Montessori Materials

SOAP-BOX ALERT! This post is about me and my reactions to current materials offered by Montessori companies. It is not about my son or his education, at least directly. It's about me and my emotions.

I will not be offended if you choose not to read this. I do not intend to offend anyone with the following words, but I feel certain that someone will think I have said something offensive.

Let me say here and NOW: each family must choose for themselves and I don't judge the "extras" that you choose. We have extras too. My soap-box has to do with the impression of Montessori in the public sphere because of these "extras".

Feel free to stop reading and join us tomorrow for our regular daily reports of Montessori elementary (or previous primary or infant/toddler) experiences.

Click the next line if you don't mind reading my soap-box ;)

Amazing Myself

Sometimes I amaze myself.

I entered a giveaway with Alison's Montessori. I won! I thought I'd won a Power of Two cube - it was a crazy time in our lives that particular week, so I didn't entirely pay attention...

I recently received my new Montessori material. It's the Power of THREE cube! It is BEAUTIFUL!

18cm cube demonstrating the power of 3
Thank you Alison's Montessori!

But see, here's the kicker: my AMI Montessori albums do not have a material for this presentation! The children should be working on some level of abstraction when they receive this presentation! I have an album page - it just doesn't require a material. (so the "amazing myself" part is that I entered to win, and WON, an item I would not have purchased to begin with - however, it is SO BEAUTIFUL! have I said that yet!?) ;)

If we provide a material for *everything* (especially at upper elementary), the children's creativity will decrease, their exploratory learning will diminish, and it will be more difficult to reach abstraction. I've just seen it happen too many times.

Our solution? We're going to use it in lower elementary as a sensorial exploration (kind of like having the binomial and trinomial cubes in primary); then I'll still give the presentation in upper elementary as-is according to my album page. And if my son or my co-op kids make the connection themselves, all the better. But since I only have my co-op kids a few times a month, the sensorial exploration will be PERFECTION for them!

As it stands, my son (just-turned-8) has already figured it out. He was putting it together blind-folded within 30 minutes of receiving it ;)

UPDATE 1/3/2016 After almost 4 years, an update is in order ;) I did end up selling this material (at cost for shipping) as we found it just wasn't necessary, it was an easy "puzzle" and nothing was really coming from it. Afterwards I saw that it is included in the Adolescent Mathematics album that does take it deeper. Ok, that is great, but honestly? The pieces are too big. the material is quite combersome. I have found a way to create this material from folded up cardstock that is not only smaller, but more enticing. Essentially, start with the Power of 2 Cube and add in the pieces you need from there. A post will be forthcoming in 2016 on this topic. ;)

Multiples in Mathematics

Lower elementary multiples example - this is typically first year in lower elementary if the child has had a decent amount of primary mathematics. It could happen in later first year if the child is brand new to Montessori altogether. 

each number is circled according to its multiples
see my son's key in the upper corner :)
who says Montessori children don't learn how to use legends?
right here it is - they just don't have an album page for it ;) 

my sample for how to highlight a particular number
again - using a key ;) 

Embellish your work!

Sample from other work I've seen
Borders around the page or around sections/problems
Separators between sections
Just to fill in some space

In Montessori we say, "DOODLE!"

Ok, so we don't say that. We DO say, "Embellish!"

We want the children to cherish their work, so we allow them the opportunity to personalize it, fulfilling the fundamental human needs towards vanitas: to embellish oneself and one's environment.

All Montessori parents and teachers reading this, raise your hand if you have NEVER been tempted to embellish the children's environment on some level or another - to the point of being TOO much?

Not ONE hand should be raised! ;)

We want the children to learn balance, so we allow embellishment from the beginning, integrating art and daily work, even when the subject matter is not necessarily art.

But isn't it all art? Math is art, language is art, music is art, history is full of art and those timelines are works of art, geometry is pure art in my mind, geography is an art --- all these things have grace, beauty, boundaries, creativity ---- ART.

