Purposeful Ramblings Through My Mind

I had a chat with my principal about the protocols involved in getting payment for lost books. Unsurprisingly, the families with the most lost books are also the families we are most worried about in other ways. Mental illness runs unchecked in these families, we regularly have to decide if such-and-such a thing is worthy of a CAS call, and when there are a collection of characters at the office, at least half of the usual suspects also have lost library books.

The bottom line: we cannot force payment of library books before letting these families do other things with the school community. We can't force payment at all. The reasoning is that for most of them, the problem isn't something fixable by more effort or better responsibility; it's about lack of resources, in particular mental health and money. The mental health issues keep them from being able to take care of their library books to begin with, and the lack of money keeps them from being able to replace the books.

The good news is that in the entire school, there are fewer than forty lost books, and nearly half of those went missing since March Break, which suggests to me that there's a good chance they'll turn up when I send home a letter with a dollar amount in it. Considering that at this time last year, there were more than three HUNDRED books listed as lost or overdue, that's pretty good. But the fact is, I'm not going to get back most of the money for those lost books. I'll get back some of it - mostly from those families where the lost book really was an accident and they're basically responsible people.

I'm of two minds about this. On the one hand, I can see where the "it's not their fault" justification comes from, and I get the equity thing. Heaven knows I struggle enough to keep organized, and I'm a functional adult by any reasonable standard. Making sure that the kids who need the library the most get a fair shot at using it, regardless of their parents' ability to pay library fines, is a reasonable goal.

On the other hand, I understand why more functional people look at decisions like this and get angry at those they perceive to be taking advantage of the system. I especially understand when it's quite obvious that they ARE taking advantage. We've heard these kids say things like, "My mom says we don't have to pay for this trip because you'll let us go anyway, so we got pizza last night instead." In an effort to understand and account for the ways in which it is not their fault, we've set up a situation where what little responsibility they might have taken is no longer necessary. We've removed any sense of agency from them.

I've run my library on a shoestring budget. I've spent just over five hundred dollars for the entire year; I've insisted on books being returned before another book goes out, though the head librarians in my board question that decision on equity grounds, too, with the result that I have one missing book for every five students instead of two missing books for every three; I've kept the place shipshape despite my own difficulties with organization, so that if a kid says a book was returned, I can pinpoint where it should be and either track it down or be very sure of myself when I tell them they didn't return it; and at the end of the day, I have no leverage to finish the job and keep my collection from deteriorating. That's incredibly frustrating.

I just realized I forgot to write about this!

On Tuesday I went to a meeting of Peer Mediator "champions" (aka the teachers running the Peer Mediator program.) The person who runs the program at the board level is a social worker, and she's been doing it for a little more than two decades; I've come across her a couple times before, though I've never been the one planning to run the program before.

More interesting than this is the fact that Hamilton's Peer Mediators program has been studied fairly extensively by a psychology team at McMaster, due to the fact that this social worker's husband is a doctor of psychology there and chose it as a study topic. He's written a bunch of peer-reviewed papers on aspects of the program, including designing the test data to see if it was working. He presented the bare bones of his findings at the meeting.

The schools he studied at first were all inner-city schools with a lot of problems. I mean, these are schools where teachers and students are regularly told to fuck off and police in the office is a near-daily event. He stationed his grad students around the playground and set up what they were counting: the percentage of ten-second intervals that contained a physically violent incident. Two of the schools had numbers approaching sixty; that is, sixty percent of ten-second intervals on those playgrounds had at least one violent incident. The third school topped seventy percent.

When the programs had been running for a month or so, he sent his grad students back to count again. Then he checked again a few years later and controlled for some other variables. Some of the results:

1) The incidence of violence on the playground at those three schools after a month diminished by about half - nearly two-thirds for the third school - into the twenties in all three cases.
2) When there were one or two peer mediator teams on the playground, the incidence remained generally around 25%, but when there were four or more teams out there, the incidence was reduced as low as 5%.
3) Teacher did not have a good grasp of what was happening on their playgrounds; they knew there was a difference but were uniformly shocked both at the original numbers and at the success rates.
4) The effects did NOT diminish over time, provided that the level of peer mediator support remained consistent; if it diminished, the incidence of violence rose again, and the teachers were not aware of it - but the kids were.

