, melancholic, sanguine and choleric -- are never mentioned to the children, and they are not discussed with them ; the pupils
should not feel they are being labeled or categorised.) She feels life to be a burden right down to the weight of her physical body, and there
is always a kind of inner despair in her. She believes that she alone suffers under the blows of fate.
What a difference the second child, the sanguine Air-Child presents. Life has no cares for her. She simply side-steps unpleasantness whenever
possible and skips on her way. The next bend in the road will always be better, and so will a new friend.
The third child is the phlegmatic, or Water-Child. Life flows steadily along like a river, or can sit like a stagnant pond for
this type of child. He does not like to make an effort and is perhaps the hardest kind of child to teach in a normal classroom. Often he may
appear lazy, but it is because of his temperament, which just cannot get along without a push.
The fourth child is the choleric or Fire-Child. An inner strength fills him with energy and initiative. He will
take risks, fight and push his way through all obstacles. A classroom in which there is no movement, drama or adventure will bore him, or turn
him into a rebel without his meaning to. All he wants in a challenge worth of his powers. He is a natural leader and the teacher who has him on her
side will have far fewer classroom behaviour problems....
Introducing the Four Processes
by Yvonne Bleach
We introduce the four processes in arithmetic in story-form, so that the children form an immediate and joyful connection with what they have to learn.
Furthermore, we introduce all four processes together, at the same time, in one story. In this way we give them an understanding of the whole: the processes
in their four different types. Working from the whole, and then later in more detail in the parts is very healthy for the children, because
they experience the unity, the completeness first, rather than working in disconnected fragments. This way of working also brings economy into teaching, saving
time and energy in learning.
Each of the four processes has a different character, and therefore the story will contain four very different personalities for the operations,
in accordance with the four temperaments (four basic types of human personalities). The names of the four temperaments -- phlegmatic, melancholic, sanguine and
choleric -- are never mentioned to the children in the same way as one would never discuss paranoia, insecurity or other such
psychological terminology with a young child. Later too, one could never directly 'accuse' a child of, say, being melancholic.
Here follows an example of an introductory story.
The Four Processes
DAY ONE: STORY
Meanwhile, in the kingdom of Numberland, on the earth above the caves (see story about the gnomes and jewels under Numberland in Chapter 6), the king was
trying to put some order into his treasure house. He had too many jewels for the shelves and so there were piles of jewels and bags and boxes all over the floor. His storerooms,
were full to the brim with grain and fruit and vegetables. (Add more detail). All the farmers in the kingdom brought him supplies, but most
of the food came from a very large farm owned by FARMER PLUS.
Now it was not only Farmer Plus's farm that was large, but he was as well. He was tall and very wide, and he wore an enormous pair of
green trousers, no shirt because of the heat, but a long green tie and a broad green belt.
(Give a description of Farmer Plus: He ambled, he puffed on his pipe, he chomped a piece of biltong... describe his comfortable, cosy house, all
the good food he enjoyed eating, etc. Talk about his farm, his workers gathering the fruit, grain, etc. You could even add his livestock. Note that all this,
his comfortable attitude to life, his interest in food and cosiness, all adds up to the fact that Farm Plus's temperament is phlegmatic.)
He went from worker to worker adding the baskets etc.
9 = 6 PLUS 3 (from the whole to the part)
activity: 6 PLUS 3 = 9. have the counters etc. available and do the activity - no writing - but many
possibilities and examples (problem solving)
Ask the children to recap Farmer Plus story and continue with "ADDING" activities (problem solving). The teacher could draw a picture
of Farmer Plus and his farm on the boar.d Start verse:
"I'm Farmer Plus and I can add
Big and small and good, not bad
Applus plus carrots and pumpkins I'll bring
To the store of our Numberland King."
Act out the Farmer Plus story (use verse). They can take turns at being Farmer Plus. Then they can draw the picture of Farmer Plus (by
copying from the board or by drawing their own version) and copy some sums from the board. Remember to make the plus sign green, the colour that
fits the phlegmatic temperament.
