"replace ambition with curiosity" - paraphrasing nancy stark smith
let go of assumption.
listen.
my ideas of the day.
Wednesday, September 30, 2009
Thursday, September 17, 2009
September 2009
I want to say a word about hope here.
I want to say a word about how the most important thing is just to show up, to have faith, to be present, to fuck up and know it and still love yourself completely, and show up the next day, still with faith and a willingness to be present, to really see what is happening in this moment, now.
I want to say a word about how a person can spend 4 years teaching and feeling incompetent and frustrated and like it doesn't matter, and then out of the blue, for relatively unimportant reasons, ten kids that you taught when you were just starting, tell you without hesitation or qualification how you changed their lives, and then go back to talking about pizza and what they're going to do after school.
I want to say a word about the importance of uncomplicated friendship that rejuvenates and inspires, clarifies, answers, supports.
I want to say a word about gratitude. To be able to notice any of this is the whole point, I think.
We are revolutionaries, all of us, each of us doing the best we can, loving and hoping and serving every day, even the ones that feel like a total sham. Eat it. Enjoy it. Live it. Trust it. Take it. It's yours.
I want to say a word about how the most important thing is just to show up, to have faith, to be present, to fuck up and know it and still love yourself completely, and show up the next day, still with faith and a willingness to be present, to really see what is happening in this moment, now.
I want to say a word about how a person can spend 4 years teaching and feeling incompetent and frustrated and like it doesn't matter, and then out of the blue, for relatively unimportant reasons, ten kids that you taught when you were just starting, tell you without hesitation or qualification how you changed their lives, and then go back to talking about pizza and what they're going to do after school.
I want to say a word about the importance of uncomplicated friendship that rejuvenates and inspires, clarifies, answers, supports.
I want to say a word about gratitude. To be able to notice any of this is the whole point, I think.
We are revolutionaries, all of us, each of us doing the best we can, loving and hoping and serving every day, even the ones that feel like a total sham. Eat it. Enjoy it. Live it. Trust it. Take it. It's yours.
Tuesday, August 4, 2009
Why does it matter?
I just read an interesting post, addressing a student's question "Why does this matter?" and it's got me thinking.
As a teacher, being prepared to answer the question of how whatever we're teaching is relevant is important. In fact, I hope that it drives our planning, that we are riveted, fascinated, engaged in the usefulness and application of what we teach. If we are clear about the context, meaning, beauty and application of a given lesson, being transparent about the topic preempts the question.
In my experience, whenever this question does get asked it's not because they actually want to know why a lesson or topic is important. It's because they're not learning. If they have time to ask this question, either they are not experiencing enough challenge or they are not experiencing enough success and one or the other is arresting their learning.
"What's the point" is code for "I'm bored and I don't want to do this because it doesn't matter" or "I'm lost, and I've been lost, and I don't want to do this because it sucks to feel lost." In either case, an explanation of the value of the topic doesn't actually address the real concern: if actually doing the math is not interesting or engaging or challenging enough to capture their interest, no amount of verbal explanation is likely to help; if they are too confused to do the math in the first place, no amount of verbal explanation is going to get them to "get it."
I think it's our job to figure out what to do to get the kids learning again. Even with an awesome explanation for the worth of algebra, if they're asking why it matters then something more basic is missing for them. When they are learning, both feeling successful and being challenged, the question doesn't come up.
As a teacher, being prepared to answer the question of how whatever we're teaching is relevant is important. In fact, I hope that it drives our planning, that we are riveted, fascinated, engaged in the usefulness and application of what we teach. If we are clear about the context, meaning, beauty and application of a given lesson, being transparent about the topic preempts the question.
In my experience, whenever this question does get asked it's not because they actually want to know why a lesson or topic is important. It's because they're not learning. If they have time to ask this question, either they are not experiencing enough challenge or they are not experiencing enough success and one or the other is arresting their learning.
"What's the point" is code for "I'm bored and I don't want to do this because it doesn't matter" or "I'm lost, and I've been lost, and I don't want to do this because it sucks to feel lost." In either case, an explanation of the value of the topic doesn't actually address the real concern: if actually doing the math is not interesting or engaging or challenging enough to capture their interest, no amount of verbal explanation is likely to help; if they are too confused to do the math in the first place, no amount of verbal explanation is going to get them to "get it."
I think it's our job to figure out what to do to get the kids learning again. Even with an awesome explanation for the worth of algebra, if they're asking why it matters then something more basic is missing for them. When they are learning, both feeling successful and being challenged, the question doesn't come up.
Thursday, July 30, 2009
Larry Zimmerman Plus
Larry Zimmerman is an extraordinary man, teacher, mind; one of those math teachers that infectiously inspires creativity and enthusiasm. As a teacher, he is alert, industrious, sensitive, clear, direct. He presents an entirely different model of teaching than anything I’ve seen before, and it made me wonder, if a little desperately, how my life would change if he had been my coach. He has recently retired from a long career at Brooklyn Tech and is pretty involved in the New York Math Circle (http://www.nymathcircle.org/)
My notes and quotes on him came from a workshop he taught on problem creation yesterday. My take on this part of his teaching is that it taps into students' (& teachers) metacognition (thinking about thinking, thinking about the fact that they are doing math while they're doing math), pattern seeking abilities and natural curiosity. I'm trying to approach planning by simply stating the questions I want to be prepared to ask during a lesson, as well as return to through the course of a unit. Here's an example of the list of questions that came from one initial problem (which I didn't initially even think was all that interesting.) I found the questions we came up with fascinating and pretty surprising.
