Zoology & Taxonomy

Ah, science.  Of all subjects it was my weakest in high school: chemistry specifically.  I did alright in biology, mostly because my best friend and I were in the same class and studies together.  If you listened closely during tests and exams you might have heard us humming softly.  We found that the best way to remember the facts was to make up silly songs.  If only I had begun learning science the Montessori way!  Here is a sample lesson, one that can be repeated indefinitely without growing tedious.

 

Above you can see the (almost) completed lesson in zoology/taxonomy.    I use it as a launching board to talk about all different kinds of plants and animals, but mostly animals.  We begin with the most basic of categories: living and non-living.  Ella sets out two pieces of paper, one labeled "Living" and one labeled "Non-Living."

I've made up many cards (just using Microsoft Word, eight cards to an 8 1/2 x 11 page), the vast majority of them animals, for Ella to sort.  I've mixed them all up and divided them into small groups so she can grab a pile and sort through those that day.

Choosing items for non-living was very interesting.  Most things I chose were no-brainers, i.e. they are obviously non-living, but there were a few that were more challenging.  Fire is an excellent one as it has many characteristics of living things (can grow, can move, needs air, needs "food", leaves waste, etc.) and there are a few others that can catch one unawares.  Above you can see that included in this pile are lightening, stalactites, rocks, and a compact disc.  There was no doubt that the rocks and compact disc were non-living, but lightening has some similarities to living things as do stalactites.  It took quite a while for her to decide where to put the stalactites because in an earlier stack she had coral, which appears to be like a rock, but is actually living.  The sneaky ones are the most fun and they help reinforce the difference between the living and non-living.

I scoured the internet for the pictures I used for each card.  While I tried to focus on variety, keeping in mind that the majority of cards would have to be vertebrates, I did make an effort to put in plenty of animals that are native to our area, such as the ruffed grouse (bottom left), which is a popular game bird in New Brunswick.

After separating living from non-living we take our pile of living and divide them up between "Plants" and "Animals."  Yes, I know that there are more categories of living things than just those two, but as they are the most common and encompass almost every living thing with which a child is familiar we focus on them.  Fungus, protozoa, bacterium, etc. can come later.

 Most of this sorting Ella found very easy, but I tried to keep her on her toes.  The Venus flytrap, being carnivorous, gave her a moment's pause.  And she was convinced for a long time that coral must be a plant, which I grant you, is not an illogical conclusion!

This particular pile of cards only had three samples of plants.  Our discussion of the tree trunk was interesting as the tree itself was dead, and therefore neither living or non-living, but it was covered in moss (which was my target species) and the moss was clearly alive.  Ella decided that rather than having just two initial categories there should be three: living, non-living, and formerly-living/dead.  After all, wood was once a tree, and the radishes can't really be living if they've been pulled up out of the ground, chopped up, and pickled!  Smart girl.

After the plant/animal division, we take the animal cards and divide them between vertebrates and invertebrates.

Categorizing animals this way is a bit more challenging.  Because you can't actually see the backbone or spine in a vertebrate you have to think through how an animal moves, how it lives, and what its surface feels like.  Ella is just beginning to remember consistently to look for segmentation of the animals' bodies, hard exteriors such as shells (an exoskeleton), and over-all "smooshiness" (that the body is completely smooshy or soft, indicating that there are no bones).  

Again, putting in tricky cards gives the opportunity to discuss the "why is it this one and not that one?" question.  Above I included a sea horse.   Ella concluded initially that it was an invertebrate because it appears to have an exoskeleton, even though it is a fish, though like catfish sea horses do not have scales. 

Following the organization of the vertebrates and invertebrates we take the pile of vertebrates and then comes the real sorting fun!

With five categories to chose from there's a lot more room for error.  Each animal has to be evaluated in several different ways: what kind of "skin"  it has and/or if it has a skin covering (hair, fur, feathers), whether it gives birth to babies or lays eggs, if it lays eggs whether it lays them on land or in water, if the offspring look like miniatures of the parents or if they have another form entirely, if it has a mouth or a beak/bill, how it breathes, where it lives, if it is warm or cold blooded, and how it feeds its babies.  There are hosts of conversations to be had as we work through these cards, and I frequently find that Ella and I end up laughing, especially at odd animal behaviour or appearance.

