Passing from One Square to Another

After our work with the cubing part 1 and part 2, I figured it was probably time to officially present "Passing From One Square to Another" since he'd already done the allegedly harder work of "Passing From One Cube to Another" (just subsequent passings at this point - not jumping two sizes).

rebuilding the square of pythagoras from primary
YES, this comes in a LOT in elementary
in particular using the bead bars! 

First he wanted to stack the squares to make a flat pyramid.
Then he turned them a bit to make them "fancy"
(think of all the art ideas a child could do with this work alone!)

Backwards order - he passed from square of 6 to 7;
then he passed from square of 5 to 8.
Hm. Looks like the binomial cube he said.
Then quickly added: but DIFFERENT colors!
(see previous posts on cubing to get the joke)

Displaying the originals with the finals. 

When we were done, we verbalized what we had done. We also noted that pattern on each side - for example, the square of 7 IS the square of 6 plus the square of 1, but with two rectangles add of 1 taken 6 times. The square of 8 IS the square of 5 plus the square of 3 plus 2 rectangles of 5 taken 3 times.

Now let's look at the values: the square of 7 (49) is the square of 6 (36) plus the square of 1 (1) plus those two 6x1 rectangles (12). It adds up!

Repeat with the second square. It still works!



Yep. We did the work out of order - some things are entirely ok to change up! This was all strong interest-driven and the main pre-requisites were in place - that's ALL that matters! We have plenty of time to review the concepts again and again to be sure of thorough understanding. (and see my previous posts this past week on that aha! moment when a child verbalizes something his actions have shown he's known for YEARS) ;)

Yes, scope and sequences are great - they get us organized - but feel free to diverge from it! Cover pre-reqs (could be informally) - that's all that matters!

God with No Hands - Some Follow-Ups

We first did the Story of God with No Hands when Legoboy was 5 1/2. He was just very, very ready for it!

But many people wonder - what do we do after? Follow the child? But how? What materials should I have ready?

Don't REQUIRE anything. Let it sit. Let it fizzle. Let it percolate. I promise in most cases, you won't be waiting long! If at all!

• Have ready everything you have demonstrated to the children - so the children can repeat. 
• Have lots of large paper on hand if they want to copy the charts. 
• Have beautiful colored pencils or watercolors on hand. 
• Have some flexibility in your schedule so you can hit up the library on any given day. 
• Keep an open, trusting mind - and have some questions of your own you'd like to research, perhaps side by side. 
• It is probably best to just have on hand what you need for the remaining geography album pages and don't worry about much else - because honestly, NO one can tell you where your child's interests will go - even I've been surprised by own son! 

My son's original interests were in the volcano (go figure!) but he didn't get into the parts of volcanoes like most children - he wanted to know about types of volcanoes, which necessitated learning some of the parts, but in a different way from a child who wants to directly know that information - and where active volcanoes sit today - and where inactive volcanoes sit. And could one be where we live. We then got into Pompeii. And two years later, our local museum hosted the Pompeii exhibit! Oh my! It was WONDERFUL! We went twice! He had other minor questions which were not as polarizing at the time.

And we moved into the other Great Lessons, instigating a study into ancient history. We began reading through Mystery of History in our own manner - reading a "lesson" each evening, creating an index card for it, then he could select any of the suggested activities from any of the listed age groups to do during school time in the coming week. Well, 2 1/2 years later, we've not quite finished the book because this study branched into Ancient Middle East, Ancient Egypt and Ancient Greece - leading to a study (when I say study, I mean reading lots of books and watching videos and having lots of discussions) of the multiple gods of their religion, leading to an interest in astronomy because of the connections of all those names, leading into a study of clocks and time-telling through history, back into astronomy. And then back into Ancient Civilizations (only reinforced since joining the level 3 atrium a year early). He really has little to no interest in modern history. Ah yes, then he discovered there were more suggested activities in Mystery of History, so he's gone back time and again to review the past stories and add more work in.

And one wonders why I post so little about the direct use of the Montessori materials ;) because it's ALL Montessori materials - the whole world! ;) 


In the meantime, we did another re-telling of the first Great Lesson when he was just past his 6th birthday, with follow-ups that time being the states of matter - heavily into the states of matter. Repeating ALL the demonstrations

At 6 1/2 to 7 1/2, with 2 more tellings during that time, the focus shifted to the layers of the earth, mostly focusing on different types of rocks. Here, he went back to the volcano to discover types of rocks around different types of volcanoes and the use of some of those rocks. Pumice and its uses; some volcanic rocks are great for closet deodorizers - put them in your closet or a polluted area, it soaks up all the smell and pollution and gets really heavy - put it out in the sunlight and the sun's rays burn out all the pollution and you can use the rocks again and again and again. He told me, "Let's buy me a bigger pair of shoes, so I can keep a stone of this stuff in each toe!" (he has raunchy-smelling feet!). I am purposely not telling you the name of this rock so you'll go look it up yourself ;) Isn't it interesting this type of rock would be spewed forth by the very volcano that it helps to "clean up". Kind of a nice balance to nature there, eh!?



