The journal question, up on the board before the lesson began, was: "Find as many different ways as possible (at least three) to represent 0.40."
I put it up before the lesson began because kids need to know what it is they're expected to learn, just as adults do. Putting up what they're expected to be able to do is one way to accomplish this. I also put up the "practice" sign, to indicate that the journal in question was not being marked for report-card purposes (that would have had the "Game time" sign.) It's a chance for them to explore what they know and for me to see where the holes are in their understanding, before I grade them on it. It reduces a lot of stress when they know that mistakes don't "count," they're just chances to ask questions.
We had already reviewed decimal tenths and fractional tenths the day before. They were fine with that, in that they could model tenths with base-ten blocks and draw them on fraction strips, and write them as fractions and as decimals. The hundredths were new to them, so we began by asking about times when they'd seen numbers like that before. Money and measurement were both mentioned, giving them a context which we'd use later in the lesson.
On the overhead, I put up a 10x10 grid, with nothing shaded. We discussed the concept of an array, and linked the idea to multiplication; that a grid like this could come in any number on either side and was an excellent way to represent multiplication when they needed to. I also pointed out the concept of a square, where the numbers across the top and down the side were the same.
We went from there to asking the kids to identify the whole, and show me how they would write it. This seems so obvious that many teachers end up skipping it, but it's a crucial piece of knowledge for kids. If they're used to thinking of a flat base-ten block as having 100 pieces in it - that is, 100 whole numbers - it's a bit of a switch to start thinking about it as a single whole divided into parts.
They didn't have a problem representing ten parts out of a hundred, but it took them some work to realize that those ten parts were equal to one part out of ten; I used the sticks from the base-ten blocks to show that there were ten of them, and each stick was going to be written in the first spot after the decimal. We didn't spend a ton of time on equivalencies, just pointing out the concepts for now, because they were to be reinforced in group work.
The centre activities were engaging and easy to set up. For the first, kids needed a sheet of 10x10 grids and a six-sided die (sometimes called a number cube, to the horror of my gaming friends.) In pairs, they were to take turns rolling the die and deciding whether the number that came up was to be a tenth or a hundredth. Then they coloured that in on one grid. The goal was to get closest to one whole in exactly seven rolls, without going over. The solitaire version is to get between 0.9 and 1 in seven rolls. The kids loved it, especially since I gave them sparkly gamer dice to use.
The second required a bit more prep. My textbook set has photocopiable sets where each page has cards of a certain way of representing decimal tenths. One page has 0.1, 0.2, etc; the next page has 1/10, 2/10, etc; the third page has squares with ten strips, and a different fraction shaded for each card; the fourth is hundredths as fractions, then hundredths as decimals, and finally 10x10 grids with whole rows shaded. The kids had to first cut out all the cards, then make sure they knew which cards were representations of the same quantity (note: I did not phrase this as "meant the same thing," which can be confusing) and then play a memory game where they had to figure out the locations of two or more cards representing the same quantity. They could also play a Snap card game, where each kid gets half the cards, they turn over one card each at the same time, and if the cards match, the first person to realize it snaps them both up. Next week, I'll be adding in other fractional equivalents, like fifths.
The kids who did those activities mostly understood what was up with the journal question. The kids who did the naming-hundredths activity need to be rotated through one of the other ones before they really get it, so the journal is due on Tuesday. We'll be moving into metric measurements by next week because they make use of the base-ten system, hundredths, and introduce a third strand to this unit.
Saturday, October 3, 2009
Monday, September 7, 2009
It's that time of year again.
Tomorrow is the first day of school up here in Ontario, at least for most school boards. (The fact that September started on a Tuesday made for some problems from the perspective of fitting enough school days into the calendar to satisfy the law, so a few school boards started before Labour Day. This is rare around here.)
I'll tell you a secret: you know that feeling you have the night before every first day of school of your life, when you're pretty sure you won't sleep and you're worried about your teacher being mean and you dream of finding yourself in the cafeteria with no clothes on and everyone laughing at you? Yeah, teachers have that too. On the night when I could most use a good night's sleep, I never, ever get one. And the reason is the same: we all know that what happens on the first day of school is going to set the tone for the rest of the school year. Teachers have the added guilt of knowing that if it all goes wrong, the blame will be mostly theirs. That's not exactly a soporific thought.
So, what to do to ensure that the first day is productive and sets the right tone? First, think about what the kids will be telling their parents when they get home from school on the first day. The first question is going to be, "Do you like your teacher?"
Not, "What did you learn?" That's the second question. The first is about relationship. It's about knowing your teacher wants you there and sees you as a valuable part of the class. It's about community, and it's about that adult who is going to shape that kid's life for the next ten months. And it's about how the other kids interact with that adult - because most kids won't have more than a few interactions with the teacher themselves, personally, so they're watching what the teacher does with everyone else for clues.
The key to the first day is to begin to establish that relationship. So, how do you want things to be in your classroom for the rest of this school year? Do you want to be the kind of teacher who doesn't smile until November? Do you want the kids to know that if they set one toe out of line, they'll be on the carpet in the principal's office? If so, come in yelling. But be prepared: once you start, it's really, really hard to stop.
I have a few catch-phrases for the tone I try to set. The first is "warm strict." The second is "community of learners." A new one, added this year, is, "Failure is not an option." Let me explain.
There are rules in my classroom. They relate to respect, responsibility, and safety. They're designed to make the classroom a good learning environment for everyone in it. One of the first things we're going to do on the first day of school is get the kids to generate the list of rules based on those three words. Usually, the kids will come up with a whole list of don'ts. Under respect, they'll put, "Don't interrupt the teacher" or "don't speak out of turn" or "don't tear up the library books." Under responsibility, they'll suggest not leaving your homework at home and not losing your pencil. I give the kids half a dozen sticky notes each (seriously, I don't know how anyone ran a classroom before sticky notes) and ask them to write down two things for each of the three words. then we stick them up on chart paper. The next step is to pare them down, because you've now got forty-odd sticky notes under each category. So you pick one of the ones that says "Don't interrupt the teacher" and one that says "raise your hand to speak" and ask, "What do you think of these two suggestions?" Someone will hopefully tell you that they mean the same thing, so you discuss which one is better to put on the wall. You write it on a different piece of chart paper, because the first one still has forty-odd sticky notes in each category.
If you're really adventurous, you can divide the class into groups and give each of the groups the job of coming up with the three or four rules in each category that seem to come up the most often. If your students haven't often done that kind of group work, you may want to leave it for another time when you can teach the rules of group work first. My kids are well-versed in it so I will probably do it this way.
Once you've got your three or four rules under each key word, you've begun to establish relationships. But there are always a few kids who want to test the rules right away. They need boundaries and they need to test if you're going to maintain those boundaries, so they start talking out. How you handle this on the first day is every bit as important as setting the rules to begin with.
