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From [ profile] pvenables: "I have a question for you about a documentary I watched recently. It's called "Waiting for 'Superman'" and (I'm assuming you have seen it but what the hey) it features the plight of the American public school system, the concept of "drop-out factories," and the perception that it is impossible to change anything that's wrong with the system due to smothering influence of the teachers unions.

One thing that particularly shocked me was the fact that American teachers can get tenure. I've never heard of that going on here-- I assume that's only in the US.

Would love to hear your perspective on the film if you've seen it and if you haven't, to hear about your impressions once you have.

The question I had for you was about Canadian (or just Ontario) schools: Do we employ what they call "tracking" for students wherein some teachers funnel students towards success while others might be destined for a lower quality of instruction or attention based on fairly arbitrary assessments? Actually, in thinking about this, I think I can probably say "yes" we do as I saw it in action when I was in school. Perhaps a better question is, how early does this begin? I know you have an objection to... what was the testing called? It was something you've asked that Elizabeth not be included in..."

I suspect this will get long. )
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The federal election isn't the only one on the horizon. There's a provincial one too, and that one will hit very close to home for teachers. The Conservatives are laying low, attempting to slide in as the only choice in the face of dissatisfaction with the current Liberal government. The probability of labour unrest, the likelihood that we will lose gains made over the last number of years, the likelihood of increased testing and decreased teaching - all of it is strong with a Conservative government.

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The Toronto Star has begun a series on this topic. The first article in the series is entitled Why Teachers Matter, and makes the case that training teachers well, paying them well, respecting them, and then letting them teach, is the best way to maximize the results of the teaching relationship. I tend to agree.

The second article strikes me as far more controversial, and I admit to arguing the same case while falling victim to it as a parent. It's called Too Many Choices and deals with school choice, and the end result of too much choice: to bring down the generic public education by removing the people most likely to insist that it be improved. I can attest to this on a personal level. French is important to me, and I teach it better than many and far better than it has traditionally been taught in Ontario, but as a parent, I didn't choose core French. Why? Because I want to be sure my kids learn French, and the advocacy required to make sure the core French system works to teach kids French just isn't there. Canadian Parents for French focuses its efforts almost exclusively on French Immersion and Extended French programs, while the core French programs that reach every kid languish in disrepair. If there were no French Immersion, would Core French be under pressure to actually teach kids to speak a second language? Probably - certainly more than it is now.

He also points out that private schools tend to perform exactly as well as public schools, and charter schools often fare worse, despite the hype associated with them in the States.

I'm looking forward to the next article; these ones were interesting and I agree far more than I disagree. Long-time readers of my blog will see many familiar themes.

x-posted to two teaching communities; sorry to those of you who see it twice.
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What a lousy, cowardly cretin! He split the union-busting portion of the bill from the part that spends money. They don't need a quorum for any bill that doesn't spend money, so they could pass the union-busting portion even without the fourteen senators who went to Illinois.

I hope they recall the bastard, but I'm terribly afraid that if they do, he'll run for President and get it.
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This short essay describes the negative and unlooked-for (but easy to predict) effects of attempting to marry measurement of results with paying people for achieving them. Someone needs to forward it to the U.S. Department of Education, and to a variety of state departments of education. It's a clear, concise explanation of why merit pay is an absolutely abysmal idea, guaranteed to result in poorer outcomes for the students most in need of better ones. It's in the context of the British health care system.
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An excellent article about the failings of the film "Waiting for Superman." I know I'm preaching to the choir, here, but have a link.
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This morning's offering: a brief discussion of This article. Exciting, I know.

The article concludes that drilling for some knowledge, some of the time, in a way that isn't boring, is necessary to academic achievement. I agree. However, I'm going to go one step further and say exactly when material should be drilled, and a little bit of how and how much.

First, when: drill should only take place after the students thoroughly understand how a process works. Drilling is then useful to fix the specifics in their heads. For example, I will never drill multiplication for a kid who can't line up a rectangle made of blocks into an array that shows a given multiplication fact, or draw that same rectangle on graph paper, or group objects in a set number of groups with a set number of pieces to show how multiplication works. While they can probably learn the facts by rote even if they don't understand them, they won't know how or when to use them and they won't be able to manipulate them - for example, they will struggle with reversing the multiplication fact to get a division fact.

This is one of the biggest mistakes teachers make in math: if a student doesn't grasp a concept on the teacher's timetable, the teacher pushes ahead anyway, saying something like, "Just learn it." If they don't have the conceptual framework in place to learn it, then they won't, and years later some other teacher is going to discover they don't know this, and that they don't know any of the things that naturally flow from it, either. When a student truly doesn't get it, the best thing to do is put more and more things in place to help them see the connection you're trying to paint for them, until the light goes on. After they get it, THEN you drill them.

