Math is more than minusing

Ruth Beechick once complained that school readers used to push all the really interesting stories to the back of the book, and maybe you got to them at the end of the year. Supplements in math class can be like that too--if you do them when you get around to them, you may never get around to them. We don't always have to be bound to the Big Fat Math Books, at least not all year long.

I think that's what was wrong with most of the math education I got during school: most of it, progressive as we were all supposed to be in the '70's, was simply arithmetic. A few angles here and there, but mostly it was about doing the basic operations. Once in awhile they hauled out the expensive kits of attribute blocks, or gave us laminated cards with "math experiences" on them, but even the teachers didn't really know how to use that kind of math stuff, so it was always back to arithmetic in the end.

Which, in a way, didn't serve us too badly; at least, as I've said before, I do know my times tables and I don't get caught too often on those silly trick questions like "what's 8 divided by 1/2?".* But I also hit that girl's grade 4 math block around long division, and it was never the same after that. I do know for sure that we never did any math research, or studied mathematicians, or looked at mathematics as something big and interesting that grownup people did. It was just what you did after reading class and before gym.

So I was very interested to read "Mild-Mannered Math No More" by Cheryl Bastarache in The Old Schoolhouse, Winter 2008-9 issue, and to also find it online. This article talks about basing your math course around a math notebook that's full of more than just sums: you can include "notes, copywork, research, challenges, responses, and fun stuff." In other words, like a scientist's journal, or a Book of the Centuries, or a Latin notebook, or any other notebook-with-a-plan like that. A book full of stuff that's actually interesting...and, as Cheryl says, if you're brave enough, you could make that "the centerpiece of your curriculum."

*The answer is 16. 8 divided by 1/2 means how many halves fit into 8?

Ooh, oxygen!

Fun with chemistry and Jean-Henri Fabre: click on the PDF of Eleanor Doorly's Insect Man and read the chapter on pages 20-21. (Penelope, Geraldine et al are an English family visiting France and trying to find all the places where Fabre lived.) We happen to have a set of Bonjour magazines from Mama Squirrel's own school days and one of them has photos of Avignon, which we used along with this chapter. Since most people haven't saved their 1977 Bonjours, you can look at these pictures on Wikipedia.

Well, at least nobody got killed.

Rummage Sale Geography

Something neat we found last Saturday: the Interfact Reference Children's Atlas. And the CD-Rom still runs on our XP system, even though it's ten years old. Not bad for a dollar!

One more reason I am still liking Math Mammoth

Is it only coincidence that the two math programs we have liked best both have the initals MM?

Actually, so did one we didn't like as much, but never mind.

This is what I'm happy about: included in the support materials with the downloadable Grade 3 Light Blue curriculum is a worksheet generator for all the Grade 3 topics! Times tables, measurement, money, clocks, addition, subtraction, everything.

I also like that you get a Canadian version of the money chapter (there's a European one as well)--very helpful.

Switching to this program is probably one of the best things to come out of the Review Crew this year for Crayons. I'm only sorry that I didn't use it earlier with Ponytails, because I think she would have liked it too. (Ponytails has been using some of the Key To books this year.) I know there are lots of other good math programs out there, but I'm happy we got a little shove into using this one.

On birthdays and frugality (links and thoughts)

Getting Freedom From Debt (or Cents to Get Debt-Free) has a guest post about DIY Birthday Cakes.

Nothing New Nothing Wasted has some thoughts on the wastefulness of birthday decorations and disposables.

Here's our own post about Birthdays, Frugal and Otherwise, from a few years ago, with a link to this frugal-birthdays post at The Common Room. And here are the posts from Crayons' Horse Party (last year), Flower Fairy Party Menu (two years ago, with extra comments about the cupcakes), and Butterfly Birthday (five years ago). Other ideas we've used are meeting friends at a park (booking a (free) gazebo in case of drizzle) or having a party that's mostly outside--does save on decorations. Or a tea party for little girls--if you already have the teacups and things, your decorating problems are solved. I read, I think in the Tightwad Gazette, about a parent who took birthday guests to either a flea market or a thrift shop, giving them each a couple of dollars to spend. As far as the issue of the guests bringing presents goes...we've struggled with that one, and solved it at one party by asking them to bring supplies for MCC school kits instead. (That inspired one of the guests, who asked the kids at her own next birthday to bring needed supplies for an animal shelter. We've also been to a wintertime party where it was requested that we bring mittens, hats etc. for a mission for homeless people.) Our kids have been to some very creative parties too where the main activity was sewing or some other craft...one of them brought home a rice-filled hot bag one time. For the Apprentice's ninth birthday, we hot-glued things on painters' caps (cheap from the paint store) and had backyard games like charades.

