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velvetpageThis is pretty rough, but it has the basic idea. I'm considering polishing it and trying to sell it. Let me know what you think.
Problems with the Ontario Elementary Curriculum
1) "Explain your thinking"
It is a truism of language education (any language, no matter how many one speaks already) that comprehension precedes expression. That is to say that language learners always understand more than they can produce themselves. For example, a baby as young as six or seven months will react to the question, "Where's Daddy?" by looking around and smiling or waving arms when he spots his father. The ability to articulate this knowledge verbally develops much later - between twenty and thirty months, a child will learn to reply with very simple language, and he will likely be about four before he'll be able to answer, "He's at work," and understand that this means he is not in the next room. The other classic example is the phrase, "I can do it, but I can't explain it." The ability to perform an operation will usually precede the ability to explain how to do it or why that method works.
Everyone has been told, "If you can explain it, that means you really know it." This is true as far as it goes. Linguistic intelligence is extremely important. However, it does not account for the many other ways to demonstrate knowledge - diagrams, performing calculations, actually building something or making it work, just to name a few. The authors of the Ontario Curriculum took this adage too much to heart. They have applied it to every area of the curriculum starting in grade one or two. In the curriculum documents, the idea is tacked onto expectations of all types with the phrase, "explain their thinking."
First, this is asked of them too early. Many grade two students simply do not have the language skills to explain what they know. In fact, it is not uncommon for students in the junior grades to have difficulty verbalizing or writing down their knowledge. This is acknowledged repeatedly in the Ministry reports on language development both at the primary and the junior levels. Secondly, it is asked too soon. Students are asked to explain a concept that has only just been introduced, leaving them no time to master the concept first. Thus the explanations are necessarily incomplete, leading to a C at best. Third, the phrasing of the expectation excludes or devalues other methods of demonstrating learning. A child who knows exactly how to do a math problem, but fails to explain it adequately, will get a lower mark than someone who makes errors in the execution of the problem but can explain the process well. The clear divide between numeric and linguistic intelligence, once a mainstay of school, has disappeared. The best marks in math go to the people who can explain their thinking, leaving many students frustrated and discouraged at low marks that do not adequately reflect their knowledge of the subject matter.
2) Learning by osmosis
The usual methodology of a well-constructed lesson includes six steps:
1) Activating prior knowledge (review)
2) Presenting new learning
3) Practising the new skill
4) Revising or correcting any mistaken impressions through assessment and reteaching
5) Consolidating new learning by asking for applications of new skills; and
6) Evaluating students' learning for reporting purposes and to plan further lessons.
Skipping or skimping on any one of these steps leads to lack of mastery of the skill or knowledge in question. If mastery of concepts is the goal, then no steps can be skipped.
The Mathematics curriculum includes five strands, or branches, of mathematics. Each strand must be taught and evaluated twice during the course of the year. This means that between September and the middle of November, a ten-week period, students must undergo three complete units and be evaluated on their knowledge. That leads to an average of three weeks per unit. If students do not immediately grasp the concept, there is no time to go back, reteach, and reevaluate. If teachers go back, something else will be missed. The timeline almost forces the skipping of steps because it is so tight.
Students end up being evaluated during the assessment and review stage of the teaching process. If errors are discovered, there is not enough time to back up and teach the lessons again. So students gain an incomplete understanding of a wide variety of topics, without ever really mastering anything. Activities like word problems, which should be used as consolidation and extension of the skill just taught, are instead used as basic skill practice. Inability to do these problems at that time is not a sign of lack of ability in math, or even in the current strand. This is an issue with the pedagogy being used. Students and parents do not realize this, however, and come away from math frustrated and discouraged. Students decide that they are not smart enough to do math. The curriculum that touted higher standards that were putting kids first has in fact succeeded in making more difficult subjects inaccessible to a majority of students. The same problems arise in the content-area subjects of science and social studies.
3) Concrete versus abstract thinking
Every teacher is familiar with the works of the famous French psychologist Piaget. His main contribution to his field was to codify a developmental timeline of which skills children master and when. It was he who noticed that small children equate "taller" with greater volume, and will not realize that a tall, slim container will hold the same amount of liquid as a short, wide one, even if they see the liquid poured from one to the other. This developmental timeline postulates that children reach stages at which they are ready for certain kinds of learning. Teaching the concept before the child has reached the appropriate stage will not work. The child will not understand, not because he is not smart but because he is not ready for the concept in question.
