Thursday, November 06, 2008

Montessori Mathematics: The Complete Bead Material - Part 1

When those who are not much familiar with the Montessori Method hear it referred to they often have interesting preconceived idea of what it entails. Some thoughts that I've heard are as follows:

--"Oh, the schools where they have no tests and they play with educational toys all day!"
--"You mean those really expensive private schools?"
--"Montessori schools are where the smart kids go."
--"Don't they mix up grades there?"
--"Children from those schools don't adjust well to 'regular' schooling!"
--"The teachers just leave the children to learn on their own."

If you are really knowledgeable about Montessori, then you can see how most of these statements have a grain of truth enhanced by a dose of ignorance. My usual response to the above includes such explanations as:

--"No, they don't have traditional type tests in Montessori schools, at least not in the early years, but the children are constantly being evaluated on what they have learned. And all of the educational materials used are graded as to difficulty, so there is a natural progression as the child learns to master each level."
--"Yes, many Montessori schools are very expensive, but in some places the Montessori schools have been adopted into the public school system. And if you cannot afford to send your child to an actual school, they can still have a Montessori education if you put your mind to it!"
--"Montessori schools are not only for children who are intellectually gifted. In fact the method began when Dr. Montessori was working in a mental institution with the severely disabled. A Montessori classroom is an excellent environment for learning for children of any age and of any intellectual ability. Whatever the level of intelligence, any child brought into such a place and taught accordingly will end up smarter, though, and at his/her own pace!"
--"In a Montessori school each classroom is composed of kids of various ages. The idea is that those who are more advanced can teach and help those who are just learning. It is a cooperative environment."
--"Children who learn through the Montessori method become used to active learning. This is the best way for children to learn because they learn best by doing, not by explanation and reading. It also engenders a love of learning so that as they grow they become independent learners, wanting to find out for themselves about subjects that interest them. Unfortunately, 'regular' schools don't often offer this to their students."
--"Teachers often work as facilitators, teaching a lesson, then re-teaching the lesson occasionally, each time becoming a little less involved in the 'teaching' as the child takes over. This continues until the child understands the lesson enough to 'teach' the teacher, or the other children!"

As for the materials themselves, if someone has heard of them or seen them the impression that they come away with is often, "that's a lot of beads!" The reason being that the Montessori method wants to start children off by learning things not in the abstract, but in the concrete. Teachers don't explain the difference between 1, 10, 100, and 1000; we show the difference! The way we do that is with beads - lots and lots of beads!

I got lucky on eBay and was able to buy the Decimal Golden Bead Material at an excellent price. Thing is, getting the complete math bead material is a massive investment. Its uses are almost endless and reach into upper elementary. It makes traditional math lessons look positively boring, and it makes it easy for children to grasp what are usually considered to be complex concepts. The decimal golden bead material is an excellent example of this.

Above, Ella and I are doing a lesson on the decimal system. The initial idea is for the child to visually and tactilely note the difference between a unit (1), a set of ten units (10), a set of one hundred units (100), and a set of a thousand units (1000). The unit bead is simply a single bead. The ten bead bar is ten beads identical to the unit bead connected in a line. The hundred bead square is essentially 10 ten bead bars connected into a square of beads. The thousand bead cube has 10 hundred bead squares connected on top of one another making (obviously) a cube. Both in appearance and in size there is a vast difference between the unit and the thousand cube.

The next stage of the same basic lesson is to bring together 10 unit beads and set them together by the ten bead bar to demonstrate the relationship between 10 ones and 10, making sure that the child counts them out. It continues by laying 10 ten bars together, counting them out, and then showing how the result is identical to the hundred square. And finally you put 10 hundred squares together so that they become visually the same as the thousand cube. (Note, though, that the hundred squares tend to interlock when placed on top of one another - so for the purposes of the demonstration, I held them up on their edges making the cube vertically, rather than horizontally, which worked very well.)

Thing is, the golden bead decimal material is all I have. And the time has come that Ella and I can't go much further in math, at least not using Montessori lessons, without getting more bead material. If you've done much searching online for Montessori materials, you know that they can be very expensive. And when it comes to bead material, there is a lot of different items you'll need. Deciding where to get it, when, how much, and in what order can be extremely overwhelming.

I've searched all over for the least expensive mathematical bead material and the least expensive buy-it-all-completed place I've found (though if you've found one less expensive, please do share!) is IFit Wooden Toy Supplier in Vancouver, BC (And at the time of this writing, they've got a good sale on - take a peek!).