Since then, he still continues to come for re-tellings of the original story - told just the same as the first time (with glass test tubes now) - and now he ponders questions of morality: how all these particles have particular laws, obey those laws, and the human race has these choices even though made from the same particles as everything else. He also ties in elements from the later Great Lessons and his own personal research, relating the particles to the planets, or to human peoples and their various methods of migration. His follow-ups these days are not as distinctly coming from just this one lesson, because he has the grand overview, told many times in the last 3 years and he is making connections and discoveries.


Some people suggest changing the story up from time to time - while focusing on just one small section has been a positive experience, I have not once had a positive experience with changing the story at all. The children seem to thrive on hearing the SAME story told over and over and over and over - much like when they were preschoolers! And each time they can listen in for a new detail, a new enticement, a new discovery, a new learning path, all from the same old story.


In upper elementary, children explore other creation stories and make comparisons, exploring how the culture and their stories tie together - what do all of these stories reveal about the Truth and about the ways of life of the people holding to their own story. At this time, it might be feasible for a child to re-write the Great Lesson, modifying it. Or they might enjoy coming back to an old friend.

Research in Lower Elementary

RESEARCH? At age SIX!? YES!!! Research at this age is as simple as asking a question and finding resources to answer that question - then just telling us the answer (or drawing it, or writing it out - or however the child wants to express himself). I guess that is the one requirement to research in the beginning: that they come up with an answer to the original question, even if they move on to other questions.

As they get older and are comfortable with knowing that they CAN do this research and that their questions WILL be honored, then we started with simple steps towards what we adults think of as research.

There is no one right way - except to follow a plan that is totally arbitrary to the child in front of you. Take a general guideline and adapt to the child's needs ;)

The first step for my son was encouraging him to write his answers in his own words. This lays the foundational skills for avoiding potential plagiarism. As he hit spots where he just couldn't do this own words because the others words were just SO wonderful and precise, I reminded him of quote marks to show the specific words of someone, and to put the name of the author and book in parentheses after his writing. Two years later, he is now footnoting these references.

When he starting getting into longer and longer research projects, he started writing his resources used on note cards. Then he could note page numbers of interesting bits of information for future referencing.

At age 8 1/2, he has not yet done full bibliographies with all the printing information --- did you at that age? Some people are aghast that Montessori at the elementary age encourages all this research, but not all the steps that you and I had in middle school and high school (and only minimally in elementary if at all!). When he puts a few paragraphs together, he does provide a list of his resources by title and author.

Speaking of plagiarizing and expectations - a girl at one of the local schools a year older than my son was talking about a report she had to write for school when she saw my son in the atrium doing some research on an ancient civilization. She saw him listing out his sources and where he got each bit of information - very loosely done but a step in the right direction. The two children talked a bit about research and I heard her comment, "I don't bother writing down where I got what, because I just copy sentences from different books and turn it in with a list of books I used." My son replied, "If you don't put direct copying into quotes, then it's not your work and you're stealing from that author who put a lot of work in that book!" (I never said those words to him! Not like that!) "Yeah, but I tell the teacher which books I used." "But if your report has your name on it, you're lying and saying it's your work when it's not. Just put it in quotes and say who said it - or say it in your own words. You wouldn't want to be a liar or thief!" She thought about it for a bit; walked away looking kind of angry and kind of sad; went back a little while later and asked him to show her what he meant. I didn't hear all the details, but I thought, "Wow - my son is really catching on!" And he wasn't being mean about things either (he can have a bit of an attitude so I was very proud of him in that moment).

Think BABY STEPS. Develop those habits in tiny steps at a very young age, and the work will just flow when they are older without having to unlearn old habits or develop new ones.



Use resources, aim for as many real experiences as possible, within research and without. This second one can't be overstated - you may not be able to take your child to an active volcano, so you may need to bring in videos or visit exhibits of as real-life as possible, but you can certainly get your children out into the community, talking to "experts", visiting those exhibits, sharing your stories of being at various places, touching the rocks that come from various types of volcanos, finding out what those rocks can DO for us, planning a real or pretend long-distance trip somewhere (and all the skills needed for that!), and definitely helping to plan real trips (errands, etc.). These skills are just part of real life and are not specific to Montessori ;) These things all help to develop planning skills, organizational skills, survival skills (even as basic as what to do if you are lost in a public place), and other life skills that we all want our children to have.

