## Thursday, January 31, 2013

In addition to the dot game, Kal-El also began using the small bead frame this week.  First he received a "tour" of the frame itself.  He learned about the "simple family" and the "thousands family" and he made the connections between the golden beads and the beads on the frame.

He counted his way through the entire frame.  He counted by ones until we reached 100.  He counted by tens until we reached 1000.  Then, he counted by 100's until we reached 10,000.  This gave him a LOT of opportunities to practice the exchange process.  I watched the small bead frame presentation videos at Montessori Live where I picked up a good teaching trick.  The presenter explained the the child that they should use their two index fingers to make an "X" for "EXchange."  Kal-El really liked this and shouts out "oops, EXchange" each time he makes an exchange.  I have a subscription to Montessori Live (it is the only place I found videos of the presentation of ALL of the upper-primary/lower-elementary math materials).  They have many videos of the small bead frame.  I've only watched the first three thus far.  They are AMS-style presentations so I adjust accordingly using my albums as I see fit.  A select few of their videos are free on their site or on YouTube.  Here is the first video.  I wish it showed the exchange process, but that took place in the second video.

T

On a different day he learned how to use the notation paper.  It was hard to get a good picture the way the sun was shining in.  But, you can tell in the photo above unless Kal-El has grown two extra arms that, much like with division, Me Too finds Kal-El's work "very interesting."  This week was the first time Kal-El has been introduced to the comma to separate the number "families."  He really thinks the comma is super neat. He is struggling a bit with when to use zero as a placeholder.  I noticed this week that  a few of his addends in the dot game were "0050" and "0125."  We talked about it.  The bead fram paper gave us another opportunity to talk about it.  I think we need to pull out the wooden number cards from the golden beads again and review how we DON'T take a card if we have zero of a category and the different ways numbers look when the zero is in different places.

Question:  Do homeschoolers often own the golden bead frame or do they often just settle on the large colored bead frame?

1. Thank you for the intro to the SBF! We have ours and are about ready to use it!

2. To the question of bead frames. The golden bead frame is quite another animal than the large frame. I've used it with children who have visual spacial issues as looking through the bead frame may be challenging. However, its original design was more along multiplication in the upper setting as an abstractor for children whose multiplication skill need help. I've primarily used it for a very short periods for 9 to 12 year-old children and only in the context of multiplication. (The children have to make their own tickets.)

I may be wrong in that, but both my AMI Bergamo mentor and my AMS elementary trainer used it for that only.

3. Eavice,

Thank you. It sounds like I don't need to worry about whether or not I need one for quite some time :)

4. A job well done KAl-El! Me Too I love your spirit!!

Thank you for sharing.

In regards to your question I am researching albums right now. I finally have come to a reality that I actually need one:) Kinda late in the game, but I have been blessed with lots of online information. Ken and DJ have now be officially deschooled(finger crossed) So now they are digging deeper, which leads me to realize I need to be better prepared. We are going Montessori all the way in due time!!

5. "Golden bead frame" - that sounds so PRETTY! I love the sound of that name (I'm going to be chanting all evening now ;) ).

AMI albums call it the "flat bead frame." I know - boring name!

I am finding differences between Bergamo AMI and AMI in the US - I wish I could take both!

In the training I had, thus in the Keys albums, the flat/golden bead frame is placed between the large bead frame (but could parallel the large bead frame) and the multiplication checkerboard, thus very much lower elementary. It has its own set of very particular nuances that it teaches - the "magical" part I think your boys would like, is that it SHOWS that "0" we add when writing the multiplication out on paper - when the slip of paper with the written multiplicand is slid over to multiply by 10 (in a manner they have learned on the large bead frame), the zero "magically" appears.

But there are few more nuances as well.

I have found it entirely worth having to provide those "baby steps".

Just another take on it ;)

6. Wanted to add: I would NOT pay \$50+ for it ;) I think I bought one of ours somewhere for \$20-ish - maybe less. I'd sell you the one I had in "my box" from a recent acquirement, but it took fast dibs and is long gone! ;)

7. Wow! Good Job Kal-El! You are doing such great work! I am planning on pulling out the bead frame again tomorrow for Bunny! I hope she likes it as much as Kal-El!