If you send the student to the office or yell at her, you give up your power and your relationship with that student. That kid is going to make your life hell for the next ten months because that kid will believe you don't like her, have never liked her, and will never like her. She's not going to do a single thing you ask without putting up a fight. And twenty-odd other kids are watching you mess it up with her and thinking, "If she talks like that to that student, how is she going to talk to me when I mess up?"
If you do nothing, you're sending the message that the rules are negotiable. That student is never going to do anything the first time you ask, because they've learned they don't have to. They can waste time indefinitely just by asking for explanations or creating minor disruptions that eventually, you have to deal with. (This, by the way, is my biggest pitfall. I hate following through on the little stuff, and it invariably becomes big stuff when I don't. New Year's Resolution: follow through on the small stuff.)
So the only course of action is to call them on the behaviour without ruining the relationship. Using a teacher look is a bad idea for this one, because, while it might work, it's not obvious enough to the other kids; they may just think the misbehaving kid decided to stop on her own. So a quiet word - "We just discussed how we don't behave like that. Please stop." is your first course of action. When it escalates - which may not happen on the first day but is inevitable at some point - you respond, "I already asked you to stop. Can you go to [designated place] for a few minutes and re-read the rules until I get there?" Your conversation about which rule was broken and what you expect can and should happen out of earshot of the other kids; but the fact that it is happening should be obvious.
You decide how to handle it at that point. I suggest recess detentions followed by a phone call home if there's a third and fourth infraction on the same day; the office is for the fifth infraction, and the principal should be there to support you in meting out discipline rather than meting it out herself.
The second question that kids will be asked when they get home is, "What did you learn?" That's a bit stickier, because the first day is generally so much about setting up for learning that it often isn't about learning anything new. I have a slew of diagnostic tests to run on my kids in the next two weeks, and the first one will indeed start tomorrow. But I can choose a diagnostic that will teach them something and give them a few concrete facts to give their parents. I give a simple multiple-intelligences quiz that asks, how many ways are you smart? By the end of it, they've figured out their two or three main forms of intelligence, which they can go home and tell their parents, and I have a crucial piece of information on each of my kids.
Another new thing I'm introducing this year is the Recess Box. It's a tote box that lives in a corner of my room that has a collection of simple games, games that can mostly be played in the fifteen minutes of an indoor recess. I have Mancala made up on cardstock and using bread tags in place of counters or stones; several Yahtzee kits, with a score card I made up myself, some scrap paper, and five dice; a couple of decks of cards; and a few store-bought games like Scrabble, Connect Four, and checkers. We're going to spend some time on Tuesday exploring the recess box, playing the games, and developing the rules for using them and putting them away properly afterward.
I'll probably start their reading notebooks tomorrow as well, including the reading logs in the back of them so I can figure out which kids didn't pick up a single book all summer and which ones had to be chased out of the library at closing time, and which fell somewhere in between. Wednesday I'll introduce math journals - duotangs with graph paper and lined paper in them, in which to do any math work that is to be marked - and begin either the DRA testing for reading or the OWA for writing. (Probably the DRA; it takes more time because there's an individual component, but they're a lot more familiar with it and it won't stress them out to do it the first week.) I will start French, because I don't want it to seem like an afterthought and because it's another great way to build community.
With any luck, being "on" the entire week won't drive me insane by Friday. It's always a danger.
The last catch-phrase is the most interesting, because school has always been designed to put the onus of failure on kids rather than on teachers. Saying that failure is not an option seems at first glance to put extra pressure on the kids. That would be counter-productive; extra stress does not lead to better work as a general rule. So what does it mean?
Teachers need to believe that all students can learn. All of them, no exceptions. Now, they may not be able to learn in quite the same ways or at quite the same speed, but they can all learn. So if they don't learn, it's the teacher's job to figure out why. Does the material need to be presented a different way to accommodate a different learning style? Did you start the material at too advanced a level, and they'd be able to do it if you rolled it back a bit? Is there a specific part of the material that is causing a roadblock? You want to set the goals well enough that every student can meet them with support, and for most students, the goals should be just this side of challenging. The key to meeting high expectations is to offer high support; high expectations without high support is setting kids up for failure.
I'll tell you a secret: you know that feeling you have the night before every first day of school of your life, when you're pretty sure you won't sleep and you're worried about your teacher being mean and you dream of finding yourself in the cafeteria with no clothes on and everyone laughing at you? Yeah, teachers have that too. On the night when I could most use a good night's sleep, I never, ever get one. And the reason is the same: we all know that what happens on the first day of school is going to set the tone for the rest of the school year. Teachers have the added guilt of knowing that if it all goes wrong, the blame will be mostly theirs. That's not exactly a soporific thought.
So, what to do to ensure that the first day is productive and sets the right tone? First, think about what the kids will be telling their parents when they get home from school on the first day. The first question is going to be, "Do you like your teacher?"
Not, "What did you learn?" That's the second question. The first is about relationship. It's about knowing your teacher wants you there and sees you as a valuable part of the class. It's about community, and it's about that adult who is going to shape that kid's life for the next ten months. And it's about how the other kids interact with that adult - because most kids won't have more than a few interactions with the teacher themselves, personally, so they're watching what the teacher does with everyone else for clues.
The key to the first day is to begin to establish that relationship. So, how do you want things to be in your classroom for the rest of this school year? Do you want to be the kind of teacher who doesn't smile until November? Do you want the kids to know that if they set one toe out of line, they'll be on the carpet in the principal's office? If so, come in yelling. But be prepared: once you start, it's really, really hard to stop.
I have a few catch-phrases for the tone I try to set. The first is "warm strict." The second is "community of learners." A new one, added this year, is, "Failure is not an option." Let me explain.
There are rules in my classroom. They relate to respect, responsibility, and safety. They're designed to make the classroom a good learning environment for everyone in it. One of the first things we're going to do on the first day of school is get the kids to generate the list of rules based on those three words. Usually, the kids will come up with a whole list of don'ts. Under respect, they'll put, "Don't interrupt the teacher" or "don't speak out of turn" or "don't tear up the library books." Under responsibility, they'll suggest not leaving your homework at home and not losing your pencil. I give the kids half a dozen sticky notes each (seriously, I don't know how anyone ran a classroom before sticky notes) and ask them to write down two things for each of the three words. then we stick them up on chart paper. The next step is to pare them down, because you've now got forty-odd sticky notes under each category. So you pick one of the ones that says "Don't interrupt the teacher" and one that says "raise your hand to speak" and ask, "What do you think of these two suggestions?" Someone will hopefully tell you that they mean the same thing, so you discuss which one is better to put on the wall. You write it on a different piece of chart paper, because the first one still has forty-odd sticky notes in each category.