So why isn't this information available online anywhere, on all those Montessori blogs and all those Montessori albums that provide samples!? I don't know! It's a bit frustrating, because it is so basic to Montessori, especially elementary Montessori. But it starts in primary with the stamp game in particular - embellishing the row between two problems.

My son's sample today. He chose to use markers
for the first time. Please note: Markers do not mix well with
colored pencils. Any work done in pencil should be
embellished with color pencils, NOT markers.
Use markers as a medium to themselves on their
own separate sheet of paper, if at all. 

My son has always done embellishment of some kind and he LOVES it. The work means something to him and he's perfecting his art skills.

 I will show you an example of one I'm not proud of because he rushed it. It was not meaningful and he even said so. We discussed the reality that if he doesn't WANT to embellish, he doesn't have to.

And we discussed the reality that markers and writing pencils and colored pencils don't mix well. The aesthetics are lost.

Therefore, all is not lost, because this experience prompted discussion on balance, necessity and art media usage.


What about work plans and work contracts? Well, these should generally not be embellished - perhaps very lightly (instead of a checkmark, a creative child could use another symbol) - now the work journal could be a place for art, if you use one for the child to document his or work! The work journal can be embellished in any way the situation allows. While it is not the place for the child to store finished work (only a place to record time spent and what was done; perhaps answer a follow-up question), many children prefer to draw their work into these journals or separate entries with fancy designs.

Playing with Language

You know when you've been doing Montessori very well in your home, specifically the grammar boxes and sentence analysis, when your child speaks in transposed sentences without even thinking about it - no hesitation. Just as natural as can be.

"Son, what are you doing right now?"

"Apple cutting core and it Mommy peeling an." With a big bright smile :)

Tessellation Patterns

While there is no specifically AMI Montessori album page for tessellations - they are just plain fun! And when presented right, with the right materials, they fit right in with Montessori.

While we do not encourage the children to create images (we want them to explore the shape, and the function of each shape - not be focused on creating boats and flowers) - elementary children do utilize them to create images. I encourage the exploration of shape and function and steer them away from creating images until it is inevitable.

Some samples of our work:

a friend's toes

exploring different kinds of flowers

what if we just use hexagons? what would happen?
note: this particular mode teaches far more
 more than creating a flower teaches a child ;) 

she was exploring pure shape; filling in gaps with other shapes,
seeing where it would lead (this is a transition stage into
creating intentional images)

Purely exploring with shapes - and look at the beautiful pattern emerging!

Long Division - Final Results

I did the writing, because he insisted on doing it with colored
pencils, which would have been too faint for our camera.
And I wanted him to focus on the step at hand: multiplication.
He has not yet embellished this page because he wants
to do more long division problems on it first. 

My son is just at the final stages of long division - writing without the beads. It is a work we started quite a while ago; he has flown through it relatively speaking, however he will continue to utilize the beads and boards for quite a while to come. (this material starts in year 1 of the elementary Montessori mathematics album - and claims to be done by age 8 - well, that's the presentations being done at age 8 - the work will continue into upper elementary --- this expensive piece of material (approximately $100 after shipping with IFit) is worth EVERY PENNY).

This is sort of bitter-sweet! My just-turned-8-year old is doing long division on paper!

Tomorrow, we will go over the basic steps of estimating the answer, then multiplying AND checking with the beads to be sure we get each step correct.

After that, the last step is using trickier numbers and estimating.

This material is beyond amazing! Once the process is mastered, the understanding just FLOWS. I recall a woman in my primary training crying when she finally understood division - and that was the same material just doing SHORT division - as an adult she was able to comprehend how the long division would work; but as a child she had been terrorized by what is now a joyful experience for her.


I strongly encourage the use of graph paper in doing mathematics. The children can embellish their work in so many ways with graph paper, plus it keeps their numbers lined up and organized. The more complicated the operation at hand for that particular child, the more you want graph paper (ie stamp game for a 5 year old is complicated; stamp game for a 8 year old maybe not so much; long division - get the graph paper!).