DAY 4: STORY
... Now the king was very worried about his bulging stores. Whenever he went for a walk in his kingdom
he saw people who were hungry and poor and he said to himself: "I must give
my people more food and riches, but how do I do it?" So he called a meeting of his council and told them his problem. One of the
councillors said, "I have a friend who lives in the next village. His name is MR MINUS and he loves to give things away." So the king
told him to summon his friend. The next day while the king was standing on his balcony, he saw a very tall, thin man walking slowly
towards the palace.
The king went out to greet him and what a sight he saw. Mr. Minus was the saddest looking fellow, tall and lean and dressed all in blue
with a dark blue belt at his waist. He looked as if he was continually looking for something he had lost or given away. (Mr. Minus's temperament
"I'm Mr. Minus, I give away
I minus everything each long day
All the jewels the gnomes have brought
I'll give them away till we're left with naught."
The king showed him to his stores and he started to give everything away.
(Description of what he gave away e.g. 10 pumpkins: gave away 4, had 6 left. Just gave anything away to anybody.
"Giving away" is far more morally meaningful to the children than "taking away.")
activity: 10 - 6 = 4 with counters and other problem solving from the story
Recap the Minus story experience. Continue with subtracting activities. No writing yet. The teacher draws a picture of Mr. Minus
giving away the King's stores. Say Mr. Minus verse.
Act out Mr. Minus. Take turns. Then draw the picture and copy sums from the board. Remember to make the minus sign blue.
DAY 7: STORY
... Now you can imagine what happened. Some of the people were very upset because they only received carrots while their neighbors
had jewels. So they sent for the king to sort it out and he promised that the next time it would be done fairly. The king was however
a bit disgruntled, because all he had had for breakfast was a potato and a turnip. Mr. Minus had given everything away. So after he had called on Farmer
Plus and had taken what few supplies were left, he realised he had to do something quickly to make his stores "more." So he called a meeting
of his council and told them his problem. One of the councillors said, "I have a friend who lives in another village. His name
is TOMMY TIMES and he knows how to make things 'more.' " So the king told him to summon his friend. Early the next morning
the king was woken up by singing, etc.
(Description of Tommy Times: He is dressed in yellow, with orange cross-over bands -- the multiplication symbol -- has a bell on his hat,
is a chatterbox, does back flips and turns cartwheels (multiplication symbol again). His temperament is very sanguine.
"I'm Tommy Times, I make everything more
And I can do cartwheels across the floor
I multiply this and I multiply that
I'm always happy so I'll jingle my hat."
So he took the king to Farmer Plus and he showed him how to multiply everything. "You only have 3 rows of carrots
and you need at least 12. So 12 = 4 x 3, etc.
Then he went to the gnomes and he showed them how to use a cart to multiply the amount
they could carry to the surface. (The cart wheels have crossed spokes, once again representing the multiplication
symbol). He showed them how to put everything into rows to make it easier and quicker to count: 5 x 4 = 20
activities: to follow with counters (problem solving)
Recap Tommy Times. Multiplying activities. Teacher to draw picture of Tommy Times on the board. All say verse.
(As for Days 3 and 6.) Act out Tommy Times. Draw the picture, etc. Remember to make the times sign yellow or orange.
DAY 10: STORY
... Now everything went very well in Numberland for a while, but soon the King's stores and treasury started to bulge again. "O dear... O dear...
what do I do? I can't ask Mr. Minus to give it all away because I'll have a riot on my hands..." So, he called
a meeting of his council and told them his problem. One of the councillors said, "I have a friend who lives over the hill. His name
is MR DIVIDE. He is very good at organising others and sorting out problems but he is very quick tempered. I will go and fetch him." The next day
Mr. Divide arrived.
(Description of Mr. Divide: Angry, short, dressed in red and dark red belt and two enormous red buttons, one for his shirt and one for his pants. In a hurry,
"I'll take charge..." His temperament is choleric.)
"I'm Mr. Divide, I'm always fair
I make sure all have an equal share
I divide up everything that I see
Equal shares for you and you and me!"
Once he saw that there was a task to be done, though, he became quite friendly and settled down to work. He divided everything
equally, and gave it to Mr. Minus to take to the people of Numberland. What was left he gave to the king and even kept a little
activity: Here are 20 tomatoes and there are 4 houses. 20 divided by 4 = 5. So we'll take 5 to each house. Continue with dividing
Recap Mr. Divide. Do more problem-solving activities. Verse. Teacher draws a picture of Mr. Divide on the board.