I asked if any studies had been done to see how far the language of peer mediation permeated the classroom environment; that is, how much were teachers using that language to solve problems in their classrooms? He didn't know, but wrote down the question for possible further study. My theory is that schools where teachers use the language of peer mediation consistently end up maintaining their peer mediation programs more effectively and report fewer instances of bullying than schools where the peer mediation stops at the classroom door.

Anyway. I've found another teacher who will be taking care of the organizational elements that I'm generally horrible at, and supporting me in the interpersonal stuff - meetings and training the kids and troubleshooting. Now the trick is to get it up and running.

Inanity of bureaucracy, example #56 439: In its infinite wisdom, the government of Ontario set out to put a law in place that would provide students with only healthy food at school, to give them good role models for healthy eating in general.

Sounds okay, right? Here's what's happened:

1) The school and school board aren't allowed to provide any unhealthy foods at in-services for teachers, or staff meetings. On their list of unhealthy foods: anything with caffeine. Someone please explain to me how serving coffee and tea to teachers at an in-service, where the kids aren't present, is setting a bad example for the kids? Because I'm not seeing it.

2) A whole bunch of small pizza places are going to have trouble surviving if they previously relied on the school market. The regulations require them to print every ingredient on the box, and only a couple of chains are big enough to be able to afford to specially-print their boxes with that information. While they're looking for allergens of course, they're focusing more on fat content and empty calories, so regular mozzarella has been replaced with a low-fat version and the crust is now whole wheat, and something was done to the sauce, too. Even if the small places could comply with the ingredients, they can't comply with the labeling so they're out of luck. All this from preventing a slice of pizza with regular mozzarella and white flour from getting into kids' stomachs at school once or twice a month. It seems like overkill to me, too.

3) Parents aren't allowed to bring in snacks for birthday parties anymore, not even if they're labeled, because they break the 80/20 rule of 80% healthy food to 20% treats.

4) Teachers aren't allowed to use candy or other treats as an incentive in class. This is the only one of the whole thing that I can get behind, and even this is taken to an unreasonable extreme: you mean I'm not allowed to hand out freezies to the cross-country team as they finish a race? Really?

5) We get a certain number of "free days" when the rules temporarily disappear, and we have to decide in September which days they will be. There will still be a Halloween party, and a Christmas party, but no, we can't hold anything a day before the rest of the school because it fits our schedule better as a class, because then it wouldn't be on the "free day."

6) Their list of healthy foods is weird. Diet caffeine-free pop seems to be fine. I'm confused; all the research is suggesting diet pop is at least as bad, or worse, than regular pop. (Yes, I drink it anyway.)

I am truly annoyed. I think I'll take a six-pack of Coke Zero (with caffeine!) to the in-service on Tuesday to share with people who don't realize they can't get coffee when they get there.

Any illustrator types want to join me in a summer project?

I need some new French plays, which I'm prepared to write myself based on fables and fairy tales. I'd love to have them illustrated into a storybook that I could use to introduce the play, and some vocabulary cards with parts of the same illustrations for the major vocabulary. I'd pay to get them printed in colour and to get the storybooks bound. If I could drum up some interest in them, I'd then approach an educational publisher about publishing them as a series.

Anyone interested? I could use a francophone editor, too.

The problem:

You've been pretty lazy about laundry lately. You've been throwing socks into the drawer without matching them up first. You also haven't taken your laundry downstairs to wash it, so at the moment, there's only two unmatched pairs of socks in your drawer - one black, one red. Most of the time this isn't a problem because you've got lots of time to get dressed, but this morning, you're being picked up to go on a trip with a friend, and your alarm doesn't go off. Your friend knocks on the door expecting you to be ready, and you need to get dressed in a flash. You reach into the sock drawer and pull out two socks.

what is the probability that they match?

Now, I can't take credit for this problem. It's straight out of the Ministry of Education document entitled "Guide to Effective Instruction in Mathematics: Probability," for grade four to six. I do take some credit for how far we took it, however.

We started with paper bags, in which were two pairs of construction-paper socks. Kids did thirty trials and then predicted the actual probability based on their experiment. Then we figured out how many possible pairs there were, and how many of those pairs gave them a matching set. We got two matching pairs out of six possible pairs, or 2/6. Using what we knew of equivalent fractions, we reduced that to 1/3.