If you're really adventurous, you can divide the class into groups and give each of the groups the job of coming up with the three or four rules in each category that seem to come up the most often. If your students haven't often done that kind of group work, you may want to leave it for another time when you can teach the rules of group work first. My kids are well-versed in it so I will probably do it this way.
Once you've got your three or four rules under each key word, you've begun to establish relationships. But there are always a few kids who want to test the rules right away. They need boundaries and they need to test if you're going to maintain those boundaries, so they start talking out. How you handle this on the first day is every bit as important as setting the rules to begin with.
If you send the student to the office or yell at her, you give up your power and your relationship with that student. That kid is going to make your life hell for the next ten months because that kid will believe you don't like her, have never liked her, and will never like her. She's not going to do a single thing you ask without putting up a fight. And twenty-odd other kids are watching you mess it up with her and thinking, "If she talks like that to that student, how is she going to talk to me when I mess up?"
If you do nothing, you're sending the message that the rules are negotiable. That student is never going to do anything the first time you ask, because they've learned they don't have to. They can waste time indefinitely just by asking for explanations or creating minor disruptions that eventually, you have to deal with. (This, by the way, is my biggest pitfall. I hate following through on the little stuff, and it invariably becomes big stuff when I don't. New Year's Resolution: follow through on the small stuff.)
So the only course of action is to call them on the behaviour without ruining the relationship. Using a teacher look is a bad idea for this one, because, while it might work, it's not obvious enough to the other kids; they may just think the misbehaving kid decided to stop on her own. So a quiet word - "We just discussed how we don't behave like that. Please stop." is your first course of action. When it escalates - which may not happen on the first day but is inevitable at some point - you respond, "I already asked you to stop. Can you go to [designated place] for a few minutes and re-read the rules until I get there?" Your conversation about which rule was broken and what you expect can and should happen out of earshot of the other kids; but the fact that it is happening should be obvious.
You decide how to handle it at that point. I suggest recess detentions followed by a phone call home if there's a third and fourth infraction on the same day; the office is for the fifth infraction, and the principal should be there to support you in meting out discipline rather than meting it out herself.
The second question that kids will be asked when they get home is, "What did you learn?" That's a bit stickier, because the first day is generally so much about setting up for learning that it often isn't about learning anything new. I have a slew of diagnostic tests to run on my kids in the next two weeks, and the first one will indeed start tomorrow. But I can choose a diagnostic that will teach them something and give them a few concrete facts to give their parents. I give a simple multiple-intelligences quiz that asks, how many ways are you smart? By the end of it, they've figured out their two or three main forms of intelligence, which they can go home and tell their parents, and I have a crucial piece of information on each of my kids.
Another new thing I'm introducing this year is the Recess Box. It's a tote box that lives in a corner of my room that has a collection of simple games, games that can mostly be played in the fifteen minutes of an indoor recess. I have Mancala made up on cardstock and using bread tags in place of counters or stones; several Yahtzee kits, with a score card I made up myself, some scrap paper, and five dice; a couple of decks of cards; and a few store-bought games like Scrabble, Connect Four, and checkers. We're going to spend some time on Tuesday exploring the recess box, playing the games, and developing the rules for using them and putting them away properly afterward.
I'll probably start their reading notebooks tomorrow as well, including the reading logs in the back of them so I can figure out which kids didn't pick up a single book all summer and which ones had to be chased out of the library at closing time, and which fell somewhere in between. Wednesday I'll introduce math journals - duotangs with graph paper and lined paper in them, in which to do any math work that is to be marked - and begin either the DRA testing for reading or the OWA for writing. (Probably the DRA; it takes more time because there's an individual component, but they're a lot more familiar with it and it won't stress them out to do it the first week.) I will start French, because I don't want it to seem like an afterthought and because it's another great way to build community.
With any luck, being "on" the entire week won't drive me insane by Friday. It's always a danger.
The last catch-phrase is the most interesting, because school has always been designed to put the onus of failure on kids rather than on teachers. Saying that failure is not an option seems at first glance to put extra pressure on the kids. That would be counter-productive; extra stress does not lead to better work as a general rule. So what does it mean?
Teachers need to believe that all students can learn. All of them, no exceptions. Now, they may not be able to learn in quite the same ways or at quite the same speed, but they can all learn. So if they don't learn, it's the teacher's job to figure out why. Does the material need to be presented a different way to accommodate a different learning style? Did you start the material at too advanced a level, and they'd be able to do it if you rolled it back a bit? Is there a specific part of the material that is causing a roadblock? You want to set the goals well enough that every student can meet them with support, and for most students, the goals should be just this side of challenging. The key to meeting high expectations is to offer high support; high expectations without high support is setting kids up for failure.
Wednesday, August 12, 2009
Multimedia Study: How Sweet is that Fairy Godmother?
I'm not going to go through every element of a language curriculum you could hit with this unit, because I'd basically be copying and pasting the entire grade five literacy document. It would work equally well for any junior or intermediate class and could probably be adjusted down to grade three. You want a rich, engaging critical-thinking unit? This is it. (Copyright E. van Hiel, 2009. Go ahead and use any or all of the ideas presented here, but only I get to publish it.)
Resources include, but are not limited to:
Ella Enchanted, book first, supported by the movie if necessary;
Shrek II, movie and/or books about the movie for later reference;
Two or three versions of Cinderella from your school library (I recommend searching out a Grimm Brothers version and a Perrault version)
The Disney version of Cinderella, with its Bibbity-Bobbity-Boo
The Rogers and Hammerstein Cinderella
1) Lesson One: Introduction
Choose a Cinderella book that you think will be fairly familiar in its storyline to your students. Before reading, ask them to think about what they know already; get a quick story outline onto a piece of chart paper. Ask students to think about the character of the fairy godmother as you read, and especially think about the question: why does she want to help Cinderella? Introduce the phrase "character motivation," and explain it as the reasons a character has for acting certain ways. Point out that they're going to have to infer, because stories usually don't come right out and tell the reader why people do things.
As you read the story, stop at various points to let students discuss their thoughts (think-pair-share) and write them down on sticky notes or in notebooks. You might take more than one day for the read-aloud, if students are getting bored. At the end of each session, gather up students thoughts and get students to organize them and summarize them. You will probably get motivations like, "Cinderella's parents chose the godmother to look after their daughter, so it's her job," "She helps because she's a nice person," and "She helps because Cinderella deserves to be helped." (If you don't get this last one, do your best to lead the kids around to it, because the rest of the unit depends in large part on the concept of "deserving.")