Act out Mr. Divide. Draw the picture and copy sums from the boar. Remember to make the division sign red.
Now the children have an imaginative picture of the four processes. They may not yet be able to calculate
freely but with group work and problem solving activities they do have a foundation on which to build. One story can
take them a long way, especially if that story is taken into the dramatic. A few simple costumes would further
enhance the picture, e.g. a green belt, tie and hat for Farmer Plus; a blue belt, blue cap and cloak for Mr. Minus; etc.
Bunches of carrots, potatoes, stones painted gold, semi-precious stones all add to the dramatic. Remedial pupils
and slow learners need the
concrete - later when they use counters they will relate to those earlier realistic or creative counters and to the images presented in the story.
I think that sewing a set of four gnomes and a king out of
and embroidering their symbols on their tunics, is well worth the time.
You could also needle felt your gnomes and king. I think that a large bag of glass flattened marbles is a good thing to buy. We also
have a sterling silver platter which adds a lot to the experience of getting out and putting away the gems. Lastly, I highly recommend
getting five play silks in the colors green, blue, yellow, red, and purple (for the king). If you want one final touch for acting
out the stories, making a felt crown for the king would be nice.
In our mixed age homeschool co-op even the middle schoolers could not wait to jump up and help act out the characters, and were excited and interested at the end of each day to know
what operation was the next to be introduced!
wool felt from Magic Cabin
glass gems from Amazon
play silks from Etsy: Beneath the Rowan Tree
For the question of making a main lesson book for this block, we chose to do little "books in a box." These
books are made using a small box. Measure a strip of paper which is the width of the box but 12 times the length of the box.
Fold the strip of paper accordion style. Do NOT glue it in the box until you have finished writing on it! See pictures of the finished books at my blog.
The 12 folds in your little accordion will be the pages of your box. Each set of two will have a topic. Ours were as follows:
first pair: title of the book "Math Gnomes", child's name and age and the school year
second pair: Plus symbol, a drawing of the gnome and his plethora of gems, a little verse about him or sentence summarizing his character
third pair: Minus symbol, a drawing of the gnome with his empty pockets, a little verse about him or sentence summarizing his character
fourth pair: Times symbol, a drawing of the gnome turning somersaults, a little verse about him or sentence summarizing his character
fifth pair: Divide symbol, a drawing of the gnome, a little verse about him or sentence summarizing his character
sixth pair: the gnome king surrounded by piles of gems and his four little gnomes
When you are done, glue the back of the first square in your accordion into the inside front of your box and the last square in
your accordion into the inside back of your box. When you open the lid of the box, your book pages will be revealed!
This is fun and it also makes a little MLB which is the perfect size for this block!
We also glued a piece of blue paper (blue is our color for Math MLBs) to the front cover of the box and decorated
it with the title "Math Gnomes" as well as some decorative gems from a craft kit.
I noticed in drawing these symbols how related the two symbols are which result in more (plus, times) and how related the two symbols
are which result in less (minus, divide). It is lovely that plus is bringing two things together (take your pointer fingers from each
hand and bring them together to make a plus sign) and the times is the somersaulting speedy skip-counting version of plus. We delighted in acting out
Tommy Times with his cheerful attitude, leaping and singing all around the classroom. And we know from our skip-counting work that
it is so true that it speeds up the work and you are cheerfully hopping from number to number. It is also wonderful to see that
the minus sign give you less but the divide sign (the horizontal bar with one dot above and one dot below) specifies right there
in the symbol that you have less BUT you have shared the amount completely fairly between the parties. What could be a better sign
to signify sharing out fairly?
Only in acting out, drawing, writing, and creating these stories and getting to know these characters so intimately do you really KNOW
the operations. It is just like the Quality of Numbers. In doing these stories this way, you get to know the Quality of the Operations.
Math Gnome Stories & Photos from my classroom.
Check out my Math Gnomes page on Pinterest for more pictures, verses, and helpful suggestions.