Then we extended it. What happens if we've got three pairs of socks? Is the probability of a matching pair better or worse or the same? I asked them to predict what they expected to find, and write down their prediction; then I asked them to prove it. Well, with three pairs, the probability is 3/15, which is 1/5. I reiterated, as I have many times, that it didn't matter too much if their prediction was wrong; what mattered was that, when they realized they were wrong, they went back to figure out why they'd made that prediction and checked to make sure they had it right now. I made sure we were using good scientific language for this process - hypothesis, experiment, proof.

Okay, so what about four pairs of socks? They figured out that the probability then was 4/28, and reduced that with help to 1/7. That was the end of day one.

On day two, I took the information we'd gathered the day before for two, three, and four pairs of socks, and organized it into a chart. Then I asked them to find the patterns, and use the patterns to predict the next term.

They came up with two patterns, only one of which I'd found myself. The first group noticed the pattern in the reduced fractions - 1/3, 1/5, 1/7 - and predicted that the next reduced fraction would be 1/9. Then they worked backwards to figure out the unreduced fraction of 5/45. The other group took the unreduced fractions - 2/6, 3/15, 4/28 - and figured out that the distance between 6 and 15 is nine, and the distance between 15 and 28 is 13 which is 9+4, and they postulated that the next term would be 13+4 more than 28, which is 45.

Anyone who got as far as seven or eight terms and gave a pattern rule that worked got a B. If they could use the phrase "theoretical probability" in their answer, that was bumped up to an A-, because the distinction between experimental and theoretical probability is a grade six topic according to the curriculum. Those who continued to develop the pattern for many more terms got an A.

Then I asked those who clearly understood that pattern to come to the carpet, and I introduced them to the concept of the nth term - when you don't know the term number, you can replace it with the variable n. If we could figure out how to get from the term number to the reduced fraction, consistently, then we could come up with any term even if they were out of order. So we looked at it, and realized that 1/3 is one less than two times two; 1/5 is one less than three times two; 1/7 is one less than four times two; and so on. So the denominator was two times the term number minus one. I showed them how to write this; 1/2n-1. To get an A+, all they had to do was show me that they could apply this to fill in two lines of the chart that were out of order, because the ability to solve an algebraic equation is a grade seven topic - two years above grade level.

In my class of twenty-five, I gave out exactly two B's. Everyone else got an A. My students on IEPs ALL got A's, and I didn't even have to adjust their expectations downwards; I just had to make sure they had access to support to clarify the patterns they saw.

The A's here are for both probability and patterning, so that's two A's on most report cards for my kids.

The grade five curriculum requires kids to develop a basic understanding of a variable for the first time: as an unknown number and as a series of values dependent on each other.

My kids already have the first definition. So yesterday we started on the second.

I put up on the board ___ + ___ = 17 and asked them to find all the ordered pairs that would fit in the blanks. I showed them how to write an ordered pair (0, 17) and then let them have at it in their groups. Meanwhile, on a piece of chart paper, I drew the upper right portion of a co-ordinate grid (because my kids haven't learned integers yet and I didn't have a lot of room, anyway.) When my kids were acting like they were done, I explained that a co-ordinate grid was a way of using math to draw things; it was just a format that everyone would use in much the same way, like a language, so that anyone who saw it would understand how it worked. I rewrote the equation on the board as x + y = 17, and asked one kid to come up and plot a point on the grid. She took (0, 17) and pointed to seventeen on each axis, saying that they were different points that were written the same way. She drew both points. I told the class that this was a problem; how could the same two numbers indicate two different points? How would that help anyone to figure anything out? I let them stew about it for a minute, and discuss how the points were different, until someone finally said, "But in the equation, x came first." I got that person up to the chart to explain what she meant, and we figured out that (0, 17) was a different point from (17, 0).

After that, we plotted each of their ordered pairs on the grid in turn, and I showed them how to label the points correctly. When we had about half the points up there, I got one of the girls who was complaining she didn't get it to come up. I handed her a metre stick and told her to play connect-the-dots.

I had expected the lesson to end there, but it didn't, because when my students notice something, I run with it. Half a dozen of my kids looked at the resulting triangle and said, "That's a right-angled triangle!" One more said, "It's a half-square triangle like in our quilt blocks!" We discussed the other two angles - both 45 degrees - and I asked the kids, "What do you think you'd have to do to get a triangle that wasn't a half-square triangle on this grid? What would the equation look like for that?"