“Theme”: How many distinct positive integer factors has the number 36?
“Variations” in no particular order:
- How many distinct positive integer factors has the number 37?
- List the factors of 36.
- What is the smallest positive integer which has the same number of factors as 36 (including 1 and itself)?
- How many distinct positive integer factors has the number 40?
- How many distinct positive integer factors has the number 49?
- How many distinct positive integer factors has the number 944?
- If x < y, and x divides y, can the number of factors of x be greater than or equal to the number of factors of y?
- Is there a positive integer for which the integer is less than the number of its factors?
- Can you find the number of factors of a number without enumerating them?
- Which positive integers have an even number of factors?
- Which positive integers have an odd number of factors?
- How many distinct positive integer factors of 36 are even/odd/perfect squares/multiples of 6/etc.?
Other inspired questions, not particularly related to the theme:
- Is zero an even integer?
- Is zero a factor of 5?
- Is 5 a factor of zero?
- Is 2 prime?
- What is the next even prime?
- Define a definition.
- What is the purpose of a definition?
My notes and quotes on him came from a workshop he taught on problem creation yesterday. My take on this part of his teaching is that it taps into students' (& teachers) metacognition (thinking about thinking, thinking about the fact that they are doing math while they're doing math), pattern seeking abilities and natural curiosity. I'm trying to approach planning by simply stating the questions I want to be prepared to ask during a lesson, as well as return to through the course of a unit. Here's an example of the list of questions that came from one initial problem (which I didn't initially even think was all that interesting.) I found the questions we came up with fascinating and pretty surprising.
“Theme”: How many distinct positive integer factors has the number 36?
“Variations” in no particular order:
- How many distinct positive integer factors has the number 37?
- List the factors of 36.
- What is the smallest positive integer which has the same number of factors as 36 (including 1 and itself)?
- How many distinct positive integer factors has the number 40?
- How many distinct positive integer factors has the number 49?
- How many distinct positive integer factors has the number 944?
- If x < y, and x divides y, can the number of factors of x be greater than or equal to the number of factors of y?
- Is there a positive integer for which the integer is less than the number of its factors?
- Can you find the number of factors of a number without enumerating them?
- Which positive integers have an even number of factors?
- Which positive integers have an odd number of factors?
- How many distinct positive integer factors of 36 are even/odd/perfect squares/multiples of 6/etc.?
Other inspired questions, not particularly related to the theme:
- Is zero an even integer?
- Is zero a factor of 5?
- Is 5 a factor of zero?
- Is 2 prime?
- What is the next even prime?
- Define a definition.
- What is the purpose of a definition?
Wednesday, July 29, 2009
Larry Zimmerman Quotes & Notes
“It is perhaps more important to be able to compose problems than to solve them.”
“Problem creation is the essence of mathematics.”
“The first effort is rarely if ever the final product.” (we must emphasize editing)
“Creating problems is theme and variations.”
“Determine what you are looking for and WRITE IT DOWN.”
“I don’t know what I want them to realize.”
“Beware of reinforced suspicion,” which is not a substitute for problem solving.
“If I’m 100% I will not forget it, I write it down.”
“There is nothing wrong with clarity by redundancy.”
Types of Problems
• Surprising
• Novel
• Fruitful
• Charming, imaginative, alluring
• Historically significant
• Haunting, musical
• Beautiful, elegant, sublime
Elements of Problems
1. a goal (construct, prove, maximize, minimize, classify, compare, compute)
2. given information
3. special rules (sometimes)
Some Big Ideas
- Plant a seed and then walk away until someone says something. Students and teachers struggle with silence, but it’s important and it saves time.
- Keep a notebook (both teachers and students) of interesting questions.
- We are well versed at turning a lot of words into symbols. Do the reverse.
- There are 3 varieties of equations: identities (always true), conditionals (sometimes true), and contradictions (never true)
“Problem creation is the essence of mathematics.”
“The first effort is rarely if ever the final product.” (we must emphasize editing)
“Creating problems is theme and variations.”
“Determine what you are looking for and WRITE IT DOWN.”
“I don’t know what I want them to realize.”
“Beware of reinforced suspicion,” which is not a substitute for problem solving.
“If I’m 100% I will not forget it, I write it down.”
“There is nothing wrong with clarity by redundancy.”
Types of Problems
• Surprising
• Novel
• Fruitful
• Charming, imaginative, alluring
• Historically significant
• Haunting, musical
• Beautiful, elegant, sublime
Elements of Problems
1. a goal (construct, prove, maximize, minimize, classify, compare, compute)
2. given information
3. special rules (sometimes)
Some Big Ideas
- Plant a seed and then walk away until someone says something. Students and teachers struggle with silence, but it’s important and it saves time.
- Keep a notebook (both teachers and students) of interesting questions.
- We are well versed at turning a lot of words into symbols. Do the reverse.
- There are 3 varieties of equations: identities (always true), conditionals (sometimes true), and contradictions (never true)
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