Thursday, December 31, 2020

Mortensen Math Materials & The Deep Well of Time

One last post and then I'm done blogging for the year! Whew! These last few days have been a marathon.

To be honest, though, this post is a bit of a placeholder because I know I won't be able to resist coming back to it later and expanding on it.

One of my goals for professional development in January is to learn more about the Mortensen math materials, since they are the newest math material I own. I keep finding articles and videos that I want to take the time to absorb. These are all FREE resources. I hope you find them interesting... and if you find more links that should be included on this list, please share!

I know it's a plastic material (although that's a blessing in the disinfect-me time of COVID) and Waldorf uses lovely glass gems and Montessori uses lovely wood materials, but there are some real advantages to Mortensen, especially when it comes to algebra. The basic idea is that there is no must-do order of concepts... as long as the presentation is consistent among them (which it is), you can follow the children's lead and do whatever is interesting for them. A child simply needs to be able to count to 9, tell if two things are different, and identify a square and a rectangle. It's pretty fascinating stuff!

So I hope you enjoy these. Here's Geoff White's website and the site for Crewton Ramone's House of Math if you're curious to learn even more!

Reconceptualizing Fraction Multiplication and Division

Algebra Visualization Book 5
Okay, so that's the mind-bending "wait a minute, I never learned it this way" stuff!! How do you get kids there?

an awesome overview in 57 minutes and 4 seconds
my colleague, Ms. Denise, traveled all the way to Hawai'i to learn from him!

Introducing the blocks and the operations

Super Simple Subtraction
immediately introducing subtraction as adding a negative number! and easily showing how subtraction is finding the "difference" between two numbers

basic operations with bigger numbers

Simple algebra

Fraction Lessons

Moving easily from percentages to fractions to algebra... and beyond!

Of course, I will continue to add links to articles & videos as I find them. And, here are all of the videos on Crewton Ramone's Youtube channel.

The other new resource which I just purchased, and which won't arrive on my doorstep until Sunday so I'll update this then, is The Deep Well of Time: The Transformative Power of Storytelling in the Classroom by Michael Dorer.

In Montessori, just like in Waldorf, teachers are supposed to teach through stories which they learn by heart and tell to their class. This not only makes the content enlivened, because storytelling is such a personal experience, it makes it more memorable! I just had a wonderful Zoom meeting with another former Montessori teacher who has become a Waldorf teacher, and is looking for places of overlap and connection, and she shared the title of this book with me. She said it was particularly wonderful for Geometry.

Even if you're not a fan of Amazon, I suggest clicking on the link I've given below and then clicking on "Look Inside" to see the table of contents and the full list of stories included.

This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Making a Hands-On Material for the Life Cycle of a Star

This material is incredible and I'm so excited to share it with you! It was made by Ms. Denise, my colleague and co-teacher at my former school, and when she retired she donated it to our classroom. It is just beautiful, and actually very simple to make, perfect if you are homeschooling! In Waldorf, Astronomy is done in grade 6. In Montessori, this would be a follow-up work for The First Great Lesson, "How the Earth and Universe Came to Be."

Although it isn't hard to make, there are lots of pieces, so I'll photograph them carefully.

This lesson would also go really well with The Stuff of Stars by Marion Dane Bauer (which I would read beforehand) and The Photographic Card Deck of the Elements: With Big Beautiful Photographs of All 118 Elements in the Periodic Table by Theodore Gray (which I would do afterwards, looking at all of the element cards and laying them out to form the periodic table).

