The other day I figured out exactly how many mpg my car gets: 31.6. Which is not bad. I'd originally estimated it at 32 based on the average miles I drove on a tank of gas and the fact that I have a 14 gallon tank. But on Wednesday, when I coasted into town on fumes, I completely filled the tank. The machine stopped at exactly 14 gallons. I looked at the odometer afterwards, before resetting it and noticed I'd gone 440 miles on one tank of gas. So, I did the math - long division, on paper, all by myself. I double-checked it on a calculator later and got 31.4 but, hey, I'm not a math whiz and there's the proof.
I've always loved numbers but because of a piss poor education, I've always done horribly in math. And its one of the reasons I want Dusty to do well in it. She doesn't have a super math whiz gene (few in our family do) but I want her set on the right track now. I don't want to her derail like I did.
Which is why I'm happy she's where she is. The school system instituted full-time gifted and talented teachers in EVERY school over the summer. We met Dusty's new G&T teacher this week and I am very pleased.
The teacher, Mrs. G, has been teaching at the school for a number of years so the environment, and many of the students, are familiar to her. She outlined how the G&T thing will work this year. Last year, Dusty worked with two part-time G&T teachers - both of them brilliant and capable but doing an impossible task. The two of them taught at four or five different schools on different days. I don't know how they pulled it off, but they did.
This year should be even better. Mrs. G explained that they have clustered the G&T students into certain classrooms. Which explains why Dusty is still with her BFF and her partner of the last two years, Nathan. All G&T kids. This cuts down on Mrs. G's workload because she doesn't have to be in every single classroom every week. But she does do that on occasion, especially when a teacher in a non-G&T cluster room discovers a possible G&T candidate.
Mrs. G and the classroom teacher co-plan their lessons and co-teach them. There are no pull-outs at this level. They co-teach and then break the classroom into groups for small group work. Mrs. G gets the G&T group, Mrs. J gets the other students.
Best of all, Mrs. G teaches an accelerated math class for 5th graders. It's a pull-out class and she's a math person so I feel really good that Dusty's in good hands. In all aspects.
Not only that, but Dusty will soon get Spanish lessons. Students at the closest high school have started a Spanish Club that will meet at Dusty's school on Monday afternoons. While the county continues to "consider" foreign language classes in the elementary schools, Dusty will get a change to learn a second language. She'll get a tiny step up.
At this point, I have zero complaints. Dusty's in very good hands.
I also learned - through Mrs. G - about the Johns Hopkins Center for Talented Youth. I'm considering signing Dusty up for the next testing date (which is in Feb or March). If she passes the test, which is given locally, she would qualify for a number of educational opportunities, classes, etc. that she wouldn't have access to otherwise. She won't run quite so far if she's not wearing the right shoes. I want to give her those shoes.
Meanwhile, I'm going to go back and check my long division work. While 31.6 is close, it's not 31.4. Maybe Dusty'll be able to point out my mistakes soon. At least, that's what I'm hoping. I only had kids so they could help me with my homework.
Showing posts with label academics. Show all posts
Showing posts with label academics. Show all posts
Friday, September 26, 2008
Friday, September 14, 2007
Chasing Vermeer
AJ is settling into first grade, but I’m still working out the kinks. One of the things the first graders have to do is to read an assigned book each night. In AJ’s case, he’s reading longer books for a total of 20 minutes a night. After AJ’s reading assessment at the beginning of the year, the teacher asked if I could help provide him with books at an appropriate level, since, as she put it, “he’s off the charts” and she doesn’t have enough books to challenge him in the classroom.
The first book AJ picked was one of his beloved Magic Tree House books. He loves the blend of fact and fiction, the associated research guides, and his old friends Jack and Annie. But the books are getting too easy for him to read and he’s not getting a lot out of them anymore. He’ll check one out from the library a mile from our house and will have finished most of it by the time we pull into our garage. So for his second book, I asked him if he could think of something new that he wanted to read.