Nouns: Singular and Plural

My son asked me to share a sample of his singular and plural noun booklet from last year.

With the study of the grammar boxes, there are many follow-up presentations for the article/noun box (grammar box 2), the adjective box and the verb box in particular.

For nouns, we have noun number (singular and plural), noun gender, noun classification of abstract, concrete, material, collective and the 3 types of abstract nouns. Number and gender can come just before or after presenting grammar box 2 (usually after), while noun classification comes at around 7-7.5 years old or at least a few months after presenting the other noun material, giving the child time to assimilate and an opportunity to come back and review those nouns.

As my son can attest, it is not necessary to do ALL the sets in a particular album page, let's say noun number, before moving on to noun gender, the next grammar boxes, and other language studies. Just exposure is necessary - there is plenty of time for review and follow-up. He likes to do things to completion in order, but even with these, I think we moved on to noun gender before finishing up the number cards.


Without further ado, here is something my son put together of his own accord - a booklet describing the rules for singular and plural - 1 rule per page or pair of pages. The translation (since he abbreviated) is in the caption. I tried to keep his punctuation and style - just writing out the words he abbreviated.

1: for some words add -s. (for example desk becomes desks) 

2: some words add -s. the difference is that
these words end with "e."
(for example ledge - ledges.)

Other things I've seen children do: create a chart or list of the rules; just state them aloud; explore more nouns that fit within each rule (we do NOT give them every example within a particular rule); create booklets of words; create additional card material.

For our material, I broke with the rules a bit. You are supposed to have a few sets of cards, then the remaining noun number sets are in booklet form for the child to study. I found it easier on me as a work-at-home single mom to just make cards of all the material; then my son (who loves booklets) makes his own and illustrates - so the singular is on the left side of the page and the plural is on the right side, and there might be two words and pictures on the left, with the corresponding words on the right. He then extrapolates the rule and writes it on the last page. If you make booklets, you'll make them as I just described, and still invite the child to extrapolate the rule (not necessarily the first time through, but they tend to be pretty quick with these).

How was the booklet made?
Take a regular sheet of printer paper (you don't want paper too thick for this or it won't fold right).
Fold it in half, unfold and fold it in half again the other way (making 4 section on your paper).
Now take the short side and fold it into the middle line; repeat with the other short side; unfold everything.
You should now have 8 sections - if you are holding the paper vertically (as if reading a printed letter), you will have 2 columns of 4 rectangles that are horizontal (longer than they are tall).
The tricky to describe part: see that long line you folded down the middle? On either side of that line are 4 pages; you are going cut ON that line just in the middle 2 section. So if you are still holding that paper vertically, your top row will be uncut, your bottom row will be uncut, but your middle 2 rows will be separated on the crease with a vertical cut.
Now fold the paper in half ON that line that you just cut. If done right, those middle pages want to "poof" out. Let them.

Ultimately you have 4 double-thick pages kind of in the shape of an x or a cross. Just fold them along their creases (don't create any new ones) and you have a book. I find I have to flip the pages around a couple of times to find the most "comfortable" fold so that nothing is sticking out at an odd angle.

Want a longer book? Make two or three of them, and glue them front to back. My son used two for his Singular and Plural Book.

Grammar Boxes - Objects

When doing the grammar boxes with your children, you want to have objects that match all the words in the boxes, so that the children can actually *bring* those objects - this is a movement work, not a sit-still-read-and-copy work.

Got a little boy? Legos work for a lot of the pieces!

Grammar Boxes without the Boxes

There was a time before we had the grammar boxes but my son was totally ready for them. 

I have NO images for what we did, but I can describe it! 

I took the images of the grammar boxes from photos taken when I was in classrooms. 

I then diagrammed them all onto posterboard (cardboard would have been better; covered with posterboard perhaps). I then cut little strips of cardboard to glue on as "edges". 

NOTE: the compartments were intentionally made just a bit wider than the cards, but not as tall, so that cards lay at an angle against the back edge. 