Possible extension for older grades: consider the character of Cinderella. Why does she do what she does? Why does she do whatever she's told to do? What is it that makes her deserving of help in the Fairy Godmother's eyes? What is it that makes the stepsisters less deserving of help? Again, summarize into a few motivations that are easily posted.
2) Guided lessons: using the resources gathered, have groups in your class read, view, or both, at least two other versions of the Cinderella story. Their task is the same each time: examine the motivations of the fairy godmother (and Cinderella, if you did the extension.) They are to present to the class what they see as the three key motives of each character. As they do the presentations, have students discuss each one and summarize the main motives given so far. It is perfectly acceptable for students to repeat the motives other students already found, since they'll be worded differently and students are still going to have to compare them against all the others to figure out which ones are saying the same things and which ones are different.
3) Ask students to choose one more version of Cinderella to study (or show the movie Shrek II or Ella Enchanted to the whole class.) Ask students to compare and contrast (or if they're younger, do a Venn diagram - it's the same thing) the fairy godmothers and the Cinderella figures in two or three of the resources they've studied. They can use software such as Powerpoint or Smart Ideas to create a Venn diagram for display. Ask students to focus in particular on the motivations they found in the very first version of Cinderella they read, especially the one about "deserving."
4) Reflection questions: What qualities did each Fairy Godmother focus on when deciding whether or not Cinderella and her stepsisters deserved help? Analyze the Fairy Godmother's evaluation of Cinderella. Was each fairy godmother being fair, in your opinion? Why or why not?
Do other versions of Cinderella give different motivations or qualities that were valued? Why do you think those versions changed the story that way?
The answers to the reflection question(s) chosen can be presented in a variety of ways. For example, students could:
1) Write an essay
2) Stage a debate between a group of students, defending or charging the Fairy Godmother with unfairness;
3) Create a visual representation of their arguments, using computer software or making a poster;
4) Write a journal from the point of view of a character of their choice, explaining their feelings on being helped or not being helped, and whether or not they deserved to be helped by the fairy godmother;
5) Rewrite the story of Cinderella to reflect the qualities you think Cinderella should have shown;
6) Another format of their choice, provided it adequately answers the reflection questions they chose and you approved.
You may wish to make up a rubric with your kids ahead of time, that will cover the expectations you're marking regardless of the format they choose.
Resources include, but are not limited to:
Ella Enchanted, book first, supported by the movie if necessary;
Shrek II, movie and/or books about the movie for later reference;
Two or three versions of Cinderella from your school library (I recommend searching out a Grimm Brothers version and a Perrault version)
The Disney version of Cinderella, with its Bibbity-Bobbity-Boo
The Rogers and Hammerstein Cinderella
1) Lesson One: Introduction
Choose a Cinderella book that you think will be fairly familiar in its storyline to your students. Before reading, ask them to think about what they know already; get a quick story outline onto a piece of chart paper. Ask students to think about the character of the fairy godmother as you read, and especially think about the question: why does she want to help Cinderella? Introduce the phrase "character motivation," and explain it as the reasons a character has for acting certain ways. Point out that they're going to have to infer, because stories usually don't come right out and tell the reader why people do things.
As you read the story, stop at various points to let students discuss their thoughts (think-pair-share) and write them down on sticky notes or in notebooks. You might take more than one day for the read-aloud, if students are getting bored. At the end of each session, gather up students thoughts and get students to organize them and summarize them. You will probably get motivations like, "Cinderella's parents chose the godmother to look after their daughter, so it's her job," "She helps because she's a nice person," and "She helps because Cinderella deserves to be helped." (If you don't get this last one, do your best to lead the kids around to it, because the rest of the unit depends in large part on the concept of "deserving.")
Possible extension for older grades: consider the character of Cinderella. Why does she do what she does? Why does she do whatever she's told to do? What is it that makes her deserving of help in the Fairy Godmother's eyes? What is it that makes the stepsisters less deserving of help? Again, summarize into a few motivations that are easily posted.
2) Guided lessons: using the resources gathered, have groups in your class read, view, or both, at least two other versions of the Cinderella story. Their task is the same each time: examine the motivations of the fairy godmother (and Cinderella, if you did the extension.) They are to present to the class what they see as the three key motives of each character. As they do the presentations, have students discuss each one and summarize the main motives given so far. It is perfectly acceptable for students to repeat the motives other students already found, since they'll be worded differently and students are still going to have to compare them against all the others to figure out which ones are saying the same things and which ones are different.
3) Ask students to choose one more version of Cinderella to study (or show the movie Shrek II or Ella Enchanted to the whole class.) Ask students to compare and contrast (or if they're younger, do a Venn diagram - it's the same thing) the fairy godmothers and the Cinderella figures in two or three of the resources they've studied. They can use software such as Powerpoint or Smart Ideas to create a Venn diagram for display. Ask students to focus in particular on the motivations they found in the very first version of Cinderella they read, especially the one about "deserving."
4) Reflection questions: What qualities did each Fairy Godmother focus on when deciding whether or not Cinderella and her stepsisters deserved help? Analyze the Fairy Godmother's evaluation of Cinderella. Was each fairy godmother being fair, in your opinion? Why or why not?
Do other versions of Cinderella give different motivations or qualities that were valued? Why do you think those versions changed the story that way?
The answers to the reflection question(s) chosen can be presented in a variety of ways. For example, students could:
1) Write an essay
2) Stage a debate between a group of students, defending or charging the Fairy Godmother with unfairness;
3) Create a visual representation of their arguments, using computer software or making a poster;
4) Write a journal from the point of view of a character of their choice, explaining their feelings on being helped or not being helped, and whether or not they deserved to be helped by the fairy godmother;
5) Rewrite the story of Cinderella to reflect the qualities you think Cinderella should have shown;
6) Another format of their choice, provided it adequately answers the reflection questions they chose and you approved.
You may wish to make up a rubric with your kids ahead of time, that will cover the expectations you're marking regardless of the format they choose.
The Quilt Project: Cross-curricular Mathematics
This project took nearly a month the last time I taught it, but it was worth every lesson. The depth of the students' geometric explorations, their artistry, and their deep empathy for slaves using freedom quilts on the Underground Railway were all wonderful to watch and valuable learning. (Copyright 2009; please, please use the unit, and please come back and tell me how it went, but all publishing rights are reserved to E. van Hiel.)
Again, the expectations outlined are from the Ontario curriculum, grade five; the project is also an excellent fit for grade six math and art and would not go amiss in grade seven history, so it's got a lot more cross-curricular potential than just math and art.
Grade 5 Mathematics:
Patterning:
– extend and create repeating patterns that
result from translations, through investigation
using a variety of tools (e.g., pattern
blocks, dynamic geometry software, dot
paper).