Real experiences :)

First Great Lesson: God With No Hands

This is one of those posts I'm not quite sure where to put. Perhaps I should really do a blog over at Keys of the Universe - but I'm not sure I can do one more blog ;)

So I'll do my best to focus this on OUR home and OUR co-op ;)

Many times, I have stated that I strongly prefer the AMI albums over AMS albums and I provide several reasons, repetitively ;) It is because I feel SO strongly about them! AMI albums are keys-based, so to use the First Great Lesson, there just won't be as many demonstrations the first time around. They USED to have a WHOLE BUNCH in the initial presentation, but over the years of careful observation, several of the demonstrations have been separated out from the first Great Lesson of God with No Hands, into their own follow-up album pages. Thus a child can focus more on the main points at hand, then have plenty of review later for follow-up and emphasis on new or additional points. States of Matter, Further States of Matter, and Attraction and Gravity are three such "additional" album pages. Hence those album pages are as brief as they are!


(I say "demonstrations" here and need to adapt my albums to say the same thing - these are truly demonstrations much more so than experiments - we know the outcome and we are seeking to demonstrate a scientific principle - when the children are working to answer a question, form a hypothesis, set up a test, see it through and evaluate, now THAT is an experiment ;) ).

AMI uses art-forms instead of photography
so the children get the emphasis on *impression*
thus providing opportunities within
their research for finding real photos
 of the various principles in action.
And it encourages the children to re-create,
thus encouraging creativity.
There are a variety of stylistic versions.
Keep them simple!

In our home, we stick with that. I at first thought I would add in all the great ideas from Miss Barbara's site (since I'd been reading that long before I had elementary training, and despite being overwhelmed by it all before going into any Montessori training, I thought it was still great and easily adaptable to my own family's needs)... but after observing and working in several Montessori classes during and after the elementary training, seeing the variety of ways the story was done, and the children's reactions....

Well, I stuck with my album page. It really hits home, focuses in, incites interests, and gets personal studying going. It didn't NEED anything else. Just those SIX demonstrations: see this link for the six.

And especially being at home, with an only child, and a part-time (one half-day a week) co-op, the minimal keys-based approach with lots of review just really made sense for us, allowing me to present in short bursts, leaving lots of time for follow-up and research, opportunity for me to observe and present another focal point of interest at the appropriate time, without feeling like I had to have to just *everything* in place at once, or (potentially) overwhelm the children with too  much information. Focus - concentration - didn't I spend all of primary focusing on keys - focus - and concentration development? ;)


So at almost age 6, my son received the first Great Lesson, along with two young ladies (ages 10 and 12 at the time) - and they were hooked!

I wish I had taken photos at the time - I didn't :(


I had my large charts from training - at-home versions are good at half that very large size - 12x18 or so is perfect when feasible, but I used what I had ;)


We also had some supplies from Magic School Bus science kits - the test tubes are not the best idea for later work when you want to hold a test tube over a heat source or place it in hot water (the plastic melts), but it all worked for the first Great Lesson. I love test tubes for demonstrating layers (introduction to density) because you such a small amount and the children LOVE to repeat this work! They can use SUCH control using just small quantities and pouring into the narrow tube - or using eyedropper to transfer various liquids - lots of fun! LOTS of concentration!

We changed up some of the stuff to be melted - I did not have time to find non-lead solder (a little goes a long way when you do buy it though - so it IS a worthy investment) so I think I used a chunk of plastic; and I used an old key for the non-descript metal (broke the rules there, but again, it is what I had!). Another alternative to the solder is that plastic craft stuff that you can melt in hot water then shape into what you want - a bit of that starting to truly melt is perfect. The idea is to use different items to demonstrate the principle at hand, without getting all technical and detailed. Display, and move on with the story.

I also subbed in quinoa for the bebes or iron shot - because it was on hand ;) No other reason! You want particles that can be seen as they roll over and around each other.



When the children have a question, write it down for them so they don't forget. These questions become their research.

RESEARCH? At age SIX!? YES!!! Research at this age is as simple as asking a question and finding resources to answer that question. As they get older and are comfortable with knowing that they CAN do this research and that their questions WILL be honored, then we started with simple steps towards what we adults think of as research. (more in the next post!)


Want to know our follow-ups to the first Great Lesson, the first time around? And other times? See two posts from now ;)

Cubing - Part 3 - Just exploring

After all was said and done, he really, really, really wanted to just build with the squares and cubes. Ok, I said - but you have to graph out your creations. He agreed and off he went:

The camera batteries died after that - and my own batteries were slowing down so I didn't replace the camera batteries until the next day. When he graphed this on paper, he did it two ways - straightening up the inside pieces as he worked:

1. straight down - so just the tops of each piece. He wasn't satisfied with this because it was a 3-d work. 
2. he tilted it and drew it out on the graph paper with diagonals in some of the boxes to show both the tops and the full fronts of each piece. That is better he said, but still tricky. He colored the sides in a darker shade of each color than the tops (outlining the tops of the white walls in gray, and coloring gray for the sides). 

