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Finding connections from math to the real world seems backwards to me, somehow. It also negates the value of the other connections students could be getting out of the same material. If you use arrays to model multiplication, you've modeled multiplication and nothing else; but if you use something built as an array (like a quilt block) and look for the math in it, you can get multiplication, but also geometry, symmetry, co-ordinate grids, fractions, growing and shrinking patterns, division, principles of design, and measurement. You might easily miss them if you start with the math. From our perspective, that makes sense; we see the job as making math real. But kids are seeing it from the other side; they need to describe reality using math. Disparate topics taught with a variety of representations don't do that as well as a single representation that is deeply explored.
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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?
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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.

Got it!

Jul. 13th, 2009 09:49 am
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I just came up with the most fabulous project EVAR to combine social studies and math.  Get a load of this:

    Project:

     

    With your partners (groups of 3) you will research number systems in at least three ancient civilizations.  One of those three must be the Hindu-Arabic system; the others are up to you and will depend on what resources you can find to learn about the number systems.  I've included a list of links, available on our class's First Class page, to get you started.

  1. Write a paragraph explaining the main features of the three number systems you chose (each group member should write one paragraph; I will be looking for rough work during conferences.)
  2. Use number cubes or other manipulatives to model each number system.  (It may be easiest to pick one number and model it in all three number systems.)  Take pictures of your models.  Don't forget to include a group member in each photo so that we know who the pictures belong to when we download them off the cameras!
  3. Make a chart that explains the main features of each number system, and compares it to our base-ten system.  Some suggestions for headings on your chart:
  4. Use of zero

    Base number

    Strengths

    Limitations

  5. Write another piece in the format of your choice, explaining which parts of those ancient number systems are still in place today, giving examples for each.  (Use the cameras or images from the internet to back up your points!)  If any of those systems have been completely abandoned, explain why you think that happened.
  6. Each group will do a brief oral report on their findings for their classmates.  Every group member should be able to discuss any aspect of the project - even if somebody else worked on it - so be sure to teach each other what you learned!

I'll be making up a rubric and some lesson plans when I get back from my swim, and I've already got a thorough list of expectations that can be assessed using this project.  When I'm done I'll post the whole thing to Ontario_teacher.  Any suggestions appreciated; this is the first, very rough draft. 

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The question always comes up in debates about teaching mathematics: how come the Japanese do so well at math, when they stress rote memorization, if memorization is the wrong way to go about teaching math? (It's usually said in a tone of smug satisfaction, as though there's no possible comeback other than to admit that a constructivist approach to mathematics must clearly be wrong because the Japanese aren't doing it.)

The answer: a little from column A, and a little from column B.

The Japanese do indeed expect kids to memorize a lot of facts, but that doesn't mean they teach by modeling procedures and then assigning students practice questions to follow those procedures. No, they present a problem which the students do not yet have the skills to solve, then the kids work in small groups to figure out the problem. At the end of the lesson, the teacher summarizes what was learned, and students are assigned a small number of questions to practise on at home.

In other words, they use EXACTLY the method we're being told to use - with the exception that they do not allow calculator use.

The single biggest difference between North America and Japan is the number of school days - Japanese students have far more. The next biggest difference is in average expectations. When American moms are asked what mark is acceptable in math, they generally say a B or a C. Japanese moms expect an A.

So - high expectations, a constructivist and problem-solving approach to mathematics, high support in the form of parental help and extra tutoring - that's nine-tenths of the items we're expected to include in our mathematics programs.

Oh, and I should point out that the rumours about this kind of math instruction ignoring basic computation skills are false. We do drill math facts; we just make sure to drill them AFTER students have achieved comprehension, rather than before or instead of.

For future reference: http://www.gphillymath.org/ExempPaper/TeacherPresent/Mastrull/SMastrull.pdf

Doing Math

Jun. 28th, 2009 09:02 pm
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I haven't been posting all my discussion posts here, but here's another one for those who care.

Doing Math )
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This is not the first big assignment I've done, but the others have all been posted to the discussion forum and have resulted in immediate feedback there; I'm not going to repost everything, I promise. :)

The question )
My answers )
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My assignment: First Journal entry
Think About It
Take a few minutes and jot down your thoughts in your Journal. Do you think we teach children mathematics or do you think they learn mathematics? What images do you think of when you think of teachers teaching? What images do you see when children are learning? Is it possible that learning can happen on its own or from a peer, with the minimum involvement of a teacher?

Teachers play an important role in the process we call learning. They become the "guide on the side" not the "sage on the stage." Showing and telling are not teaching. Rather, we hope that children can be actively engaged in learning, questioning, analyzing, predicting and constructing knowledge from meaningful contexts and real-world experiences.