The back of each compartment was covered with an appropriately colored piece of construction paper (hint: don't use construction paper - it tends to FADE - I ultimately colored over each one with colored permanent marker). 

I then proceeded as usual with the presentations, except the cards were placed mostly flat within each "compartment" (leaning against the back "edge"). 

Interesting tidbit: the original grammar boxes as imaged in the Advanced Montessori Method book also do not have tilting insides. The compartments were vertical and the card fit in them such that they lay flat against the bottom of the box. If I were to make ours from wood, with my simple scroll saw, I would make ours similar, but with the compartments narrower from front to back, so that the cards tilt against the back of the compartment. I could have made them out of cardboard that way too - but had made the poster boards already; then was gifted with the modern style wood ones. 

Grammar Boxes - Review

Just for kicks, my son and I are reviewing the earlier grammar boxes - mostly to check out the material I've recently developed, make sure there are no errors.

I figure we'll do videos of this work another time.

Even though I am *not* requiring him to bring each object for grammar box 2 (the first grammar box), he is bringing EVERYTHING! I actually told him to stop and he just really doesn't want to. He is giggling SO hard!

What a hoot!

he brought a box for the table, since we were working on the floor :)

Oh the humor of little boys!


(note: please ignore the colors of the cards - my printer is out of some colors and this is just review for my son - we're just assuring the proper words and sufficient amounts :) )

Keys of the Universe - Mother's Day Special

Ok, I have this idea worked out and I am happy to be able to offer it to everyone!

As a Mother's Day gift and preparation for the coming school year, I would like to offer anyone who has entered a Keys of the Universe giveaway on any site $15 off a new enrollment in the course, if they join before Tuesday May 15; and $10 off if they join before Saturday May 19.

8-month courses are $40/month - 16-month courses are $20/month - full-pay is $300.

All you'll need to do is go to http://keysoftheuniverse.com/elementary, create a new account; then send me a message with the e-mail used on that account, which course you want to join (8-month, 16-month, or full-pay) and the location of your giveaway entry (only one gift allowed per person ). I will send an invoice for the adjusted amount and add them to the proper course manually.
OR you can send the proper amount to jessica@keysoftheuniverse.com using Paypal, including a message with the location of your giveaway entry and which course you are joining; and I'll know to add you that way too 

Primary albums in our family

The primary albums I used for my son were my AMI primary albums in exercises of practical life, sensorial, language and mathematics. All the other subjects were interspersed into appropriate places therein (ie art was spread out, music, geography, botany, zoology - all was spread out in the appropriate subjects).

I am slowly adding these albums for sale at Keys of the World. While I found them complete in themselves, many people may like to use other albums available online for supplementing for interested children or just for another perspective.

While I am entirely sold on pure AMI for elementary, I feel there is more flexibility with the primary years. As long as the same topics are covered; a child is neither forced ahead and intentionally held back, most of the primary albums available are wonderful options. I'm just throwing my own into the mix for a good AMI balance. I will not be specifically providing online support for the primary albums, however most people reading this blog know that I am more than happy to be of service privately or at any of the online groups where we meet :)

TIP: No matter what albums you use, start with the theory album - at the appropriate level. It's the nitty-gritty and allows you to utilize ANY album in the proper manner. It's where the "real Montessori" is.


UPDATE: I have primary and elementary theory albums, as well as the elementary Biology album posted at Keys of the World. Online access and online support are available for the elementary albums at Keys of the Universe Course Access Site.

Sneak Peek - Montessori Nuggets on Grammar Boxes

There is a series of Montessori Nuggets coming up on the grammar boxes.

The one I include here is not scheduled until June 9 - but I am fielding so many questions about this material, so thought I would share it here.

UPDATE: There is one coming up on June 9 but I have changed that upcoming Montessori Nugget to provide a more detailed *suggested* outline for presenting the grammar work (the entire "Parts of Speech" section of the elementary Montessori language album).