If you want to get every component needed for everything - i.e. every lesson, game, and bead activity, you don't have to buy everything. You need only buy the parts that have enough components for every lesson, game, and activity. For example: the decanomial beads have 55 of each of the bead bars for the numbers 1 through 10. If you use material from the decanomial beads, you won't have to buy any other bead stairs, nor will you have to buy additional golden 10 bead bars for the golden bead material. Albeit, you won't have all the tidy boxes and cabinets for storage, but if you can contrive to make those you'll cut down on your costs considerably.

For enough components to do all bead activities, you'd need to buy:

  • the Decanomial Bead Bar Box
  • the Elementary Negative Snake Game
  • the Complete Bead Material
  • Forty-five Golden Bead Units
  • Forty-five Golden Hundred Squares

Today (November 6th, 2008) the price for the above materials from IFit Wooden Toys is $523.28 CAN or $422.00 USD - which is partly because of the fantastic sale they have on. But don't forget shipping costs when you make up your budget! For example, if I were to order it, I'd have to add 5% GST (Goods & Services Tax - Canada's national sales tax) and shipping costs ($62.86), so my total would be $612.30.

Unfortunately, that's a lot of money to spend all at once, and most homeschool families just don't have it! After all homeschool families rarely have two salaries! So even though this price is phenomenal considering what you get, it's still beyond many, myself included. Therefore you might want to consider going the route I've taken: making the bead material yourself.

My first piece of advices is: don't go tripping off to Michael's or a Wal-Mart and think that you can buy the beads there. I did and once I began to calculate I realised that it would be much cheaper, and much more efficient to buy the bead material outright! That's provided they even have enough beads in enough colours.

You'd do much better to order the beads, possibly from a wholesaler. Some of the least expensive places I've found online for buying ridiculous numbers of beads are as follows:

Lure Making - Yes, it's a fish-oriented place. But some fishing lures need beads, and they have a decent price!

John Bead - A Canadian company, although, as a wholesaler, they have some restrictions as to whom they will sell. But if you have a friend who works in a craft store...???

Consumer Crafts - Which seemed my best option until I discovered they don't ship to Canada! So, for non-Americans, you may as well just skip this link!

Bolek's Craft Supplies - The company I decided to go with for three main reasons: they will ship to Canada, and they were the least expensive, and they have a big selection of colours.

Now, before you say, "But pony beads are much cheaper! And they're available everywhere in bulk!" let me warn you: pony beads are marvelous for children's crafts, but because they are not round they cannot be used for bead material. Here's why. Pony beads work well for the unit beads, and even for the bead bars, but when you begin to make bead squares and cubes you'll notice right away that the squares are not squares but rectangles, and the cubes are not cubes but rectangular prisms! To make Montessori bead material you need beads that are as long as they are wide, as they are high, which limits you to either cube beads (and you'll never find enough of these in enough colours to use) or round beads. Faceted round beads will work as well.

The traditional colours for the Montessori bead materials are: red, green, pink, yellow, light blue/aqua, purple/lavender, white, brown, dark blue, and golden. And for some special-use beads you'd have to add: light grey, dark grey, black, and a second shade of pink. Obviously, not all companies have all these specific colours, so you might find yourself having to improvise, but if you do, you certainly won't be the first one to do so!

So, how many beads, exactly, does it take to make the bead material? And how many do you need of each colour? Well, you've struck a goldmine now, because I've already done all the figuring out for you! Hopefully all my figures are right!

  • 55 RED BEADS
  • 273 PINK BEADS
  • 35 PINK BEADS (for the pink/white bead stair in the snake game, you may wish to use a different shade of pink)
  • 1194 PURPLE or VIOLET
  • 1777 WHITE BEADS
  • 2488 BROWN BEADS

Well, that's about all I can write for tonight! There will be other posts regarding the making of bead material in the future, as this is a topic that takes a lot of time, for the Montessori material maker, the Montessori teacher, and eventually the Montessori student!

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At 11:36 a.m. , Anonymous Anonymous said...

Just today I was talking to a friend about how I'm becoming quite curious about the Montessori method and have decided that I need to get some books out about it. I really enjoy thorough postings like this one - it's great knowing there are such handy resources available if we do decide to go down this route with our kids (our daughter turns 2 this month, and we have a 2 month old son). Thanks for sharing so freely of what you're learning.

At 8:28 a.m. , Blogger HomeSchooler said...

The first book I would recommend to those new to the idea of Montessori and are considering using it in a home environment would be Elizabeth Hainstock's Teaching Montessori In The Home: The Pre-School Years. It's a fast and easy launching point. Then, if you are still very interested, I'd read Montessori's The Absorbent Mind. Good luck with your decisions!