Well, they tried x + y = 12, though my gifted kid told them right off the bat it was going to just make a smaller version of the same triangle. It did. When it seemed they were stumped, I took the metre stick and drew a line from (7,0) to (0,14). Then I asked them to figure out the relationship between seven and fourteen. They eventually got it, with a bit of help to get the form right: 2x=y, where x=7.

Every kid in the class understood the basics of the co-ordinate grid. Every kid as far as I could determine understood the ordered pairs and how they were graphed. A few kids couldn't wait to pull out the graph paper and try some equations on their own. They were tickled by the idea that I did this math in grade nine and it's currently in the curriculum in grade eight.

Today's lesson: Explain why x + y = a whole number is always going to produce a half-square triangle, no matter what the whole number is.

The grade five curriculum says that students are only supposed to measure angles up to 90 degrees this year. In grade six it's 180 degrees, and by grade seven it's the whole circle.

Of all the ridiculous and counter-productive divisions of concepts they could have made, this one has to be near the top of the list.

My kids were having difficulty understanding exactly what it was they were measuring with a protractor, and understanding the units was even worse. So I drew a co-ordinate grid on an overhead (no numbers, just the lines.) They told me it was a t-chart, it was an X, it was four triangles - that's when I stopped them. Where are the triangles? So one kid came up and drew the lines that connected the four points of the grid into a square, bisected diagonally twice. We measured the angles in the middle and the angles on the outside and discovered they were ninety degrees and added up to 360 degrees.

Then we talked a bit about the Babylonians, who came up with a number system with a base of sixty. They figured out that they needed a way to divide up a circle into even fractions. Since they did things in base 60, when they divided a circle their first instinct was to divide it into six parts, each of which was 60 degrees, and the 360 degree circle was born. We talked about why you might need to measure angles, and how that was used. I gave them the vocabulary words they needed: bisect, radius, diameter. At this point I'm well into the grade seven geometry curriculum, and they're eating it up.

Then I pointed out that you can draw a triangle in a circle by going through the centre point of the circle, using the radius as sides. We measured the inside angle of that triangle and found it to be 58 degrees. With one more line, I showed them the complementary triangle: the one made with the 122 degree angle.

They spent the rest of the period exploring triangles as fractions of circles and investigating the number of degrees involved. I have three different kids who realized that the sum of the outside angles would be greater than 360 because they were measuring a radius but also a line that went through two points on the circumference. I had a fourth kid who realized that if she drew the X so that the angles weren't all 90 degrees, she could figure out the measure of all the other angles if she knew the measure of any one, by doubling it for the opposite angle, subtracting that number from 360, and then halving the result. (Convoluted but it works just as well as figuring it out using 180 for the straight angle. Efficiency will come later; right now I want comprehension and wonder.)

I'm going to get those four kids to present their findings to the class tomorrow so the rest of the class can be exposed to those ideas and play around with them themselves. So basically, I can give a B to any kid who can measure an angle less than 90 degrees accurately, and an A to those who can explain how angles are related to circles and why triangles add up to 180 degrees.

I love it when lessons become kid-directed explorations of important mathematical ideas.

I've just been reading the short stories written by my students. The assignment was for a realistic story, with characters similar to themselves experiencing everyday problems.

Now, my class is quite diverse. Out of 24 students, 14 speak a language other than English at home. Of those, three are white (Eastern European) and the rest are mostly from the Indian sub-continent. Five are Muslim, one is a Coptic Christian, the rest are Hindu or Orthodox Christian.

So it was with some surprise that I noted that all of their stories, without exception, used Anglophone names. There was a full complement of Melissas, Jessicas, Amandas, two different Sams, two Maxes, and a few slightly less-common ones. But not a single name in the bunch that seemed to come from their cultures. Not a single reference to cultural food or religion or clothing that wasn't North American. To read the stories, you'd think my class was white-bread middle class from the Prairies.

I find this rather disturbing. We've read more than one story from their cultures, we regularly discuss how each culture in the room has something special to bring to the table, I make opportunities to discuss the things that each culture has in common with the others and the things that set it apart, and yet when it comes to a story that was supposed to relate to their own lives, I get nothing so much as classic examples of acculturation.