One idea that was less successful for us was the time we took little Apprentice and her friends to a McDonald's playland--I posted about that a long time ago. That was a year when we opted for "simple" (as in "make it simple for us") instead of "frugal"--but some of our "frugal" parties have gotten better reactions from the guests. This weekend's bowling party was more on the "simple" than "frugal" end, and we did use some disposables (because it's hard to manage china plates at the bowling alley), but there's nothing to say that you should never have parties like that either. We like to support that family-run business, they charge a reasonable price for an hour's bowling plus free chips and drinks, and it was something that Crayons was really looking forward to. We thought about doing a home-based superheroes party, but this time around, she really wanted to do something like bowling...and after a busy rest-of-the-weekend, I was just as glad not to have to figure out party games. So I don't apologize for that. (Besides, we lucked out--the people who had the party room just before us left all their pink balloons up on the wall!)

Anglewings or angelwings?

We're not sure--anyway, this looks just like the butterfly that Crayons found this morning. Folded up, it looks like a dead leaf--but when it opens, you can see the tortoiseshell pattern.

Forgotten fractions?

I found this article (and quiz) by Brian D. Rude through a comment on another blog.

Can you pass the fractions test he gives his first-year college students? Can your kids? And what does that say about the success/failure of North American education?

A Month with Charlotte Mason, #30 (On Dandelions)

How are we supposed to end this?

We started with A Leisurely Education. Freedom from the small round of busywork, opportunity to grab hold of something bigger, learning to see ourselves (including our children) more as we are in God's time and in God's universe. Living without futility.

And I'm ending with dandelions.

The Treehouse backyard this week has been covered with yellow dandelions. Much-maligned little flowers that provoke criticism from the neighbours (spraying's in disfavour, but they would like to see us at least hard at work rooting them out). They're not good for much except making more dandelions (okay, I know you can eat them too). The first big batch are either going to seed or were cut off last night with the lawnmower, but they'll be back. [As in, within 24 hours.] Nobody really gets rid of dandelions forever, even if they want to--they're stubborn. And we don't want to get rid of them. In spite of the seasonal allergies kicking in around here, we like our dandelions.

I get the feeling that cultivating a yard full of unfashionable dandelions is somewhat like our approach to education, and maybe our approach to life. This is a time of too many conflicting ideas, at least around lawn care. Lawn spraying is now illegal here (we didn't spray anyway), but people still expect you to have a weed-free, dandelion-free, well-trimmed piece of grass around your house...more or less the same as anyone else's. Educational powers talk about diversity while squeezing out the individual. They dump a lot of fertilizer, if you'll pardon the metaphor, and try to control what grows and what doesn't.

Keep the dandelions growing, if only as a reminder that our natures are stubborn and won't be satisfied with educational sludge. Leave enough room for the intangibles and the poetry--as Cindy said, we can always catch up on grammar later.

A game of romps (better, so far as mere rest goes, than games with laws and competitions), nonsense talk, a fairy tale, or to lie on his back in the sunshine, should rest the child, and of such as these he should have his fill.--Charlotte Mason

A Month with Charlotte Mason, #29: Fragmentation, trivialization, and redemption

"Our four children came home from their private boarding school in Rhodesia for the last time. They were well-dressed, well-shod, well-fed, prosperous-looking children. Only when one listened to their vapid chatter, limited by both vocabulary and knowledge, did one glimpse the distressing poverty of their minds."--Joyce McGechan, "To Prosper in Good Life and Good Literature," Parents Review, 1967

I've been struggling to write the last two posts in this series, trying to decide on an ending. I think I just had this one handed to me in one of Grandpa Squirrel's Toronto weekend papers. Click over to Saturday's Globe and Mail and read Margaret Wente's interview with Camille Paglia. [LINK FIXED] (Warning: several of the comments afterward contain language that is just not nice.)

I do not agree with her viewpoint on other important issues, but she has gotten the problems of education absolutely correct. Just--wow.

"When I went into graduate school at Yale, the professors of poetry were the leading lights on campus. Can you imagine anything comparable today?"

"Art history survey courses are in the verge of extinction. Teachers have no sense that they are supposed to inculcate a sense of appreciation and respect and awe at the greatness of what these artists have done in the past. The entire purpose of higher education is broadening. But since then we've witnessed the fragmentation and trivialization of the curriculum."

"The long view of history is absolutely crucial....I believe in chronology and I believe it's our obligation to teach it. I've met fundamentalist Protestants who've just come out of high school and read the Bible. They have a longer view of history than most students who come out of Harvard."

"Educators need to analyze the culture and figure out what’s missing in the culture and then supply it. Students find books onerous. But I still believe that the great compendium of knowledge is contained in books."

"At the primary level, what kids need is facts. They need geography, chronology, geology. I'm a huge believer in geology – it's all about engagement in physical materials and the history of the world. But instead of that, the kids get ideology. They're taught that global warming has been caused by factories. They have no idea there’s been climate change throughout history. And they're scared into thinking that tsunamis are coming to drown New York."