8. Whilst the Golden Bead Frame does have its own little gems to teach - I only had one - yes one! - child that used it in 3 years of LE and UE classroom teaching. Everyone else had already abstracted naturally by that point. So I wouldn't bother buying one unless you find it for a great price :)

9. At Home - that is very interesting! It gets me thinking which schools I've seen it in, and which schools it collected dust. In the schools it collected dust, the children weren't really doing the checkerboard until upper elementary either (for us is solidly a lower elementary work). In the schools where I saw it in use, it was used by every child of the appropriate age (1st-2nd grade, early 3rd grade for just a few children who joined the class in late 1st grade).

I have personally always done it with late 1st/early 2nd graders, regardless of their previous Montessori experience - because they just get there; as well as 3rd-8th graders just coming in who needed math tutoring. Many aha moments with these guys (but they were truly new to Montessori). Legoboy points out (at almost 9 (3rd year), he still uses it to check his work from to time), that he likes the lines showing him which bar to multiply, the same bead color, the magic zero, the up and down nature like on paper (we don't really have another material that replicates that up/down nature), not writing multiplications by 10/100/1000 then multiplying by the number of 10/100/1000 but doing it like on paper, and (typical Montessori child!) he loves doing bigger numbers than on the large bead frame. Checkerboard goes bigger of course, but doesn't have the other features.

I wonder if it is something that depends on what scope/sequence one is following? I just see upper el being presented with the checkerboard, they like it, they get it, but it obviously doesn't meet their needs compared to other schools that finish that work up by 3rd year and work on the decimal board and decimal checkerboard in 3rd-5th years, who are already fading out from as much use with the beads. Something to consider as I am about to visit a few more schools. :)

10. Jessica,

It WILL be interesting to hear about what you see on those visits. As we have discussed in the past, I have a lot of trouble finding evidence online and in our local Montessori schools of kids that are finishing the primary AMI albums in primary. I see most early elementary kids using the "primary" materials...and that's in schools not homeschools. Obviously they exist because you have seen it and already done extensive visiting in the past. I just wonder if it is particular to certain trainers and geographical areas.

I thought of this line of discussion earlier this week when I was looking for two and three-digit division videos for DM. One of the stamp game videos I came across was called "long division with the stamp game" which demonstrated division with a SINGLE divisor. http://www.youtube.com/watch?v=fCDNoyBMHnk The presenter stated in the video "Typically children in first grade will get a preview of the stamp game but it is used most extensively in second and third grades." The DIY stamp game that I have was given it to me by a friend whose daughter attended a traditional Montessori school from ages -8 and needed it because her daughter, whom she homeschooled starting in second grade, was JUST STARTING the stamp game when she finished first grade.

Anyway, I agree with your idea that the differences that people see in materials use may have to do with the fact that different people are using them at very different ages. I think about the scope and sequences a lot because Me Too is ahead of where Kal-El was in the math sequence at his age but it doesn't feel as "right" as it did as when Kal-El moved through the materials. I feel like he's less independent and I have to force it more. However, I clearly see that his mind is more "absorbent" and he's having better success with things like the memorization materials.

11. MBT,

I think you are right in the trainers and geographical areas. I had nice phone visit with an old friend earlier this afternoon who currently works at an AMI elementary school that is "fed" by a mix of AMS and AMI primary classes. There is no training center nearby, but the nearest is an AMS center. She finds that the AMI children come in with some last remnants of the AMI primary album, and they still DO all the later work while she is providing elementary presentations. So they come in with stuff to do they already know: fractions, bead frames, stamp game. They are indeed still working on the material, but she does little in the way of "giving" - she simply reminds them of the material. She said she pulls some of the more primary level work out of the classroom by early November at the latest (they start in mid-August). It is similar across all subjects, the exception being history (aha!).

On the other hand, the AMS children come in with no bead frame work, limited fraction work, lack of memorization experience, and lower reading levels. But they much more readily jump into the history presentations and are generally bored with the initial biology and astronomy-related presentations because they had some of that more specifically (these things being fleshed out more in the AMS albums for primary). She has to work with them on math and language, and there is little for them to do in those two areas until she actually works with them.