In Waldorf, a study of Chemistry begins in grade 7. So if you didn't do this lesson in Astronomy, I would definitely suggest it for the beginning of Chemistry and the Elements. A wonderful book of science experiments for the elements in grade 7 is The Book of Ingeniously Daring Chemistry: 24 Experiments for Young Scientists by Sean Connolly.

you will need 118 tiles to represent the elements
write the symbol for each on its tile on both sides with a sharpie

you will need colored paper or felt (but felt is better because then the circles won't slide around so much when they are stacked on top of each other)

here are her colors and the diameter of the circles

Hydrogen - yellow - cut eight 8" circles

Helium - orange - cut seven 7" circles

Carbon - purple - cut six 6" circles

Oxygen - green - cut five 5" circles

Neon - dark pink - cut four 4" circles

Magnesium - blue - cut three 3" circles

Silicon - red - cut two 2" circles

Iron - black - cut one 1" circle

the circles will be stacked on each other -- eight stacks in all -- to show the layers progressively building up at the core of the dying star

the cards are for students to read as they tell the story, either aloud when presenting to a friend or to themselves if they are doing the work alone

card #1

card #2

card #3

card #4

card #5

card #6

of course, because it's Montessori, the cards are numbered on the back so the child can read them in the correct order while doing the work

alternatively, a child familiar with the lesson can try to lay out the steps in order and then flip them over to if he/she is correct

when the child gets to card 4, with the steps in the dying star, he/she would then lay out the circles and their labels, to show the story

it's a long presentation so I would allow at least 8 feet of space

for everything to fit in the photo I had to put my supernova below which is not ideal... I just did this for the photograph and would have it all in one long row for the students... it is important that they see it is a linear progression

for card 5, which describes the dying star exploding and throwing out all the elements it has created (and many more which are created instantly from the heat and pressure of the explosion), all over outer space, the child will lay out all of the 118 tiles which show the elements, as shown below

I realize that some of the most-recently discovered elements were artificially created in the laboratory by scientists, but I would not go into that at this time... the idea here is that it is an impressionistic lesson which deeply affects the child in a hands-on and visual way, and those more abstract details can be addressed in grade 7 during a study of the atom and its parts

This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!

Fun Picture Books to Inspire a Simple SWI Lesson

SWI and Waldorf... something I am extremely passionate about!!!

SWI stands for "Structured Word Inquiry" and is a specific classroom approach for logically studying English spelling.

In all of its facets it can be used in grade 3 and up, but the foundation to it can be laid in grade 1 & 2 as we are first introducing letters and words.

Steiner's native tongue was German -- which is very phonologically based and spelling is easy -- and so there aren't many indictions about spelling instruction. But if you read what he wrote about language arts it is very clear that SWI is in perfect alignment with his method and views overall.

Some of its basic principles include the ideas that English spelling is logical and makes sense, that every word has a story, that every letter in a word has a job and is there for a reason, and that spelling in English primarily carries the MEANING of the word and is less about representing SOUNDS.

One of the things my friend Virginia, class teacher at the Portland Waldorf School who has used SWI with her students, and I are trying to figure out is how to get people confident to take that initial leap. After all, almost all of us were told all throughout our childhood that English is full of exceptions and that it is the most difficult language in the world to read and spell. It's a huge mind shift to have someone tell you that the language makes sense... so much so that it can be investigated by children simply using the scientific method! In fact, some teachers call it "Scientific Word Investigation."

So here are a few fun picture books and for each one I will give a simple SWI lesson idea. If you try one, let me know how it goes!

For the idea that every word has a story

For the idea of the word sum (every word either is a base or has a base)

    How the Grinch Stole Christmas!

    by Dr. Seuss

    "Pooh-Pooh to the Whoos!" he was grinch-ish-ly humming.

    Even though Dr. Seuss made up the word grinch-ish-ly, we all know what it means! That's because English operates on a system of morphemes (little bits that make up words) and you can add lots of different prefixes or suffixes to a base to make a new word. It is kind of like a set of Legos. We understand morphemes very early on, which is why children who are just learning to talk say things like "runned." In fact, keeping a list of the cute incorrect things that children say gives you a great start to a lesson on morphemes.

    In SWI, we show the base with its affixes by writing a word sum.

    grinch + ish + ly

For the idea of a matrix (putting your word sums into Mini Matrix-Maker)

    Builders & Breakers

    by Steve Light

    This is a perfect book for practicing word sums! Then you can put all of the word sums built on the same base (which we call morphological relatives) into the FREE website Mini Matrix-Maker. To make it work, remember to capitalize the part of the word sum which is the base... and hit Update. It will create a wonderful visual which we call the matrix. These are especially helpful for dyslexic children.

