Purposeful Ramblings Through My Mind

We, the female gamers of the world, are FUCKING tired of this.

Who in the world thinks this could possibly be anything but a sexist, classist clusterfuck?

No, this is not sexy. No, this is not funny. It is demeaning and rage-inducing. A pregnancy tracking sheet? Really? It's like a bad Youtube satire of playing with girls. "Roll to see if you're menstruating!" Filling in your bust and waist measurements on your character sheet? Really?

We are more than our genitalia. We want to play characters who are more than their genitalia. We want you to respect that we're fully-fledged human beings. Why on earth is that so difficult?

*Disclaimer: the men I play with, to the best of my knowledge, will all see this as just as jaw-droppingly disgusting as I do. That's one reason I continue to play with them.

American students tend to misunderstand the meaning of the equal sign far more than international counterparts.

The article is decent, and the study says exactly what I'd expect it to say. The idea of balancing numbers on both sides of the equal sign is crucial to algebra, but most students taught procedurally understand the equal sign to mean, "This is where I put my answer."

However, the article attributes the problem to poor textbooks. While this is probably a factor, I'd call it correlation rather than causation, because over-reliance on textbooks for mathematics instruction is symptomatic of the poor teaching that leads to the misunderstanding of the equal sign. Studies have shown that teachers who teach from the textbook most of the time generally rely on the textbook to lay out their plans for them. They'll spend exactly as much time on a topic as the textbook will - even if their students don't yet understand. Any mathematical concept that the textbook is unclear on, the students will be unclear on too, because the teacher is unlikely to address it outside the framework of the textbook.

Solution: get kids as young as grade one working on addition and subtraction sentences that involve balancing equations: 4+2=9- ___, for example. For primary classrooms, have a graphic of a teeter-totter with the equal sign on the fulcrum, and make it clear that the idea is to balance the teeter-totter in the middle. Do this all the way through the primary grades with increasingly complex problems and manipulatives.

By grade five, kids are ready to be introduced to the idea of a variable to take the place of the blank; they're also ready to solve problems by making tables of values that rely on one thing being equal to another: "A spider travels 19 cm every second. How long will it take her to travel the perimeter of a room that is 3m x4m?" One logical starting point is 1 second = 19cm, and the table of values can be built up from there, provided the students know they have to keep counting the number of nineteens in order to balance the equation.

Thanks to ankh_f_n_khonsu for the link.

x-posted to 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.

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? :)

Edgerton Ryerson, the father of public education in Canada (and arguably in Western culture) called it the Hidden Curriculum. Back then, it consisted of neat, clean uniforms, washed hands and face, shoes, standing when spoken to, lining up, and other niceties of polite behaviour. It didn't change too much for a very long time.

No one really questioned the rules at the time, with the possible exception of the children themselves. Middle-class people believed in cleanliness and obedience for children and expected their schools to mirror those values. Lower-class people got no say in the matter. Upper-class people were sending their children to private schools that had similar rules for public behaviour, with a few additions (such as uniforms.) Since the middle class was driving the public school system and middle-class values were self-regulating their homogeneity, it was understandable and expected that middle-class values would dominate the school system. This was right and good.

We still use school to instill middle-class values in kids. We still teach them the rules of behaviour. We still expect them to speak politely and work hard and obey their teachers. But some of the other expectations we have for public education are changing, and they're creating a conflict.

Pedagogical research is clear: the deeper and higher the question, the better the learning that accompanies it. That means that a book about the Underground Railroad won't just be discussed in terms of theme and characters and history; it will also spark questions about points of view, both missing and present, the meaning of freedom, and rights. A book about the water cycle will be discussed in terms of what children can do to conserve water in their own country and to help other people around the world who don't have enough fresh water. A poster about diamond mining may lead to discussions of diamond cartels, sweat shop labour, and capitalism. (All of these examples come out of my own classroom, and I'm not alone; I'm using the materials bought for me by the school board at the behest of the Ministry of Education.)