I'm not sure what to do about it, though. A classroom is a place where children are enculturated, and if their culture is not the dominant one, some acculturation is almost unavoidable. That said, I want them to feel that their culture is valuable and valid in my classroom, and that a story that involves their experiences as minority cultures in Canada is not only acceptable, but perhaps preferable in this situation because it's closer to their experience. I wouldn't expect all of them to write that way, but I would have expected a few of them to do so.

I'm going to post this to racism_101 as soon as someone over there approves me for membership, and see what they have to say.

I hate marking math tests.

I thought I'd gotten past this particular affliction of the teaching profession when I switched to a problem-solving, constructivist approach to teaching mathematics. Unfortunately, I still have to give kids a grade, often before they've had the time to explore topics as thoroughly as they needed to. So I end up on someone else's timeline, giving math tests that I know kids aren't going to do well on because they haven't had enough practice, and then I have to mark and report on the results.

If report cards weren't due next week, I'd put the quilt unit on hold, go back to measurement, and do a few more questions. I'd get small groups discussing their strategies, have them write some journal entries about their struggles and successes, and coach the struggling kids using guided math. Then in a couple of weeks, I'd test them again and bask in the glow of a class full of B's and A's. But with report cards due next week, I have to take the marks I get on the first test.

Realistically, I know that their marks aren't going to improve on this kind of question until I've taught more multiplication and elementary algebra strategies. They're not sure of how to deal with an equivalency in a problem (If Adrick takes three steps in each meter, how many steps is he going to take in two kilometres? How far will he have to walk to go 10 000 steps?) and for that, they need a lot more practice at multiplication and division. I could probably come back to this type of problem in April and they'd be much more ready for it than they are now.

Even so, I hate giving out C's to kids who could probably get a B if I could give them an extra week to work on it.

On the other hand, I have no trouble giving C's to kids who measure in centimetres and give units in kilometres. Seriously, it was on the board in three different spots, in their notebook in at least two, and I pointed it out before they started the test. Not a whole lot of excuses, there. Careless work doesn't get my sympathy.

Full-day kindergarten, learning hubs, and extended parental leave are all here, and I think the vision is fabulous.

Nevertheless I have some reservations.

First, I think combining Early Years centres with schools and kindergartens has the potential to be excellent for kids. I'll be waiting to see how my union responds to this, because so far, they've been against the idea of full-day kindergarten unless it's staffed by their own members. I can see why - ECE workers do not have the training in literacy and assessment that a certified teacher has in Ontario. The only reason the government would like to put ECE workers into that job is that they're an awful lot cheaper. In Ontario, ECE is a two-year community college course, versus teaching's average of five years university. As a result, ECE workers top out at about the salary where teachers start.

The second big problem is physical. Kindergarten and early years centres need classrooms with bathrooms and sinks and water fountains right in the room, and for the early years centres, probably an area that meets Department of Health regulations for preparing snacks. Even schools that have empty rooms don't have rooms that are set up like that. Expanding kindergarten from half-day to full-day requires us to double our space for kindergarten classes, and portables won't cut it. Even empty rooms in most schools will need significant modifications to meet criteria. The result is obvious to me: the schools that are going to get this first are the new schools, the ones that have been built with the knowledge that this was coming down the line and have the extra space with its amenities already accounted for. That means schools like ours - medium needs, small, old, and around the corner from a Catholic school that has all the amenities and has an Early Years centre already - are going to be at the bottom of the list for improvements. I'd be surprised if our school sees this before 2015, with the way the government is hemming and hawing about money.

The last thing I would like to see would be a change to parental leave to allow extended leaves to be taken half-time, rather than full-time as they are now (and as this report suggests.) I know a fair number of people who would be better off working half-time for a few years when their kids are small, rather than going back full-time the minute their leave runs out, but the option doesn't exist. What if that extra six monthe they're suggesting could be spread over a year of every-other-day or half-day work? I'm sure I wouldn't be the only parent thinking that would save my soul alive.

Though the report doesn't detail how, there's also a suggestion to make the early years centres and possibly early kindergarten a year-round thing. The biggest stumbling block to this is probably the teachers' contracts; the second-biggest stumbling block is, again, physical plant issues. Summer downtime is when maintenance is done on school buildings. I think they could probably make this work by using ECE workers for non-school days and certified teachers for the rest. But it will be both tricky and expensive.