My answer:
I don't think this should be an either/or question; that is, I don't believe there is a great divide between teaching and learning. They are two parts of the same whole. Facilitating learning is called teaching, and it can take many forms. When I think of teaching, I generally picture direct instruction, the teacher modelling and then the students practising with guidance. Then I think about the activities I have students do that look nothing like that - jigsaw activities, where my whole role is to write questions on chart paper and let groups come to their own answers through exploration; whole-class discussions, where my role is to moderate who speaks and when, and possibly ask leading questions if the discussion stalls; critical literacy and exploration activities, where I provide materials and guide students to see them in light of certain key questions. I'm not doing much modelling or direct instruction in any of those situations - and together, they make up well over half of the classroom activities I plan.

I don't think the traditional teaching methods - imparting knowledge to students who lack it, in a top-down model - is really as traditional as recent research would have us believe. It seems to me that the method we're being told to consider, including the one hinted at in this journal entry with that very leading question, is just a variation on the age-old Socratic method, where we teach by asking questions that lead students towards more, deeper questions, and the knowledge they require to ask the next level of questions. Indeed, in the Socratic method, the students ask at least as many questions of each other as the teacher asks of them, resulting ideally in a depth of discussion that is totally lacking in so-called traditional educative methods. (I call it a variation because the Socratic method is mostly a thought exercise, with the students studiously avoiding getting their hands dirty, whereas the modern version of it requires kids to get up to their elbows in manipulatives of all kinds.) Most learning has been done like this since the beginning of time; it was the people we think of as traditional teachers who changed it, bringing Skinner's behavioural model of teaching into the forefront of pedagogy.

So, to bring this journal back around to its point, students learn mathematics in a variety of ways, including direct teaching, exploratory learning, peer interaction, and observation of the world around them. My job as a mathematics teacher is to highlight the connections between mathematical concepts, to ask the questions that will lead to students deepening their understanding of those concepts and their connections, and to facilitate their exploration of their world through the language of mathematics.
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I occasionally (or not so occasionally) come across people who believe that the way they were taught math before all this problem-solving mumbo-jumbo was superior, not because it worked better at the time but because, after learning the steps without understanding them, they developed the ability to problem-solve and reason mathematically later on. Their reasoning: kids don't need to learn to reason mathematically from the outset; they'll learn to think procedurally and then as their brains develop, they'll fit their procedural knowledge into a growing problem-solving framework. The end result will be adults who reason well AND are good at arithmetic (these are usually the people who believe that New Math creates kids who can't add or multiply, to which I say: then the person who was teaching it didn't really know what they were doing.)

I used to think this way, because in math, this is what I did. School taught me the traditional algorithms, my dad taught me to add and multiply quickly in my head, and I made connections between concepts without being encouraged to. (When I first learned fractions, they were already old friends - I'd been seeing them on sheet music for two or three years at that point.)

It occurred to me last night, in conversation with [livejournal.com profile] wggthegnoll, that there is a better metaphor in my life for old math versus new math: music.

Now, I have some natural talent for music. There was never a time when I couldn't carry a tune, and some of my earliest memories are of singing interesting and difficult music at the Salvation Army, sometimes before I could read. I started taking piano lessons at the age of eight, and continued taking them until I was sixteen, at which point I started teaching piano instead. My training on the piano was classic. I was given a piece of music in a book geared to the level I was supposed to be at. I read through that music with my teacher there to point out anything I didn't get or some new technique for fingering. Then I went home and practised that piece of music until I could play it well. When I was done most of the songs in that book, I moved on to the next one. My education in music theory was mostly taken care of at music camp, and I ended up skipping Grade One Rudiments entirely (though I did do the Grade Two exam - it was necessary to get a high school credit for my piano lessons, along with my grade eight piano exam.) I learned my scales, I did fingering exercises, I knew how to play tonics and dominant sevenths and minors harmonic and melodic.

However, I was not the kind of kid who thought outside the box that was presented for me. I didn't start listening to the radio until years after my friends did, and I was fifteen and already had my grade eight exam under my belt before it occurred to me that I could play music that didn't come out of a Royal Conservatory Repertoire book. I rarely tried to figure out for myself how something was played, and other than a few hymn tunes, I had little experience with playing anything that wasn't classical. In short, I never learned to play by ear, and more importantly, nobody ever drew for me the connections I would have needed to develop that talent (which, btw, I have when I'm singing, though it's undeveloped.) I never learned about modes; no one pointed out to me what standard chord progressions were and how I could play with them to make them sound different using those arpeggios and scales I'd memorized so assiduously. Though my dad pointed out that I didn't have to play a hymn tune exactly as it was written, I could break up the notes for better rhythm, no one showed me what the chord notations were or how to read them or how they connected to each other. The advanced harmonics, which I was perfectly capable of playing, were not taught to me as something I could reason my way through.

