comments on learning and living, mainly taken from the email lists and forums on which I have far, far too much to say. Hopefully, this is the good stuff.
9.09.2011
anger and communication
6.18.2011
can't do it
6.13.2011
specialty math manipulatives
centimeter smaller in each direction than the prior cube -- with the smallest
cube being a perfect cubic centimeter. When the tower is aligned on one corner,
the smallest cube can "walk" up (or down) the tower and can slide around two
sides of each of the other cubes -- the perfect alignment is a point of interest
for the child.
Those kinds of sales pitches sound so appealing, don't they? But in terms of evaluating their actual value, it can help a lot to step back and look at the underlying principles. The Montessori-Method "Pink Tower" communicates, with proper instruction, a set of mathematical principles, but those same principles can be discovered naturally by a child playing with any set of unit blocks - and sets of blocks have a far, far wider range of applications than the Pink Tower, which is used for... what a dozen exercises at most? The graduated blocks of the Pink Tower can't be used for much beyond building the tower and a few variations because there's only one of each, but a set of blocks - ah! Blocks can be used to build a million different things *and* used to represent other things. The
Pink Tower is only ever the Pink Tower.
The best math manipulatives in the world are unit blocks and some of the best unit blocks ever made are, frankly, Legos. Yup, a big commericial toy wins the day, I'm afraid. With legos you could build your own Pink Tower... but why bother? Kids will learn exactly the same concepts playing with the blocks in their own way - or with other types of unit blocks. Not every child loves Legos.
The significant aspect to consider, when it comes to blocks, is that they are *unit* blocks - there are regular units of increase between one block size and the next. Most sets of plain wooden blocks are unit blocks because it's utterly logical to make them that way. (And wooden blocks are great for toddlers and younger children, a muuuuuuuch better investment than a Pink Tower, and probably a tenth of the cost, even if you buy a really nice set!)
the light reflecting differently off the different flat planes of the tower
when the child walks around it to admire his work is a point of interest.
This is a point I find, frankly, amusing. For a theoretical system that shies away from plastic, it's a little ironic that one of the selling points of the a toy is that it's smooth and shiny.
The tower has ten cubes because our number system is based on ten, and the
knobbed and knobless cylinders, pink tower, brown stair, and red rods are all
meant to reinforce that.
Okay, my math button has been pushed! Since base 10 is everywhere in the real world, why would you need to teach it? This is a case of Montessori toys being made to turn a sterile classroom into a substitute for a rich home environment. A noble cause, but not particularly applicable to home educators. There's no real need, if you live in any developed nation, to "reinforce" base ten. Kids figure it out (arguably they derive it) without specific lessons in the subject.
Besides, in the real world we use multiple bases every day, not just base ten. Consider: How many days in a week? How many seconds in a minute? And if you live in a country like the US which still uses inches and ounces....? Reinforcing base ten, under those sorts of circumstances, is counter-productive, and lessons with reinforce base ten have the side effect of then requiring additional lessons to give kids the tools they need to work with other bases. Montessori does this better and sooner than mainstream education, it is true, but at the cost of needing yet more, highly specific teaching tools. The Pink Tower is a one trick pony.
Now Legos, by contrast, do something that's far better than reinforcing base ten, they give kids a format to construct mathematical concepts in multiple bases simulateously and in the process give kids tools with which to derive the principles of mutiplication and division/fractions. How do you build a wall when you have a mix of 2x2, 2x3, and 2x4 blocks? That's the most basic Lego problem, one with which every Lego builder is familiar, since those are the most common building blocks - and it involves the principles of converting from one base to another... the same principles which are needed to add fractions.
Also, a very important part of this material is its baric and sterognostic
value -- "Montessori-speak" for the way the weight and feel of each piece varies
in a precise order -- the largest cube is 1000 times the weight of the smallest
cube
Once again, I'm amused. The above is going to be true of any set of wooden unit blocks where the pieces are solid.
One of the problems with placing too much value on this idea, though, is that in real life objects do not, in fact, increase predictably in weight based on size - composition and construction matter. An empty 55gal drum weighs substantially less than a fairly small farrier's anvil. A 2x4 made of oak weighs more than one made of pine or poplar. A laundry basket full of laundry weighs and carries differently than a laundry basket with a cat in it.
So like base ten, this particular Montessori lesson is one that needs a hundred other lessons to modify and give kids a picture of the real world - lessons in empty vs full, lessons in pouring, lessons in lifting chairs and pulling drawers - because all the specific materials can do is give simple lessons. They're all one trick ponies, which is a big, big percentage of the cost - it's not just a matter of shelling out for one great toy but of getting a hundred items that you won't need a year
later.
very orderly environment in which they can notice very small differences
(something that most toys and the natural world don't often provide).