The biggest leap, after the acquisition of basic language skills in the first four years of life, happens sometime between the ages of eleven and thirteen. It is the jump from primarily concrete thinking styles to the ability to manipulate abstract concepts. Before this, the best teaching methods are highly visual and tactile. The best way to explain multiplication to an eight-year-old is to give her fifteen blocks and let her divide them into groups of five. A child will learn from this to the point where they do not need the manipulatives to do multiplication each time. But explaining multiplication with only pictures and no blocks is much harder than using the blocks, because the tactile element has been eliminated. Explaining multiplication with neither pictures nor blocks is doomed to failure, because it does not recognize how children think.
The previous curriculum introduced very, very few highly abstract concepts until the middle grades or higher. The difficult concept of integers used to be a grade eight subject because the pictures and abstract manipulation of numbers on the other side of zero was something that required some mastery of abstract thinking. Even in grade eight, many students had difficulty with integers. The Ontario Curriculum currently in place introduces integers in grade seven, and expects mastery of them before high school. Many children will not be developmentally ready for this concept until near the end of grade eight. The result is two years of thinking they are bad at math, when in fact they are being asked to learn that which they are not yet capable of grasping.
The other example is basic algebra. Using a variable to replace a blank space in a question is a highly abstract concept. Even very mathematically adept ten-year-olds will often not truly understand it, though they can be taught to manipulate it without comprehension. Yet monomial algebra is now taught in grade six.
The truly interesting aspect to this problem is that this curriculum recognizes the need for concrete learning in many areas. Most math expectations include a mention of "using concrete materials and drawings" to demonstrate understanding, up to an including grades seven and eight. Science strands include building bridges and structures in grade one, using materials such as toothpicks and marshmallows. The expectation to explain one's thinking often includes the suggestion that this be complemented by diagrams or manipulatives. Yet, while the recognition of the need for concrete, kinesthetic learning is there, the assumption seems to be that any concept can be mastered if the teaching technique is tactile enough. This is simply not true. One has the impression that the people writing the curriculum never glanced at the research surrounding how children learn while they were deciding what should be learned and when.
Next Steps
The Ontario Curriculum needs to be reevaluated and revamped by teachers and other professionals in education-related fields such as child psychology and linguistics. There are parts of it that are salvageable, and even parts that are good; but several steps need to be taken to ensure that the good is maintained while the elements that are hurtful to our students are removed.
First, we need to scale back the amount of knowledge our children are expected to master. There is simply not enough time to grasp it all, and some of it is being introduced too soon for the children to master it in the first place. Science strands need to be reduced to three per year, allowing for one complete unit to be taught each term. The Data Management and Probability strand needs to be removed from the math curriculum entirely until middle school. Data management in the form of simple graphs can easily be taught as part of science or social studies, and probability is too abstract a concept for most children before about age ten. Certain elements of the junior math curriculum need to be moved to middle school, allowing more emphasis on the basic computation skills that are not currently being mastered at all. Social studies should be streamlined and reduced to take advantage of the widening focus and increased background knowledge a child achieves with age and exposure to information. The requirement to explain one's thinking should begin after grade 3, and be limited to concepts that have been taught in at least one previous grade. Children should be given several opportunities to master new concepts before being expected to explain them.
Problems with the Ontario Elementary Curriculum
1) "Explain your thinking"
It is a truism of language education (any language, no matter how many one speaks already) that comprehension precedes expression. That is to say that language learners always understand more than they can produce themselves. For example, a baby as young as six or seven months will react to the question, "Where's Daddy?" by looking around and smiling or waving arms when he spots his father. The ability to articulate this knowledge verbally develops much later - between twenty and thirty months, a child will learn to reply with very simple language, and he will likely be about four before he'll be able to answer, "He's at work," and understand that this means he is not in the next room. The other classic example is the phrase, "I can do it, but I can't explain it." The ability to perform an operation will usually precede the ability to explain how to do it or why that method works.
Everyone has been told, "If you can explain it, that means you really know it." This is true as far as it goes. Linguistic intelligence is extremely important. However, it does not account for the many other ways to demonstrate knowledge - diagrams, performing calculations, actually building something or making it work, just to name a few. The authors of the Ontario Curriculum took this adage too much to heart. They have applied it to every area of the curriculum starting in grade one or two. In the curriculum documents, the idea is tacked onto expectations of all types with the phrase, "explain their thinking."