We came up with Chasing Vermeer by Blue Balliett. We were both interested in the book for several reasons. AJ likes the math manipulatives at school and has been wanting to get some for home. I’ve been wanting to try working with pentominoes and tangram puzzles with him. Pentominoes play an important part of the book. AJ was also excited about the secret code that is used in the book. Some passages have to be deciphered. AJ has been fascinated with codes and codebreaking lately after finding a book about it at a library sale over the summer. Third, as the title suggests, there is art involved in the plot. AJ loves going to the Art Institute of Chicago, where some of the book takes place, and I thought it might be a good way to bring some more discussion about art into AJ’s world. I was envisioning reading through the book slowly and taking time out to pursue some of the affiliated digressions, perhaps ending with a field trip to some of the places mentioned in the book, like the University of Chicago and the Art Institute.
But AJ is still in the mindset that he should read books as fast as possible, just because he can. The problem with Chasing Vermeer, though, is that he misses a lot when he reads in his usual way. There are words he doesn’t know. And even more complicated than the vocabulary, which is largely explained in context, is the frequent use of metaphors with which AJ is unfamiliar. I’m getting the sense that his experience of the book is probably somewhat like that of a person from a foreign country reading the book. He doesn’t have all the cultural references.
To deal with this, he’s been reading it out loud to me and we’ve been discussing the phrases he doesn’t know and looking words up in his dictionary.
“What does it mean when the teacher says, ‘I’m not letting you off the hook this time!’?”
“What do you think it means?”
“I don’t know.”
“I’ll give you a hint. Think about fishing. What happens when you let a fish off a hook?”
“He escapes.”
“Right. And if the teacher’s letting them off the hook?”
“They’re escaping?”
“Sort of. They’re escaping having to do what she asked them to do. But she’s saying she’s not letting them off the hook. That means they’re not going to escape this time.”
“They’re going to have to do the work.”
“Exactly right.”
I’ve been worried that I’ve been pushing AJ too hard on this one, mainly because I haven’t yet encountered a book that elicits quite so many questions. But AJ is loving it and is not at all daunted or discouraged by what he doesn’t yet know.
Then I was worried that it wasn’t quite what his teacher was looking for. Was she trying for more fluency and independence?
I got the chance to talk to her today and she confirmed all my positive first impressions of her (no doubt because we had the same opinions on everything). She thought it was great that he was doing a challenging book, suggested maybe alternating harder and easier books to give him both the sense of independence and the chance to expand his reading skills, and thought the book discussion format sounded great. And she filled me in on some of the things she’s doing with him in the classroom, which include some followup on the books he’s reading at home. AJ signed a Reading Contract with her to do some extra work, which is including some discussion of literary elements as well as some creative writing. For his first assignment, he was to find the longest sentence he could and bring it in to class. Later he’ll be writing new endings for books he’s read, writing stories, etc.
Because the school’s been doing reading placement testing for the last week or so, they haven’t done much with math yet. I’m hoping we’ll be hearing more about math in the weeks to come. In the mean time, AJ has been busy playing with his pentominoes at home. And that’s enough for now.
C
The first book AJ picked was one of his beloved Magic Tree House books. He loves the blend of fact and fiction, the associated research guides, and his old friends Jack and Annie. But the books are getting too easy for him to read and he’s not getting a lot out of them anymore. He’ll check one out from the library a mile from our house and will have finished most of it by the time we pull into our garage. So for his second book, I asked him if he could think of something new that he wanted to read.
We came up with Chasing Vermeer by Blue Balliett. We were both interested in the book for several reasons. AJ likes the math manipulatives at school and has been wanting to get some for home. I’ve been wanting to try working with pentominoes and tangram puzzles with him. Pentominoes play an important part of the book. AJ was also excited about the secret code that is used in the book. Some passages have to be deciphered. AJ has been fascinated with codes and codebreaking lately after finding a book about it at a library sale over the summer. Third, as the title suggests, there is art involved in the plot. AJ loves going to the Art Institute of Chicago, where some of the book takes place, and I thought it might be a good way to bring some more discussion about art into AJ’s world. I was envisioning reading through the book slowly and taking time out to pursue some of the affiliated digressions, perhaps ending with a field trip to some of the places mentioned in the book, like the University of Chicago and the Art Institute.