The original post:

The child in question is not my son - he is another little boy I once knew. My own son loves to do things sequentially, so wants to do all the grammar work grouped together as much as possible - so all noun/article; then all adjective. Now, he does plateau at times and we move on, returning at the appropriate time to review previous learning and build more on the nouns and verbs. (in the between times, he chooses the work for his own follow-up, so he is reviewing in between presentations; as well as participating in my large group presentations with the co-op children).

Homeschools will have to consider the best method of ongoing review for their particular situation. Classrooms have other children working on the material, so it is reviewed by mere observation and by jogging the child's memory - "ah yes, I remember working on that! that is the "past simple tense" work" - and this keeps review going by keeping it in the forefront of their minds.



Without further ado - the (original) June 9 Montessori Nugget:


There is no ONE proper sequence for presenting the Grammar work at elementary, except perhaps to do anything that kills interest ;)

The grammar boxes with all language work should be presented before the child's 9th birthday - this does NOT mean the children need to have mastered it all. It just means the child has other things that require grammar as a strong foundation.

But what about all those exercises? 

Well, "all those exercises" really refer to the noun and the verb. The remaining parts of speech (grammar boxes) do not have so many associated activities. And those exercises are mostly the *contents of the remaining filler boxes* - therefore can only come AFTER the grammar box has been presented.

While I have personally seen many Montessori schools presenting the grammar boxes in the 1st and 2nd years of elementary and I have not personally witnessed a new introduction of the grammar boxes in the 3rd year (unless the child is altogether new to Montessori elementary) and I have never seen the grammar boxes presented as the "capstone" of all grammar work, I do see these references online in various places - in charts and diagrams on how to present what/when.

That method might work too.


This Montessori Nugget is focused on two things: Follow the Child - and Have Fun.
Grammar is a fun game - keep it that way! :)



Let's take a look at one particular child:

He received all the grammar work at primary; he moves into elementary and has quick review with those parts of speech and even begins hearing the name of the part of speech. The noun activities by themselves do not have a grammar box (it would be grammar box 1 as the boxes are labeled by compartment number) - so this child moves right on to the article, where he may have an oral introduction to the noun, some noun activities, and then immediately do Grammar Box 2 on the article (which includes the oral introduction given in primary).

Now he MAY do some of the noun activities; but he needs time for them to percolate, so he goes on to the adjective (grammar box 3) before finishing all the noun activities.

He has an oral introduction (a review of what he learned in primary); does Grammar Box 3 with the first filler box; then proceeds through some of the associated activities; alternating between more noun work and more adjective work.

In the meantime, he is exploring the other parts of speech as well - like an introduction to the verb followed by that grammar box; then more review work; then another grammar box. And suddenly he does 3 grammar boxes in the same week and he's done with "new" presentations - now he just keeps working with the previous filler boxes (not all children need all filler boxes; but they tend to be fun enough for the children to WANT to do most of them - just don't require them to copy out the phrases).

This all happens rather quickly - within a few months at the most. And well-run Montessori classrooms have at least an introduction to every grammar box with some activities long before the end of the first school year the child is in elementary Montessori. With plenty of work left for review in the 2nd year. By the 3rd year, many children might have received everything; and those who haven't (because they have been focused elsewhere in their studies or are new) will receive the remainder. There is time for percolation, and those who are ready can move into logical analysis in usually their 3rd year, sometimes starting in 2nd year and some children not until 4th year of elementary.


And again - those later grammar boxes don't have as many associated activities; and some of those few activities are best done AFTER the grammar box presentation. So things DO move rather quickly as you reach the final grammar boxes (and again, there may be more activities in nouns and verbs even after a child has done ALL the grammar boxes).


A good deal of the verb work is intended for approximately 8-10 year olds - after they've worked with ALL the grammar boxes and are simultaneously working with the sentence/logical analysis material - it means more to them now as they are evaluating those different parts of speech, trying to classify them.


The grammar boxes and associated activities lay the foundation for further work in language analysis.

Language analysis extends the work of grammar into practical use.