I was taught the arithmetic of music. I was taught, "If you follow these steps, you can play any piece of music you pick up. You'll learn how they work later." I was not taught to think critically about the form of the music I was playing. All of that was saved for after I had the rudiments; it would have come about during Grade Three Harmony, which I started but never finished. It was assumed I'd pick it up on my own - but I never did.

Because of all that, I'm a very limited pianist. I know the most basic chord structures, the ones that show up in most pop music and a wide variety of hymn tunes, and I can generally figure out how to make them sound cohesive if I work at it. I can read music, though I can't sight-read very well - that is, if you put a piece of difficult music in front of me and ask me to play it, it's going to take me a week of painstaking work to get to the end of it and be able to play it back to you. (That one is a confidence issue: I don't like to keep going if I make a mistake at something, but when you're sight-reading, that's exactly what you need to do so that the person you're accompanying doesn't have to stop in confusion when you break rhythm.) I still know very little about modalities and harmonies. I still can't play by ear or even chord by ear most of the time, though I can come up with vocal harmonies with no trouble at all. I can hear in my head what it is supposed to sound like, and I'm frustrated trying to bridge the gap between how it should sound and how I'm able to make it sound.

I'm going to bring this up with my uncle when he starts teaching Elizabeth in the fall. I've taught the way I was taught, and passed on these same errors out of ignorance, but I'd prefer that my daugthers' talent for music ends up better developed than my own, so I'm going to talk to him. I want to figure out how to apply New Math strategies to elementary music, and I won't take the platitudes - they'll figure it out on their own later, don't worry about it, one step at a time, basics before critical thinking - at face value. While it may work for some kids, it didn't work for me. I don't settle for, "They'll pick it up later" when I'm teaching math. Why should I settle for that when teaching music?
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I had a parent ask me if her daughter could come in for some extra help after school.

Um, no, and here's why.

First, she doesn't need extra help - she needs encouragement to use her own judgement on her work to improve it. She knows what she needs to do, and doesn't do it because she's relying on me to point it out to her. This particular kid needs more independence, not more dependence.

Second, and more to the point, is the concept of "extra" help.

How much help is extra? Where do I draw the line between the help I'm required to offer my students, and the help that is extra? Clearly, some kids will "get it" quickly and not need very much help at all. If I expect them to be in that group and it turns out they're not, is the help I offer them extra? How about a kid who usually has trouble? Is it "extra" help when she gets more of my attention than the kid who usually gets it right off the bat?

The idea of extra help is rooted in a concept of education that is out-dated. It's a view of children as passive receptacles, whose job is to soak up learning that the teacher tells them they need. If they're not soaking it up, it's their own fault. They need to seek out extra help to soak up what everyone else is soaking up. This is the view of education that gives us sentences like, "I taught it - it's not my fault if they didn't learn it!"

If they didn't learn it, then how well did you teach it?

My job is to teach, which means my job is to get kids to learn. If they aren't learning, part of my job is to identify and overcome the roadblocks to learning. Their responsibility is to be honest with me about what they can do and participate to the best of their ability in their learning. Asking for help during the school day is part of that - as is me offering suggestions as they're learning. That's not extra. It's integral.

So what does it look like when I'm doing my job? First, there's a pre-assessment. Do they already know the skill I'm setting out to teach? What will it look like if they already know it? For that matter, what is the skill I'm setting out to teach? I need to have it laid out and so do they, so they can start to develop the metacognitive awareness of when they've learned it. So, we do a pre-assessment, and I figure out some loose groups - who gets it completely; who gets it sort-of and is going to need enrichment, or to prove that they can do it on a higher level of material; who can see what the concept is but doesn't know how to do it; and who can't even formulate the questions to figure out what's going on. With any luck, most of my kids will fall in the last two groups, with four or five in the second group.

Since the material I'm teaching is about strategies for comprehending and communicating, it's rare for a student in my class to truly get it right off the bat. Pretty much all of them can benefit from practising the skill on reading materials that are at their level, because the questions I'm asking are the same big questions they're going to get in every class right up through university. What is the main idea? What is the author's message or theme? What does the author want us to think and feel about the topic/characters/themes? What are the clues to that? What techniques has the author used to get us to think or feel these things? How effective was the author at communicating their message? What can I learn from the author's techniques, which I can then apply to my own writing/media creations? Even gifted students can apply these same techniques and become better readers, writers, and thinkers, by using them - on material that interests them and is closer to their level.