Amphibians.  They have slimy skin, live in or near water, are cold-blooded, lay eggs in water, have babies that look nothing like themselves and whom they completely ignore, and usually can breathe right through their skin.  Their appearances have little variation: frogs and toads look similar as do salamanders and newts.  To give a bit more variety I've tried to include pictures of amphibians at various stages of development.

Mammals.* We are warm-blooded, have fur or hair, live all over,  breathe air with lungs, give birth to babies that look similar to the parents (usually!), and feed our offspring with milk from our own bodies.  Isn't it great to be a mammal?  There are quite a few unusual mammals, like whales, manatees, platypuses, etc.  It can be fun to emphasize the similarities between humans and other mammals, as well as the differences.  Thank God for opposable thumbs!  Plus, as a nursing Mum, it's interesting to discuss how other species nurse.  In the case of whales, Ella would not believe me that they were mammals until I found a video of a beluga whale giving birth and nursing her baby!

Fish.  They live in water, are cold-blooded, and breathe through gills.  Some species give birth to live young, but most lay eggs.  The level of parental involvement is usually low to nonexistent.  Although there are three different classes of fish, for the young child and early elementary student so many details can be confusing, so I lumped all the fish together.  When (or if) I ever have time to set up an aquarium again we will certainly get into closer examination of fish classes.

Birds.  Feathers, beaks, wings, and two legs are the most easily recognizable traits.  They are warm-blooded, breathe air with their lungs, lay eggs, and are frequently attentive parents.  One of their families (the penguins) are even able to survive in the harshest climate on earth and one of their species (emperor penguins) stay in that climate during its harshest season in order to go to extraordinary lengths for the purposes of mating, bearing, and raising offspring.  In my opinion, birds are way cool!

Reptiles.  Some like life where it's hot and dry and others would prefer to stay wet all day long.  But they all have scales, breathe with their lungs, are cold-blooded, lay eggs on land, and their babies look like miniature adults.  They are also very good for frightening grandmothers and mothers when brought in from outside with a cheerful, "Look what I found, Mum!"  (Please note: this refers to something my brother did to my mother and grandmother, not something my children did to me.  I would not be so chicken-hearted... I hope!)

After all the sorting has been done, we clip each section together with other cards of the same category, to play with and discuss later.

Eli added his own artistic touch to the non-living card!

And, as is so often the case with homeschooling Montessori Mums, how to store materials effeciently is of great concern, so here's what I did.  I found this tray and this box at the local Dollarama store.

The tray perfectly fits half of an 8 1/2 x 11 piece of paper (or cardstock), which is what I used for the category titles, and the small crate is perfect as a card holder!

*Please note:  While all the photographs taken above were mine, the pictures in the photographs are not.  They were all found online through Google search.  The human family in the mammals is unknown to me, but it was the best photo I could find of nude humans that was neither graphic (in the negative sense) nor of poor quality.  Since all the other animals were au naturel, I figured it was only fair that the humans were as well.  For the record, I think it is a beautiful and tasteful photo... though I don't think I'd be comfortable with my family posing in such a manner, or at least displaying it!

Square of Pythagoras - First Presentation

Thanks to all who inquired.  No, I'm not dead!  It's been almost a year and a half since my last post, and while my life has been moving quickly onward I've been facing it mostly with glazed eyes and an air of confusion.  Such is life with twin boys.

My sons are now 2 and are healthy, mischievous little fellows.  I've begun to do some early Montessori work with them, which you will hear about in an upcoming post.

Ella is now "officially" grade 1, in that she is 6 and that is the typical grade 1 age.  And there ends all that is "typical" about her.

Evidently she's doing some things on a grade 4 level, and she was teaching our 17 year old babysitter about geography.  Her reading is about average, or perhaps a bit above average for her age, and her handwriting in abominable!  Though much of what she writes looks like the hen-scratchings of a preschooler, what she writes is very well done.  I guess we just didn't do enough of the sandpaper letters or the metal insets.

I have a vast backlog of photos and lessons to share and I hope to do so over time.  For today, here was our afternoon lesson: the first presentation of the square of Pythagoras (also called the deconomial square).

The square of Pythagoras is basically the multiplication times table in visual form.  The smallest square is 1x1 cm and is red in colour, which coordinates with the colour of the bead bars.

The next three shapes are green, like the "2" beads and are 2x1 cm, 2x1 cm, and 2x2 cm square.