First, this is asked of them too early. Many grade two students simply do not have the language skills to explain what they know. In fact, it is not uncommon for students in the junior grades to have difficulty verbalizing or writing down their knowledge. This is acknowledged repeatedly in the Ministry reports on language development both at the primary and the junior levels. Secondly, it is asked too soon. Students are asked to explain a concept that has only just been introduced, leaving them no time to master the concept first. Thus the explanations are necessarily incomplete, leading to a C at best. Third, the phrasing of the expectation excludes or devalues other methods of demonstrating learning. A child who knows exactly how to do a math problem, but fails to explain it adequately, will get a lower mark than someone who makes errors in the execution of the problem but can explain the process well. The clear divide between numeric and linguistic intelligence, once a mainstay of school, has disappeared. The best marks in math go to the people who can explain their thinking, leaving many students frustrated and discouraged at low marks that do not adequately reflect their knowledge of the subject matter.
2) Learning by osmosis
The usual methodology of a well-constructed lesson includes six steps:
1) Activating prior knowledge (review)
2) Presenting new learning
3) Practising the new skill
4) Revising or correcting any mistaken impressions through assessment and reteaching
5) Consolidating new learning by asking for applications of new skills; and
6) Evaluating students' learning for reporting purposes and to plan further lessons.
Skipping or skimping on any one of these steps leads to lack of mastery of the skill or knowledge in question. If mastery of concepts is the goal, then no steps can be skipped.
The Mathematics curriculum includes five strands, or branches, of mathematics. Each strand must be taught and evaluated twice during the course of the year. This means that between September and the middle of November, a ten-week period, students must undergo three complete units and be evaluated on their knowledge. That leads to an average of three weeks per unit. If students do not immediately grasp the concept, there is no time to go back, reteach, and reevaluate. If teachers go back, something else will be missed. The timeline almost forces the skipping of steps because it is so tight.
Students end up being evaluated during the assessment and review stage of the teaching process. If errors are discovered, there is not enough time to back up and teach the lessons again. So students gain an incomplete understanding of a wide variety of topics, without ever really mastering anything. Activities like word problems, which should be used as consolidation and extension of the skill just taught, are instead used as basic skill practice. Inability to do these problems at that time is not a sign of lack of ability in math, or even in the current strand. This is an issue with the pedagogy being used. Students and parents do not realize this, however, and come away from math frustrated and discouraged. Students decide that they are not smart enough to do math. The curriculum that touted higher standards that were putting kids first has in fact succeeded in making more difficult subjects inaccessible to a majority of students. The same problems arise in the content-area subjects of science and social studies.
3) Concrete versus abstract thinking
Every teacher is familiar with the works of the famous French psychologist Piaget. His main contribution to his field was to codify a developmental timeline of which skills children master and when. It was he who noticed that small children equate "taller" with greater volume, and will not realize that a tall, slim container will hold the same amount of liquid as a short, wide one, even if they see the liquid poured from one to the other. This developmental timeline postulates that children reach stages at which they are ready for certain kinds of learning. Teaching the concept before the child has reached the appropriate stage will not work. The child will not understand, not because he is not smart but because he is not ready for the concept in question.
The biggest leap, after the acquisition of basic language skills in the first four years of life, happens sometime between the ages of eleven and thirteen. It is the jump from primarily concrete thinking styles to the ability to manipulate abstract concepts. Before this, the best teaching methods are highly visual and tactile. The best way to explain multiplication to an eight-year-old is to give her fifteen blocks and let her divide them into groups of five. A child will learn from this to the point where they do not need the manipulatives to do multiplication each time. But explaining multiplication with only pictures and no blocks is much harder than using the blocks, because the tactile element has been eliminated. Explaining multiplication with neither pictures nor blocks is doomed to failure, because it does not recognize how children think.
The previous curriculum introduced very, very few highly abstract concepts until the middle grades or higher. The difficult concept of integers used to be a grade eight subject because the pictures and abstract manipulation of numbers on the other side of zero was something that required some mastery of abstract thinking. Even in grade eight, many students had difficulty with integers. The Ontario Curriculum currently in place introduces integers in grade seven, and expects mastery of them before high school. Many children will not be developmentally ready for this concept until near the end of grade eight. The result is two years of thinking they are bad at math, when in fact they are being asked to learn that which they are not yet capable of grasping.