While the first part of that statement has some validity, the last, parenthetical statement is false - it sounds good, but it's not true at all. The natural world is full of order and small differences - heck there's a Montessori material which compares leaf shapes and sizes! Show me a bouquet or roses or a litter of kittens and I'll show you order and small differences.
And since commercial toys are made to appeal to children (unlike many "educational" toys which are made to appeal to parents) they include a lot of order and small differences. As much as parents deride this aspect, it's part of what makes some toys successful. Some examples of popular commercial toys designed around those concepts: My Little Pony, Littlest Pets, Barbie, Hot Wheels, American Girl dolls, Legos... and then there are toys and themes with more substantial differences like Pokemon, a wildly successful series of games, toys and shows because it so very much appeals to kids' interest in order and classification.
The basic principles of Montessori are excellent: learning is intrinsic for all people; learning flows best when it is chosen by the learner; observe the child to discover his or her needs and priorities; see behavior as a way of communicating needs; set the child up for success; when something isn't working, change the environment and recognize that you, the adult are part of that environment; punishments and rewards get in the way of ethical development, so avoid them. All of those principles have been re-discovered and derived again and again in the century and more since Maria Montessori first articulated them - not merely by wild eyed dreamers, but by serious scientific research into education and learning.
All the techniques and materials special to Montessori are just tools to help teachers and classrooms mimic the benefits of a rich, responsive home environment. It can be useful to read about the techniques and materials as a way of learning more about how children develop and learn - I've learned an enormous amount by reading the "whys" of various apparatus. The trick is not to get bogged down in the specifics but to discover the principles. The Pink Tower is pretty, but the principles are everywhere and human beings are wired to understand them - otherwise human kind would have never invented mathematics, much less the Pink Tower, to begin with.
5.21.2011
not so bad, being the grown-up
I love the fact that I can take "no" for an answer from my kids, that I'm secure enough, mature enough, and mindful enough to know that my agenda doesn't always have to come first. My kids don't have to eat my cooking for me to feel special. My kids don't have to dress in ways that make me comfortable in order for me to feel secure or limit themselves to my preferences about technology for me to feel competent. My kids can be who they are even when it is inconvenient and disconcerting to me, and that's a marvel.
2.20.2011
fact or fiction
> The really fascinating thing for me as I experience my son's questions is that the most correct answer to each of them would be "I don't know."
Correct answer? As in "this will be on the test"?
Its worth thinking about why you want a single correct answer, like that, but more than that, its worth thinking about why your child is asking you a question in the first place. Doling out single, correct answers, including "I don't know" can shut down conversation and erode a relationship.
There's an idea that some parents have that a sense of wonder is something that needs to be promoted and encouraged - and that can turn into a kind of closet curriculum for parents, as if children can be taught to wonder by being given vague answers, regardless of what the child is looking for. In that sense "I don't know" can become as dogmatic as "this is The Truth".
Trust that your kids already have a sense of wonder and excitement about the world. You don't need to push it along! And you don't need to define it in your own terms. Maybe its exciting *to you* to wonder at the potential for beyond the rainbow, but your child isn't you - he may rather wonder at the physics of refraction itself and find all the stuff about magic misses the beautiful paradox of the photon.
> The world gets bigger and bigger, more and more open. I was taught in fact and limits, and now each question reveals an assumption with a jello-like foundation. Fun to explore.
Fun for you. Maybe fun for your child - but that's the question, isn't it. Are you letting your own ideas about what's important get in the way of what your child would rather explore? Are you letting your closet-curriculum of mysteries get in the way of someone looking for data?
It doesn't have to be one thing or another, fact Or Fiction - and maybe that's what J. means. Recently Mo and I have been reading a fantasy series about dragon riders set in a facsimilie of ancient Egypt. As a result of that, she's been curious about real Egypt, so we've been looking through books and websites and talking about what's known and not-known, about archeology and history, alphabets and customs... and in the last couple weeks about politics and democracy since Egypt has been in the news in exciting ways. So learning is swirling around, in and out of fact and fiction and the gray area that is "history" - and there's a Lot of that gray area in Egypt! There's a lot of "no-one really knows for sure, but...". A lot of wondering to be done. And, at the same time, there's a chance to see how wondering fades into true fiction. I'm not pretending that maybe there used to be dragons in Egypt - but know that part is pretend doesn't make the stories less fun, or the people we're reading about less wonderful. It doesn't automatically make the world smaller to say a fantasy isn't real - it can make our human capacity for imagining all the more miraculous.