– create, identify, and extend numeric and
geometric patterns, using a variety of tools
(e.g., concrete materials, paper and pencil,
calculators, spreadsheets);
Geometry and Spatial Sense:
– identify, perform, and describe translations,
using a variety of tools (e.g., geoboard, dot
paper, computer program);
– create and analyse designs by translating
and/or reflecting a shape, or shapes, using
a variety of tools (e.g., geoboard, grid
paper, computer program) (Sample problem:
Identify translations and/or reflections
that map congruent shapes onto
each other in a given design.).
Grade 5 Art:
– identify the three pairs of complementary
colours (red and green, purple and yellow,
blue and orange);
– describe how line may be used to define
shapes and forms and to create movement
and depth;
– identify negative and positive shapes in
works of art and the environment
(e.g., shapes created by both the branches
of a tree and the spaces between the
branches);
– produce two- and three-dimensional
works of art (i.e.,works involving media
and techniques used in drawing, painting,
sculpting, printmaking) that communicate
a range of thoughts, feelings, and ideas for
specific purposes and to specific audiences
– identify, in their plan for a work of art, the
artistic problem and a number of possible
solutions (e.g., identify different types of
subject matter that they could use to
express their concern for the environment);
– describe the connection between an
element of design and a specific artistic
purpose, using appropriate vocabulary
Overview: Students will view, analyze, deconstruct, plan, and create quilt squares, both traditional forms and those of their own design, using a variety of materials. They will explain the elements of geometry and design that went into creating the squares (e.g. Names of shapes, symmetry, transformations, line, colour, and form.) They will explain the effects they were hoping to achieve through the use of those elements in their original work, and indicate other patterns from which they took their inspiration.
Lessons:
1) Introduction: Bring in a vintage quilt or reproduction that has several different quilt squares in it; spread it out and let students identify the patterns and colours. (If you don't have a teacher on staff who has one of these, as I do, I suggest calling your local quilter's guild, or talking to a local museum that documents the Underground Railway. Antique quilt collectors may be able to help you out, but a reproduction is better because it's not as fragile, and you want the kids to be able to move around on it to point things out.) Name some of the quilt blocks for them, and ask them to explain where they think the quilt block got its name. Begin to direct them towards describing the shapes mathematically by pointing out right-angled triangles, and how putting two triangles together in a quilt block almost always makes a square. Discuss the use of colour, particularly in blocks that rely on it for effect, like Log Cabin or Around the World; negative and positive colour values can be introduced here. If possible, point out how the squares look different if they are put together differently, and remind students of the transformations they're familiar with (reflections, translations - rotations are a grade six expectation but there's no reason they can't be mentioned if someone points them out.)
2) Using the book "Sweet Clara and the Freedom Quilt," by Deborah Hopkinson, review the use of patchwork quilts to guide slaves to the North on the Underground Railway. Discuss the quilt blocks used on each page. Challenge the students to use the other quilting resources, including the internet sites listed below, to find other examples of the same quilt blocks. Reflection question: how do quilters use colour to change the way a quilt block looks? How do they use transformations of blocks? (Other reflection questions and activities related to language may be pulled in here as well.)
3) Pick a relatively simple quilt block such as Ohio Star (nine-patch with triangles in the middle squares of the outside strips.) Using geometric software on a SMARTboard or an overhead transparency of the square and some shapes in different colours, model reproducing the square using blocks and/or paper cut-outs. Point out the grid pattern (three by three) and the way each block of the grid is further divided into triangles to form the pattern. Brainstorm ways the pattern could be adjusted just slightly to make a different look with the same pieces; see if you can find any of those variations in the resources we've collected about quilt blocks. (Since the Ohio Star is the starting point for at least a dozen other classic patterns, it's a good one to start with.) This lesson will likely take several days and may need to be done with more than one block as students become familiar with the language used to describe transformations and patterns.
4) First mini-assignment: Using either a website (listed below) or a quilting book provided, find a block that you like. Print it or photocopy it so you can mark up the original as you analyze it. Reproduce it on graph paper, paying attention to the proportions. Most quilts are designed along grids that are made up of two or more similar-sized squares within the block, so to reproduce the design, you have to figure out what grid the quilter used for the proportions. Materials may involve pattern blocks, square counters, symmetry mirrors, rulers, graph paper, and colouring tools. (Note: this is where the connection to area and multiplication comes in, and possibly to fractions and ratios.) Reflection: How could you make this quilt block look different by changing just one thing about it?
5) Using a double-nine-patch quilt block, investigate growing and shrinking patterns in quilts. Problem-solving question: using this double-nine-block pattern, how would you extend the pattern to a quilt-sized square? (i.e. A triple nine-block) Find another quilt block pattern that involves growing or shrinking patterns in our resources, and explain why the pattern is a growing or shrinking one.
6) Culminating Activity: Design a quilt block of your own. Use what you've learned about traditional quilt blocks. You are welcome to take an existing block and change a few elements of it to make it your own. Explain the pattern in your quilt block in terms of geometry, symmetry, and the elements of design such as line, form, and colour. Create your quilt block using the materials provided or ones you bring in yourself. (Provided: construction paper, origami paper, scraps of felt or other fabrics) Bonus: describe the steps to go through to create your quilt block by cutting each piece from a bigger shape (for example, "The triangles in the corners are made by cutting a 5cmx10cm rectangle into two 5cm squares, and then cutting these diagonally to get two right-angled triangles with the sides on either side of the right angle measuring 5cm.")
Quilt block websites:
http://www.blockcrazy.com/index.htm
http://oldsite.mccallsquilting.com/qb/
http://www.quilterscache.com/QuiltBlocksGalore.html
http://www.quilt.com/Blocks/AlphaBlockList.html
If internet access is not stellar in your class, a few quilting magazines will provide lots of examples of patterns, and the quilters of the quilting guild you contacted at the beginning of the unit may be willing to lend some pattern books as well. Many crochet or cross-stitch patterns are also based on quilt blocks.
Book possibilities:
Hopkinson, Deborah. Sweet Clara and the freedom quilt. Illustrated by James Ransome. New York, Knopf, 1993.
ISBN 0679823115 ages 4-8
Howard, Ellen. The log cabin quilt. Illustrated by Ronald Himler. 1st ed. New York, Holiday House, 1996.
1 v. (unpaged) col. ill. 21 x 26 cm. ISBN 0823412474 ages 4-8
When Elvirey and her family move to a log cabin in the Michigan woods, something even more important than Granny's quilt pieces makes the new dwelling a home.
Polacco, Patricia. The keeping quilt. New York, Simon & Schuster Books for Young Readers, c1988.
[32] p. all ill. (chiefly col.) 23 x 28 cm. ISBN 0671649639 ages 4-9
A homemade quilt ties together the lives of four generations of an immigrant Jewish family, remaining a symbol of their enduring love and faith.