    (In the case of < breakthrough >, which is a compound word made up of two bases, I will capitalize both to have the matrix reflect this.)

    Here are a few word sums from the story, but there are more!

    build + er
    build + er + s
    build + ing

    break + er
    break + er + s
    break + ing
    break + through

For exploring compound words

For the idea of affixes that do and do not work

    Is there a limit to the number of affixes that can be attached to a base? No, but they must make sense. It's so fun to play with this.


    by David Macaulay

    Is unbuilding a word?

    The World Is Not a Rectangle: A Portrait of Architect Zaha Hadid

    by Jeanette Winter

    What about unbuildable?

    What about build-ish? Or re-unbuilding? Where is the limit?

    The Quicksand Book

    by Tomie dePaola

    For the experiment in the back, is "quicksand" a verb?
    Can you "quicksand" regular sand, "unquicksand" it, "requicksand" it, and "reunquicksand" it?

For introducing the game In the Family / Not in the Family

    The Unbeatable Bread

    by Lyn Littlefield Hoopes

    I learned this game from Rebecca Loveless and Fiona Hamilton, who both share excellent introductory SWI lessons. They use them in Early Childhood but in Waldorf education this would be suitable for grade 2. I have a little fabric pouch that I use as a word bag.

    Having a hula hoop on hand is also fabulous, but you can also just lay out a piece of string in a circle. Introduce the base and then pull out the cards from the bag one at a time. You can do this whole group or give the children a set of cards and have them work in small groups or individually.

    If the word is in the family (meaning if you did a word sum it would be built on the base in question), it goes in the hula hoop. If the word is not in the family, it goes outside. If you are not sure, place it on the rim of the hula hoop.

    I happen to love this story, but any story about a baker would work. Words that are built on the base < bake > include baker, bakery, baking, and baked. Each of these words would go on an index card and go in the bag. You should also put some cards in the bag with words that are not in the family. These are words that are NOT built on the base; relatives must share both a meaning conneciton and a spelling connection. Some foils might be cake, bread, and oven.

    Cake is an especially good one to use. Sometimes children are presented with lists of rhyming words as they are learning how to read, and these make them feel capable in their decoding skills. But these rhyming words are NOT a word family. Words are not morphological relatives unless they are built on the same base!

For introducing letters as markers

    It is natural, as children begin to understand that every letter in a word is there for a reason, for them to wonder about the job of some letters. Some letters may do more than one job, so there's a lot to explore here. However, here is one of my favorites that is super-easy to teach, and it is one of the many jobs of the single final nonsyllabic e (that's the official name for the "silent e").

    The Little Mouse, the Red Ripe Strawberry, and the Big Hungry Bear

    by Don and Audrey Wood

    Why is there an < e > at the end of < mouse >?

    It is there because a final < s > in English words is used to signify a plural, like cats or needles. Without that final e, the word would be


    which would look like the plural of mou.

    So, this single final nonsyllabic e is a "plural-cancelling e."


For introducing the language of "represents" instead of "says"

    One important way that we can refine our speaking about spelling with children is to start to use the word "represents" intead of "says." For example, you could say in THIS word < b > represents / b /.

    The angle brackets show spelling and the slashes show sound. Yes, the letter < b > is often a match with / b / but not always, and so we don't want to give children wrong information... especially when we will have to go back and unteach it later when we teach them how to read the word < doubt >. The < b > in doubt is there for a really good reason (which is to show that it is related to double and carries a sense of two) but it is NOT doing the job of representing / b /.

    After all, if you say < p > says / p /, what are you doing to say to children when they try to sound out < pterodactyl >?

    P Is for Pterodactyl: The Worst Alphabet Book Ever

    by Raj Haldar and Chris Carpenter

    Instead of seeing English as having a bunch of not-very satisfactory rules (like, when two vowels go walking the first one does the talking, which isn't true in mouse, for example, and neither does the e in mouse make any letter say its name) and a ton of nasty exceptions, let's see it as a really interesting language worth exploring!