So what did this work entail: 

• geometry
• art
• aesthetics
• architecture
• planning
• viewpoint adjustment

Good skills going on!

Algebraic Trinomial Cube

This cube goes by several names - but the most important fact is that it is NOT the trinomial cube.

As Legoboy so recently and astutely discovered:

Poorly cropped - but
1) someone skipped getting dressed
2) I wanted to include an image
 of the squaring/cubing

"It's just like the trinomial cube!" He proclaimed when he first saw it. "But the colors are different," he side-commented to me to be sure I didn't ask him about the changing colors as I did with the tower of cubes versus pink tower.

But I still had him one-upped ;) "Hmm. Different colors, alright. I'll let you explore this while I go do something else and keep myself from interrupting you!" He just smiled and proceeded to work.

When he was done, he brought it to me, and said, "Oh Mama! The colors were VERY different! They didn't even match the lid on every layer like the trinomial! This is a CRAZY cube!" (keep in mind our trinomial cube is not in our home right now - it's over at the local school building).

I told him as soon as we get our trinomial cube back into our hands, I will show him the story of the Three Kings. Of course, just to be contrary, he says, "I already know about the Three Kings! I can skip that presentation!" (sound like some adults we know? I already know it (based solely on the title or perhaps the title and the main headings, then skip the actual content, which just MIGHT actually be nuanced different, if not entirely different... and then wonder why things aren't working right;) hehe - Yep, that describes me!)

"Oh no, my son, not THOSE three kings! These are the Cubed Kings!" That got his interest up! He's been asking for a week now. Perhaps next week we'll get to it. I like to keep up some anticipation (and I do want to review a couple of other concepts before working with the Kings.).

Yeah, we had fun with this one!

Stylized version - I know how tricky the illustrations can be!
Tricky - but NECESSARY
for each and every step!

Don't know the Kings?

Pick up a Keys of the Universe mathematics album ;)

HONEST review here - from a homeschooling mom - NOT from a Montessori trainee:
There is a free elementary math album available online, with which I usually agree as to the order and general set up of presentations, but I am thoroughly perplexed by its version of the Three Kings - (this part comes from me as a trainee: and I KNOW it! And I know what is trying to get across and what comes next.) Back to being JUST a homeschooling mom: But the instructions are confusing, the story is BLECK-boring until you realize that the *actual* story comes after the presentation in the album and is actually mildly interesting but leaves some strange questions, the whole set up begs to know what pieces to move when and as a mom I want it all together so I can SEE what is going on, and I really-really want those black pieces to be the same height as their king - it just makes sense when you see the other attendants the same height as their own king. But this album has them all laid flat.    It just does not look appealing - while mathematically correct, there is another way that makes the math more clear, leaves out the strange questions and keeps the appropriate parts of the presentation together in order. I'll stick with the Keys of the Universe version ;)
Sorry! I really do LIKE that album - I just don't "love" it and I'm very honest about things these days.

Cubing Material - Part Two - the REAL fun begins!

We had a fun morning exploring all of our "new" materials and it was too much for just one post ;)

After building the pink tower with the cubing material:

He finally asked me, "So what is this material for?" He has seen it at work in a classroom but it has been a while and he was not yet ready for it. He has been working with the early squaring and cubing and playing the decanomial games and calculating the values of pyramids and towers (with the bead cabinet material). So now we are on to something new.

I challenged him (before doing the actual album page) to construct one cube into its next cube.

Little secret - shhhh! Don't tell Montessori "purists" (of which I consider myself one, but with a different definition)... but Legoboy has not officially done the work with building from one square to the next square! Ahah! I have RUINED MY SON! Hahahaha - not really! I have followed an interest, in the moment of pure joy over discovering he already knew something about this material, helping me organize it - now is the perfect moment to introduce the concept!


Thus, the challenge:

Can you turn the cube of 3 into the cube of 4,
using ONLY the materials here????? 

Well, he tried all sorts of ways - some with relative success - some were just tedious and annoying (a wall of 1s) and he started figuring out where he could exchange squares of 1s for squares of larger numbers. He was presenting a series of problems (issues) to himself - knew I had an answer, so he continued to keep working, to 1) see if he could figure it out himself and 2) see if he could formulate the right question to get the answer he wanted (he knows I don't easily answer questions - that I am going to guide him in his thinking anyway, and he finds it "easier" to do as much himself first ;) ).

eh!? it was a first attempt to see what he could find
in patterning and sizes.... 