But AJ is still in the mindset that he should read books as fast as possible, just because he can. The problem with Chasing Vermeer, though, is that he misses a lot when he reads in his usual way. There are words he doesn’t know. And even more complicated than the vocabulary, which is largely explained in context, is the frequent use of metaphors with which AJ is unfamiliar. I’m getting the sense that his experience of the book is probably somewhat like that of a person from a foreign country reading the book. He doesn’t have all the cultural references.
To deal with this, he’s been reading it out loud to me and we’ve been discussing the phrases he doesn’t know and looking words up in his dictionary.
“What does it mean when the teacher says, ‘I’m not letting you off the hook this time!’?”
“What do you think it means?”
“I don’t know.”
“I’ll give you a hint. Think about fishing. What happens when you let a fish off a hook?”
“He escapes.”
“Right. And if the teacher’s letting them off the hook?”
“They’re escaping?”
“Sort of. They’re escaping having to do what she asked them to do. But she’s saying she’s not letting them off the hook. That means they’re not going to escape this time.”
“They’re going to have to do the work.”
“Exactly right.”
I’ve been worried that I’ve been pushing AJ too hard on this one, mainly because I haven’t yet encountered a book that elicits quite so many questions. But AJ is loving it and is not at all daunted or discouraged by what he doesn’t yet know.
Then I was worried that it wasn’t quite what his teacher was looking for. Was she trying for more fluency and independence?
I got the chance to talk to her today and she confirmed all my positive first impressions of her (no doubt because we had the same opinions on everything). She thought it was great that he was doing a challenging book, suggested maybe alternating harder and easier books to give him both the sense of independence and the chance to expand his reading skills, and thought the book discussion format sounded great. And she filled me in on some of the things she’s doing with him in the classroom, which include some followup on the books he’s reading at home. AJ signed a Reading Contract with her to do some extra work, which is including some discussion of literary elements as well as some creative writing. For his first assignment, he was to find the longest sentence he could and bring it in to class. Later he’ll be writing new endings for books he’s read, writing stories, etc.
Because the school’s been doing reading placement testing for the last week or so, they haven’t done much with math yet. I’m hoping we’ll be hearing more about math in the weeks to come. In the mean time, AJ has been busy playing with his pentominoes at home. And that’s enough for now.
C
Orienteering
While I was in the middle of a post about AJ in first grade, it occurred to me that I should probably fill you in on what this blog is likely to be about this year. For those who haven’t read my main blog spynotes at either its present or former locations, you might not have followed our every angst-ridden, self-imposed crisis as we try to figure out how to arrange the best possible education for our high-achieving kid.
We have a number of issues. First, AJ is an only child and he needs and craves normal social interaction with other kids. He doesn’t want to hang out with his boring and sometimes embarrassing parents for the rest of his life. So we were interested in putting AJ in a traditional school situation rather than home schooling or some other type of arrangement. Second, while AJ, a first grader, is reportedly reading at the level of a “very smart sixth grader,” and is also engaging with math and science tasks at an as yet undetermined level higher than his grade, we want to make sure AJ is kept interested and challenged at school. It is important to us that he continue to like and get something out of school. It is also important to us that we are not responsible for all of his education because, well, we have jobs to do to pay the bills. We are, however, more than willing to assist classroom teachers and do lots of enrichment projects at home. In fact, we love it.
After much soul-searching (and, perhaps more importantly, piggybank shaking) and exploration of multiple possibilities, including private schools, schools for the gifted, tutors, enrichment programs, and shipping him off for a stint at the International Space Station, we’ve decided to send AJ to the local public school while maintaining our civic right and duty to be a pain in the ass if necessary to get him what we think he needs.
As it happens, we haven’t had to do much injury to anyone’s posterior. The school has been remarkably enthusiastic about trying to help, from the principal to the classroom teacher. We are, however, working with some handicaps. For one, the school, like most public schools, has limited resources. Among the things it does not have is any kind of formal program for gifted kids before the third grade. After that point, high achieving kids are tracked into groups within classrooms and receive special programs once a week or so. But for the next two years, we’re making it up as we go along.