So, I have the pre-assessment in hand, and I know where my kids fall on the rubric related to this specific skill set. I have tentative groups. I also have a specific goal for each kid. Not every kid is going to get it at the end of the unit. That's unrealistic. But my goal is for 75-80% to get it, and for every kid to make progress in at least a couple of the sub-skills involved. They can't articulate the author's message? I'll concentrate on getting them to pick out the main idea and some supporting details, because that's an important background skill for evaluating, and it can be taught as part of my regular lessons.

Now I design my whole-class lessons, which introduce the topic and provide an example. I do a read-aloud, I think aloud as I'm reading, and I write down my thoughts on chart paper. I focus on one or two of the questions for the unit - at the moment, I'm focusing on, "What does the author want us to think or feel about the topic? How do we know?" I pick a reading selection that will be interesting to everyone, even though the reading level will be too easy for some and too hard for a few others. When we've done one or two of these whole-class lessons, I do another small assessment. This time, I get the kids to talk with their peers about the answers to the questions, then I get them to write their answers. At this point, I solidify the groups. There are usually a couple who have moved and don't need much more direct instruction, and the lowest group should by now have a way to frame their questions.

Now I assign practice work to the kids who are ready for it, according to their reading level, and the kids who need more direct instruction come to see me for guided reading. Usually there are two levels of this - those who only need a bit of help to be ready for independent practice, and those who are barely able to grasp the meaning of the question. I take the first group first, while assigning different (busy) work to the lowest group. When I work with the lowest group, it's intensely. The other kids have probably finished their independent practice at this point and are doing independent reading, or the assignments related to independent reading. I work with the lowest group on a subset of the skill in question - probably main idea and supporting detail. This process generally takes a couple of days.

Now I do another whole-class lesson, this one involving a lot more student participation. I want the ones who have got it to practise in a way that lets the lower-functioning kids listen to their thinking and see what they're doing. This whole-class lesson will usually involve mixed groups at some point, where I send kids off to answer questions on chart paper in groups that include a few people from each of my levelled groups. I get the groups to present their findings; other groups are responsible for coming up with a summary sentence of each group's presentation. The goal of all this talking is three-fold. First, it helps the kids themselves to articulate what they are starting to understand, and it supports the writing they'll eventually be doing about this topic. Second, it provides language for the kids who have trouble articulating it - a hook for their understanding and a vocabulary base for them to talk about it. (This is the point where the Word Wall is updated with vocabulary the kids decide is important to this topic.) Third, it allows for several levels of accountable talk - group talk, paired talk, and presentation-talk - which allows for the use of different levels of language, practice in various group-work skills, and practice in presentation skills and listening skills. This is where my oral communication marks come from, most of the time.

Now we do another assessment, a brief one. By this point, most of the kids who are ready to really get it, are getting it. I give them one more practice assignment for consolidation purposes, and then they have to demonstrate their learning.

The lowest group probably hasn't gotten to the point where they get it yet, but hopefully they can now find the main idea when they look for it and point out some supporting details. I will usually try to get them to begin to practise the skill everyone else has been working on, so that it won't be brand-new to them when they see it the following year.

Demonstrating learning takes several different forms. I usually break up the "understanding" part from the "creating" part, because being able to create using these concepts is a higher level thinking skill than being able to explain the same concept. So there will be a small task where I find out if they get it, and a bigger task that ties everything together. This stage generally takes half an hour a day for a week or two. This is also where I do writing conferences, so I can address any small misconceptions or issues with writing form or style that crop up. I strive to see every kid for at least two writing conferences. Usually, I see every kid at least once and about half of them twice.

The only part of this where I might conceivably feel the need to offer what most parents think of as "extra help" is right at the end, if I don't have time for all the writing conferences I want to do. (See previous post about smaller class sizes - 27 is just too many.) For the rest of it? The scaffolding of learning, the gradual release of responsibility to the kids, the pointers on what to do and how to improve their answers, are built so carefully into each step that 80% of kids won't need any mroe help with the concepts - only with the execution. The remaining twenty percent are probably being pulled by the spec. ed. teacher a few times near the end so that we can get a final product out of them, and they're getting a bunch of guided practice time directly with me. If they're still not getting it at the end, the reason probably has more to do with outside factors than with my teaching - which means extra help might not help them, anyway, at least not right now.