Replaced the cube with a series of squares
just to see what could be done.
he recognized patterns from the decanomial work! 

Not bad - and getting there. But what about all those squares?
isn't there something easier?
I modified the challenge to state, "build this cube of 3
into the cube of 4" (I'd reviewed my album page
in the meantime - yep, even I have to review ;) )

Back to the original cube.

A wall of ones - this got tedious - FAST. 

  

But he managed to get it. Then it all fell off. 

He thought, "what if I use the cube AND add squares?"

I didn't tell him - but this is VERY close to the actual
presentation - all the right components -
just in the wrong spots.
He built the squares at odd angles around the cube. 

It's kind of pretty from this angle ;)
But doesn't express the mathematical formula.
So I told him, "Ah, you are so close!
Is there one more easier way to rearrange just
THESE pieces???"

SUCCESS! And now the mathematics is displayed!

 Yes, I then presented him with the actual album page presentation.

Cubing Material

Last week we received two large boxes of our final Montessori materials order. Turns out there will be a few more things that need replacing - sigh (my own fault for not checking!), but at least we have something for everything, in some state or another ;)

Some of the items we purchased ARE replacements; some are brand new to my son; and some are materials he has worked with elsewhere and only now has a set at home.

We had an open exploration morning with the materials - FORGET the "perfect" presentation - what better presentation than to JUST EXPLORE!?

We had SO much fun!

One of the first favorites was discovered when he was helping unpack the box of squares and cubes - it is introduced in lower elementary (around age 8) and continues into upper elementary - at least according to my albums and if a child is on top of the squaring and cubing concepts. There is obviously going to be a wider range of ages for various children - us adults in training loved these ;) But I have been astounded to hear time and again that this material isn't touched even in upper elementary - on a *routine* basis; and that many elementary teachers don't even bother getting the material because it is more appropriate to adolescence  REALLY!? Tell that to my (non-genius, totally normal) 8 year old son after our experience last week --- and all the children I've shown this work to in schools at ages 7-10. They won't tell you it's for adolescence!

As the styrofoam and bubble wraps was removed from each set of squares and cubes and put into place in the box, Legoboy suddenly said - "Wait a MINUTE! I bet this makes a PINK TOWER!" and proceeded to count how many there were ("darn! number 10 is missing! but I can make the rest of the pink tower!"), and started stacking them. I gave him a quizzical look and asked, "You're going to stack those up and it's going to become pink!? Really!?"

Note the styrofoam still all over the floor.
That stuff is a PAIN -
so we ignored it and got to work ;) 

He just looked at me, all serious, and said, "No." Then he paused. Looked at the half-done tower and said, "It looks like like the cubes from the bead cabinet. Wait.  You mean the bead cabinet cubes are the same as the pink tower, too? I didn't know that!"

Aren't those just the cutest little toes!? ;) 

(this is one of those aha! moments when a child who has already been demonstrating clear understanding of a concept for literally YEARS, suddenly "gets it" - the light bulb turns on and the child can VERBALIZE it; it makes us wonder if he didn't really get it before - but he did, it was just unconscious before - and by allowing the child the JOY of discovery, it is truly his own learning!)

He wanted to build it corner-aligned -
he likes that layout so the #1 can "fall"
down the stairs of the tower!

Music Scale Construction

I want to share this post over at Montessori Station:
Montessori Station - Music: Major Scale Construction

Having found this image over at Junk Seller (doing a Google search for C Major charts), I fell in love with this as a potential Montessori activity. The children can build this!




I am going to introduce it to my son later in the month of December - as a manipulative. I'll let you all know how it goes!

Language - An Early Book

Going through some of our previous work and found this booklet in its earliest stages - on the city of Ancient Rome:

"Hello, I am (Legoboy),
I will a(ccompany) you t(hrough) Rome."
Note the lack of spelling, thus abbreviation ;)
I did edit out his name which he had beautifully
written in all lower-case cursive ;) 

Some tracings - some free drawing

He is hiding on every page in addition to his spoken blurb. 

on the left is a helmet - he says "scary!"

This was entirely free work - not directly related to any particular school work at the time. It could have been connected and if he went to school, and did it there, it would be "school" but at home we have re-define what is school and what is home ;)   So this one was personal interest work, thus I did not critique spelling, etc - instead mentally noting what needed work during our regular school time and presenting the appropriate album pages (lesson plans) for those skills in our usual fun Montessori way :) 

Impressionistic Charts - Storage

Here is how the impressionistic charts were stored at the elementary training center I attended, as well as in all of the first elementary schools I was in that I actually recall see the charts in use (some schools I subbed for a short times and the charts were not in use on those days). I have since been in schools that have different organization, from keeping them near their corresponding subject areas, to laying flat on shelves - I personally prefer the storage showed in the first two photos here.