So my posts for this space are likely to be about, in one way or another, what it’s like to put a gifted kid in a public school.
We don’t really have a plan. We’re improvising as we go, as we’ve always done: responding to AJ’s questions by showing him the ways to find the answers. One of the things I’m finding liberating about AJ being in formal school is that I am free to follow his whims at home without the burden of having to stick to a curriculum.
I expect that my posts over the next few months will deal with activities with which we supplement AJ’s school work as well as information about how we’ve been working with AJ’s classroom teacher and his school in general. I hope that others will find our experiences helpful and I hope that, you, the readers, will share your experiences as well. We feel like we’re embarking on an adventure in a strange place without the luxury of compass or map. It’s exciting and a little big scary. And sometimes we could use some help. Or a snack. Or maybe a nap.
We have a number of issues. First, AJ is an only child and he needs and craves normal social interaction with other kids. He doesn’t want to hang out with his boring and sometimes embarrassing parents for the rest of his life. So we were interested in putting AJ in a traditional school situation rather than home schooling or some other type of arrangement. Second, while AJ, a first grader, is reportedly reading at the level of a “very smart sixth grader,” and is also engaging with math and science tasks at an as yet undetermined level higher than his grade, we want to make sure AJ is kept interested and challenged at school. It is important to us that he continue to like and get something out of school. It is also important to us that we are not responsible for all of his education because, well, we have jobs to do to pay the bills. We are, however, more than willing to assist classroom teachers and do lots of enrichment projects at home. In fact, we love it.
After much soul-searching (and, perhaps more importantly, piggybank shaking) and exploration of multiple possibilities, including private schools, schools for the gifted, tutors, enrichment programs, and shipping him off for a stint at the International Space Station, we’ve decided to send AJ to the local public school while maintaining our civic right and duty to be a pain in the ass if necessary to get him what we think he needs.
As it happens, we haven’t had to do much injury to anyone’s posterior. The school has been remarkably enthusiastic about trying to help, from the principal to the classroom teacher. We are, however, working with some handicaps. For one, the school, like most public schools, has limited resources. Among the things it does not have is any kind of formal program for gifted kids before the third grade. After that point, high achieving kids are tracked into groups within classrooms and receive special programs once a week or so. But for the next two years, we’re making it up as we go along.
So my posts for this space are likely to be about, in one way or another, what it’s like to put a gifted kid in a public school.
We don’t really have a plan. We’re improvising as we go, as we’ve always done: responding to AJ’s questions by showing him the ways to find the answers. One of the things I’m finding liberating about AJ being in formal school is that I am free to follow his whims at home without the burden of having to stick to a curriculum.
I expect that my posts over the next few months will deal with activities with which we supplement AJ’s school work as well as information about how we’ve been working with AJ’s classroom teacher and his school in general. I hope that others will find our experiences helpful and I hope that, you, the readers, will share your experiences as well. We feel like we’re embarking on an adventure in a strange place without the luxury of compass or map. It’s exciting and a little big scary. And sometimes we could use some help. Or a snack. Or maybe a nap.
Thursday, September 13, 2007
Little Man on Campus
Over the summer, my six year old went to college. No, he’s not that kind of a super-genius – keep in mind that this is the kid who, just this very minute, shouted from his bathtub, “Mommy! I just made my armpit fart!” He participated in a program run by our local community college that offers enrichment courses for elementary school kids on the college campus.
I first heard of this program through AJ’s school’s gifted teacher, who recommended it and was one of the program’s ffounders. After third grade, the programs are limited to kids who have been defined as gifted either by their schools or through formal testing. But for younger kids like AJ, the programs are open to all who are interested, which I think is great. For one thing, testing is expensive and of dubious value. And for another thing, why shouldn’t any kid have a chance to pursue his or her curiosity about something?
The college for kids offers a variety of courses, most of which, for AJ’s age group at least, seem to be centered around science topics. We saw that there was one about space, AJ’s favorite subject, and signed up for it right away. It was the first thing on our summer schedule.