Previously, she worked in an area with a very strong AMS presence, with an AMS training center nearby. Being AMI trained working at a school trying to work towards AMI affiliation, she had to continually work through the remedial sections of math and language with almost all the children, and just thought it was par for the course until she moved to her current location. She saw what the other teachers did (keep using what to her were primary albums, but to them were their actual training manuals) and tried it for a bit, but it didn't feel right for her, because she saw how the children just latched on to the elementary work.

Most of my own employment, student teaching, required observations, subbing and optional observations have been in areas with a strong AMI presence or an AMI training center. The city I am near right now has a strong AMS program and the school where I typically sub currently is an AMS school. The principal has both AMS and AMI training for primary and sees the benefits to both. He wishes he could have half of each in his staff, but the AMS training center is right here and handy, so only 2 of the staff members currently have AMI training. This school does a LOT of adaptations - bringing in Orton-Gillingham, textbooks in upper elementary (actually used as textbooks), some of the materials literally collect dust (I have a box of them in my living room ;) including more items that I can't find in Montessori catalogs or albums... ;) ).

My plan is to visit the remaining Montessori schools in the two nearest cities to me - I've been to many, but not all. I always learn something new and am so inspired when I visit schools :) (not to mention the subbing and old materials possibilities!).

So it will indeed be interesting to see what I see, especially because now I'll really be paying attention to this particular area ;)

12. I would agree with Jessica. AMI Primary children seem to lag behind AMS children at the beginning, but then in the late 2nd and 3rd years, they gain momentum.

I rarely had children from an AMI background that needed be to have golden bead materials in elem, but often we needed them for AMS children as place value was a bit wobbly.

This sounds so judgmental.

I will throw in that the AMS children were more creative and artsy than the AMI children - as a rule. Plays and visual projects were better for their mix in the class.

The AMI manuals have less additive lessons and distill the core of Montessori to a fine point. The AMS manuals are two to three times larger and paint with a wider brush.

I would also add that the children begin to spread out in their abilities in elementary as their gifted tendencies begin to truly assert themselves. So much so that one of my trainers would never split the upper and lower elem classes at her school (apparently Mario recommended that the classes be one) so that the children can spread across the materials and lessons to adjust to their aptitudes. It worked for her and the culture of her school.

This is so useful.

I want to say that I love to pull out the golden beads when first introducing stamps, bead frame, bead boards, etc... Some teachers skip this part but it is SOOO important. Just like in the video the students keep internalizing the values.

Thank you!

14. Eavice,

I always appreciate it when you add your two cents, thank you. It has been quiet on your blog lately! I miss it!

You are right, this discussion is super interesting but does border on judgmental if everyone commenting didn't "know" one another. The good news, no one here means for it to be...

15. Gigi,

In light of all the training you've had, I don't know if you would consider them "good" or not. I don't have much to compare them to, but think they are great. I don't always do things quite the way they are done on the videos but I love knowing that I can pull up most of the upper primary/lower elementary math and see nearly every step. It's a lot more consistent than digging around on YouTube.

16. So, now I am sitting with my SBF and I can't find enough on how to use it. I am still searching, but the paper confuses me. Do I have her write 1-10 and then 20-100 by tens, or does she move them back and write 11, 12, etc? Other then the pay video, have you found any good tutorials. I suspect I'm over thinking this, but I'm actually confused! Thanks for any help you can offer :)!

17. Lisa,

The AMI Primary Guide lessons are not bad:

I didn't look very hard for other videos because I already have the subscription to MontessoriLive. Your frustration is exactly why I have the subscription. Some things you just have to see. I think they have seven videos covering the small bead frame and I think those are JUST for numeration and addition. Anyway, she would NOT move them back and do 11, 12, etc.., That would take forever. Kal-El did some of that (his idea) the third time through after learning to exchange but he eventually gave up. I think the biggest mistake I see people make is to write the numbers inside the empty squares instead of on the lines. Also, notice how putting the zeroes on the paper is its own presentation.