Smucker, Barbara Claasen. Selina and the bear paw quilt. Illustrated by Janet Wilson. New York, Crown Publishers, 1996.
ISBN 051770904X ages 4-8
When her Mennonite family moves to Upper Canada to avoid involvement in the Civil War, young Selina is given a special quilt to remember the grandmother she left behind.
Stroud, Bettye. The Patchwork Path: A Quilt Map to Freedom
ISBN - 10:0763624233
ISBN - 13:9780763624231
A young girl and her father escape from slavery and make their way north with the aid of a quilt map.
Again, the expectations outlined are from the Ontario curriculum, grade five; the project is also an excellent fit for grade six math and art and would not go amiss in grade seven history, so it's got a lot more cross-curricular potential than just math and art.
Grade 5 Mathematics:
Patterning:
– extend and create repeating patterns that
result from translations, through investigation
using a variety of tools (e.g., pattern
blocks, dynamic geometry software, dot
paper).
– create, identify, and extend numeric and
geometric patterns, using a variety of tools
(e.g., concrete materials, paper and pencil,
calculators, spreadsheets);
Geometry and Spatial Sense:
– identify, perform, and describe translations,
using a variety of tools (e.g., geoboard, dot
paper, computer program);
– create and analyse designs by translating
and/or reflecting a shape, or shapes, using
a variety of tools (e.g., geoboard, grid
paper, computer program) (Sample problem:
Identify translations and/or reflections
that map congruent shapes onto
each other in a given design.).
Grade 5 Art:
– identify the three pairs of complementary
colours (red and green, purple and yellow,
blue and orange);
– describe how line may be used to define
shapes and forms and to create movement
and depth;
– identify negative and positive shapes in
works of art and the environment
(e.g., shapes created by both the branches
of a tree and the spaces between the
branches);
– produce two- and three-dimensional
works of art (i.e.,works involving media
and techniques used in drawing, painting,
sculpting, printmaking) that communicate
a range of thoughts, feelings, and ideas for
specific purposes and to specific audiences
– identify, in their plan for a work of art, the
artistic problem and a number of possible
solutions (e.g., identify different types of
subject matter that they could use to
express their concern for the environment);
– describe the connection between an
element of design and a specific artistic
purpose, using appropriate vocabulary
Overview: Students will view, analyze, deconstruct, plan, and create quilt squares, both traditional forms and those of their own design, using a variety of materials. They will explain the elements of geometry and design that went into creating the squares (e.g. Names of shapes, symmetry, transformations, line, colour, and form.) They will explain the effects they were hoping to achieve through the use of those elements in their original work, and indicate other patterns from which they took their inspiration.
Lessons:
1) Introduction: Bring in a vintage quilt or reproduction that has several different quilt squares in it; spread it out and let students identify the patterns and colours. (If you don't have a teacher on staff who has one of these, as I do, I suggest calling your local quilter's guild, or talking to a local museum that documents the Underground Railway. Antique quilt collectors may be able to help you out, but a reproduction is better because it's not as fragile, and you want the kids to be able to move around on it to point things out.) Name some of the quilt blocks for them, and ask them to explain where they think the quilt block got its name. Begin to direct them towards describing the shapes mathematically by pointing out right-angled triangles, and how putting two triangles together in a quilt block almost always makes a square. Discuss the use of colour, particularly in blocks that rely on it for effect, like Log Cabin or Around the World; negative and positive colour values can be introduced here. If possible, point out how the squares look different if they are put together differently, and remind students of the transformations they're familiar with (reflections, translations - rotations are a grade six expectation but there's no reason they can't be mentioned if someone points them out.)
2) Using the book "Sweet Clara and the Freedom Quilt," by Deborah Hopkinson, review the use of patchwork quilts to guide slaves to the North on the Underground Railway. Discuss the quilt blocks used on each page. Challenge the students to use the other quilting resources, including the internet sites listed below, to find other examples of the same quilt blocks. Reflection question: how do quilters use colour to change the way a quilt block looks? How do they use transformations of blocks? (Other reflection questions and activities related to language may be pulled in here as well.)
3) Pick a relatively simple quilt block such as Ohio Star (nine-patch with triangles in the middle squares of the outside strips.) Using geometric software on a SMARTboard or an overhead transparency of the square and some shapes in different colours, model reproducing the square using blocks and/or paper cut-outs. Point out the grid pattern (three by three) and the way each block of the grid is further divided into triangles to form the pattern. Brainstorm ways the pattern could be adjusted just slightly to make a different look with the same pieces; see if you can find any of those variations in the resources we've collected about quilt blocks. (Since the Ohio Star is the starting point for at least a dozen other classic patterns, it's a good one to start with.) This lesson will likely take several days and may need to be done with more than one block as students become familiar with the language used to describe transformations and patterns.
4) First mini-assignment: Using either a website (listed below) or a quilting book provided, find a block that you like. Print it or photocopy it so you can mark up the original as you analyze it. Reproduce it on graph paper, paying attention to the proportions. Most quilts are designed along grids that are made up of two or more similar-sized squares within the block, so to reproduce the design, you have to figure out what grid the quilter used for the proportions. Materials may involve pattern blocks, square counters, symmetry mirrors, rulers, graph paper, and colouring tools. (Note: this is where the connection to area and multiplication comes in, and possibly to fractions and ratios.) Reflection: How could you make this quilt block look different by changing just one thing about it?
5) Using a double-nine-patch quilt block, investigate growing and shrinking patterns in quilts. Problem-solving question: using this double-nine-block pattern, how would you extend the pattern to a quilt-sized square? (i.e. A triple nine-block) Find another quilt block pattern that involves growing or shrinking patterns in our resources, and explain why the pattern is a growing or shrinking one.
6) Culminating Activity: Design a quilt block of your own. Use what you've learned about traditional quilt blocks. You are welcome to take an existing block and change a few elements of it to make it your own. Explain the pattern in your quilt block in terms of geometry, symmetry, and the elements of design such as line, form, and colour. Create your quilt block using the materials provided or ones you bring in yourself. (Provided: construction paper, origami paper, scraps of felt or other fabrics) Bonus: describe the steps to go through to create your quilt block by cutting each piece from a bigger shape (for example, "The triangles in the corners are made by cutting a 5cmx10cm rectangle into two 5cm squares, and then cutting these diagonally to get two right-angled triangles with the sides on either side of the right angle measuring 5cm.")
Quilt block websites:
http://www.blockcrazy.com/index.htm
http://oldsite.mccallsquilting.com/qb/
http://www.quilterscache.com/QuiltBlocksGalore.html
http://www.quilt.com/Blocks/AlphaBlockList.html
If internet access is not stellar in your class, a few quilting magazines will provide lots of examples of patterns, and the quilters of the quilting guild you contacted at the beginning of the unit may be willing to lend some pattern books as well. Many crochet or cross-stitch patterns are also based on quilt blocks.