The next five shapes are pink, representing "3" and are (2) 3x1 cm, (2) 3x2 cm, and a 3x3 cm square.

In the above photograph, Ella is laying out the 4s.

I find that she really enjoys making the square of Pythagoras as she thinks that the pattern is beautiful.  I think so too.

The completed square (as done by Ella).  As you can see it goes from 1x1 cm to 10x10 cm.  It is meant to coordinate with the pink cubes, the brown/broad stair/rectangular prisms, and ultimately can be used as a guide to laying out the bead bars in the deconomial.  Hopefully I will be showing these extensions in the near future.

As for the Square of Pythagoras material itself.  It is really hard to find to purchase. Ideally it is supposed to be made out of wood, but I found it much easier to make it out of foam sheets using a large paper-cutter.  (An office-sized paper cutter can be invaluable when making materials.)  I've also seen beautiful square of Pythagoras lay-outs made of felt or other fabrics, plastic duo-tang covers (though I don't know how easy or difficult it would be to find the colours you want), and painted cardboard or bristol board (though they can tend to warp).

Initially I planned on making it using inches as a base, rather than centimetres.  Bad idea!  It was HUGE and very unweieldy.  I'm very glad I downsized, though what I'm going to do with all that extra foam is beyond me!

The first presentation of the square of Pythagoras is not meant to teach the multiplication table, but like the binomial and trinomial cubes it is a sensorial introduction to a more complicated mathematical concept.  Right now we call all the green rectangles and square the "twos,"  all the pink the "threes" and all the yellow the "fours."  It will be some time before we begin to name individual rectangles 2x1 or 4x3.

To present it I simply named the material, "This is the square of Pythagoras." and I began making the square, beginning with the red, then the green, then pink, and so on.  It didn't take long before Ella got the idea and just took over.

She was rather frustrated by the fact that her square of Pythagoras wasn't as "perfect" as mine, but with a bit of reassurance that it took practice she became satisfied with her results.  I'm looking forward to her reaction to the extentions.

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
• 142 GREEN 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)
• 476 YELLOW BEADS
• 775 LIGHT BLUE or AQUA BEADS
• 1194 PURPLE or VIOLET
• 1777 WHITE BEADS
• 2488 BROWN BEADS
• 3411 DARK BLUE BEADS
• 10 LIGHT GREY BEADS
• 265 DARK GREY BEADS
• 8095 GOLDEN 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!

My Completed Pink Tower

Okay, after sanding and sanding and sanding and sanding, going to Dad's to use his belt sander, then went home and sanded some more. In the midst of all that sanding I was repeated told by Dad, "Don't be so picky!" Can you guess which of the two of us is the perfectionist?

(If you happen to be looking for instructions on how to make the pink tower or broad/brown stair, go to Make Your Own Sensorial Materials, Part One and Part Two.

I gave all the blocks a coat of latex primer, then did multiple layers of "cherry blossom pink" acrylic paint. Finally, I gave them all three coats of acrylic varnish. Here's the results:



You can see more detail when I do the pink tower shell-shape:


From a distance, they don't look too bad. But if you take a closer look, you can tell that they weren't professionally made:

On the 10cm x 10cm x 10cm block, you can see the "dip" in the wood. If I had sanded much more, it would not longer have been 10cm x 10cm x 10cm, so I cut my losses and voila!

Here's another view of the 10cm x 10cm x 10cm block. You can tell here that one of the corners isn't really a corner. That was another fault in the log. Also (but not shown) is a large knot in the wood that, despite substantial wood fill and sanding, still has enough of an indentation to make it noticeable.

Just for comparison, I put the teeny-tiny 1cm x 1cm x 1cm block atop the 10cm x 10cm x 10cm block. Theoretically, it would take 1000 of the former to make the latter, and when you look at it this way, you can really see that.

Ella can do the pink stair with little-to-no difficulty, although sometimes it's hard to tell, as she often has a "friend" (be it little monster, Mayas the rabbit, Lambie, or some imaginary person) who just can't figure it out on his/her own, so mistakes are made which Ella has to correct! It's not always clear to me if she's making the mistakes deliberately in order to get to "correct" her friend, or if it happened by accident and she's just using her imaginary friend/stuffed animal as a scapegoat for her mistakes. In some cases, I can tell one way or the other, but sometimes... Well, let's just say I know her better than anyone, but there's plenty of times when I have no clue what's going through that little mind of hers!