Oh, as for keeping them busy? I've got another smaller topic, text features, coming up the middle between the Big Idea we're just finishing - inference - and the one we're just starting - Evaluating. And of course, it's all tied in even there - how does the author use X text feature to make you think or feel something in particular? Everything is tied together.

Traditional teaching decides what the kids need to know, teaches it, and then evaluates it. It skips the practice steps and scaffolding that are the heart of my program. In a traditional model, yes, extra help is essential - because there was so little help built into the lessons. The smart kids are the ones who play the education game well enough to produce good work the first time they're asked for it, but they never get the chance to go deeper into their topic or Big Idea because they're focused on the fact that they're going to be marked on whatever they produce. My kids know which parts of their lessons are practice and which parts are evaluation, and they know that if they do poorly on the evaluation, I'm going to give them another opportunity to get it right and more teaching first, so there's little stress and absolutely no incentive to cheat.

In the end, I get kids who can talk intelligently about the author's message, techniques, use of text features, attempts to provoke an emotional response, and effectiveness. I was an advanced reader - but no teacher ever taught me that until grade eleven, and even then it was an accident.

x-posted to [livejournal.com profile] ontario_teacher.
velvetpage: (teacher)
Background: Ontario teachers have been without a contract since the end of August. This happens regularly; strikes in teaching generally only happen when contract negotiations have gone on for several months with no progress. In this case, the negotiations have two parts: the first with the provincial team for things that are common to all teachers, and then with our individual boards of education for things specific to our own local area. At the moment, I'm discussing provincial negotiations.

Some time ago, ETFO (Elementary Teachers' Federation of Ontario - my own branch of the Ontario Teachers' Federation, aka "the union") signed a media blackout agreement with the provincial negotiators. This was requested by the province, and today I found out why. The blackout has been lifted, btw, and the Board of Education lost no time making its elementary teachers look like greedy bastards, intent on sinking the province financially and failing our students at the same time. (It's worth your time to read the link if this matter interests you, because I'm about to point out all the ways it's wrong.)

Here's what I found out from the union steward at my school today. She only found this out herself a few days ago, when the media blackout was lifted.

That bit about the boards of education proposing things that would improve student learning? It's a flat-out lie. The union proposed taking no salary increase at all for one of the four years - that's three percent less than the province was offering us. In return, we wanted smaller class sizes in the junior and intermediate grades (that is, a cap similar to what exists in primary but higher - the proposal was 23 for junior classes and 25 for intermediate.) We would have been willing to accept no other changes whatsoever to our existing contract. Instead, the provincial team wanted to give us the 12% raise that others negotiated, with the following strips from our contract:

1) Extra prep time would be at the discretion of principals, meaning it could be taken away at will as teachers were asked to fill in for missing colleagues. That's code for, "We're freeing up classroom teachers to be supply teachers so we can cut back on the supply list."

2) The improvements that we won at the negotiating table three years ago around supervision time would be gone, allowing for an extra 100 minutes a week of supervision duty. That's more than double what we currently have, which we fought for long and hard. What good is an extra forty minutes of prep time if it can be taken away at will and is replaced with a hundred minutes of supervision duty?

3) They wanted to add a preamble to the Education Act, stating that teachers and schools are wholly responsible for student success. Translation: they want to be able to reward teachers with extra pay in schools that are doing well, and penalize teachers financially in schools that aren't. Can we say No Child Left Behind? The result: excellent teachers would be fleeing failing schools in droves, trying to maintain their salaries, so the schools that needed their expertise the most would then be without it, and the schools where students were already doing well would get better teachers. It's a route to adding a new element of classism into Ontario's school system. I've written about this before in my POAC about treating schools as businesses. It's disgustingly discriminatory. When 69% of student achievement can be explained by socio-economic factors, blaming teachers for lack of success - when success is determined, not by each student's individual improvement from previous years but by a statistically-invalid "standardised" test - is wrong and unfair.

There were also a few strips related to capping benefits at current levels for four years, which were not a sticking point in the face of everything else, but really did add to the camel's load when looking at the whole picture.

People of Ontario: when you see in the newspapers that teachers turned down the deal because they wanted more money or things that would end up costing more money, DON'T BELIEVE IT. The union's proposal wasn't going to cost one red cent more than what the Boards were proposing. The Minister of Education agreed with that. It's the provincial team negotiating on behalf of the boards of education who turned down an agreement that fit within the provincial framework, allowed for a smaller pay increase than was being offered, and respected previous negotiations. We don't want more money. We DO want to be respected for our work, we DO want to protect ourselves from being unfairly blamed for being unable to rewire students' brains, and we DO want to keep the benefits we've negotiated for in good faith in past rounds.