Book possibilities:
Hopkinson, Deborah. Sweet Clara and the freedom quilt. Illustrated by James Ransome. New York, Knopf, 1993.
ISBN 0679823115 ages 4-8
Howard, Ellen. The log cabin quilt. Illustrated by Ronald Himler. 1st ed. New York, Holiday House, 1996.
1 v. (unpaged) col. ill. 21 x 26 cm. ISBN 0823412474 ages 4-8
When Elvirey and her family move to a log cabin in the Michigan woods, something even more important than Granny's quilt pieces makes the new dwelling a home.
Polacco, Patricia. The keeping quilt. New York, Simon & Schuster Books for Young Readers, c1988.
[32] p. all ill. (chiefly col.) 23 x 28 cm. ISBN 0671649639 ages 4-9
A homemade quilt ties together the lives of four generations of an immigrant Jewish family, remaining a symbol of their enduring love and faith.
Smucker, Barbara Claasen. Selina and the bear paw quilt. Illustrated by Janet Wilson. New York, Crown Publishers, 1996.
ISBN 051770904X ages 4-8
When her Mennonite family moves to Upper Canada to avoid involvement in the Civil War, young Selina is given a special quilt to remember the grandmother she left behind.
Stroud, Bettye. The Patchwork Path: A Quilt Map to Freedom
ISBN - 10:0763624233
ISBN - 13:9780763624231
A young girl and her father escape from slavery and make their way north with the aid of a quilt map.
Metric Conversion Lesson: Differentiated Instruction in Action
This lesson is applicable in particular anywhere where metric units are standard, though it wouldn't be such a bad thing to teach it in a place where they're not, since the lesson so beautifully reinforces the base-ten system and multiplying by tens. In Ontario, this is a grade five lesson because of all the conversions; lower grades aren't expected to be able to go quite that many. It could easily be adapted for grades four and six.
Metric Conversions Lesson: Differentiated for Special Needs
Expectations:
– select and justify the most appropriate standard unit (i.e., millimetre, centimetre, decimetre, metre, kilometre) to measure length, height, width, and distance
- solve problems requiring conversion from metres to centimetres and from kilometres to metres
– multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies
Materials: Base-ten blocks, graph paper, rulers and metre sticks, calculators
Prior knowledge: pattern rules, basic multiplication, use of calculators
Lesson:
Problem: Mr. Johnson (the gym teacher) is setting up an obstacle course in the form of a maze, using string. He's calculated the perimeter of the course to be 1.24 kilometres, but the balls of string he is using are measured in metres. Each ball contains 50 metres of string. How much string does he need? If one ball of string, from a different company, is listed as having 400 cm, how does that change your calculations?
Allow students to work in groups to solve the problem. When one group comes up with the conversion for metres to kilometres, get everyone's attention and point it out to the class. Discuss how we need a manipulative that can be divided into a thousand parts, so the whole will represent one kilometre and the parts will represent one metre. As students realize the metre sticks and base-ten blocks both fit that bill, the ones who get it will start to solve the problem quickly. Assess who is getting it easily, who needs more practice, and who is lost.
After that, divide students into centre groups to work on related activities. Kids who got it can write a math journal or create a video explaining how they got the answer, using manipulatives as examples. Kids who need more practice work on similar problems at centres to practise conversions, possibly using calculators to come up with a pattern rule for multiplying and dividing by multiples of ten. Kids who were lost come for a guided math lesson using metre sticks and string. They can set up a mini-obstacle course using fifty metres of string, and mark off the string in one-metre lengths as they unravel it. Explicitly teach the strategy of measuring a small amount, then multiplying to get a big amount; allow for calculators and multiplication charts for this. Practise with the string and metre sticks. Once they're comfortable with the smaller amounts of string and measuring for centimetres, then multiplying, go back to the original question and help them draw the connection between centimetres, metres, and kilometres. Kids with spatial sense deficits or visual deficits will have the most trouble with this activity, and will need the most opportunities to develop and apply pattern rules using manipulatives and calculators. There is a good chance this part of the lesson will take several guided math sessions, so centre work to extend the understanding of the kids who get it will be necessary while working with this group.
Extensions:
1) Research the metric system in detail. Why did our problem skip decimetres and decametres? Are these units used elsewhere in the world? Develop a pattern rule that covers conversions in the metric system (or extend your pattern rule to include these two units, if you've already made one.)
2) Use our measuring cups and beakers to extend your understanding of the metric system into litres. Do you need to make any changes to your pattern rule to make it work for measurements of volume?
Metric Conversions Lesson: Differentiated for Special Needs
Expectations:
– select and justify the most appropriate standard unit (i.e., millimetre, centimetre, decimetre, metre, kilometre) to measure length, height, width, and distance
- solve problems requiring conversion from metres to centimetres and from kilometres to metres
– multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies
Materials: Base-ten blocks, graph paper, rulers and metre sticks, calculators
Prior knowledge: pattern rules, basic multiplication, use of calculators
Lesson:
Problem: Mr. Johnson (the gym teacher) is setting up an obstacle course in the form of a maze, using string. He's calculated the perimeter of the course to be 1.24 kilometres, but the balls of string he is using are measured in metres. Each ball contains 50 metres of string. How much string does he need? If one ball of string, from a different company, is listed as having 400 cm, how does that change your calculations?
Allow students to work in groups to solve the problem. When one group comes up with the conversion for metres to kilometres, get everyone's attention and point it out to the class. Discuss how we need a manipulative that can be divided into a thousand parts, so the whole will represent one kilometre and the parts will represent one metre. As students realize the metre sticks and base-ten blocks both fit that bill, the ones who get it will start to solve the problem quickly. Assess who is getting it easily, who needs more practice, and who is lost.
After that, divide students into centre groups to work on related activities. Kids who got it can write a math journal or create a video explaining how they got the answer, using manipulatives as examples. Kids who need more practice work on similar problems at centres to practise conversions, possibly using calculators to come up with a pattern rule for multiplying and dividing by multiples of ten. Kids who were lost come for a guided math lesson using metre sticks and string. They can set up a mini-obstacle course using fifty metres of string, and mark off the string in one-metre lengths as they unravel it. Explicitly teach the strategy of measuring a small amount, then multiplying to get a big amount; allow for calculators and multiplication charts for this. Practise with the string and metre sticks. Once they're comfortable with the smaller amounts of string and measuring for centimetres, then multiplying, go back to the original question and help them draw the connection between centimetres, metres, and kilometres. Kids with spatial sense deficits or visual deficits will have the most trouble with this activity, and will need the most opportunities to develop and apply pattern rules using manipulatives and calculators. There is a good chance this part of the lesson will take several guided math sessions, so centre work to extend the understanding of the kids who get it will be necessary while working with this group.