The other example is basic algebra. Using a variable to replace a blank space in a question is a highly abstract concept. Even very mathematically adept ten-year-olds will often not truly understand it, though they can be taught to manipulate it without comprehension. Yet monomial algebra is now taught in grade six.
The truly interesting aspect to this problem is that this curriculum recognizes the need for concrete learning in many areas. Most math expectations include a mention of "using concrete materials and drawings" to demonstrate understanding, up to an including grades seven and eight. Science strands include building bridges and structures in grade one, using materials such as toothpicks and marshmallows. The expectation to explain one's thinking often includes the suggestion that this be complemented by diagrams or manipulatives. Yet, while the recognition of the need for concrete, kinesthetic learning is there, the assumption seems to be that any concept can be mastered if the teaching technique is tactile enough. This is simply not true. One has the impression that the people writing the curriculum never glanced at the research surrounding how children learn while they were deciding what should be learned and when.
Next Steps
The Ontario Curriculum needs to be reevaluated and revamped by teachers and other professionals in education-related fields such as child psychology and linguistics. There are parts of it that are salvageable, and even parts that are good; but several steps need to be taken to ensure that the good is maintained while the elements that are hurtful to our students are removed.
First, we need to scale back the amount of knowledge our children are expected to master. There is simply not enough time to grasp it all, and some of it is being introduced too soon for the children to master it in the first place. Science strands need to be reduced to three per year, allowing for one complete unit to be taught each term. The Data Management and Probability strand needs to be removed from the math curriculum entirely until middle school. Data management in the form of simple graphs can easily be taught as part of science or social studies, and probability is too abstract a concept for most children before about age ten. Certain elements of the junior math curriculum need to be moved to middle school, allowing more emphasis on the basic computation skills that are not currently being mastered at all. Social studies should be streamlined and reduced to take advantage of the widening focus and increased background knowledge a child achieves with age and exposure to information. The requirement to explain one's thinking should begin after grade 3, and be limited to concepts that have been taught in at least one previous grade. Children should be given several opportunities to master new concepts before being expected to explain them.
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(no subject)
Date: 2005-03-14 05:19 am (UTC)(no subject)
Date: 2005-03-14 03:26 pm (UTC)(no subject)
Date: 2005-03-14 05:30 am (UTC)My impression is that selling opinion pieces is hard unless you're a regular writer for the publication or an expert in the field. I don't know if any paying education-focused Canadian markets would consider someone with your background to be an expert or not, but it is certainly worth a try. You're more of an expert than me, and your background in linguistics gives you an interesting and unique perspective.
Having said that, I confess that I disagree with a lot of what you're saying, while also recognizing that I'm less of an expert, can't back up my views (at the moment), and likely have a warped perspective on learning given my academic record/history.
(no subject)
Date: 2005-03-14 11:13 am (UTC)(no subject)
Date: 2005-03-14 03:01 pm (UTC)Their website is currently down, but it is cached by google.
Their attitude towards education is the right one, but implementation requires smaller classes and brilliant teachers, as I understand it. Obviously, this isn't really within the budget of the public school system, but I'd like to believe that there is a sane way to implement this philosophy of challenging, early intervention in spirit, at least, en masse. That belief may be unfounded though.
Anyway, I got the impression that you feel that the curriculum should be easier than it already is, whereas I feel that it isn't hard enough or engaging enough, and that children will excel when challenged in the right way. I don't agree with all you've said, of course. Just the impression of wanting to teach less earlier on, and the belief you seem to have that students can't learn certain types of stuff before a certain age.
(no subject)
Date: 2005-03-14 03:24 pm (UTC)Keep in mind also that for you, the system worked. Much of what you saw as a student would have been successful learning, because you were a successful student. For the kids like you, this curriculum is working fairly well. It's the other eighty percent of the population that I'm worried about.
(no subject)
Date: 2005-03-14 05:19 pm (UTC)My brother, who is about as smart as I am, took an extra year to graduate high school with horrible grades. He did horrible in school because they didn't challenge him or motivate him early on. The system failed him even though he was just as smart as me.
Anyway, I confess I'm skeptical about this research you're citing -- not because I think you're lying or anything like that, but just because I like to read these things myself and have a chance to consider their methodology before accepting their study.
