The topic of “whole to parts” is pretty central to the Waldorf method of teaching – more than just on the math front, as children advance in age the whole to parts theme is evident in their study of zoology and botany as well as other places in the curriculum. When we teach using whole to parts, it is easy for the children to pick up everything around them as a whole. For instance the number 12 doesn’t stand alone, many things come together to make up 12, and 12 is also a component of many other larger parts. 12 can be 6 X 2, it can be 2 + 2 + 2 + 2 + 2 + 2, it can be 4 X 3 – in our story we are looking at 12 as part of 48. I hope you will enjoy how it comes together.
Today we are focusing on the introduction of math to a child in grade one. I like to start the introduction with Roman numerals during the tail end of the letter introduction block via the container story I wrote for the grade, and then do a combination number qualities block before I start the introduction of the four math processes. During the number qualities block I like to review the Roman numerals (through 12) and also introduce the written word, even if they are not yet reading it is good for them to see the qualities of the number. We took this time to work on shapes too and would see just how many pictures could be drawn only using triangles or squares, remember that it isn’t a geometry lesson, you are just getting them familiar with common shapes, especially ones they may see day to day. Once you feel like they have a good grasp on number qualities and they are beginning to count, then you can introduce the four math processes, it is traditional Waldorf to do it through story. While I use gnomes, if gnomes don’t do it for you then change it up, I know others have used squirrels, angels, and fairies – use what speaks to you.
Also the use of gnomes in Waldorf education can largely be traced back to Margaret Peckham, she wrote many gnomes stories and it has been said in several circles that she was the inspiration for Dorothy Harrer’s work with gnomes. Where ever the stories come from, they are all fun – make teaching math as experience you enjoy.
While traditionally the counting materials of the gnomes have been jewels, I have always felt like gnomes loved all things beautiful so our gnomes count flowers, fairies, butterflies and ladybugs just as often as they count the king’s jewels. I also have told my children a series of gnome tales through their childhood and these gnomes grew out of those stories. In our gnome world all the gnomes know each other and each gnome has a job, when all the gnomes work together our Mother Earth is happy and healthy. The Number Gnomes are part of this.
Some folks think that all gnomes live under ground, we believe differently, we believe that gnomes and fairies and other nature creatures lurk in places we often don’t expect doing good deeds and working kindness for each other. Our gnomes also have a great and wise king, he rules over other wise kings and many, many gnomes, all working together. The king’s name is Melchizedek. He is married to Mother Earth. This story though is about one of Melchizedek’s counselors, a gnome king named Equals.
King Equals is the wisest of the Number Gnomes, he takes great care to make sure the entire natural world and the world of numbers work together properly. His gnomes help the root gnomes so they are sure all the flowers have the right number of petals! King Equals has four special gnomes that help him with all the counting that must be done to keep things moving smoothly, these gnomes have special names. There is a fiery yellow gnome with beautiful golden hair, her name is Times Multiply, most people just call her Times. She is happy and fun and loves to bring happiness to others. Next to her stands a chubby little green gnome, his name is Plus Addition, folks call him Plus, he’s happy too but he’s also greedy, he loves to try and get as many things as he can, his gnome robes have many pockets. Next to him stands a sad looking gnome, he is wearing blue robes that need mending, his pockets all have holes and he is often sad, his name is Minus Subtraction, Minus for short. The last of the special helpers is a pretty little red gnome named Divided By, she has pretty dark hair and she is a great problem solver often thinking of all the ways she can be helpful. King Equals loves his gnomes – they work so hard. These counting gnomes help the gnome world stay running by mining and gathering jewels for King Equals each day. Equals requires 48 jewels per day. At the end of each day the gnomes come into his counting house and this is what they usually see…
Times skips into the treasury room with a large bulging bag full of stones, some blue sapphires, some red rubies, some diamonds, and some emeralds – she dumps her bag out on the table and begins counting for Alpha, the treasury gnome.
She lays out her piles in twos and counts: “2, 4, 6, 8, 10, 12, 14, 16! Oh my I brought home too many! I’m sure the king won’t mind.”
In waddles Plus, looking like his bag is full and his pockets are nearly touching the ground. He puts his bag on the table and with that Alpha spies his pockets – “Plus, are you leaving anything behind?” Plus stares at the floor and tries his best not to lie, Alpha doesn’t give him the chance and gives Plus a big gnome hug with a little shake and all of Plus’s pockets empty out onto the treasury floor.
Alpha counts them up: “20 jewels! Most of them are pretty green emeralds, what a great collector you are!” Plus adds “Green is my favorite color!” as he steps aside to make room for Divided By.
Divided By begins to explain to Alpha: “I had my twelve jewels, all pretty indeed, but then I came across poor Minus and he again lost everything because of the hole in his robes, so I helped him. I divided my batch in two piles and gave him some, so I fear today Alpha, I have only brought six jewels.”
Alpha gave her a hug and thanked her for all her hard work.
In came Minus and the whole room looked a little gloomier. “What’s wrong Minus?” asked Alpha. “I lost my jewels again and Divided By had to help me.”
“There is no shame in getting help! We all need help from time to time Minus. Perhaps you should visit one of the sewing elves and see what they can do for your robes; I know they’ve done wonders for a special cobbler friend of mine. Now let’s count your bag.”
“Very good, six jewels, very pretty jewels, the king will be so pleased. Today we have gathered all 48, great work Number Gnomes. We’ll see you tomorrow.”
With that the gnomes bid Alpha good bye and went to play in the meadow – they loved to count flowers. That’s tomorrow’s lesson!
For drawing from this story, we draw the gnomes and for writing you could write out their names or if your child would like, you can also write a short summary. After this introduction, I would be done for the day, then the following day you can go over counting them again from this story and also begin counting other things. Our math book “A Journey through Waldorf Math” includes many more ways to practice these new skills.