Please note that these two images are from a Catechesis of the Good Shepherd atrium within a Montessori school - they created their song charts and typology charts the same size as the impressionistic charts from the elementary classrooms, thus they chose a similar storage system.
(note 2: the typology charts have now been replaced by the typology timelines - for more information on this aspect, please see Seeking the Plan of God.)

large boards the same size or just
slightly larger than charts - with tabs

the bottom on this one is tipped inward -
this allows the charts to lean properly
without curving; ones with straight sides
in front and back are less efficient.
Wheels on the bottom allow it to be
moved around. 

In my co-op last year, I started to make something similar to above, but time got away from me and Joann's Fabric Store was closing - I picked up several of their fabric shelving units for $5 a piece. 

I nailed 2 large boards across the front
 and removed all shelves. I added
tabbed boards after this photo was taken.
The timelines are in a small tray at the
bottom so they stay upright. 

showing the top-most shelf which held
various supplies for use with the charts
and timelines. 

Finally, here is how we are storing various timelines in the level 3 atrium, that could be modified for some of the timelines in the elementary Montessori:

See the basket to the very far right -
some of our timelines are rolled up inside of it.
Some small timelines belong in the basket on the
3rd shelf down, next to a basket of rocks to hold
down the edges of the timelines. 

UPDATED to add a better photo of that basket. 

Montessori Homeschooling - Socialization

Every homeschoolers faces the socialization question at some point or another, and usually repeatedly. And frankly, the answer lies in what definition for socialization is being used in the question.

• getting along with age-based peers in a group project
• getting along with age-based peers on the playground
• interacting with adults as co-learners
• interacting with adults as teacher-student (boss-employee)
• sitting still in a desk when told to; waiting in line when told to; ask to use the bathroom every time; other incidents related to being a very large group

Socialization is all of these - and more. Homeschoolers can gain all of those skills - it will just look different, though the skills remain the same. My son learns to wait in line at the various stores we visit, when waiting to get into the museum, when more than one of his mates/friends in various activities all need a drink at the same time --- it is natural learning, not arbitrary. 

but... 

My all-time favorite line? It was said with ALL sincerity and love. And seriousness.

You should really put Lego Boy into public school. 

Why is that, dear Grandma? Not even a private school?

A public school. Yes. So he can learn to be teased. And he needs to ride the bus. 

Ok. So we'll ignore that private schools in our area share bussing with the public school kids, who all spend anywhere from 20 minutes to 90 minutes (yes, 90 minutes!) on the bus each way.

And we'll ignore that teasing can happen anywhere, any time, any place.

And we'll ignore that not all children ride the bus anyway.

And we'll ignore that I spent 13 years in public schooling, sometimes riding the bus and sometimes walking (sometimes walking when I should have been on the bus and usually begging rides to avoid the bus!). And all the "teasing" left me was bitterness, a refined talent for nasty come-backs, a brick wall surrounding my true self, and hopelessness.

Did public school do that? Not directly. It was a much larger picture. There are fantastic public schools and private schools available; there are fantastic teachers and fantastic classrooms.

But of all the wonderful reasons to send my child to school, learning to be teased isn't anywhere near the list.

Would I send my son to school? Yes. When it meets our family's needs. He has already attended school. He attended a private Montessori school at age 3, 50 hours a week (coming from my having been a stay-at-home mom with a daycare in our home...); he attended a 3-day-a-week non-Montessori preschool (full days) at age 4; and he attended another private Montessori school for 3 months in kindergarten (I was subbing in another classroom). He spends an hour a week at the local public school. And he currently participates in a weekly middle school literature class (it's online).

This is in addition to the other daycares, camps and other educational institutions that met our needs from time to time.

And we sometimes ride the public transportation bus (or subways or other forms of public transportation). It's not the same bus experience from public school - but for those who live in the city, it's the bus that they could be riding a lot longer. Doing it every day doesn't make it a better thing. It just is.




So what about socialization?

What activities can fulfill this "socialization" without going to rows of desks in a line with the teacher gabbing on and the students sneaking notes to one another? or falling asleep? or (gasp!) doodling? Does it have to be either/or?

Yes, all of the following can be done by families who use public school as well. The point is that public school doesn't provide the be-all-end-all. And neither does homeschooling. There are options. You can't do it with public school alone, but neither can you do it sitting in a desk or at a table in your own home all day. REAL socialization happens in society. Period.



Please add your ideas below!