For four days, AJ spent three hours with three other kids and a teacher talking and learning about space. Three hours is a long time, even for graduate students. I dread the day I have to teach a three hour seminar. I’m not sure I have the attention span. But space is AJ’s favorite subject and as far as I can tell, three hours is not enough. He comes home still asking questions, wanting to look things up and begging to watch his favorite space videos.
The teacher seemed to have tailored the class for the interests and abilities of the kids who showed up. They played games, did art and did research. They were each assigned two planets to research and had several worksheets with questions they had to find the answers to. They were given books and several recommended websites and more or less turned loose to see what they could find. AJ learned a lot, not so much about space, but about how to find out the answers to things he didn’t know. That’s something a lot of kids don’t get in school until much later. The teacher treated it like a treasure hunt and they loved it. AJ learned to love the process of finding things out, not just the end result.
Currently AJ is busy with first grade and football and friends. He doesn’t have as much time to do research with 30 minutes of homework a night. But I know there’s more research in his future because the to-do list on his desk reads:
1. Do reading log.
2. Write to pen pal.
3. Research chromosomes.
I first heard of this program through AJ’s school’s gifted teacher, who recommended it and was one of the program’s ffounders. After third grade, the programs are limited to kids who have been defined as gifted either by their schools or through formal testing. But for younger kids like AJ, the programs are open to all who are interested, which I think is great. For one thing, testing is expensive and of dubious value. And for another thing, why shouldn’t any kid have a chance to pursue his or her curiosity about something?
The college for kids offers a variety of courses, most of which, for AJ’s age group at least, seem to be centered around science topics. We saw that there was one about space, AJ’s favorite subject, and signed up for it right away. It was the first thing on our summer schedule.
For four days, AJ spent three hours with three other kids and a teacher talking and learning about space. Three hours is a long time, even for graduate students. I dread the day I have to teach a three hour seminar. I’m not sure I have the attention span. But space is AJ’s favorite subject and as far as I can tell, three hours is not enough. He comes home still asking questions, wanting to look things up and begging to watch his favorite space videos.
The teacher seemed to have tailored the class for the interests and abilities of the kids who showed up. They played games, did art and did research. They were each assigned two planets to research and had several worksheets with questions they had to find the answers to. They were given books and several recommended websites and more or less turned loose to see what they could find. AJ learned a lot, not so much about space, but about how to find out the answers to things he didn’t know. That’s something a lot of kids don’t get in school until much later. The teacher treated it like a treasure hunt and they loved it. AJ learned to love the process of finding things out, not just the end result.
Currently AJ is busy with first grade and football and friends. He doesn’t have as much time to do research with 30 minutes of homework a night. But I know there’s more research in his future because the to-do list on his desk reads:
1. Do reading log.
2. Write to pen pal.
3. Research chromosomes.
Friday, March 16, 2007
Everyday Mathematics
Scene: Harriet’s car. Harriet and AJ are en route to the local ice rink, as they are at this time every Friday morning.
AJ: You know what I think?
Harriet: What?
AJ: I think that if there’s no end to how big numbers can get, then there’s no end to how small they get either.
Harriet: Interesting theory. Why do you think that?
AJ: Well, because if a number can always have a bigger number, then there should always be a smaller number too. But I can’t figure out zero.
Harriet: (parking in front of the ice rink). There’s another way to think of it. What if you were trying to go somewhere but you could only go halfway at a time?
AJ: Then it would take you two times. You’d go halfway and then you’d go the other half.
Harriet: But what if you could only go half of the distance to the door. Here, I’ll show you what I mean. (They grab their skates and gear and lock the car). We’re going to walk halfway to the door of the skating rink and then stop.
AJ: O.K. (He eyeballs the distance and walks to the halfway point). I’m halfway.
Harriet: Good. Now we’re going to walk halfway between here and the door.
AJ: Oh, I see. And then we’ll go halfway again.
Harriet: That’s right. What’s going to happen?
AJ: We’re never getting to the door. The door is zero!
Harriet: What happens to the distance we walk?
AJ: It gets smaller and smaller to infinity!