The Giles School accepts children on a first come first serve basis. There are no admissions tests, and financial aid is available for families having difficulty paying for the schooling. Supposedly, the children nonetheless thrive in this environment. I'd love to talk to the folks there and ask them some hard questions. Do they really feel that their students are mostly about average in base intelligence? What is their "dropout" rate? What reasons are usually cited for students who choose to leave and/or transfer? How big are their classes, and how many hours do their students spend in school per year? What kind of background do their teachers have? That's just some of the questions I'd like to ask.
(no subject)
Date: 2005-03-14 05:48 pm (UTC)That suggests the children at Giles have been raised in an environment that puts a strong emphasis on learning. They've been pre-programmed to thrive in the Giles environment. A lot of kids just aren't raised that way. Their parents may approve of scholastic success and encourage it, but simply don't go about instilling that properly.
(no subject)
Date: 2005-03-14 05:54 pm (UTC)Good point, though.
(no subject)
Date: 2005-03-14 06:17 pm (UTC)(no subject)
Date: 2005-03-14 06:02 pm (UTC)That would be the ideal solution, one that recognizes that kids are not all created equal and will not benefit from a curriculum that treats them like they are. It's a long way off, though, mostly because we don't have the money for it.
(no subject)
Date: 2005-03-14 06:08 pm (UTC)I love streaming. I think it is a great idea. However, I do think that there needs to be a mechanism for switching between streams. Sometimes children grow up and realize they care about their future. Having them be stuck in the stream they are in would be most unfortunate.
(no subject)
Date: 2005-03-14 06:30 pm (UTC)Actually, there would still be one issue - the self-esteem one. How do you convince a kid that they're capable and intelligent when the other kids of their grade are doing harder work than them and they know it?
(no subject)
Date: 2005-03-14 03:30 pm (UTC)From what I read, it doesn't seem to be a case of "can't," but a case of "not ready to," combined with "rushrushrushhurryhurryhurry."
I know that the guidelines in velvetpage's post aren't set in stone; I was playing with probability when I was seven years old. But the idea appears to be pushing all the subjects, at everybody, at the pace that I took for most math, while ignoring anybody who can't keep up with that pace.
This is the method I was taught by, although the Ontario Curriculum seems to be worse. In my case, it meant that I could spell well, and I understood grammar, but I could not organize my thoughts into paragraphs. Twelve years of schooling, and I couldn't write.
And yes, smaller classes make it possible to avoid such problems. But since nobody is willing to pay for that for everybody, only a few children will get it.
(no subject)
Date: 2005-03-14 03:32 pm (UTC)As an aside, ever tried explaining the phrase, "in a nutshell" to a ten-year-old?
(no subject)
Date: 2005-03-14 05:05 pm (UTC)Actually, I'm not sure I could explain it to myself. There are some phrases that I only understand from context, including "in a nutshell," and "the whole nine yards."
(no subject)
Date: 2005-03-14 05:08 pm (UTC)Thanks for clarification (and choosing that particular quote so that I could notice my mistake)!
(no subject)
Date: 2005-03-14 05:13 pm (UTC)I swear, I knew what you meant, and I read it exactly that way. It's only when you pointed it out that I realized that what I read wasn't what you wrote, even if it was what you meant.
(Ghidrah's claws, that's convoluted.)
In any case, I tend to do that.
(no subject)
Date: 2005-03-14 05:58 pm (UTC)(no subject)
Date: 2005-03-14 06:08 pm (UTC)As things stand, though, I'd like to see the curriculum loosened up enough that teachers can work within it to seek out each child's potential and do what's necessary to develop it. Our current curriculum doesn't do that.
(no subject)
Date: 2005-03-14 07:12 pm (UTC)Re: streaming: I'm of two minds about it. In my day, streaming (at the high school level) was closely related to family income and to known learning disabilities (and that was not entirely their or their parents' choice). I would of course hope that the mindset behind that would've become extinct by now, but frankly I'm skeptical. Also (though this is somewhat outside of the scope of the grades you're dealing with, it does factor in eventually), it is not reasonable to expect a child of 13 to know what they're going to do after high school. G-d knows I sure didn't.
On the other hand, I don't believe that it's reasonable to lump all kids together regardless of ability and inclination and so on. The freedom to cross over between streams without interference or judgement would have to be mandatory, IMO, before streaming would be workable.