18. I actually read the AMI lesson and it was confusing to me! I did finally find Jenny Yen's http://faculty.fullerton.edu/syen/mts/math/11-1.htm. It's been so long since I read hers that I forgot she was out there. Usually AMI is all I need! Thank you for the tip about writing on the line. I'm doing the work myself right now to make sure I understand it and I had put my numbers in the box :). And the zeros in their own lesson, did you follow that? Or did you follow up the first lesson with zeros right on the same day? I'm afraid that Mustang will look at me like, duh Mom. The video subscription looks great. Something to add to my want list!

Oh, and thank you so much for your help!!

19. This is definitely an area where a picture (of the paper) and a video (of the presentation itself) is worth far more than a thousand words!

For when to do what - just follow your child. Some children are ready to move on, some not so much. I highly suggest keeping all the stages and in order, to emphasize the point; but many children can move on quickly. This material (small bead frame) can be used by 5 year olds, and my AMI albums say that if elementary children didn't get in primary to just move into the large bead frame because all the same exercises can be done, they'll just be done more quickly; so there is a lot of wiggle room here :)

I would strongly recommend not doing any operations on it until the child is confidently reading the numbers with minimal errors.

By the by - why DO we leave out those zeroes at first? To show place value. On the cards with the golden beads, we don't "place" a zero if there is nothing there - it just appears on the cards. So here we are only "writing" when we have a "quantity" - but that quantity by itself, without a zero, by the mere fact of its placement has varying values (a precursor to the checkerboard work in elementary - just the mere fact of the numbers placement determines its value).

:)

20. Ok, now I'm curious and I've not looked at differences on this one in so long - for those of you who have just recently done some comparison, here are the exercises as my primary AMI albums have them - for both the large and small bead frames - I wonder how these compare to others?

Presentation: Notation with no zero
Presentation: Notation with zeroes
Composing Numbers Stage 1: adult writes and builds the number
Composing Numbers Stage 2: adult writes and the child builds
Composing Numbers Stage 3: the child writes and builds
Composing Numbers Stage 4: child builds, reads, writes the number
Static Subtraction
Dynamic Subtraction
Dynamic Subtraction with a zero in the minuend
Subtraction with multiple zeroes in the minuend

Wooden Hierarchical Material
(various stages)

Presentation: Notation with no zero
Presentation: Notation with zeroes
Composing Numbers Stage 1: adult writes and builds the number
Composing Numbers Stage 2: adult writes and the child builds
Composing Numbers Stage 3: the child writes and builds
Composing Numbers Stage 4: child builds, reads, writes the number
Dynamic Subtraction
Dynamic Subtraction with a zero in the minuend
Subtraction with multiple zeroes in the minuend
Multiplication Introduction
Multiplication using the Notation Paper

21. Lisa, Jessica,

Lisa..the AMI Primary presentation makes a lot of sense IF you've seen the video LOL! The Jenny Yen IS a better verbal explanation, I forgot about hers too...but the pictures in the AMiP are sorta helpful. Even my beloved Montessori by Hand presentations don't have any pictures and have a confusing verbal explanation. She managed to cram the whole bead frame onto a page-and-a-half.

The steps in my albums...both AMS and AMI are similar or identical to what Jessica listed. I'll look harder later. Lisa, instead of doing the two steps separately we first did the sheet with NO zeroes and then thought back on our work "when we made 20 did we have any units?" "No?" and added the zeroes to the paper. This is how they did it in the video and one of my albums suggested this as well rather than fill out the whole paper twice. Otherwise, we did all of the steps (up to where we are) that Jessica listed, we just did a lot of them on the same day. So, it took us three days to get all the way up through dynamic addition. Day one was introduction and counting beads (no exchange). Day two I taught the exchange and then did notation without zeroes then notation WITH zeroes. Day three we did all the composing numbers work, static addition (not on Jessica's list) and then dynamic addition. We only did one or two static addition equations before Kal-El asked "lets write one with an exchange." I'm letting him write all of his own equations for this work (after the first few I used to demonstrate).

Jessica,

I have to go but I can do a better comparison of your list to some of my other albums later.

22. No hurry on my part - I'm just curious (and you know others will be too - and next time web searches are made, everyone will end up here ;) ).

Which one is not on the AMI list?