Second, how: for heaven's sake make it FUN. I don't care how you make it fun. Games between two or three students are a great way to do it. Flashy computer games to drill those facts are wonderful if you have access to computers in your classroom. Some kids like flash cards. Most kids like the feeling of being tested briefly on something they know, and getting a reward for it - a quick oral test of one multiplication table gets them a sticker on a chart and they're puffed up with pride. And there's nothing wrong with that. The two keys are that it doesn't feel like heavy work, and once they know a certain set of facts, they stop practising those facts. Giving students work to do that they already know is just as soul-killing as giving them work to do that is way above what they know.

Third, how much: it should be less than 20% of a math program. The bulk of math instruction should be problem-solving, analyzing strategies for problem-solving, and extending the problems. Drill fills in the gaps in this program. It does not replace it, ever, even for low-functioning students, because the studies show that teachers tend to underestimate the abilities of those who came to them with a label of "level 1" student already attached. So we give all students the opportunity to problem-solve, adjusting the numbers or number of steps in the problem rather than eliminating the problem itself, and follow up with drill for those students in about the same quantity as we do for those more able. I can guarantee that sometimes, those level 1 kids will surprise their teachers if they're given a chance to do so.
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"It's not the school's job to cater to [insert student with a specific difficulty which they may or may not have brought upon themselves here.] It's the student's job to figure out what they have to do and do it."

The specific scenario, in this case, was a teen mom who gave birth two weeks before the end of the school year. She got up from her hospital bed, left her baby in her mother's care, and went to write a couple of tests so she could graduate.

I have a really, really big problem with this.

First, I can't imagine who the school thought they were serving by requiring this. Most women are not at their best intellectually or emotionally a few days after giving birth, so it's not hard to imagine that the young woman in question might have seen her marks suffer when she wrote those tests. That makes the assessment invalid, because it doesn't match her usual abilities. If the test is not a valid measure of her abilities, then it's not serving her needs for her to write it.

She wanted to graduate and go to college in the fall, so the argument could be made that the college needed her marks to know exactly what she could do and to decide on admissions. I'm not buying it, again for the reason of the test's lack of validity: the college was getting a skewed view of her abilities unless she managed to pull some excellent grades on that test. So an invalid test doesn't serve the purposes of the institute of higher education, either.

So whose needs were being served? The school's, of course. The flexibility required to let her graduate without the week or so's missed work required extra work on the part of the school, and a lack of (what the school would call) fairness to other students. They might have to recalculate a GPA to exclude those tests, so she wouldn't be penalized for missing them, or they might have to give her an alternate, less-stressful assessment, or they might have had to plan in advance for her to finish her schoolwork (or at least finish enough of it that she could be said to have been evaluated on the full content of the course) a bit early due to the likelihood that she'd deliver around the time of her final exams.

I don't believe that's what real fairness looks like. Real fairness evaluates students in a variety of ways, giving them lots of opportunities to show what they know and can do. Real fairness can and should look different for different students. A rigorous adherence to a marking system based on tests and GPAs is inherently unfair, not just to our new mom in the example but to every kid who has test-taking anxiety, or a learning style that makes test-taking a problem, to name a couple of possibilities.

If some bureaucracy is inevitable in a public school setting (a debate for another day) then the least schools can do is ensure that what bureaucracy they have is essential to be fair to the students.
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I followed some links on a friend's page and found a PDF of the new Core Common Standards, which are now adopted by 34 states and the District of Columbia, making them the basis for curriculum across most of the U.S. For the sake of simplicity, I'm starting with the math standards. Language standards tend to be harder to compare because they often differ by only a word or two from one year to the next.

I was hoping to find that the standards were based on the NCTM standards for primary/junior math. I confess myself somewhat disappointed in this regard. While the language all points to a constructivist method of instruction, it seems to move faster than the NCTM standards in a couple of areas, specifically multiplication and division, and much slower in others. There's no introduction of probability at all until grade seven, no statistics at all until grade six, no measurement of angles in any capacity until grade seven. These are all key mathematical understandings that can be taught effectively much earlier, and provide a context for other mathematical understandings.

Meanwhile, the standards for multiplication and division lead me to suspect that the authors of the curriculum subscribe to a back-to-basics model. The level of multiplication and division expected of grade fours is very high, and without the added context provided by a firm basis in measurement and probability, it looks like the constructivist language is nothing but lip-service. It's too fast, and the size of the numbers the students are expected to master goes past the level of abstraction that most kids in grade four are developmentally ready for.