Extensions:
1) Research the metric system in detail. Why did our problem skip decimetres and decametres? Are these units used elsewhere in the world? Develop a pattern rule that covers conversions in the metric system (or extend your pattern rule to include these two units, if you've already made one.)
2) Use our measuring cups and beakers to extend your understanding of the metric system into litres. Do you need to make any changes to your pattern rule to make it work for measurements of volume?
Tuesday, August 11, 2009
Catapulted out of the rift between paradigms
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, often referred to as "traditional" though it's not as old as that word would imply, 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, if I recall correctly. 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.)
It didn't take me long, as a new teacher, to realize that the dominant paradigm at that time was failing my students. I was teaching in a medium-needs school, which is to say, approximately half my students were from families receiving government assistance in some form, usually several forms. It was middle school, so my students had already figured out the hierarchy in the class. They knew who the smart kids were, and they knew who the dumb kids were. The smart kids expected A's and the dumb kids expected C's and D's. The dumb kids had already pretty much given up on education. They were passing time, filling out their social lives, waiting until they were old enough to drop out, and many of them thought it great fun to make my life hell along the way. Some didn't wait long - I know of at least four kids from that class who effectively dropped out of grade nine.
At first, I did what teachers used to do in the face of kids who weren't succeeding. I dumbed it down. I went back to grade five topics, and taught lessons that had the smart kids bored and even a lot of the dumb kids complaining. I went back to basics and taught only easy stuff. I skipped any questions that smacked of critical thinking - my students weren't ready for it! And still they failed, and still I felt like a failure, and considered leaving teaching. I was following in the footsteps of many an early burnout in my profession. What I needed was to change what I was doing. Fortunately, change was coming - a change that took me some time to catch up with, because it was so all-encompassing. I had to re-examine everything I thought I knew about how to do my job, and replace it with a new paradigm of education.
The paradigm shift started 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 in the U.S. 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 fact, many of the notable failed trends of the eighties were attempts to implement this half-formed paradigm. Whole language, anyone? It was on the right track, but it didn't have enough theory or power behind it to make it work.
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. MathQuest fell into this category, as did the Origins series of history textbooks.) 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. Also interestingly, at least one state - California - had the new paradigm but took it out again due to parental and teacher pressure, at least as it referred to mathematics.)
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.
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.
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, often referred to as "traditional" though it's not as old as that word would imply, 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, if I recall correctly. 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.)
It didn't take me long, as a new teacher, to realize that the dominant paradigm at that time was failing my students. I was teaching in a medium-needs school, which is to say, approximately half my students were from families receiving government assistance in some form, usually several forms. It was middle school, so my students had already figured out the hierarchy in the class. They knew who the smart kids were, and they knew who the dumb kids were. The smart kids expected A's and the dumb kids expected C's and D's. The dumb kids had already pretty much given up on education. They were passing time, filling out their social lives, waiting until they were old enough to drop out, and many of them thought it great fun to make my life hell along the way. Some didn't wait long - I know of at least four kids from that class who effectively dropped out of grade nine.
At first, I did what teachers used to do in the face of kids who weren't succeeding. I dumbed it down. I went back to grade five topics, and taught lessons that had the smart kids bored and even a lot of the dumb kids complaining. I went back to basics and taught only easy stuff. I skipped any questions that smacked of critical thinking - my students weren't ready for it! And still they failed, and still I felt like a failure, and considered leaving teaching. I was following in the footsteps of many an early burnout in my profession. What I needed was to change what I was doing. Fortunately, change was coming - a change that took me some time to catch up with, because it was so all-encompassing. I had to re-examine everything I thought I knew about how to do my job, and replace it with a new paradigm of education.
The paradigm shift started 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 in the U.S. 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 fact, many of the notable failed trends of the eighties were attempts to implement this half-formed paradigm. Whole language, anyone? It was on the right track, but it didn't have enough theory or power behind it to make it work.
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. MathQuest fell into this category, as did the Origins series of history textbooks.) 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. Also interestingly, at least one state - California - had the new paradigm but took it out again due to parental and teacher pressure, at least as it referred to mathematics.)
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.
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.
Raison d'etre
I'm a teacher.
That's not all I am. I'm also a mother, a writer, a friend, a student, and many other labels which I don't always acknowledge in public. Like the rest of the world, I'm multi-faceted and like to think that sometimes I sparkle.
But this blog is about my professional life and thoughts, not those other things. They'll show up here, because multi-faceted people can't hide all but one facet at will, even if they try. I don't see a good reason to try that hard. Mostly, though, this blog is for discussing big issues in education, especially the shift we're in the middle of right now - the shift towards a constructivist model of education.
I'll talk about the theories, and the research that backs them up. I'll talk about the theories that are being replaced, and why, as I respectfully relegate them to the history books. They've served their purpose. I'll talk about the specifics - the lessons, the groupings, the reasons for classroom decisions that may make those unfamiliar with this trend in public education raise their eyebrows or call me a fool. I'll even talk about my failures and what I've learned from them.
I am based in Ontario, Canada, which is why my posts center around public education in my province. When I'm aware of trends elsewhere, I'll talk about them. The big lines of my experience are, I believe, applicable everywhere. Change is coming, slowly as institutional change does, hopefully to every jurisdiction that purports to provide an education for its young citizens. I hope you can take my experience and use it to create change where you are.
That's not all I am. I'm also a mother, a writer, a friend, a student, and many other labels which I don't always acknowledge in public. Like the rest of the world, I'm multi-faceted and like to think that sometimes I sparkle.
But this blog is about my professional life and thoughts, not those other things. They'll show up here, because multi-faceted people can't hide all but one facet at will, even if they try. I don't see a good reason to try that hard. Mostly, though, this blog is for discussing big issues in education, especially the shift we're in the middle of right now - the shift towards a constructivist model of education.
I'll talk about the theories, and the research that backs them up. I'll talk about the theories that are being replaced, and why, as I respectfully relegate them to the history books. They've served their purpose. I'll talk about the specifics - the lessons, the groupings, the reasons for classroom decisions that may make those unfamiliar with this trend in public education raise their eyebrows or call me a fool. I'll even talk about my failures and what I've learned from them.
I am based in Ontario, Canada, which is why my posts center around public education in my province. When I'm aware of trends elsewhere, I'll talk about them. The big lines of my experience are, I believe, applicable everywhere. Change is coming, slowly as institutional change does, hopefully to every jurisdiction that purports to provide an education for its young citizens. I hope you can take my experience and use it to create change where you are.
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