Middle-class liberals are familiar with these topics. They come up in their perusals of the internet, they get discussed amongst friends, they spark donations and outreach in their communities, and they appear in newspaper articles aimed at this group. But other middle-class groups may not have the same values. Will a discussion about diamond mining be neutral territory and fair game in a public school in the Yukon? Will a discussion of water cycles and pollution be fair game in Sudbury or other heavily-polluted mining towns? It's extremely difficult to moderate that type of discussion in a classroom without the teacher's own views coming through; how much politics in the classroom is too much? When does enculturation - the introduction of children to their own culture - become acculturation - the introduction of children to a dominant culture not their own?

The clearest indication of this disconnect at the moment in North America is the Conservative movement to homeschool. The reasons for homeschooling are complex, but they boil down to a belief that liberals (especially secular liberals) are using the school to brainwash kids into accepting liberal values without question. The belief is that teachers' job is to teach reading, writing, and arithmetic, and maybe some history and geography. In other words, a teacher's job is to deliver facts and basic skills. According to this view, it's the parents' job to give these facts and skills a cultural context. Children should be studying culturally neutral material and learning the skills everyone agrees they need. The critical thinking, the higher-order questions, the debates - all these things are too culturally charged to be left in the hands of a group well-known for their liberal leanings.

I'm certainly not going to pooh-pooh their concerns. They're right in several ways. We have changed what we expect kids to learn in school. We have changed the behaviours we expect of them. We have changed the questions we ask and the materials we ask them of. And "liberal" is indeed a good way to describe much of it. While the intention is to get children thinking critically about what they read and view, the fact is, teachers' biases are going to come out in those discussions, and the students - beginning critical thinkers as they are - will not always realize it.

How much right do teachers have to go against parental requests in the name of better teaching?

Statement: people who are insecure in their own intellectual pursuits find intelligence and higher learning intimidating. This effect is magnified when the higher learning is in a field seen as esoteric, particularly abstract, or which most people see as "other." (For example, few people are intimidated by a graduate degree in teaching, because people see teaching as something they can relate to; they were in school themselves, after all. But a graduate degree in microbiology or physics is an entirely different story.)

Discuss.

(Note: this topic came up a few weeks ago and I never got back to it, and I was just reading back in my journal and spotted it. I am about to take pain meds and have a hot shower to get the knots out of my shoulders before I go to bed, so play nice until tomorrow morning!)

When I started teaching, I taught the way I had been taught.

In fact, regardless of the quality of teaching in a faculty of education, most teachers start out this way, because that first year of teaching is a trial by fire and when under stress, people fall back on what they know. So, having come through a school system where grades were used to determine who was smart and who wasn't, where the only way to prove your knowledge was to write about it, where marks were taken off for poor spelling or less-than-perfect handwriting or not underlining the title in red with a ruler, I taught that way, too.

The paradigm was deeper than those things, which were just a surface expression of it. The paradigm said that school needed to teach the basics to everyone as a baseline for the middle class, but it also said that some people would never achieve in school because they were not smart enough. It said that basics had to be taught before enrichment, and that enrichment - as the name implies, which is why I no longer use that term very much - was for the top students, the ones who proved they could do it. If you hadn't mastered the basics, you were doomed to read books and regurgitate their information, practise handwriting and multiplication, and get more and more bored of the whole thing until you eventually dropped out of school, thankful that it was finally over with. The only ways to master the basics were through rote learning, called "drill and kill" by its detractors. You had to learn either orally or through reading or writing - but orally didn't mean talking, it meant listening or repeating by rote. The whole class was given the same things to learn and it was the students' job to keep up with the teacher.

It worked for a lot of people. It worked for me. In fact, I was probably one of the kids for whom it worked best, because I had a good memory for lecture-style learning and I loved to read and write as my primary modes of learning. There were a lot of other people for whom it worked sufficiently, like my brother, who managed to come out of school with a massive chip on his shoulder from the methods used on him that didn't work, but also with a good education to take with him to university. (I'll talk more about this second group further down.) It worked all right for a lot of people in the middle - people who assumed that B's and C's were fine, they were just that kind of student, and they could get what they needed out of education so long as they were allowed to drop math (or some other subject they were having trouble with - math was the most common example but not the only one.) Many of this group did just fine in university later on - they'd learned to play the game of school and they'd learned enough about how to learn to make up for the deficits in their actual knowledge and problem-solving skills. In fact, having to work hard and work through boredom usually worked to their advantage later on. (Again, more about them later.)

