I don't know much about math or teaching it. But I like the idea of teaching mathematical thinking instead of calculation. I defer to Conrad Wolfram, an actual mathematician who is actually concerned with education.
So? What do you think?
Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Monday, November 15, 2010
Tuesday, April 27, 2010
Applying problem solving to...uh...solve problems
"Recall a time when you really loved something: a movie, song, an album or a book. You wholeheartedly recommend it to someone you really like. You anticipate that reaction, you wait for it. It came back, and the person hated it. That is the exact same state I spend every working day of the last six years. I teach high school math."
--Dan Meyer, March 6, 2010, addressing a TEDx. Dan teaches high school math outside of Santa Cruz, CA. In this brief 12-minute talk, he explores the intersection of math instruction, multimedia, and inquiry-based learning. His blog can be found here.
As I think I've mentioned. I don't teach math, but I think that understanding how math is taught and how it can be taught can be instructive to all teachers. Because it is a process about process. At the risk of belaboring the obvious, a math teacher cannot fall into the trap inherent in Social Studies, Science and sometimes in English, in which we become enraptured by our content and we start shoving the kids a big pile of "stuff", often referred to as "facts." Math, as a discipline, must always be a verb and not a noun.
At their best, Science teachers know this--that's why they have labs. Hopefully, they do not tell the students too much about how a given experiment should end up. (I can remember fudging results to match the prediction--don't blame me, it started with Gregor Mendel.)
In Language Arts, this is why I argue against diagramming sentences. It tells you a lot about what things are called and how to categorize them. It's a very useful tool for linguists studying syntax, especially in comparing languages or dialects. One teacher friend who advocates diagramming tells me the students love them. But that is not an argument in their favor. One thing students really like is questions for which there are certain and "right" answers. They hate uncertainty, ambiguity and personal interpretation. But that's the way the world is built.
And most importantly, I do not know any way to draw a line between skill in diagramming and improved writing. There may be a connection, but it has not been demonstrated to me. I believe the only way to teach writing is to (a) require a lot of it; (b) give a lot of feedback; (c) require rewriting. And the writing task must itself be authentic and have an intrinsic interest to the student. Exercises in literary analysis are lovely for college students of literature, but to induce facility in writing (if not love for it), there must be motivation.
My greatest music teacher was Lew Spratlan, not because of any information or wisdom he imparted. I took Composition with him and there was one simple, hard and fast rule of the class. "Come each day with a new piece of music to demonstrate, or don't come." We learned that the most important tool for writing music was the seat of the pants--that is, learning to apply that portion of the body to a chair in order to write. And write. And write.
When I taught general music, I made sure that students were making some kind of music at least two or three times a week--not just listening, or learning terminology or other non-functional facts. (I can't tell you how much commercial music instruction material tells you all about how many children Bach had, while telling you nothing about how he put music together.)
This corresponds with Mr. Meyer's example of waiting for the container to fill. Everyone wants to know how long that will take, even if they don't care the least about how to calculate the volume of an object. A more detailed explication of this approach to math instruction is Lockhart's Lament, which I stumbled across for obvious reasons.
This is hard, it's labor-intensive, and it means you won't "cover" as much "stuff." This runs counter to the politically-driven high-stakes testing system we have in place now. But this is what we teachers must juggle today. (I just hope the politicians who advocate these multiple-choice tests have got lots of jobs waiting for our students which involve taking multiple-choice tests. Because that system will not teach anyone to think.)
"'You can know the name of that bird in all languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird. You'll only know about humans in different places, and what they call the bird. So let's look at the bird and see what it's doing--that's what counts.'" -- Richard Feynman, quoting his father in WHAT DO YOU CARE WHAT OTHER PEOPLE THINK?
--Dan Meyer, March 6, 2010, addressing a TEDx. Dan teaches high school math outside of Santa Cruz, CA. In this brief 12-minute talk, he explores the intersection of math instruction, multimedia, and inquiry-based learning. His blog can be found here.
As I think I've mentioned. I don't teach math, but I think that understanding how math is taught and how it can be taught can be instructive to all teachers. Because it is a process about process. At the risk of belaboring the obvious, a math teacher cannot fall into the trap inherent in Social Studies, Science and sometimes in English, in which we become enraptured by our content and we start shoving the kids a big pile of "stuff", often referred to as "facts." Math, as a discipline, must always be a verb and not a noun.
At their best, Science teachers know this--that's why they have labs. Hopefully, they do not tell the students too much about how a given experiment should end up. (I can remember fudging results to match the prediction--don't blame me, it started with Gregor Mendel.)
