UPDATED past post: Fraction Materials

I recently updated this post on superfluous Montessori materials. Mostly just tweaks.

But I added the information below about the fractions materials and thought it deserved its own post because of the strong emotional response that has been sent my way when I calmly say, "This material is unnecessary." So yes, here I am a bit more emotional ;) Because I really stand behind the Montessori principles involved.


As I state in my other post, I am not intending to offend anyone, but I know this will sound that way to some people. Please consider the Montessori principles at hand; the century that has passed with consistent observations and the development of album pages appropriate to the various stages of childhood. While not everything may be solidly set in stone, the youngest ages do have a very firm foundation. It is the adolescent age where we are still playing with the details.


Fraction sets for 1/11 through 1/20 - there is a keys-based presentation for helping the children work with fraction above 1/10. If a child is given the material for fractions 1/11 and higher, he is losing out on the opportunity to explore on an abstract level. He will always be hindered in his work because he was given "the fish" when he needed directions on "using the fishing pole".

I have had 3 moms tell me their 5 or 6 year old was SO STRONGLY into fractions and since the child was SO young, this hands-on material would be appropriate for them. NO! Can I say that loud enough!? NO!!! NO! NO! NO!
(before we go on: my son at age 4 1/2 was there too - ALL things fractions! a "fraction genius" even! I really thought I had a guru on my hands - and I was ready to feed that guru-ness wherever it took us, but something happened...)


There is a reason that fractions are in the primary album for children ages 5 and 6 - BECAUSE they have an intense interest! So we are already feeding that interest! But we are feeding that interest by providing the FOUNDATION. A STRONG foundation in the basic facts and uses of fractions.

Then if your child is truly a fractions-genius and his interest hasn't yet waned (most children's intense interest in fractions wanes for a year or two, because they 1) need to consolidate and 2) are moving on to other areas of development and 3) there is just so much else to DO) - there are a series of elementary level presentations that are worked on FIRST (and the little genius can certainly do them all in 1st grade if he wants! rather than spread them across 1st-3rd), before you even get to the need for doing 1/11 and beyond. Once you get to the presentation for 1/11 and beyond - WE DON'T STOP AT 1/20! We go to 1/100 and 1/360 and BEYOND even that! So when a child is ready - he's READY! And we don't hold him back! But we lay the foundation FIRST.

Therefore the fractions materials for 1/11 through 1/20 are superfluous at best; a hindrance and a crutch at worst. Don't bother with them!


SUMMARY:
If a child is a fraction genius and it HOLDS, then he has all the primary presentations AND all the elementary work at his fingertips, before he is presented with how to address fraction smaller than 1/10 --- and at that point, a true fraction genius, will be entirely ready for that materials that are provided, or he will be genius enough to make his own material - thus consolidating and applying the fraction concepts at hand in a much more efficacious manner than just handing him the material.

:)

It all works out in the end :)

Elementary Language Materials: A Photo Journey

You may notice some matches to the primary level - you should! Many of the materials transition over from primary to elementary but are used in different ways. 

Legoboy made a booklet of the rules.

Sentence Analysis is FUN!

Sorting all those nouns!

grammar box work - he wanted *real* items -
no miniatures this time!

Wood grammar symbols - worth buying the wood ones.
They are SO NICE!

small movable alphabets for word study, dictation,
spelling practice, and SO much more!
We have three at home: black, blue, red

Grammar boxes are worth having, but could also be
made of posterboard with cardboard strip "trim". 

Beginning definition stages for elementary
(moves into the definitions cut into strips)
Don't have these for just every topic - but a few key ones
 to develop analytical thinking skills and extend previous work. 

Impressionistic charts tend to inspire copying and research.
(do not require the copying or tracing -
let it be a true work of the child - but you can model it! 

Analysis of Dwyer Booklet - compared to AMI Primary Language Album

I am short on time, but I have several people interested in my analysis, so here are my notes. If I have a chance I will freshen these up in the near future with a bit more narrative.

Please DO ask if something doesn't make sense!



In Complete Agreement: 

0+
Developing language at home - absorbing it
speak, sing, poems, rhymes, read books
REAL language - diverse vocabulary
explore with the sound games (spoken language section of the language album - can begin when a child starts speaking, maybe even before - attune his ear to sounds)

2 1/2 +
Development of vocabulary
Primary Language album: spoken language - heavily emphasized (there are a lot of games in the spoken language section that are excellent for the children's exploration!)
Stories, poems and songs

Emphasis on key sounds - but not on early sandpaper letters! Be sure to have those sounds down pat! But also start them when the child is very young. I add that starting with an older child (4, 5, 6), it may be necessary to introduce some sandpaper letters very soon into it, so that the child "sees the point". Otherwise, the earliest introduction of the sandpaper letters is between 3 1/2 and 4, after just about the all sounds are known.