I want to see my union getting its message out. I want to see editorials that explore both sides fairly - because I believe the truth reflects better on teachers than on the boards. I want to see the union respond to the slanders that have already begun in editorial boards, asking why teachers aren't making salary concessions. We are. Now it's up to the boards of education to accept them, and bargain in good faith.

Edit: Here is ETFO's breakdown of what happened in the negotiations.
velvetpage: (oxford comma)
This is from Piet's journal, still screened over there because he's getting a better night's sleep than I am, on the education thread from a few days ago. I don't think [livejournal.com profile] professormass will mind me reposting his comment, and I'm pretty sure [livejournal.com profile] oakthorne won't mind being referenced in it, either. I'm leaving it unlocked because those gentlemen aren't on my friends list and have a right to see this. And I'm posting it here because, until Piet unscreens the comment, I can't answer it over there. :)

First, [livejournal.com profile] professormass's comment:

Something occurs to me (and I apologize for butting into the conversation -- as you know, velvetpage, I'm keenly interested in education):

The sweeping generalizations and the arguments against making those generalizations are missing a key point — the education system must address generalization, because it's trying to work for the mythical "average student," casting a net that catches as many kids as it reasonably can. The exceptions will always and must always be the issue. No bureaucratic system can account for the wide variety of learning styles present in the complexity of human nature.

People oakthorne and myself are exceptions. So, yes, much of pyat and velvetpage's arguments hold water, with the percentage of the population who aren't exceptions.

I think that the biggest point of difference I'd have with them is what percentage of the population represents exceptions to things like "
A middle-class person who doesn't get that education might be able to keep their middle-class status with a job that doesn't require it", where "requiring it" is a highly subjective thing, in most cases. My field, for example, routinely requires anywhere for 6-12 years of degrees, diplomas and certifications; I have none, and still operate at an executive level.

A friend of mine, a schoolteacher, told me that he thought the percentage of exception was something like 1%. I think it's more like 25%.

Modern school systems have almost always served the needs of the majority. When pyat says "it's getting better," I read, "it's serving a broader swath of the majority."

There will always be exceptions to the rule. After having done much research, I'd tend to say that public education has succeeded in catching a slightly broader swath than when I was trapped in the system. I don't think it will ever catch all the exceptions.

So, really, the question is: what to do with the exceptions? What safety net can be cast for people like oakthorne and myself? Can one be cast?

Now my reply:

Arguably, Piet and I are exceptions, too. As I believe Piet stated somewhere else, he was identified “gifted” but nearly flunked out several times, getting by with barely-passing grades. I was at the opposite end – I excelled with so little effort that I spent much of my class time in elementary schools with a novel open under my desk, because I was bored silly. And yet we managed to make system work for us, in our own ways.

That said, you’re right – the education system works best for the people who test out as average and slightly above-average in intelligence. It generally works all right for those slightly below-average, because they’re able to access extra help that is sent their way, and it often works just fine for those at the top of the intelligence scale because they learn to play the system. But for all the special placements, resource help, gifted classes, and what have you, that the school boards put in place to cast that wider net, there will always be those who don’t quite fit it. Most of those will benefit by taking everything they can out of the education system and then going their own way. But the fact that it doesn’t work for them doesn’t diminish the value of education overall; it only speaks to the need to address individual needs as broadly as possible, or as you say, to cast a broader net.

In terms of the number of kids with a diagnosed exceptionality (at the top or bottom – this number includes gifted) you and your friend are both wrong: it’s between ten and fifteen percent, statistically. But the school board makes concerted attempts to catch most of those within their net.

I believe my school, and for that matter a fairly large chunk of the schools in Ontario (not all, yet, but we’re moving that way) are doing a better job of this than ever before. I now routinely teach to four or five different levels in my classroom at a time. I have smart kids who are feeling challenged and rewarded, and I have low-average and below-average kids who are learning as fast as their brains will let them, and the kids in the middle aren’t being forgotten, either. I have a learning-disabled gifted kid (neither of those are official diagnoses, the first because his parents don’t want him labeled and the second because the LD got in the way of the intelligence testing when we did it) who is enjoying school for the first time in his life. I’m teaching him to game the system – how to get what he needs from it as he goes on to grade six, what it’s important to do, what can be ignored – because there’s no reason this kid can’t succeed at the highest levels and get the kind of career you only get through education. (He wants to be a lawyer.)