As I go deeper into the primary grades, I'm looking for references to constructing understanding using manipulatives. I'm not finding them. There are occasional uses of the word "represent," which could mean anything from writing number sentences to elaborate models. It's so vague it might as well not be there at all. But the absence of specific expectations related to manipulatives really worries me. It strikes me that it would be very, very easy to teach to these standards using nothing but pencil-and-paper activities. Manipulatives should be an accepted part of the curriculum at all levels - yes, even high school, though obviously they'd be very different manipulatives there - and the lack of references to them is another indication of a back-to-basics philosophy. It's destined to fail because it pushes students to a level of abstraction they aren't ready for, without giving them the opportunities they need to move from concrete concepts to representations of those concepts to symbolic and then to abstract reasoning.

In short, after this very brief look at the core common standards, I'm beyond unimpressed - I'm actively concerned for the colleagues whose attempts to teach constructively are about to be undermined and for the children. They're going to get the kind of math instruction that led to a society where it's perfectly acceptable to ask someone else to calculate your portion of the tab in a restaurant because you're not very good with numbers. They're going to get that instruction on the basis of a political climate that sees knowledge in an outdated way that fits a certain political agenda, and the U.S. public education system will continue to be undermined by it as they see that, exactly as has happened before, it doesn't work.

Has anyone taken a closer look at the other subject areas?
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A U.S. court upheld the expulsion of a counselling student who could not reconcile her religious belief that being gay was immoral with her ethical requirement to counsel anyone who needed her help. There's at least one similar case elsewhere in the country, and if it gets decided differently, the matter could very conceivably go to the Supreme Court.

Kudos to [ profile] cereta for this one.
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x-posted to [ profile] ontario_teacher

It is time for the teachers of Ontario to take a personal stand against the EQAO test by withdrawing their children from it.

My daughter is entering grade two in the fall. I have started to consider the possibility of withdrawing her from school the week of the EQAO testing in grade three. It's a difficult decision to make alone. On the one hand, my daughter doesn't need to do well on a standardized test to prove that she is working at grade level. I already know how advanced she is, and so does her school. She tends to get nervous before events she sees as tests, and I don't want her developing that nervousness at the tender age of eight. Furthermore, I know that as a French Immersion student, she's at a disadvantage: the inclusion of good spelling to get a level 4 is prejudicial to students who don't study English until that same year, though they catch up later. I'm not interested in putting that level of stress on her for no gain.

On the other hand, her teachers are my colleagues. If she doesn't write the test, she counts as a zero. Having taught in a turnaround school, I know what kind of pressure low scores put on a school, and I know that they'll be predicting a high score for my daughter. Withdrawing her from the testing hurts her school and potentially hurts my relationship with her teachers. I don't want to do that.

This decision should be supported by the union. The union has a role to play in asking teachers who are also parents to boycott the testing, not for their students, but for their children. At an individual level in our schools, we can't force this testing to stop; but collectively as a group of concerned parents, we can significantly impact its validity in a way that is completely legal and without repercussions for our jobs.
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Gender gap persists at highest levels of math and science testing

The authors of this study point out that the achievement gap between boys and girls, when testing gifted seventh-graders, has narrowed dramatically in the last thirty years. When it was studied in the eighties, the number of boys scoring above 800 on the math SAT outnumbered the girls 30 to 1, and that gap has narrowed to about 3 to 1. That happened in the first fifteen years - that is, the 3:1 gap has been consistent since 1995.

So the authors are postulating that the persistence of this 3:1 gap indicates a difference in innate ability between boys and girls in math and scientific reasoning (where the same gap is evident.)

I'm not buying it. Here's why.

First, for every elementary school teacher who is well-versed in constructivist teaching methods as they relate to math, there are a bunch more who aren't. The NCTM (National Council for Teachers of Mathematics) put out the original version of their constructivist curriculum in 1989; I suspect if one were to break down the changes further within that thirty-year time span, it would be the years between 1990 and 1995 that would show the biggest change. But the uptake is, at best, piecemeal. Teachers still teach from textbooks, which short-circuit the problem-solving process by their very nature. Manipulatives still start to disappear from ready availability in classrooms as early as grade four. The higher one goes in math, the more likely it is that manipulatives will disappear almost entirely from the classroom, to be replaced with purely abstract problems and procedural methodology - not because those are the end goal of mathematics instruction but because that's how the teachers were taught, and when they get out of the comfort zone of their pedagogical instruction which is generally aimed at the middle of the expected outcomes for their grade level, they tend to fall back on what they know.