How can we stay out of this "landscape of death" and create an oasis of hope? According to Camille Paglia, the answer is not in teaching critical thinking, ideology, or hysteria over drowning polar bears. It's in poetry, geology, the long view of history, physical books, geography, art appreciation. It's the struggle against fragmentation and trivialization. Question is, will anyone listen?

"Our shabby little crew, with few material advantages, have a good life. They work hard at lessons and on the farm. Then duties done, they run free on the veld, catching butterflies, collecting stones, watching birds, gathering wild flowers. Evenings for them are all too short. Specimens must be identified, labelled, catalogued. There are still unread books on the bookshelves, as well as old friends to be re-read. Daddy must hear someone's latest effort at poetry composition, or told the anecdote about George IV's false teeth.

"Thanks to Charlotte Mason and the PNEU school these children of ours are, in fact, rich."--Joyce McGechan

A Month with Charlotte Mason, #28: Sunday Ponderings from the Parents Review

"Geology I dabbled in, having met with "Lyell's Principles" in the School Library. A piece of spar still remains which I obtained from the lowest Lias at the deep cutting, then being made, on the London and Birmingham Railway; I loved to gaze from the top of its banks on the three spires of Coventry. The slight knowledge acquired of what was then a new science was like a seed thrown into the ground, which did not germinate till long years after. I still eagerly pursued Entomology, chiefly with Wratislaw."--"Memories of Arnold and Rugby 60 Years Ago," by a Member of the School, in 1835, '36 and '37. Parent's Review, Volume 7, 1896, pg. 127

"Fifty years ago, when that famous pioneer of science, Dr. William Buckland, was Professor of Geology in the University of Oxford, it was his pleasant custom on occasion to announce to his class at the close of a lecture, 'Tomorrow, gentlemen, we shall meet at the top of Shotover, at ten o'clock.' And to the top of Shotover Hill the class would ride or walk from Oxford the next morning, and there the professor would talk to them in his vivacious, impressive fashion about the formation of the hill on which they stood, its limestones, clays, ironstones, gravels or fossils, on the evidences of denudation or the methods of stratification. And if things got a bit dull he would take especial delight in giving the most fastidious of the equestrian freshmen a practical lesson in geology by leading their horses through the stickfast mud on the slopes so that they might remember the nature of the Kimmeridge clay. And, doubtless, they did remember it, with the help of Common Room jokes thereon.

"Dr. Buckland, like every great man of science (and if one may presume to judge from programmes alone, like the truly scientific promoters of the work of this Union) was thoroughly convinced of the supreme importance of the school out of school, of out-door education. Buckland used often to say that such geological terms as stratification, denudation, faults,--to mention only a few of the commonest--could never be understood through lecture-room teaching alone. Shotover Hill was to him a lesson in geology, far superior in force to any which could be learnt from books or lectures, however admirable, and however rich the illustration by diagrams or pictures, or even by actual specimens of rocks and fossils. And all such illustrations in the lecture-room itself, Buckland used with a liberality that was utterly astounding and disconcerting to the academic Oxford of his day.

"Yet Buckland was teaching young men, not mere children, and might justly have relied to some extent on their fairly mature intelligence to grasp his verbal explanations of geological phenomena. But with the true teacher's instinct he studied his own mental processes, and asked himself, 'Now, could I really, thoroughly understand what a fault looks like, could I have a vivid mental picture of it from books and diagrams if I had never seen the thing itself in the rocks?' And being aware that the intense reality of his knowledge came purely from his early friendship with the rocks themselves at Lyme Regis, and Bristol, and elsewhere, from a long-continued intimacy with the thing and not the name or even the picture of the thing, he made it his business to bring his students to see the thing itself, since in such a case the thing could not be brought to the students.

"This, then, is the testimony and the practice of one who was a master of earth-lore. No less significant is the evidence of one whose study lay amongst the great stone-books of art. As Buckland was the pioneer of geological studies in Oxford, so was John Henry Parker (now resting in the quiet of St. Sepulchre's, near Jowett and T. H. Green) the pioneer of the study of Historical Architecture. In one of his books on Gothic Architecture, which have been the source of a new joy in life to throngs of students, Mr. Parker tells us with the brief unmistakable words of a master: 'The only real way of thoroughly understanding architectural history is to go about and see the buildings themselves.'"

"If Buckland and Parker thus insist on the necessity of bringing the real thing before the eyes of students of university age so that the thing may teach its own lesson, how much more essential to right understanding is this 'real' teaching for children of school age, and how absolutely the only right sort of teaching for the very young whose school days have not yet come."

--"At School on Hampstead Heath," Parent's Review, by Mrs. Grindrod, 1897