Part of the reason he’s going to make it is that nobody’s telling him that school isn’t important, or that many people can succeed without it, or that the system is out for its own benefit. Those things are true some of the time, but they’re not helpful overall. They’re excuses for people who did not succeed within the education system. Some of the time, those who didn’t succeed within the system manage to succeed outside of it, as you and oakthorne have done. More often, that is not the case.

And here we get to the crux of the matter. I’m quite willing to admit that school doesn’t work for everyone, and that some people succeed just fine without it. What I’m NOT willing to admit, and indeed will argue against with all the force at my command:

1) that this is the rule for most, even for most of those we would classify as exceptions;
2) that the existence of holes in the net in any way diminishes the value of the educational system;
3) that teaching the conclusion we’ve been arguing against (that advancing your education through traditional channels is a worthless endeavour) is going to help the people who take the lesson to heart;
4) that in fact, people who hear that lesson and learn it well stand an equal chance of succeeding at their various endeavours in life, as measured by the level of control they have or can access over their own workplace and community, as those who remain within the educational system.

Please note that I think it’s possible to enter the education system at differing points and still succeed within it. A child who is homeschooled until high school often ends up doing better when they finally do access formal education, in large part (I believe) because their parents took a very active interest in their education and made sure that they understood the value of an education – traditional or otherwise. But sooner or later, most people who succeed at the highest level they’re capable of, do it by making use of some facet of the education system.

So, to answer your question: I think the net that is catching more and more kids still has something of value to offer to the exceptions, especially the exceptions at the top of the spectrum. The clearest evidence of this is the fact that three exceptions have now come forward in this journal or another, to argue their case. They've done it with varying degrees of rhetoric, but they've all done it with a good grasp of written English. Put simply, they're attacking the educational system with tools that they accessed through an educational system. It didn't fail them as far as they say it did. (Yes, I include you, [livejournal.com profile] professormass, in that assessment.) The higher up one goes in education, the smaller the net the system is attempting to cast, for exactly the reasons you've stated - not everyone needs it. For an adult, the choice to work within the system or circumvent it (or simply ignore its impact) is a choice. There should be (and are) mechanisms in place to help those who wish to access that system but are having difficulty doing so. But the onus is on the student to take what they need from the system - not on the system to offer whatever the student needs. The focus shifts further and further away from the responsibility of the system and more and more towards the responsibility of the student. The student who either fails at that responsibility, or decides not to take it on, needs to take a hard look at where the problem was. Many of them cut their own hole in the net.
velvetpage: (teacher)
Also, thanks to [livejournal.com profile] anidada who suggested I get this book. :)

"Notice that this argument for the abolition of traditional grades isn't based on the observation that some kids won't get A's and, as a result, will have their feelings hurt. Rather, it is based on the observation that almost all kids will come to accept that the point of going to school is to get A's and, as a result, their learning will be hurt."

So, what happens to a "good kid" like me, who internalizes that second message?

First, one of the things that made me a good kid was that I almost never experienced a lack of understanding; I could do pretty much anything I needed to do with minimal effort. So I was mostly spared the anxiety of a fear of failure. Even so, it reared its ugly head a few times in my school career. There was my father's jocular habit of looking at a grade of 95% and remarking, "Not bad - but it leaves room for improvement." There was the internal, quickly-suppressed panic when I didn't understand something instantly. I suppressed it because it was imperative that NOBODY KNOW I didn't understand. I knew I was capable of pulling the wool over everyone's eyes and making them think I understood just fine, until I figured it out. There were my siblings' efforts to be different from me, often by underachieving so as not to compete.

Even so, when it came to school work, I put in minimal effort to get the grades I wanted. Grades were everything in school, from - as best I can remember - about grade three. That was partly because my grades at the end of grade two were among the lowest I ever experienced in my school career. My parents' and teachers' disappointment in the grades - not in the learning they represented, because I actually knew everything they were teaching, notably in phonics in which I got a C - was like a slap in the face. I knew even then that I'd been shafted. The teacher hadn't marked how well I understood the phonics - I was reading "chapter books" fluently by then. She'd marked the answers in the workbook, which, because I was bored and slightly depressed from a recent move to a different province, were incomplete. Not wrong - INCOMPLETE. What did I learn? I learned that what you knew in school didn't matter, unless you answered the questions correctly, no matter how boring you found them.

So I coloured my title pages, underlined my titles in red pen with a ruler, whipped through spelling exercises without ever paying much attention to them - I was a natural speller with a good grasp of phonics, so this didn't matter - and spent my daydreaming time with a pencil in hand, writing stories. My teachers loved that, and the rote learning was so boring that I had plenty of time for cooking up stories, often while my pencil was busy with the "real work." The stories always got A's.