23. Jessica,

I swear I checked your list three times and static addition wasn't on it this morning and it is now. Obviously I'm not a morning person.

24. Okay, SO not a morning person. I inadvertently misrepresented when I said the Montessori by Hand album crams it all into a page and a half. What I've done SO FAR is crammed onto a page and a half. There are a few more pages I have yet to do. The orientation presentations barely tell you what to do at all. It talks you through up to ten and tells you to "let the child take over" without explaining if you'll be counting by ones the whole way or by tens and hundreds as you go.

25. Okay, last note on the Montessori by Hand album...it has all of the steps you outline Jessica but not fleshed out like your bulleted list implies for your album. For example, here is the ENTIRE Large bead frame info:

Presentation 1.) Make the connection with the Hierarchical Material.
2.) Introduce the features, focusing on new
categories and families. We have new black family.
3.) We orient the child in a similar way, understanding that there is new language to attach. 4.) Once we feel the child is comfortable with forming, writing and reading numbers, we can move on to
operations.
5.) Begin with static operations first, shortly moving on to dynamic operations.
6.) All three operations, addition, subtraction, and multiplication, can be done on this frame.
7.) The child will be more independent with this work.
8.) Sit with the child if needed, especially during the dynamic multiplication presentation.

Now I'll peek at my AMS albums.

26. Okay, from the Karen Tyler album...Jessica as you know the frame isn't in a "passage to abstraction" section as in AMI but rather tucked in at the end of the addition sequence. AMS doesn't introduce the materials one at a time in the album and tell you how to use them for each operation but rather divides the album by operation and puts each material under each operation. Also, the KT album doesn't happen to include the hierarchical material or the large bead frame. Here are the categories for the small bead frame:

Notation Paper 198
Subtraction 206
Subtraction - Regrouping 208

Some of your steps are consumed by her larger steps but are still there. Obviously the golden beads category is listed here and isn't in the Montessori by Hand album but it is perhaps assumed you would do that.

27. The Mid-America (AMS?) lower-elementary album that I have is not very user friendly so I had to dig a bit. The small bead frame is recommended for year one for addition and subtraction static and dynamic. The hierarchical material listed as a possible "year two" material. The large bead frame presentations are included and are in the album after the hierarchical but is not listed in the possible year-by-year scope and sequence. It starts the small bead frame right at static addition with none of the previous presentations. The large bead frame has all of the presentations you listed from introduction thru composing numbers stage four. However, in the album at least no addition or subtraction is done with the large bead frame, only multiplication.

28. And finally (In think) the Montessori R&D elementary math manual level one.

introduction to the bead frame with notation paper

Like the Karen Tyler primary album, R&D elementary level one (which I understand is identical to the primary math album) does not cover the hierarchical material and the large bead frame. Those are in the table of contents for level two which I don't own. The R&D albums is less organized by operation and more organized by Material than Karen's but not quite as much so as an AMI album. So, it was not very accurate of me to say that AMS albums are organized that way. Some are. I feel that the above presentations include all of the steps you outlined in your comment.

29. Lisa is probably wondering what this all has to do with her questions (which were about a couple of particular steps within a presentation or two). Lisa, I think we are talking about other questions at this point, LOL! No, I don't know how that happened.

30. Lol! I just came back to see if there was any follow up and found all this :). You reminded me of my Montessori By Hand Album, too. Thanks! I had been using the online AMI for pretty much everything, I guess I should look at all my stuff from time to tome. I'm actually taking Jessica's class, too, so I am interested to read all your thoughts on this.

What ended up happening: Yesterday I gave her the intro to the SBF. Today, I just ended up doing the first exercise without the zeros. I could tell that she could use a review of writing the first numbers without me sitting there giving directions anyway. We will add zeros in our lesson on Monday.

She, like me, had a strong desire to write NEXT to the line, so I have to make sure she is at least trying to stay on the line.

Also, I had no idea there was even a golden bead frame until this post. I find out so much from you :). Thanks!!

31. To help myself remember to write on the line (and I've said it to children too) - is that the lines are the wires, so we write a number on the "wire" instead of having all the beads.

MBT - Thank you for all the comparisons - it is interesting to note how each are laid out and the different nuances on one particular topic :)