1.22.2011
Origami Lesson
I’ve been paper-folding most of the morning; first working through an origami bird kit with Morgan watching and playing with the birds and then folding one particular form over and over and over. I’ve had lots of thoughts in my head as I fold and refold, and most of them have had to do with learning and creativity and – surprisingly – with limits.
Origami kits and instructions can be a nightmare until you get the hang of the principles of paper folding. The instructions are baffling and senseless until you understand the quite literal ins and outs of the technique. I remember thinking origami unreasonably difficult until my mid-twenties (and I’m good with my hands, good at puzzling out directions from a diagram, too) until someone sat down with me and showed me a few basic folds. I’m still not any kind of paper folding expert but I’ve become a fairly confident dabbler, intrigued with the idea of limiting a creation to something made from a single square of paper.
On a radio program the other night, some artist or other (Stewart of the Daily show, I think, in an interview with Terry Gross) commented that creativity comes from limits. I don’t disagree with that in the least, but I do think it’s important to point out that those limits do not necessarily come from outside the artist.
Take origami, itself. Sculptor Eric Joisel discovered it years ago and changed his whole body of work as a result. He chose to limit himself to the magic of one sheet of paper, no tape, glue, or cutting, and then expanded very slightly from those constraints. Other artists make similar choices: only found objects, only haikus, only fully functional musical instruments, only hats. Artists can rise to the challenge of a limited environment, but that limited environment is unnecessary to the process. In an environment of abundance, artists naturally self-limit for the sake of art.
Today, after years of dabbling I finally have the gumption to modify the designs – first “correcting” a bird I mis-folded at an earlier stage so that it still “works” and then subtly altering the wings of another to make “chicks” instead of elegant flying adults. I am thoroughly impressed with myself and begin folding another bird, thinking of more modifications. Mo stops me mid-fold.
“That looks like a rocket,” she says. I agree, impatient to continue folding. “Can you make me a red one?”
I set aside my bird and make a red rocket. Morgan begins folding, too, but is quickly frustrated; the quirky ins and outs of origami folds are too much for her, yet, and she has folded something backwards. She hands the page to me. “Make another,” she says. “This one is for a mutant mouth.” I fold a mutant mouth and she hands me two more pages. “Now make two more; these are hands.”
“Do I need to make them different?” I ask hopefully.
“No, I’m making a giant mutant plant monster with hands and feet that are mouths.” She returns to her portion of the work, rolling paper into arms, legs, the main stem of the plant. In her lack of attachment to the idea of a bird, it seems, she has found another use for a form that arises half-way though the parrot’s construction. Not just one use, either; limiting her creation to one form, she sees multiple uses for that form.
I have a moment’s resentment (who does she think I am?) but I keep on folding. Yesterday we went to see an exhibit of the glass work of Dale Chihuly, including a film about the making of some of the pieces. They are massive glass works and as the artist has gotten older he relies on others to do the bulk of the fabrication while he directs and adds details. I remind myself of that: today Morgan is The Artist and I the assistant, fabricating parts that her hands can’t produce although her mind knows what they shall be and how she shall use them.
A nose-cone has been added to one form for a rocket and she begins to explain a story that draws from a variety of influences: the Eds, Ratchet and Clank, and something else… where did that giant mutant plant come from? I search my memory, thinking of the Day of the Triffids. Morgan has yet to see the Day of the Triffids, or Little Shop of Horrors for that matter… aha! I have it! Rocky and Bullwinkle’s Pottsylvania Creeper. Morgan’s plant, a native of Planterra, she tells me, has no need to creep, it can stride across the paper boulders to devour the paper rocket whole. Good thing the Eds never made it on board! I rest my hands awhile and return to folding birds.
It doesn’t matter if Morgan never “gets” origami or learns to create her own origami designs. It doesn’t matter if she accepts or eschews the limits of origami, itself. She already instinctively knows the most important artistic principles: to let the materials “speak” to her, to let her knowledge of other artwork (including nature) inform her, to follow her muse, to collaborate when appropriate, enlist help when needed, and most of all, to tell her stories. And curiously enough, in the midst of freedom to use whatever materials in whatever way she wants, she understands the value of self-imposed limits. I’m not trying to say my kid is some kind of genius, but that this kind of self-selection is so natural, so obvious to the human mind, that we adults don’t need to set limits on children in order to encourage creativity. What we do need is to be a little less attached to our own ideas so that we have a better chance of re-envisioning the world through the eyes of our children.