    And one of the ways to make it interesting instead of infuriating is to introduce it correctly. Saying, in THIS word < sh > represents / sh / leaves room for children to discover that the sound / sh / is represented by < t > in lotion, < c > in ocean, < ch > in machine, and < s > in sugar.

For introducing the fact that you don't need to know it all

    It is my firm belief that people don't start SWI because they now feel not very informed about their own native tongue, and are uncomfortable to teach children something before they themselves reach expert status. However, we can't very well talk about teaching children the value of grit and grappling and being life-long learners if we aren't going to also model it for them. SWI is the perfect opportunity! It's okay that you didn't learn the English spelling system this way. SWI was only developed within the past few years. None of us did (except our lucky students).

    So I think it's important to just start with it. You will still teach grapheme-phoneme correspondences, you just will always place that within its correct context, which is that spelling in English primarily carries the MEANING of the word and is less about representing SOUNDS. Thus the < b > in < doubt >.

    Believe me, I have plenty of SWI questions of my own still. I also have a-ha moments all the time, almost daily! You can be an excellent reader and speller and still discover amazing things about our language. When reading the Grinch book this Christmas and thinking about grinch + ish + ly, I suddenly realized that the word sum for selfish is self + ish! And when we studied Astronomy I had a student tape up little notes by the moons of Mars, Phobos and Deimos (who are named for the horses which drew the chariot of that mythological god), so that we would remember which one was which. Until I connected Phobos with < phobia >... of course! Fear!

    Here is a great book for a word family that I'm still wondering about:

    The Brave Little Parrot

    by Rafe Martin

    This is a wonderful Jataka tale and would be perfect for grade 2. And there are many words in the family of < fire >, which children could brainstorm. But one of the words I wonder about putting in a word sum and a matrix is < fiery >. Its spelling is unusual and comes from the days of Old English, when < fire > was once spelled < fyr >. Would I put it in the hula hoop for < fire > or is it outside the hula hoop but still a relative? This can happen, and it's the other kind of relative, an etymological relative. These are words which no longer share a modern day spelling pattern but share a historical root word from Greek, Latin, Sanscrit, Old English, etc.

    So, for < fiery >, I would put it on the hula hoop, straddling the inside space and the outside space, and I would leave it there. It's the thinking that matters... just like in any experiment where we are teaching the children to think like scientists. Fyr ---> fier ---> fier + y? A draft word sum is exactly like a hyopothesis in science! And I don't know what to do with it and that's okay. Pete Bowers says that it is okay to say to children "this is my current understanding" and to go back to them later and say "I have a deeper understanding now."

    The important thing is NOT to guess! I ran into this when I taught the 4th grade Man and Animal block and expected the dent in < rodent > to mean teeth. Nope! The word sum for rodent is NOT ro + dent. Here's my blog post about it: The Many Surprises in Our Exploration of < Rodent >.

For exploring the Online Etymology Dictionary,

    Hildegard of Bingen

    by Jonah Winter

    true or false:
    the word < shine > is related to the word < cheetah > ?

    If you would like to play around with Doug Harper's wonderful free online etymology dictionary, and explore some words, here is a long blog post I made up of possible SWI investigations in the Saints block, including the one listed above and many others. Enjoy!

There are many resources on SWI as it continues to spread around the world, shared by enthusiastic teachers. And I know that my penchant for making looooong lists of links isn't always helpful! So I will refrain and simply say that, if you were going to just click on one follow-up link, I highly recommend Fiona Hamilton's wonderful website wordtorque, blog, and online courses. She is fantastic and very accessible for people who are new!

In the coming year I will be working on expanding my number of online course offerings for Waldorf main lesson block planning. I already have one on the Capital Letters block in grade 1, so if you are curious about how SWI influences the introduction of the letters please join our conversation there!

This post contains affiliate links to materials I truly use for homeschooling. Qualifying purchases provide me with revenue. Thank you for your support!