[AJ runs into the ice rink and spots his friend D., who is waiting for him inside the glass doors.]
AJ: Hey, D.! I just ran infinity!
* * * * *
Blazingstar recently left me a link to a contentious debate about the teaching of math in elementary school that is being waged on YouTube. One of the subjects of the debate is Everyday Mathematics, the curriculum that has been adopted by AJ’s school. The first of the videos can be seen here. There is also a series of responses, most of which I’ve had a chance to watch yet. The basic problems the first video has with Everyday Mathematics is that 1) it doesn’t teach the traditional algorithms for mathmatics, 2) it teaches math in a way the parents don’t always understand 3) it forces the students to come up with more than one way to do a problem (which apparently prevents “mastery” that is better acquired through rote memorization) and 4) it relies on calculator use.
Everyday Mathematics’ take on the teaching of curriculum as well as the rebuttals to the video, believe that the problem with teaching rote memorization is that we’re not teaching comprehension but the following of instructions. Everyday Math seeks to teach children how to problem solve. They spend a lot of time on the practical uses of math, having children figure out how to find math problems in everyday life.
I find the debate interesting, because I was one of those kids who balked at rote memorization. I’m still like that. If I didn’t know why I was supposed to memorize something, then I just wouldn’t remember it. AJ is the same way. AJ is, however, quite good at traditional algorithmic-based math. He likes practicing counting by 3s or 5s or 10s. He likes doing pages of problems. And he also craves the sense of mastery that the completion of a task, like the memorization of times tables or finding quick and accurate solutions to a page of problems provides. The big question I have is why does asking “why” and showing “how” necessarily mean that no memorization is happening? Can't they be used in tandem?
I feel like AJ’s current way of learning math is ideal for him. It is “Everyday mathemetics” at its fundamental sense. He thinks about something he notices in the world and we try to figure it out together through numbers. Numbers, to AJ, are yet another way of exploring meaning, the same a language or art or music. He plays in the real world with numbers, but he also likes to play with the numbers themselves to see what they will do. It's like the way he plays with Legos, sometimes building buildings -- a house, the Sears Tower-- sometimes just experimenting to see how he can put them together
After the conversation about infinite smallness, I found myself noticing AJ’s mathematical mind at work on the ice rink. Or rather, what I noticed was that other kids run into each other all the time but AJ almost never does, unless someone gets him from behind, out of his line of vision. Why? Because AJ triangulates with amazing accuracy. I’m sure this is more an issue of his attention than his ability – he doesn’t like to get run into. He’s never been the kind of kid who hurls his body around without fear of the consequences. But it struck me what a complicated skill it is to figure out how you, a moving object, might intersect another moving object, where that intersection is likely to take place, and then adjust your own speed and direction to avoid an intersection. That could easily be another math problem from the everyday, although I’m not sure I’m qualified to do the calculations.
But it is still a mathematical skill, and a much more useful application of math than pretty much anything I remember ever doing in an elementary math class. You do the math, you stay on your feet. You fail the problem, you hit the ice. It’s that simple.
[Crossposted at Spynotes]
AJ: You know what I think?
Harriet: What?
AJ: I think that if there’s no end to how big numbers can get, then there’s no end to how small they get either.
Harriet: Interesting theory. Why do you think that?
AJ: Well, because if a number can always have a bigger number, then there should always be a smaller number too. But I can’t figure out zero.
Harriet: (parking in front of the ice rink). There’s another way to think of it. What if you were trying to go somewhere but you could only go halfway at a time?
AJ: Then it would take you two times. You’d go halfway and then you’d go the other half.
Harriet: But what if you could only go half of the distance to the door. Here, I’ll show you what I mean. (They grab their skates and gear and lock the car). We’re going to walk halfway to the door of the skating rink and then stop.
AJ: O.K. (He eyeballs the distance and walks to the halfway point). I’m halfway.
Harriet: Good. Now we’re going to walk halfway between here and the door.
AJ: Oh, I see. And then we’ll go halfway again.
Harriet: That’s right. What’s going to happen?
AJ: We’re never getting to the door. The door is zero!