Eyes of our children. I’m not a fantastic typist and wrote “yes of our children”. A serendipitous mistake in this context. Sometimes unschooling isn’t so much about saying yes as stepping beyond our attachment to “the right way” in order to experience the yes of our children.
11.02.2010
excess
"natural mommy" wrote:
>If I could, sometimes I would just veg out and do all my computer tasks and fun for a few days straight
You "can" though - you could decide that leaving out a few boxes of cereal and the tv on constitutes taking care of your kids and do what you want to do. You could put them in school or daycare and forget about them for hours at a time. You're choosing not to do those things, choosing to set aside what you want for other things that you value as much as your desires. It helps to see those behaviors as choices. You're not "stuck" being someone's mom, you are actively choosing to parent because doing that is meaningful to you in some way.
The economics of limits can skew choices in big ways, they can make choices feel like chores vs luxuries. If getting on the computer feels like an escape from “have to” then that’s going to affect your reasoning. My MIL, for instance, spends the day on the computer for her work, so the last thing she wants is to be on email lists or social networks – getting out in her garden feels like a luxury so she’ll spend hours there
>>Fact is,there ARE plenty of kids (and adults) that would spend all day watching t.v, playing vid games or whatever suites their fancy, so when are they taught about balance vs. excess?
Plenty of people do those things who *have* been taught about balance vs excess, though. There are tons of messages in the world about moderation and what one "should" do to be good, be healthy, be productive... yada yada. The trouble is, teaching doesn't "get" people to produce specific behaviors.
A lot of people spend time watching tv or playing games or surfing the web as a way to de-stress, or step back from other parts of their lives that are unpleasant - school or work for the most part. School isn't an issue that unschoolers need to worry about outside of deschooling - but its Very common for kids to spend a lot of time watching tv or playing games while decompressing from schooling. If a family member is needing time to de-stress from work, then other family members can help with that by bringing food and offering companionship so the person isn't having to choose between one value (connection) and another (decompressing).
One of the fascinating aspects of parenting as a partner is getting to see kids choosing to do things for reasons other than “whatever suits their fancy” even though they have the freedom to do exactly that.
>>This topic particularly concerns me since our family is loaded with people who like to go to the side of excess and in an unhealthy way.
It can help to think about what those people have experienced in terms of both limits and support. In conventional parenting a lot of support only happens within a context of limits, so "no limits" looks a lot like "I don't care". But support doesn't have to involve adding more limits to a person's life. Its important to articulate real limits! Drivers unable to see little children is a real limit in a parking lot. Mommy too hungry/tired/hormonal to deal with taking kids to a playground is a real limit. Not enough money for certain foods or toys other things is a real limit. The wonderful part of unschooling though is that limits aren't an end game. They're a chance to find other options.
Mo likes to do things in big chunks - if she's going to play a game, it will be for hours and hours. If she's going to watch a movie, she'll watch it a bunch of times. It doesn't help her to pull her away from what she wants to do - its more helpful to find her ways to "fill up" as it were so that moving on to the next thing feels good and right to her. That can look a lot like "excess" and I could point to others in the family who tend to excess, but I can also point to people with a lot of drive and focus, too - a lot of drive and focus is another kind of excess!
Why one and not four? Why one and not ten? It’s a little ironic, that you’ve picked a fairly extreme limit if your goal is to coax your kids more toward moderation. Why not, instead of a number limit, put the candy up out of the way and say “yes” whenever asked? Those are things to think about.
How sick is sick? That’s something else to think about. Would they get a belly-ache or would they need to be hospitalized? There’s a lot of ground in between those two options, too. Would it be a catastrophe if they ate it all in one day?
How much do you want to emphasize that candy is a luxury item? That’s something else to consider. A whole lot of food issues arise from limiting Because of the economics of limits – limited foods are luxuries so its natural not just to crave them but to binge on them.
It isn’t a horrible thing to eat to excess now and again – arguably, its part of human nature. This spring I discovered a new source of fresh, organic fruit and went a bit overboard on fruit. I made myself a little sick and rebalanced. That’s part of balance, if you think about it – its not some kind of middle of the road stasis, our human bodies and interests often swing wildly in one direction and then swing back to equilibrium. Its unfortunate that we’ve developed a lot of culture pressure saying the extremes are “bad” and the middle is “good” because it skews our ability to see what natural learning looks like. A lot of natural learning involves extremes. Passion is an extreme, and it’s a really common way for people to learn about the world.