• martial arts: typically multi-age settings, with ranks according to skill not by arbitrary age. Children and adults of all ages have basically the same expectations to promote to the next belt, for which a test is provided when people have met the requirements and are ready - not forced ahead or held back arbitrarily. 
• cub/boy scouts: typically the smaller groups meet within their age groupings, but the  boys are able to move ahead at their own pace and there are bigger meetings with boys of multiple ages. They focus on skill and character development. 
• why not girl scouts? most troops tend to be focused on one grade level; if you have access to a multi-age group that allows for the girls to move ahead when they are ready and not too muh before/after, then great. There can be other issues present, so be on the look-out.  
• Other sports - whether personal or otherwise. As long as they don't rule your life (unless that is what you want) - that provide personal growth and team-playing. 
• just play with other kids. Nothing fancy - this is where MOST socialization happens - in the adult-left-out interactions between children - whether at recess, on the playground, playdates, just getting together with other people of all ages. The adult guides moral behavior, but the children work most things out on their own. Older children will naturally lead into group projects, short-term or long-term. 
• Goings Out: this is a Montessori concept of a "field trip" - the child helps to plan the outing, it is usually related to other things going on in the child's life or education. The children make the phone calls, map it out, interact with the other people involved, all with an adult's guidance. 
• Being out in society: interacting with the people at stores, the employees at various businesses, people on the street, just being out there - and working through the various customs of various cultures. Isn't this the society that the children will have to interact with as adults? Might as well start now! 
• All the better if you can visit as many other cultures as possible. 
• church groups can count, depending on the situation. Multi-age settings such as Catechesis of the Good Shepherd atriums, Godly Play worship centers, youth groups and the like. 
• other classes: whether for fun or for specifically academics. Face to face is best, but online classes can provide for certain socialization skills. 

What to look for: 

• multi-age - to reflect real society. My mother works with someone with whom I went to high school. They are co-workers. My first "real" job outside of summer camp programs, I had higher qualifications than the 40-60 year old women working there - and I quickly had authority over them. Yet I still needed to respect their years of experience and they respected my educational background. We learned a LOT from each other. This was not something to be gained from "school" of any sort. 
• respect for all members - my son's tae-kwon-do has 3 rules: never mis-use martial arts, never criticize, and never forget your instructor's name ("master ___ "or "sir"). If they follow those rules, they are laying a strong foundation for RESPONSIBILITY when they have a power that someone else does not; RESPECT for those in authority over them; and respect for those under you and equal to you ---- they must NEVER laugh or make fun of someone else in class or out of it. There is also a foundation of respect, period; found in all 3 rules. No name-calling, no inappropriate fighting... that sort of thing. 
• let the adult in charge BE in charge - we parents have to back off and share our authority. We will not always be there for our children despite our best intentions and desires. We need to help our children discern appropriate authority figures, so they do not naively put themselves in danger later in life. If YOU don't trust, then pull out of that activity (at an appropriate time - because we also want to teach our children commitment) - do not stay without that trust and that ability to pass the baton - it will only set up the children for confusion. 
• fit with your family's values - yes we want to expose our children to other ideas and develop discernment in them; but that doesn't mean we "throw them to the wolves" until they are ready. :) 

Command Cards - Elementary Montessori

This post started as a quick note about Geometry Command Cards, but quickly got off on other tangents as 3 ladies asked me related questions at the same time ;) Talk about coincidence! (or alignment of the moon or something!)


ORIGINAL POST: 

Fast drawing the concept on paper
From a command card for "two lines"
note the opposite direction of the stick work
showing mastery of the concept in a different layout

Just a quick post to say that I have added sample basic geometry command cards at the end of the following previous post:

Geometry Command Cards Original Post

This file includes additional pre-formatted pages to add your own additional ones; I have left it in Word so you can edit it as you like.

More advanced versions are being added to the Keys of the Universe Geometry album.





ADDING ON: 

NOT ALL CHILDREN need these command cards. Sometimes (in the case of my son) they are a great way to provide quick reviews for a slightly older homeschooled child without the benefit of having watched his peers doing the work, or helping younger ones, before moving on to more advanced work.

Sometimes a child just needs a little push into ways that he can work independently with a material.

In pure Montessori terms, the command cards should be presented only when needed to get work going, then pulled out as the children are finding ways to work independently and come up with their own ideas.

EDITING (11/27/2012) TO ADD this sentence:
*Writing* command cards is an excellent exercise for a child to develop skills in planning and organizing --- especially when there are many ideas going through his mind at once and he can't go all directions at once! So if a child hears a lesson and has 5 ideas, he can write out each of his ideas on a card - choose one to work on now, and now he has 4 ideas in back-up to pursue later that day, later that week, or just later in life.





Again - in the homeschool, I see more of a use for them from to time.

• get work going
• encourage working independently when toddlers and babies and teens or home businesses need a parent's attention
• as review for that middle aged child (8-9) to review concepts not explored recently before moving on to more advanced work. 
• As a way of monitoring work, combined with the work plan and work journal. 
• I DO NOT recommend using as your child's sole source of inspiration for work. Use them judiciously. 