In short, how much of this is the fact that girls learn mathematics differently, and their learning styles for mathematics aren't being supported in their gifted classrooms? My gut instinct says that's a huge part of the reason for the gender gap, but of course I don't have the stats to back it up.

Second, their base data is of twelve-year-old gifted kids. Leaving aside the selection criteria for giftedness (which honestly I question, knowing as I do dozens of people who are very clearly gifted academically but were not identified as such in school) there's the question of socialization. Girls are still socialized away from mathematics, more subtly perhaps than they used to be and less often by teachers, but it still happens. Twelve-year-olds are at the point in their lives when they're really struggling to figure out their place in the world. How many of those gifted kids have already decided that math isn't their thing, due to a couple of years of the poor teaching I mentioned above? How many of them will be talked out of that thinking once it starts to establish itself? Or will it simply be seen as her choosing what she's best at, and hey, there are great careers in language-based subjects, too, so what does it matter if she gives up on the highest levels of math?

In short, socialization has been downplayed as a reason in this study, probably erroneously. The cultural myopia of the data selection is in my favour, here: there is no gender gap in several Asian countries when it comes to mathematics, which makes me question why there should be a 3:1 gender gap here. But the study is done entirely on American students using American tests.

Third is the issue of NCLB. It started in 2001. It short-circuits attempted improvements in instruction because so much of the testing is knowledge-based rather than based in a problem-solving model. Because the testing has such very high stakes attached to it, teachers teach to the test, meaning that improvement in instruction has been stymied in favour of getting the test scores up. You'd think that wouldn't affect gifted education, but school culture affects everything, including the kids who otherwise might not have to worry about it. If the teachers' PD is all about getting test scores up, the teacher of the gifted students effectively is getting no PD at all. His kids are going to do just fine. But he's not then getting trained in the enrichment methods which would really serve everyone much better and are absolutely essential for the highest-functioning kids.

In short, if you want to see problem-solving in students, you have to ask for problem-solving on the tests. The US as a whole is not doing that, so the level of problem-solving isn't improving.

Should I email the authors of the study and point out the problems in their methodology? :)
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I think maybe I'll make this a weekly feature, just for the heck of it. It reminds me that I'm doing a good job.

So, this week in math, we started by reviewing what little we'd learned about equivalent fractions before the March break. Since exploratory learning is starting to become de rigeur for my students (as it should be) I took them to the computer lab and let them play around with the fractions manipulatives on the national library of virtual manipulatives website. The differentiation was easy. Don't get this at all? Try the basic fractions manipulative. You've already figured out the pattern rule? Great, do the grade six one.

On Monday, I gave them an assignment to do. They would get four or five pieces of regular paper in different colours, their choice. On each one, they'd write a different common fraction. The example, which I made up with my six-year-old on Sunday, was one half. Then they'd come up with three or four equivalents for it, and represent those equivalents in pictures. They had to explain the fractions and how those fractions were connected to the original fraction. There is a rubric - let me know if you want it.

The kids who were having trouble even accessing one half came for some guided math with me. We did fraction strips, and played around a bit with blocks, until they got to the point where they understood that if you divided all the pieces the same way, you had an equivalent fraction.

Then, because an abstract understanding is important to work towards, we took the equivalent fractions they'd come up with and analyzed them. How do you get from 1/2 to 4/8? If they expressed it as adding, I told them they were right, but they'd see the pattern faster if they thought of it as multiplication. So what would they multiply by? Some figured out the pattern independently; others needed to be shown several times, and finally got it with the help of more manipulatives. Then I encouraged them to use the pattern rule they'd found to come up with what they thought was an equivalent fraction. They had to come up with the proof that they were right by drawing a representation they could connect back to the original fraction.

As of this writing, most of my kids have finished two or three sheets of equivalent fractions. The rubric gives an A to kids who can connect their equivalents to decimals or percents, so I've explained the idea of repeating fractions to the kids trying that for 1/3. I suspect most will finish on time - the assignment is due on Monday.

Next Week: comparing and ordering fractions is so much more interesting when the denominators are different.


Mar. 20th, 2010 11:56 am
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I hate giving marks.

I hate the process of figuring out how a dozen different assignments, all relating to different expectations and all taught, supported, and assessed in different ways, go together to create one overarching letter that is supposed to sum up a kid's work for a term.