When sounds are known, quickly go into the sandpaper letters - 2-3 weeks should see them all mastered (AMI says "less than a month" so corresponds). Remember, the child KNOWS the sounds; he is just learning a graphic symbol and tracing it right now. Nothing more.


There are many references to "proper" presentations; full exercises; all the stages (of handwriting for example); children "lucky enough" to have had it all done right for him.... The booklet does not provide these details; the details are found in the language album. Some sample stages of the sound games, which seems sufficient to get the heart of the matter; other stuff too lightly touched on to be in-depth.


DIFFERENCE: 
Up until the booklets/folders, references of activities are to those found in the Primary language album. Activities are very similar, with Dwyer providing few details that are then found far in-depth in the Primary Language album.

DIFFERENCE: The primary language has a "photo album" filled with a set of phonogram card. There are no folders such as described in Dwyer's booklet. They may have been at the time this booklet was originally written. The booklets described are stage 1 of the booklets described in the primary language album. There are two more stages of booklets, which can be hand-made or suitable sets purchased.

SIMILARITY: For the dictionary of phonograms, the album page in the primary language album is "Research".
Dictation is done with the materials at hand - and is done in similar manner - the child can either handwrite or use the small movable alphabet to spell out the words.


SUMMARY OF INITIAL THOUGHTS: 
All in all, the Dwyer pamphlet seems to be summarizing and providing the framework for what was possibly AMI's specific approach at that time. In the meantime, only the minor differences noted above have made their way into AMI; these differences based on observation and needs of the children.

I feel that her approach is straight-forward, but knowing what I personally know, it leaves out a lot of details and leaves me hanging! Understandable given the format she was working with as compared to the size of the language album! I do NOT know how I would have felt about this booklet if I had found it before I had AMI training. I think I would have loved it for the framework it provides along with the bit of details to help me be looking for the right resources to fill in the pieces. I think I would have appreciated it and I do know that I would have mostly understood it better than the p/b/g scheme. But I do think it would have left me with a lot of hanging questions (like what are these activity word games!?).

I highly recommend this booklet for parents homeschooling their 0-6 year olds, but with a caveat: since it is only the structure AND the points of emphasis, it should utilized along with the AMI Primary Language album. The booklet will provide the necessary introduction and practical application, while the album will provide all the details on the materials and presentation styles.

The album can feel overwhelming and for a non-AMI-trained parent definitely could use more of a "guide". It seems that together, this booklet and the AMI primary language album fit well together to provide the homeschooling mom (or other adult) what they need to know to work with their child(ren).


(I have received some offline questions on this topic and am putting them all together in one post - it will go up on January 3rd, but please keep asking questions and I'll keep editing that post as needed so everything is in one place :) How to Use Dwyer with AMI Primary Language (linking to post ahead of time - it will be available on January 3rd). The post includes a chart with each step in Dwyer aligned with the corresponding section of the Primary Language Album.)




Click her for a link to the Montessori Trails page correlating Dwyer with AMI with Pink/Blue/Green - aligned next to each other according to stages.

Multi Base Material - Upper Elementary Mathematics

(UPDATED! For clarity and to add search results at the end)


We strive to be keys-based around here. I provide the keys and the opportunities, my son uses them to their fullest potential at the right times.

Great.

Until I won a giveaway through Alison's Montessori for a beautiful, non-essential, non-keys Power of 3 Cube. This is an *abstract* presentation in my album - it is not intended to utilize a material because at that point, the material becomes a crutch to the child. If the child needs a material at this point, the child *creates* the material himself.

So. We're using that one for sensorial exploration for now - as a puzzle - in lower elementary; then I will pull it from the available materials for upper elementary. It's a neat little "puzzle" so I'm ok with that.


But then I placed an order for our remaining Montessori materials several weeks ago. Received everything; then realized I still have a couple of small purchases to make. Oops. That company doesn't have those things anyway, so it's fine. I get my list ready and figure out how much money we'll need to save and I have it ready for the right time. Ok :)

But then I went and pulled this out of storage (given to us a while back - I'd tucked it away without thoroughly checking it beforehand). I thought it was the Non-Decimal Base Board, but I never thought to wonder what was in the BOX (non-decimal base board does not require a box).

This is the one sold at Alison's' - ours is identical, but I don't know where we got it.
It's pretty - it looks neat - but it is definitely NOT an essential material.
Why do companies sell the non-essentials and LEAVE OUT so many of the essentials? 