Harriet: What happens to the distance we walk?
AJ: It gets smaller and smaller to infinity!
[AJ runs into the ice rink and spots his friend D., who is waiting for him inside the glass doors.]
AJ: Hey, D.! I just ran infinity!
* * * * *
Blazingstar recently left me a link to a contentious debate about the teaching of math in elementary school that is being waged on YouTube. One of the subjects of the debate is Everyday Mathematics, the curriculum that has been adopted by AJ’s school. The first of the videos can be seen here. There is also a series of responses, most of which I’ve had a chance to watch yet. The basic problems the first video has with Everyday Mathematics is that 1) it doesn’t teach the traditional algorithms for mathmatics, 2) it teaches math in a way the parents don’t always understand 3) it forces the students to come up with more than one way to do a problem (which apparently prevents “mastery” that is better acquired through rote memorization) and 4) it relies on calculator use.
Everyday Mathematics’ take on the teaching of curriculum as well as the rebuttals to the video, believe that the problem with teaching rote memorization is that we’re not teaching comprehension but the following of instructions. Everyday Math seeks to teach children how to problem solve. They spend a lot of time on the practical uses of math, having children figure out how to find math problems in everyday life.
I find the debate interesting, because I was one of those kids who balked at rote memorization. I’m still like that. If I didn’t know why I was supposed to memorize something, then I just wouldn’t remember it. AJ is the same way. AJ is, however, quite good at traditional algorithmic-based math. He likes practicing counting by 3s or 5s or 10s. He likes doing pages of problems. And he also craves the sense of mastery that the completion of a task, like the memorization of times tables or finding quick and accurate solutions to a page of problems provides. The big question I have is why does asking “why” and showing “how” necessarily mean that no memorization is happening? Can't they be used in tandem?
I feel like AJ’s current way of learning math is ideal for him. It is “Everyday mathemetics” at its fundamental sense. He thinks about something he notices in the world and we try to figure it out together through numbers. Numbers, to AJ, are yet another way of exploring meaning, the same a language or art or music. He plays in the real world with numbers, but he also likes to play with the numbers themselves to see what they will do. It's like the way he plays with Legos, sometimes building buildings -- a house, the Sears Tower-- sometimes just experimenting to see how he can put them together
After the conversation about infinite smallness, I found myself noticing AJ’s mathematical mind at work on the ice rink. Or rather, what I noticed was that other kids run into each other all the time but AJ almost never does, unless someone gets him from behind, out of his line of vision. Why? Because AJ triangulates with amazing accuracy. I’m sure this is more an issue of his attention than his ability – he doesn’t like to get run into. He’s never been the kind of kid who hurls his body around without fear of the consequences. But it struck me what a complicated skill it is to figure out how you, a moving object, might intersect another moving object, where that intersection is likely to take place, and then adjust your own speed and direction to avoid an intersection. That could easily be another math problem from the everyday, although I’m not sure I’m qualified to do the calculations.
But it is still a mathematical skill, and a much more useful application of math than pretty much anything I remember ever doing in an elementary math class. You do the math, you stay on your feet. You fail the problem, you hit the ice. It’s that simple.
[Crossposted at Spynotes]
Wednesday, January 10, 2007
School Cards
One of our challenges with AJ, an only child with two work-at-home parents, is encouraging him to play by himself. He is so used to being around all the time, that he would usually rather be entertained. It’s not that he doesn’t like playing alone – he gets into his own little world. But sometimes he has trouble getting started.
Yesterday we invented a new game, which AJ has dubbed “School Cards.” AJ loves to play school and we also want to encourage him to work on some of the subjects he doesn’t yet get at school. So we sat down together and came up with a list of all the things we could think of that you could do at school. My list included:
Language Arts
Math
Science
History and Geography
Foreign Language
Gym (indoors)
Recess (outdoors)
Art
Music
AJ added:
Rest time
Snack time
Story time
We got a stack of 3x5 cards and wrote the name of each subject on the back of one card. On the other side, we started writing lists of possible activities. For example, for Language Arts, we included things like “Read a book,” “Write a story,” “Write about something that happened to you yesterday,” “Do one handwriting worksheet,” “Take a vocabulary quiz,” “Play Mad-Libs.”