You know what? It doesn't. There's no way that it can. The same kid can be at three different levels in three different key expectations, and giving them the middle level doesn't recognize either their weaknesses or their strengths well enough to satisfy my professionalism, much less well enough to really represent the kid.

Furthermore, the parents don't look at that A and say, "Wow, you did really well on that brochure assignment! You put a lot of effort into it and used your information well, and your research came from lots of different sources! I'm impressed with your work!" No, the vast majority of parents look at the A and say, "You're really smart in English!"

Then they look at the C+ in number sense and numeration, and instead of saying, "It seems you were really struggling with multiplication. What can we work on together that will help you with that?" they say, "It's okay. Some people just aren't good at math." Which is a better message than the other most likely one: "You're stupid and lazy and that's why you got a low mark." But it's still not the truth. Neither of them are the truth. And since a parent's opinion is necessarily and properly more important to a kid than a teacher's, my repetition of the first message gets drowned out by their repetitions of the other messages.

For the parents out there, please, please, know this: no matter what your personal relationship with grades was in school, you need to put it aside. If there's one message I want to give you, as a teacher trying to improve your child's learning and give them hope for their future, it's this: marks are not a reflection of the child's abilities. They're a reflection of the child's achievement on a certain number of assessment tasks which may or may not accurately reflect the child's understanding of the material and almost certainly do not reflect the child's full potential. If you treat marks as indicators of work already done, and tie them directly to the learning that went into that work, then you'll probably avoid this trap. If you interpret marks as a reflection of your child's aptitudes, you are doing your child a significant disservice. Marks are only as good as the expectations they relate to and the tasks used to assess the child's achievement of that expectation. They do not reflect the child well at all. They're at best a necessary evil, at worst a horrible setback to kids who might otherwise be making great gains.

This rant brought to you by my second-term report cards and the letter C+.
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I don't think I posted this here before, so I'll do it now. It was one of the initial assignments for my specialist course.

The assignment has become a standard one for grade one students in Ontario: gather a collection of 100 items to bring in and explain to the class on the hundredth day of school, usually in mid-February. It filled my six-year-old with glee. She knew exactly what she wanted to bring in. I was less thrilled, because the collection she chose did not belong to her, but to me: my dice.

Nevertheless, we spent an hour one Sunday afternoon gamely dividing dice into baggies, categorizing them by number of sides, then by colours. Along the way, we explored concepts relating to the base-ten system and the absolute basics of multiplication.

My daughter has plenty of experience with dice. They’ve been a part of her life since birth. Plush dice, foam dice, and the vast array of dice used for roleplaying games by both her parents and all their friends, were her first introduction to numbers that weren’t on her fingers. For her, dice represent fun times with friends, groups of people laughing and telling stories around the dining room table, the adults who take an interest in her life even though they aren’t related to her – and math. So it was natural that when she needed a real-life collection to bring in for Hundreds Day, her first thought was dice. Dice are math as it is in her life.

There is a great deal of emphasis in mathematics education on making math real, on finding the ways to make the numbers concrete, tactile, visual. This emphasis is a vast improvement over numbers that never left the page, because it does facilitate a deeper understanding of mathematics, and that is the ultimate goal of mathematics education. (1) But my daughter’s experience with dice is evidence that it doesn’t go far enough. For her, dice are not something a teacher brings out to show how numbers work; dice are real life that we describe using numbers. The educational establishment has been getting it backwards. The goal is not to make math real. Math is already real. The goal is to teach how reality can be described using math.

Paul Lockhart, in his article, “A Mathematician’s Lament,” discusses how mathematics is the art of pure idea. (2) When we teach it procedurally, we strip from it the inherent creativity and beauty of it; but when we use it to describe our ideas, and engage students in describing progressively more complex ideas with mathematics, we find that everything is math. There’s no need to make it real because it already is. As teachers, our vision for our students should be to bring their mathematical understandings into the classroom. Where is the math in their lives? What forms of art exist in their cultures, and in the culture to which we’re introducing them, that can further their understanding of number and pattern and relationships? It is when we follow students’ mathematical understandings and extend them that we get the deep understanding of mathematical ideas that creates lifelong learners and problem-solvers.


1. Carpenter, T.P, Hiebert, J., Fennema, E., Fuson, K.C, Wearne, D., & Murray, H. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth. Heinemann.

2. Lockhart, Paul. (2008) “A Mathematician’s Lament.” Mathematical Association of America Online.
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Attention, parents of school-age children! Are you frustrated by the fact that your child's math homework doesn't bear even a passing resemblance to the method you were so painstakingly taught? Is your child frustrated at getting one method at school and another at home?

Never fear, help is here!

Read more... )

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