I am now the keys-based, flummoxed owner of TWO non-keys-based materials that I didn't know I was getting! ;)


I *thought* it was the board for Non-Decimal Bases. But it's not. And I have *nothing* in my albums for this Multi-Base material. Thus it could be a great work to do! But it is not keys-based - it is an extra. I am "ok" with that to an extent, but if I can't figure it out in under 30 seconds, with my experience and training, then is it really going to be necessary for the child?
NO.

But my son MIGHT be interested in it and it might make a FANTASTIC follow-up if that is where his interests go (no, the local educational requirements in our area will not require what this board teaches, so I can't even pull it in for that purpose!).

Wish I'd double-checked first! Because now I don't have the Non-Decimal Bases board - but that should be easy enough to just draw out on posterboard. And anyone else who needs Non-Decimal Bases Board and you've already made a chart for primary use of organizing the golden beads into their categories (that chart being another non-essential material that could be useful and even necessary in some cases - it is 4 columns, with a row at the top to designate that units, bars, squares or cubes go in a particular column)... Just use that! Fine. I'm good with that. Easy and cheap!


But what do I do with this Multi-Base material? I am flummoxed and, frankly, borderline annoyed - both at myself for not checking a long time ago and at companies for making this stuff. I am looking for an album page, a set of album pages - or someone to just tell me which company sells an album that has it - just to save me time figuring it out and making up the album page(s) myself.

Any ideas?


I have contacted 5 companies who sell it, of the 3 who have responded thus far, they have no idea either! So my next question is where did they get the instructions on how to make the material? Many of the discount places get their materials from the same place in China I am sure, but not everyone gets their stuff from there; so where did the original pattern come from?

It is very sad and very disheartening that the gray line between "essential" and "extra" (but could still be good) is so blurred, that there are sometimes "extras" that just aren't even good, but are still being called Montessori - but that is for other posts!


Downer post - sorry! It gets better tomorrow!


(UPDATE 12/29/12: All but two companies have responded back to me; I contacted 3 others who all responded. Not a one of them has any clue how to use this material, or even where the pattern actually came from. Wow.

This pdf document makes ONE reference to it:
Workshop
“How Mathematics forms the brain–Montessori and
Multi-base Material” by Ms Han Kamphuis, pedagogical
consultant at Nienhuis.

Thus it appears to be AMI, and it appears to be relatively new.

Not one AMI elementary training center has responded to my messages, to date. Not even the one I attended.)

Will update further as anything new comes up.

Dot Game Fun!

I love the dot game - I don't know what it is - all the dots maybe? Nah - it's the organization of it - the beauty of it - the essential teaching of it!

And it is the one time that markers are typically used in a Montessori class - if the dot game is kept in a glass frame or laminated and mounted - the children can use a dry erase marker and eraser and use it again and again!


Legoboy did it at school, and wanted it to do it at home (that year I alternated subbing at Montessori schools and working at home - and homeschooling - it was a crazy, but wonderful year!) --- well, I just printed it out and he filled it in. We downloaded this version from Montessori Materials - a great place for some of the printable materials.

Then I had to print more - because he just ate it up!

Here is his first one... It's so pretty! I wrote the first set of numbers and everything else was on him.

The children check off as they do a row, so they can track where they are. They connect up the dots to create a "bead-bar of ten"; then carrying over is noted in red the first several times they do it, to really reinforce the extra work that goes into carrying. But these are all concepts that are actually KNOWN - the child has been doing this work throughout use of the golden bead material - for Legoboy, it had been almost two years with the golden beads, probably a year and a half with carrying, before he actually did the dot game. 

Montessori works in baby steps - so there are only two new things here: 

1. doing the work ALL on paper, in typical addition format (on the right side) --- but connecting it back to their previous work of no more than 9 in any category! 
2. introduction of the comma. Until this time they have not really been using the comma. There are many adults (ahem, me) who try to sneak that comma in there sooner - before the child is ready (too many new things at once if it is introduced sooner!) and most of the time the adult doesn't even realize he or she is doing it! It's so instinctive! But we want the children to focus on place value, so we don't worry about the comma until around this time - this is close to the time they will also learn about millions with the wooden hierarchical material - so the next step is to be introduced to the repetition of the categories (unit, ten, hundred; unit of thousand, ten of thousand, hundred of thousand, etc.). 

This material is only used for addition although multiplication could be done on it. There is more other work for the child to do and the point here is the two points listed above. So further operations are not necessary. 

By the 3rd sheet of this work, the Dot Game turned into a balloon popping game - pop 1, pop 2, pop 3, etc. until number 10 was the biggest POP of them all! 

oh the days when it wasn't about battles and weapons.... it just balloons popping! How I miss those days ;)