Then there were the ones for whom it didn't work. Some of these people would have been invisible to me as a student. It wasn't until the early 1980's that Ontario law even required that this group all be in school, so some of them wouldn't have been part of my primary experience until much later - middle school, IIRC. Some of them didn't appear different, and I know I didn't really notice most of them when I was a student, but they were there. There were the kids labeled as stupid because their learning disabilities were such that pencil-and-paper, drill learning was the worst possible way to get them to learn. There were the ones who spent most of the time in the principal's office for not doing the homework, or for acting out in class, or whatever it was. For whatever reason, an estimated 20% of kids did not receive enough education to be considered literate when they left school. A further 10-15% were able to function at literacy tasks, so long as they weren't asked for anything too strenuous. The system's answer? Of course some students aren't going to do well. It's normal, and we can't give them intelligence if they have none. They'll find perfectly good jobs as workers and they'll be fine. (More on this later, too.)

The paradigm shift started just before I entered teacher's college. Most of it hadn't made its way into the faculty of education at that time; it was still new enough that the research was being done but the application wasn't. It was being applied in Australia, consistently, via a program called First Steps - an early developmental model of learning that has had profound effects on the research over the last two decades, though Australian teachers don't use its specific formulae anymore. The National Council for Teachers of Mathematics had come out with a document some years earlier that espoused the new paradigm - and it was met with such stiff resistance by everyone involved that it's still being slammed nearly twenty years later.

In Canada, textbooks were being written that would work well with the new methods, but since the new methods were not yet being taught to teachers with any consistency, many teachers didn't know how to use them to best effect (if such a thing were even possible - it's actually really hard to use a textbook as a primary resource in the new paradigm, but those textbooks were a good starting point to do so.) It took several years for the paradigm shift to make it as far as the revised Ontario Curriculum, which started to be released shortly after the current Liberal government took power in 2003. (This paradigm was in the documents that the Harris government released starting in 1997, but it was not fully-developed in them and that government didn't support the teacher learning that would have been necessary to ensure full implementation.) I've looked at similar curriculum documents for three provinces and half a dozen states, and all of those that have been revised within the last ten to fifteen years contain varying levels of the new paradigm. (Interestingly, the further south one went, the less of that paradigm was evident in the curriculum for the public school system.)

The new paradigm states that all students are capable of learning, given high expectations and high support. It grew out of psychological research begun by Piaget and continued in theories of multiple intelligences. (One of the great tragedies of the former paradigm was that it looked to Skinner's behavioural model instead of Piaget's developmental model for its research base.) The key points in this model are:
1) Students learn in many different ways. It's the teacher's job to find out how his students are learning and design lessons that will activate as many different ways of learning as possible, so that the maximum number of students will be able to access the learning.

2) Students bring a great deal of knowledge and experience of the world into the classroom with them. The corollary here is that all new learning is built on previous learning (this is called "constructivism" and it's the central tenet of this educational paradigm.) The teacher's job is to find out what the student already knows and help them build on it, again by accessing as many modes of learning as possible.

3) All students can and need to learn to think critically and present their thinking to others in a variety of ways. Critical thinking and problem-solving are not add-ons for after kids have mastered the basics; they're vehicles through which the basics can be taught. Bloom's taxonomy has pride of place in this model, because the upper levels - especially synthesis - are where student should spend the overwhelming majority of their time.

4) When students aren't succeeding, the correct response is to increase the support through group work and/or individual help, paired with resources that meet the student at their level. It is not to dumb things down, go back to low-level questions, or limit the student to drill and practice. Those things perpetuate the problem instead of solving it.