Time passed, and I began to read more outside of school than in it. This is where the really interesting part comes in, in terms of pedagogy. I was a reader by nature and nurture. While I didn't read earlier than kindergarten, I did read better, faster, than most of my peers. When I learned, it was with a sudden light bulb rather than a slow progression. The important part is that I didn't see reading as a school activity. I saw it as something people do for fun, because that's how my parents saw it and how they encouraged me to see it. The things I saw as school activities were still done well, mostly because I was too much of a pleaser ever to risk the displeasure of the adults around me by doing a half-assed job. But most of my learning didn't come from those activities. I can't remember more than a handful of activities I was actually assigned in school, nor more than a few things I was told to read. The books I remember, the books I learned from, the books that informed my worldview and gave me the historical background colour on which to pin real historical understanding - ALL of that came from reading that I did for the love of reading.

Which makes me wonder: what happens to the kids who don't grow up with the knowledge that reading is something people do for fun, and who don't have the benefit of reading early and well? I can answer this, this time from looking at my students: they see reading as an in-school activity, and they see it as something on which they will be graded. The "good kids," that is, the pleasers, will do fairly well at it in the context of school work - but they'll stick to reading material with no meat to it, whenever I let them get away with it. They'll refuse to challenge themselves, and they won't think about what they're reading unless I can get them to forget about the grade. The not-so-good kids, that is, the ones who don't read early or well, will start to give up by the end of grade one, sometimes sooner. They'll have their failure to read on the school's timetable reinforced as a failure of their ability, and each time they fail at a reading task (in their own estimation) a failure becomes more likely the next time.

I continued in much the same pattern through high school and even into university. Coursework was a slog that I had to get through - often even if the topic was fascinating. I managed not to read half the books I was supposed to read, because I knew I could pass the tests by regurgitating what the professor had told me, especially since my own ideas were unwelcome and got lower marks on those tests. If the prof only wanted his own ideas given back to him, why would I read the book and risk getting some of my own? That way lay frustration - so I avoided the frustration by eliminating the learning in favour of getting the grade.

The courses where my own ideas were welcome got far more of my effort and taught me far more lasting lessons. Still, much of what I've learned about subjects that interested me came because I read about them on my own. The more I think about it, the more I realize that my success in school is more an indictment of the system than an advertisement for it. I succeeded at school while learning as little as possible in it.

If the goal of school is to educate, then we need to consider: are our methods of assessing students undermining that goal? Are kids learning what we want them to learn, or are they learning to please teachers and parents while avoiding practically all valuable thinking? Are we setting them up for failure by grading their successes?

And if so, how do we fix it, in such a way that ALL students come out educated?
velvetpage: (teacher)
Every conservative government I'm familiar with in North America occasionally brings up the issue of school choice - that is, the right of students and parents to choose the school that best fits their values and will give their kids the best education. The mantra usually includes several elements of a moral conservative and economic conservative standpoint: the problem of religious education; the idea that competition provides a motivation to improve; and that engagement increases with the level of choice.

Cut for length. )
velvetpage: (Default)
I have a request for you.

I need a poster to put up in a couple of classrooms in my school, and I don't know how to design such a thing myself. The idea is this:

There is a large umbrella on the poster. On the umbrella are the words: "This ___________ we are working on:" followed by two blank lines, with "Math" written under one of the lines (on the left side of the handle) and "Literacy" written under the other line (on the right side of the handle.)

Down the handle itself are the short forms for the five school days - Mon, Tues, Wed, Thurs, Fri - and on either side of the handle are empty text boxes corresponding to each day of the week (so, five on the left and five on the right.) This part of things should take up at least two-thirds of the space, because those boxes are where the important day-to-day information is going to go. I'd like a strong background colour behind the white text boxes. I don't really care what the colour scheme of the background is, as long as it's fairly bright and cheery. The lettering needs to be legible from a distance (say, the back of the classroom if the poster is on the blackboard) and in a fairly simple font.

Any takers? I don't think I can pay anyone to do this, but you could try to pitch it to an education materials company when you're done. All teachers in Ontario are being advised to post their lesson goals for every lesson, every day, and I suspect if you came up with half a dozen different ones of a similar type and offered them, you'd get a good response.

I just need the image itself, which I can then get printed at Staples and laminated.
velvetpage: (Default)
For my American teacher friends, in particular - it's somewhat less applicable in Ontario:

Not on the test."
velvetpage: (cat in teacup)
An interesting article about children's, adolescents', and adults' lies: http://nymag.com/news/features/43893/

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