At 11:15 a.m. , Anonymous Anonymous said...

I'm just getting started with montessori homeschooling. Thank you for this post. I am excited to learn how you have made yours, I am hoping to make my own beads as well. I also can't wait to see what all those beads will be used for, and all the different colors, I don't know anything beyond the very basics with the beads.

At 9:26 a.m. , Anonymous Anonymous said...

Thanks for your posts.
It has been very informative indeed.

I am trying to decide how much materials to get.

Same like you, I am hunting for beads materials.

Alisons is offering 20% off and free shipping for $500 and above.

At 9:22 p.m. , Blogger Mel said...

I'm wondering whether pixos / joining beads would work. I'm envisioning turning the creation of the beads themselves into a project for my daughter and myself and imagining that learning would take place in the invention of our own beads as well as their future uses. I've found pixo replacements on ebay costing $35 for 4000 beads. I'd love to read some thoughts from experienced Montessori parents on this possibility.

At 6:32 p.m. , Blogger HomeSchooler said...

Mel, I couldn't say for sure. I've looked at a few pictures and it's hard to tell. Basically, if the beads are perfectly spherical they should work in theory. My next question would be - how would you attach the bead bars together to make the short and long bead chains? Let me know if you try them and it works!

At 2:33 p.m. , Blogger Smith said...

Thank you soooooo much for this. Can't wait to see part 2.

Out of curiousity, is it a significant savings to make them yourselves (not including labor)?

At 5:00 p.m. , Blogger HomeSchooler said...

Smith - Depending on where you'd purchase your loose beads and where you'd purchase your complete bead material, you'd save in the vicinity of 300-1000 dollars. In my case, I saved about 480 dollars, so it was definitely worth it.

At 5:06 p.m. , Blogger Nicole said...

This was so helpful! But I didn't see part II on your website! Did I just miss it?

At 6:30 p.m. , Blogger HomeSchooler said...

Ah... The elusive part II. I know exactly what I want to write. Now I actually have to do so! It will be coming in the near future.

At 6:46 a.m. , Blogger Nicole said...

That would be so helpful!

At 11:02 a.m. , Blogger Stacy said...

I gained much inspiration from your effort. I would like to link to your blog. I am currently writing up my entry about my progress making the bead material making.

At 12:14 a.m. , Blogger Aimee Moisa said...

Hi, I'm new to reading your blog, and newish to Montessori in general. (My daughter's just over 15 weeks old and I started "preparing" to Montessori homeschool when she was 4 weeks.) Your blog is a really great resource for the Montessori homeschooler, I am very much enjoying your insights and experience. Since I've started learning about the activities and materials, I've felt kind of lost, but some of the ideas in your blog have given me a few "A-HA!" moments. I'm definitely going to keep my eye on your blog. Thanks for all the wonderful articles you write! Your do-it-yourselfing has really inspired me.

At 8:31 a.m. , Blogger Kerryanne Cummins said...

WOW, you have done all the leg work for me!! Your amazing. Like some of the others have said, I too have just started and have been overwhelmed by all the info and the materials, I did go to Michael's last night! forget it! I was just about to search for beads online, when I found your blog! Thank you so so much!

At 8:55 a.m. , Blogger Smith said...

maybe i missed it, but i'm wondering...if i made all the bead material you mentioned, do i still need to buy the wooden 100 and 1000 squares?

At 2:59 p.m. , Anonymous Anonymous said...

I'm fascinated by your patience and ingenuity in creating all the bead material DIY.

One thing I haven't seen explained well on ANY montessori site or blog, is how to introduce the bead material? Which order do you introduce the games in? Are the beads all connected or are some of them loose? I feel like I have a good concept and grasp of the MOntessori method in every other subject until it comes to the bead material. I'd very much appreciate it if you made a blog post about it or linked to where I could find that information!

At 5:30 a.m. , Blogger Smith said...

I'm wondering...if I purchased all the beads you have listed to make the bead material, do I still need to buy the wooden 1000cubes and 100 squares from the bank game?

At 10:35 p.m. , Anonymous Anonymous said...

Thanks so much for the information. I am inspired to make my own materials and save money in the process. Could you please tell me the exact type of bead you ordered from Bolek's?

At 2:27 p.m. , Anonymous Anonymous said...

I'm not sure if I just missed it or not but what exact beads did you order from Bolek's Craft Supplies? (size, name). Thanks for posting this, it helps me ALOT!

At 4:02 p.m. , Anonymous Anonymous said...

I used the pony beads for squares but I turned them so you could see the holes and glued them to card stock, I haven't done cubed yet....


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