Now, I'll be the first to admit this is a dramatic shift in focus. It changes the entire purpose of public education, which has traditionally been to prepare the middle class to be worker drones in an industrial society. The new purpose of education is to maintain the middle class while also preparing students for an information-based economy. In other words, it's not good enough now that nearly 50% of our students will graduate unable to function in an information-based economy. Our society will collapse in on itself in a few generations (if it's not already) if we continue to teach in ways that encouraged that rate of failure. At its best, this paradigm should allow students to acquire basic skills while pursuing the topics that are of interest to them, developing a deep level of reflective learning to support future learning - starting from the very beginning. (Yes, I do ask my three-year-old reflective questions about what she's reading, starting with, "Why do you think x happened?" And yes, she answers them in a three-year-old way. I'm not expecting rocket science, but I am definitely expecting that she will learn her ideas have value and should be expressed and used as the basis for new knowledge.)

It's not surprising, though, that the people for whom the old system worked just fine are up in arms about it. They don't see the need for change, because it worked just fine for them and would probably work just fine for their children. (If their kids turn out to be LD, they often change their tune on this.) Their worldview when it comes to human intelligence and psychology leads them to believe that basics first, enrichment second, works better than a problem-solving approach. They're building on their previous knowledge, which isn't broad enough to support the need for change. They didn't see the kids for whom the system failed, or they did but felt it was acceptable, or inevitable, for them to fail. Or they blamed the failing students for their failure rather than the system. Or some combination of the above - I've known them to switch back and forth on these points, apparently not realizing that some of them are contradictory.

The second and third groups - the people for whom the old system worked all right - may see the need for change. They may also have a lot of trouble with certain elements of the new model, especially the bit where advanced students get more independent work while less-advanced students get more individual attention. They're right to have concerns about this, because it's one of the stickiest areas of the new model. When they express those concerns, they often fall back on what they know again, which is streaming into advanced classes for those who are capable of handling it. Most of this should be unnecessary if the new model is being implemented fully - only the top and bottom 3-5% should need more than the classroom teacher can provide. But this group is also the group with stable jobs, the group most likely to vote, and the group most likely to write to their political representatives or their newspaper. They're the group most likely to show up for parent-teacher interviews or to take concerns to the principal. And they often don't realize that they're operating under a different paradigm from their children's teachers. So when they ask for something that would have been forthcoming under the old system and find that it's no longer available, they get upset. It's a lack of communication on the part of the school and school board, but it's a serious one because it leads to parents thinking the new paradigm isn't working.

The last big problem: paradigm shifts do not happen quickly. They take a bare minimum of fifteen years, according to some business theory experts. So far, in education, we're at 12 years and counting in Ontario, and we're not there yet. My student teacher last year had a placement in a grade two classroom before she came to me. That teacher had her class sitting in desks arranged in rows, doing worksheets and then being tested on their contents. Sound familiar? That's the old paradigm in action. My student teacher was totally flabbergasted to realize that the number of fill-in-the-blanks worksheets I gave in a year could be counted on one hand; that kids sat in groups not because it made better use of space, but because I paused lessons every three or four minutes to get the kids to discuss an idea or problem amongst themselves; that anytime she suggested a drill-style activity, I was going to veto it and suggest ways to add higher-order thinking into it.

The reason I am so well-versed in this paradigm is quite simple: my school used to be one of the ones failing under the old paradigm. The Ministry and Board of Education decided to pour money and training into our school and others like it, to make them models of the new way of teaching. They did this right across the province, with the result that perhaps 20-30%% of Ontario teachers have now been immersed in the new model for several years running, and have seen its results. Teachers' colleges are actually teaching it now, though they still have trouble finding mentor teachers who know these methods well enough to mentor all the new teachers. (My school was approached by three different teachers' colleges for this fall, and I've got two who want me to take a student teacher this year. I know of another school where teachers have taken on three or more student teachers EACH per year, so great is the need for teachers who understand these methods and apply them well.)