The process of writing our ideas was interesting for AJ, because he had to think about what kinds of skills went into some of the things he likes to do. We included some games like Uno and Sorry under math, because they require addition and subtraction. We put Rush Hour under Math too, because it involves spatial imagination. We also considered putting it under art, though, because AJ thought he cars were like sculpture and because spatial ideas are important in art too. We put other games under language arts (Guess Who) and gym (Twister, Hullabaloo) and even science (Mousetrap).
I didn’t have any particular plan for how to use the cards. I just wanted a tool we could turn to when we were short of ideas for things to do. I wanted it to be a tool we could use to play together but one that AJ could also use to jumpstart his own play.
AJ definitely has his own ideas about the cards. Yesterday he divided them into work and break time (the latter included gym, recess, snack, story time (because that’s when I read to him instead of him reading to me), and rest time). He alternated pulling cards out of each deck, balancing out work and play. It kept him busy all morning. At lunch time, he was begging to do “just one more.” In the morning, we practiced addition and subtraction to four columns, read a book about China and looked at it on our globe, wrote in his journal, read a book in English and another in Spanish, wrote down some new Spanish words, looked through the telescope and microscope, built an obstacle course in the family room and raced through it, had a snack, and played music and danced to it.
Today he tried another tack. He arranged the cards into a schedule and is going through it systematically. This morning we had science (more microscope investigations) and gym (his weekly gymnastics class) before we had to go run errands.
I like the way this game is making his mind work. He’s thinking about how skills learned in different activities relate to one another. He’s also aware of keeping some balance in his pursuits. I hope to keep adding to our activity lists over time.
Yesterday we invented a new game, which AJ has dubbed “School Cards.” AJ loves to play school and we also want to encourage him to work on some of the subjects he doesn’t yet get at school. So we sat down together and came up with a list of all the things we could think of that you could do at school. My list included:
Language Arts
Math
Science
History and Geography
Foreign Language
Gym (indoors)
Recess (outdoors)
Art
Music
AJ added:
Rest time
Snack time
Story time
We got a stack of 3x5 cards and wrote the name of each subject on the back of one card. On the other side, we started writing lists of possible activities. For example, for Language Arts, we included things like “Read a book,” “Write a story,” “Write about something that happened to you yesterday,” “Do one handwriting worksheet,” “Take a vocabulary quiz,” “Play Mad-Libs.”
The process of writing our ideas was interesting for AJ, because he had to think about what kinds of skills went into some of the things he likes to do. We included some games like Uno and Sorry under math, because they require addition and subtraction. We put Rush Hour under Math too, because it involves spatial imagination. We also considered putting it under art, though, because AJ thought he cars were like sculpture and because spatial ideas are important in art too. We put other games under language arts (Guess Who) and gym (Twister, Hullabaloo) and even science (Mousetrap).
I didn’t have any particular plan for how to use the cards. I just wanted a tool we could turn to when we were short of ideas for things to do. I wanted it to be a tool we could use to play together but one that AJ could also use to jumpstart his own play.
AJ definitely has his own ideas about the cards. Yesterday he divided them into work and break time (the latter included gym, recess, snack, story time (because that’s when I read to him instead of him reading to me), and rest time). He alternated pulling cards out of each deck, balancing out work and play. It kept him busy all morning. At lunch time, he was begging to do “just one more.” In the morning, we practiced addition and subtraction to four columns, read a book about China and looked at it on our globe, wrote in his journal, read a book in English and another in Spanish, wrote down some new Spanish words, looked through the telescope and microscope, built an obstacle course in the family room and raced through it, had a snack, and played music and danced to it.
Today he tried another tack. He arranged the cards into a schedule and is going through it systematically. This morning we had science (more microscope investigations) and gym (his weekly gymnastics class) before we had to go run errands.
I like the way this game is making his mind work. He’s thinking about how skills learned in different activities relate to one another. He’s also aware of keeping some balance in his pursuits. I hope to keep adding to our activity lists over time.
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