In Language Arts, this is why I argue against diagramming sentences. It tells you a lot about what things are called and how to categorize them. It's a very useful tool for linguists studying syntax, especially in comparing languages or dialects. One teacher friend who advocates diagramming tells me the students love them. But that is not an argument in their favor. One thing students really like is questions for which there are certain and "right" answers. They hate uncertainty, ambiguity and personal interpretation. But that's the way the world is built.
And most importantly, I do not know any way to draw a line between skill in diagramming and improved writing. There may be a connection, but it has not been demonstrated to me. I believe the only way to teach writing is to (a) require a lot of it; (b) give a lot of feedback; (c) require rewriting. And the writing task must itself be authentic and have an intrinsic interest to the student. Exercises in literary analysis are lovely for college students of literature, but to induce facility in writing (if not love for it), there must be motivation.
My greatest music teacher was Lew Spratlan, not because of any information or wisdom he imparted. I took Composition with him and there was one simple, hard and fast rule of the class. "Come each day with a new piece of music to demonstrate, or don't come." We learned that the most important tool for writing music was the seat of the pants--that is, learning to apply that portion of the body to a chair in order to write. And write. And write.
When I taught general music, I made sure that students were making some kind of music at least two or three times a week--not just listening, or learning terminology or other non-functional facts. (I can't tell you how much commercial music instruction material tells you all about how many children Bach had, while telling you nothing about how he put music together.)
This corresponds with Mr. Meyer's example of waiting for the container to fill. Everyone wants to know how long that will take, even if they don't care the least about how to calculate the volume of an object. A more detailed explication of this approach to math instruction is Lockhart's Lament, which I stumbled across for obvious reasons.
This is hard, it's labor-intensive, and it means you won't "cover" as much "stuff." This runs counter to the politically-driven high-stakes testing system we have in place now. But this is what we teachers must juggle today. (I just hope the politicians who advocate these multiple-choice tests have got lots of jobs waiting for our students which involve taking multiple-choice tests. Because that system will not teach anyone to think.)
"'You can know the name of that bird in all languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird. You'll only know about humans in different places, and what they call the bird. So let's look at the bird and see what it's doing--that's what counts.'" -- Richard Feynman, quoting his father in WHAT DO YOU CARE WHAT OTHER PEOPLE THINK?
Wednesday, March 31, 2010
Inspired and inspiring teacher gone
Jaime Escalante, who taught AP Calculus to inner city students who weren't supposed to be able to master arithmetic, died yesterday. If you haven't seen Stand and Deliver, or you haven't seen it in a long time, put it in your Netflix queue to remember why we do what we do.
Incidentally, there is a "rest of the story" as the late Paul Harvey would put it. Escalante's program faded and died because of the lack of continuing administrative and district support. Persistence may be the hardest accomplishment in education. Read about it here.
Sunday, February 21, 2010
A quick commercial
My son works for Wolfram Alpha, an online computation engine which attempts to understand and answer any question asked in plain language, the answer to which is susceptible to computation. One of the side effects of this powerful tool is that astute math students who discover it could use it to simply do their homework for them. This is because WA doesn't just answer questions, but shows you how it computed the answer. The smart math teacher (of smart math students) will take account of that and figure out how to incorporate it in their instruction. Here is Conrad Wolfram, one of the key figures in this project, explaining how computers can be integrated into math instruction to promote higher-order learning. (Sorry, this is a YouTube video, so it cannot be viewed within New Milford High School, for reasons which defy rational explanation.)
I am not a math teacher, and my math instruction ended just short of calculus, but I can appreciate the concept of moving math away from mere calculation toward the analysis and the solution of real-world problems and questions. This is akin to where I would like to see Language Arts education to go--away from the study of literature and mechanistic writing skills such as forming paragraphs and punctuating them, and toward locating and de-coding real-world texts for real world purposes, and synthesizing the material found there with other material, such as what the writer generates into a text with a real audience. You know, like writing a comment on a blog and stuff.
And in any case, I'm way proud of my son and the people he is associated with.
I am not a math teacher, and my math instruction ended just short of calculus, but I can appreciate the concept of moving math away from mere calculation toward the analysis and the solution of real-world problems and questions. This is akin to where I would like to see Language Arts education to go--away from the study of literature and mechanistic writing skills such as forming paragraphs and punctuating them, and toward locating and de-coding real-world texts for real world purposes, and synthesizing the material found there with other material, such as what the writer generates into a text with a real audience. You know, like writing a comment on a blog and stuff.
And in any case, I'm way proud of my son and the people he is associated with.
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