I used to teach the old way. I did not simply accept everything I was told by a faculty of education. I am not a parrot. I worked through the old paradigm, and it did not work for what I needed it to work for - educating my students. Gradually, I switched to the new paradigm, adding pieces, discussing, reading, arguing about pieces I felt were wrong, and eventually coming to the place I'm at now. I can look back at the route that brought me here and know beyond a shadow of a doubt that I'm serving my students far better than I ever did before; that I'm serving my students better than any of my own teachers ever did; and that the shift of paradigms must continue, because it works. I look at the road ahead of me and know, again beyond a shadow of a doubt, that my career will be spent teaching within this paradigm and teaching other teachers to implement it; that my master's degree will investigate this trend and suggest ways of speeding up the implementation process; and that at the end of it, I may not win accolades in the profession at large, but I will have contributed to society at large on a much broader scale than a classroom teacher gets to do.

That's not arrogance, as some have alleged. It's professional expertise, and it was hard-won.

This very good article describes an American ex-pat's experiences with the Dutch social system. A few points resonated with me in particular, since I live in a socialist system as well:

1) More social safety net does not translate to more laziness or less work for the vast, vast majority of people. On the contrary, it makes people more secure, which means they're able to pursue work they might not be able to afford if they were tied to a health insurance provider (for example.)

2) The roots of socialism in Canada, as in the Netherlands, are deeply religious. They grew out of the Reform Protestant movement to find the most efficient ways to help widows and orphans and anyone else who needed it. The difference is primarily in who we expect will pick up the tab. When times get tough, it gets harder to rely on voluntary charity, because people who lose their jobs tend to stop giving out of necessity. The government has much better resources at its disposal for tiding itself over the lean times. The other difference, of course, is that the non-religious or non-organized religious can buy into a social welfare system where they may not be willing to buy into an overtly religious one.

3) There's a sense of community in Canada, a feeling that if everyone is pulling along fairly well, we're all better for it. The individualism in the States puts a high value on charity being voluntary, theoretically as opposed to the forced charity of taxes. But voluntary charity is charity that can't be counted on to be there when you need it.

It's a good article, especially if your worldview leans towards a strict division between left and right politically.

No, she doesn't want you to stop breastfeeding. She wants women in America to stop being guilt-tripped into pumping at work.

The key quote, for me - and it's restated further up the article in a different way - is this: Why, as a society, have we privileged the magic elixir of maternal milk over actual maternal contact, denying the vast, vast majority of mothers the kind of extended maternity leave that would make them physically present for their babies?

That's it. Right there. Her hyperbole about relegating the pump to the history books is just that - hyperbole. There are plenty of babies who need that pumped milk to live, and I would certainly not deny any mother the right to do that for her preemie or sick child. Nor do I dislike extended nursing or any of the other variations on nursing that are out there. The problem I see with America's push to get women breastfeeding is that all the push is on the moms. There's very little societal investment in it. There's no paid maternity leave. There's no cultural assumption that the best place for the mother of a child under a year is at home with that child, where they can then nurse their baby as much (or as little) as they want to. There's guilt, and there's resources to help a woman figure out how to "make it work," but there aren't enough resources to actually take some of the pressure off her so she CAN make it work.

I have never seen a breast pump at work in Canada. I work in places where there are constantly women having babies, because teaching is a female-centered profession. I don't know anyone who has pumped at work or even suggested doing so, and the reason the movement hasn't caught on here as it has in the States is that women are on maternity leave when they're breastfeeding exclusively. By the time they go back to work, it's no longer quite that crucial that their babies get nothing but breastmilk. They're getting solids, maybe juice or water, and their nursing has naturally tapered off. And that's the way it should be.

Breast pumps are a wonderful stop-gap measure. They keep preemies alive. They're great for increasing milk supply before the growth spurt so that you've got a supply in the freezer and don't have to deal with OMGsoHUNGRYbaby when the growth spurt starts.

But if the breast pump is ubiquitous in the workplace, it's because the whole culture surrounding motherhood in that place has got it terribly, terribly wrong.