I hope this is not overwhelming. The point is this:

FOLLOW THE CHILD.

Follow the child's interests and abilities. The child is using interjections and conjunctions every day, why wait until age 7 or 8 to introduce them? Why turn a fun interesting game (the grammar boxes) into a tedium of a series of exercises that may or may not be beneficial at this time (and can be harmful if it kills the child love of language study)?



Have fun with it! 

Short Division and Long Division with Racks and Tubes

In primary, we give the children short division on the racks and tubes (test tube division). They use just the units board, dividing a 7-digit dividend (into the MILLIONS!) by a 1-digit divisor. This would come after their experience with the wooden hierarchical material (golden beads on steroids - it goes into the millions!).

Children CRAVE big numbers - and using big numbers gives a great deal of repetition without it being a worksheet drill.

We write the problem in a linear fashion at this level. The focus is on the sensorial experience of short division. Only one board is used (for the 1-digit divisor).

When they have completed this work, they will have done
the equivalent of 6 division problems on a worksheet.
Except that sensorially, they understand the
concept on a much deeper level.
They are actually DOING the division.

In elementary, whether they have done that work or not, they move into the racks and tubes fairly early (assuming a mostly full primary experience), using a 4-digit or 5-digit dividend and a 2-digit divisor. They then  make up their own problems with as many digits in both dividend and divisor as the material allows (7 is the max for the dividend; 4 for the divisor).

• They work with combinations of zeroes in various places. 
• They record their answers in the proper places using long division notation. 
• The slowly build up through a series of exercises to writing more steps on paper. 
• Finally they do the work on paper and only check with the beads (usually somewhere between age 8 and 10). 

Some of my son's work when he first began this work at elementary:

8,492 / 34 

He then extended into his own problems, including 3-digit divisors and just being plain silly.

3,457,486 / 9 - just to prove to himself he could do short division. I modified one of the digits to be sure there would be no remainder (a great control of error in the beginning)

8,457,486 / 6 - just to use a similar number with fewer beads - it was a bit ungainly at first

9,999,999 / 99 - his first completely on his own (he was surprised at this answer!) - he only needed reminder where to place the answer; otherwise he covered all the steps himself.

7,657,776 / 214

8,222,743 / 1,234 

This was ONE afternoon, not even the entire afternoon. How many 1st grade worksheet problems is this equivalent to? For most curricula - NONE. They don't do division in 1st grade. But for the sake of counting it up anyway, I'm still not sure - how do you quantify the number of individual division problems in 8,222,743 / 1,234 - technically, there are 4 distribution steps, but over 4 boards each time. Essentially we are looking at 12 division problems, but there is also the sensorial understanding of how it all works that just doesn't come from facing a worksheet of repetitive math problems.

My son made these numbers up himself. They mean something to HIM. And in these 4 division problems he has covered the concepts of 3 years of division work by most curricula.

And that's only exercise 1. Follow-up exercises introduce the writing out of the problem in stages.



   


HOW TO CHOOSE A DIVIDEND WITH NO REMAINDER:
You can see a lot of my own writings - helping him to find a problem that had no remainder just for the sake of focusing on a different skill at that particular moment - choose your divisor and quotient and multiply them; this provides the dividend; just don't share the quotient with the child until they've discovered it themselves - for some children this is like MAGIC! It's a fun game to play - "I have written a number on this piece of paper, I wonder if you will get the same number if you divide out this really large number, but I'm not going to show you until you've done the work - we'll see if we get the same number!" (if the child makes an error in the beginning, ah well, the numbers don't work and the magic wasn't active that day) :)

LONG DIVISION IS JOYFUL:
This work brought a lot of joy on an otherwise very rotten day. Who'd've thought that long division brings JOY!? :) This was big work, it was meaningful (he turned it into food distribution for a king whose populace were facing a drought and had to come to the king for a fair amount of food), it was long, it was challenging, but he was ready and capable. He was playing a game with numbers and finding some patterns.