How do I feel about the curriculum cards created by Albanesi?
You are about to read a completely wide open, honest and blunt response.

You have been forewarned ;)

• I think (my opinion!) they are ridiculously expensive for a homeschool (even though homeschoolers might have a greater use for them, supplementing the cards where 30-35 children are not present; but then you have to buy the materials too!? And still have the albums!? NO WAY!?)
• And entirely unnecessary in such large quantities and sets for a classroom where there IS the influence of so many other children. 
• These curriculum cards are not command cards so much as almost everything is done by the child, with very minimal work with the adult. This is NOT Montessori - this is independent learning - not really the same thing at all. And it is too "curriculum-like" to borrow my primary trainers term (for another Montessori-styled item) - it's not about following the child or meeting the child's needs of the moment. 
• Yes, there are a couple of yahoo groups that are trying to do something like these sets for homeschool purposes. They (we, actually - since I am in on those groups), continue to hit brick walls because of these conflicting notions of what they are meant to be and how they are meant to be used. So yes, I have looked into these cards extensively. And a homeschool version is likely to be created at some point in the next year or two - but it won't be like what the original project set out to do. 
• I do NOT recommend purchasing them, for home (expense) OR for school (appropriateness in the environment). If someone gifts them to you, then great - use them as you see fit. But don't spend your own money on them! 

How's that for an honest response? ;) 

Fractions in Lower Elementary

My Boys' Teacher over at What Did We Do All Day just posted about fractions and asked for some samples.

His chosen embellishments for this page
include math signs and the number 3 ;)
He mounted this paper onto colored paper
and inserted into a 3 ring folder as a portfolio.

I went to pull my son's math folder... and found in our recent un-organization of our home... the folder is pretty much missing. I did find the folder Lego Boy started in the co-op with some of that year's sample work.

















And he so graciously offered to create some samples on graph paper to show how he has written fractions on graph paper in the past. Unfortunately he did not go back to the basic-of-basics and instead did what "he" considers basic which is equivalency within operations. ;)

This is smaller graph paper than the first graph paper he used, but it hopefully still gets the idea across? There is no one right way...




But I did have an order of operations in fraction writing, not so much from any album but from what seemed to follow the child at the time:

• start him on blank paper - showing both ways in our culture for writing fractions (horizontal line and slanted line)
• then large large squared paper (each fraction in a square); 
• then larger graph paper, with a number, then line, then number, then space - each in their own squares ---- in order to align numerators, denominators, fractions bars, equal signs, etc. 
• regular graph paper, with the entire fraction written within a square - he can now write smaller AND this gets him ready for writing mixed number (whole numbers with a fractional portion). The whole number written big in the square and the fraction written within its own square. 
• He can write them out on lined paper as well, but true to Montessori, we try to stick with graph paper for math work. The graph paper helps with organization, mathematical principles, drawing out samples in geometry and multiplication  etc. --- it just FEEDS that MATHEMATICAL mind, where lined paper feeds the LANGUAGE of writing. 

Later, we will explore other cultures' ways of writing fractions. 

Also, I offer this file I created when my son was in primary. It is a printable file for the labeling and basic operations with fractions - I'd forgotten about this one and was about to share a funny looking one that worked and fit into our tacklebox we used - but is not "ideal" - I am so happy I found this one for you all!

Montessori Fractions: Labels and Simple Operations

I did start another file for sample elementary level problems; I will fix it up and have it included in the elementary albums at Keys of the Universe - if you're in that course and don't see it up soon, please do bug me about it ;) I am good-natured about those sort of things ;)

Last Elementary Montessori Order

I just placed our final Montessori materials order - and couldn't believe what a struggle it was to reach the free shipping level! We had all else we needed!

Wow.

One more year of lower elementary, 3 more years of upper elementary to come... and we have everything???

Ok, we'll still be purchasing and borrowing things along the way - items to correspond with interests, replacement chemicals and other supplies - but the Montessori-specific items are done.

Overall... elementary is no more expensive, Montessori-wise, than primary, perhaps cheaper (I'll look at actual numbers another day!) - and covers SIX years.

And the re-sale value canNOT be over-stated!

He was still sleeping in this photo,
but he reached out to me as I sat down next to him.
Those hands that were so tiny at birth.... 

This is a bittersweet day. It means a preparing for a closing of one area of life (browsing Montessori catalogs, determining what to make and what to buy and from whom), but it also means a true settling in. Settling in for the next 4 years. Settling into just BEing in elementary. Then on to adolescence.


Ok, scratch that last sentence. Just focus on this time. Right now. The moment we have - right now - together.




ETA: November 12: IT'S HERE!