The math department has five amazing student teachers this semester. They eat lunch together and we talk math. They are like a team, and they provide a sort of community of support for each other and for us. Our tutoring program has a new feel because we have the presence of an army. Partly by luck, partly I think because of the safety that so many of them can provide, they are more confident and comfortable in our school than any student teachers I've ever seen. They are going to learn a lot because they are already so willing to throw themselves into this. It's so beautiful to see their generosity, their new bright eyes, to hear their arguments and passionate brainstorms.
It's my second time having a student teacher. Last semester when I dropped off my blogging, it was in part because I was so humbled by the constant witness of my student teacher that I hardly ever had anything positive to say about what was happening in my classroom. In many ways, having a student teacher brought me back to the ego bashing of my first year. Who was I to teach anyone how to do this? Lord oh lord.
This time around, I know what to expect a bit more. I know that it can be hard to have someone watch me do this job every minute. It's hard just to have someone else that I've got to be around all day long. It's hard to have anyone else that I'm responsible for teaching. But I'm ready, I'm brave, I'm humble, I'm honest. I'm trying to trust that just by doing the job that I do and being the person I am I can support this new addition to our field. I know a bit better what it is that I'm good at. It's worth it to try to share that.
This feels better from my perspective of course, but it also makes it easier to encourage him to critique me, to ask me why I'm doing what I'm doing, to question my motives and offer his own ideas to improve my classroom. That's half of what I can do for him, and it's a wonderful thing to let go of my own pride enough to let him do that without letting it get under my skin or make me question myself on a fundamental level.
Of course the other half of what I can do for him is to be the best and clearest model of passionate, mathematical, thought-provoking, community-supporting teaching that I can. That practice, that aim, can only be great for me and my students.
--
This afternoon my student teacher and I went to chess club together. He reminded me how to set up my pieces and then I got to play LOJ, an 11th grade kid I taught when he was in 9th grade. This kid is truly one of the most distracted students I've ever taught. He's spent three years wandering around in the halls and talking through his classes, mostly about whatever the class wasn't. He's more mature now, and I don't get frustrated with him anymore, but I also don't know how useful school has been for him. I've always known he was capable and smart but today was the first time I had ever seen him focus on one thing for more than 2 minutes. And the kid was freaking awesome. A great player, schooled me in a serious way, beat the crap out of me, and was utterly focused on his game when he needed to be. He was quiet, thoughtful, generous in his advice to me. Beautiful.
Also beautiful was my explicit willingness to lose this game to a student. I haven't played chess more than four times in my life because I hated feeling so bad at something. Today was the first time in over a decade that I've touched a chess piece, and I feel like I let go of something adolescent that was holding me back. Hoorah.
As always, may this find you all happy and inspired, able to love yourselves and your students.
Thursday, February 11, 2010
Wednesday, February 10, 2010
Slide Rules with John Ewing
The Math for America President John Ewing lead a workshop on slide rules last week, and I was really excited to have the opportunity to get to know him better and learn about slide rules. At 29, I had literally never seen a slide rule. I had no idea how they worked. I will be forever grateful to John for changing this.
Caution: I was confused off and on throughout this workshop because, never having seen a slide rule before, I had no idea which indices to look at when, or how to keep track of decimals when I chained operations. If you are like me you will need to play around with these a bit to figure them out.
Classroom benefits of integrated slide rule use:
- Estimation
- Scientific Notation
- Complex arithmetic
- Number sense
- Meta understanding of accuracy (how close to actual), precision (how reproducible), significance (related to precision…how many digits?) and difference b/w those.
- What makes an answer foolish. (Don’t need 100 digits to decide how much paint to use.)
- How functions work: increasing, decreasing, even concave up and down all were natural notions
John's questions:
How did the advent of technology and the handheld calculator affect the way that people approached and thought about calculation? How does it affect us? John is interested to think about why some things are harder or just different to teach today without slide rules.
Interesting History:
First handheld calculator, the HP-35, cost $395 in 1972 (~$2000 today)
People used to carry around book of log and trig tables…had interpolation tips as well to increase accuracy by 1 digit or so.
The Regents exam provided log tables
Gauss complained about the time consuming annoyance of calculation, and he’s famously good at it.
John Napier’s 1614 invention of logs was revolutionary. Before every calculation was done by hand. Napier got a really good feel for what the log function looked like (do high school students know what it looks like?)
Log xy = log x + log y (converts mult into add)
Log x/y = log x – log y (converts div into sub)
This is what was revolutionary, since addition & subtraction are way easier than multiplying and dividing.
Reverend William Oughtred (www.oughtred.org) used this trick to manipulate logs:
- Label rulers with numbers 1-10 but at log distances
- Developed within a decade of Napier’s work, but took two centuries to catch on
- Need increased in 19th century with engineering and war (cannon aiming) and so got popular in 1850, with the addition of the middle slider.
Tricks with slide rules:
- easy to chain calculations
- squaring things just means double log
- geometrically, just double the scale
- reverse to find square roots! (sq on A scale, root on D scale)
- cube the number on the K scale (and cube root backwards!)
Problems:
1. Want to paint a large sphere with radius 12.5. Paint label says 1 gallon covers 450 sq ft. How many gallons do you need?
2. Cylindrical tank has radius .82’. How tall should it be to hold 65 gallons? (NB: 1 cubic ft = 7.48 gal)
3. Have a tank 5.2’ high. Want it to hold 63 gallons. What is the radius? (uses sq root)
My inspirations after this:
- Teach decimal addition with just regular sliding rulers, play with measurement and perimeter. Use as a way of building meta-cognition about the sense of answers.
- Do a calculator correction activity, e.g.: Fix the problem: 42/85 = 2.0238
- Adapt what John did and run a math circle style workshop in which we re-discover the concept of sliding rulers to do arithmetic, the amazing transformation that happens when the rulers have logs on them instead of our regular rulers (I’d be interested in constructing a log table for that matter), how to chain operations, etc. Apparently real engineering slide rules have log log scales, so play with those too.
This pdf is what John gave us (kindly already cut out, just not folded) to make our very own slide rules.
Caution: I was confused off and on throughout this workshop because, never having seen a slide rule before, I had no idea which indices to look at when, or how to keep track of decimals when I chained operations. If you are like me you will need to play around with these a bit to figure them out.
Classroom benefits of integrated slide rule use:
- Estimation
- Scientific Notation
- Complex arithmetic
- Number sense
- Meta understanding of accuracy (how close to actual), precision (how reproducible), significance (related to precision…how many digits?) and difference b/w those.
- What makes an answer foolish. (Don’t need 100 digits to decide how much paint to use.)
- How functions work: increasing, decreasing, even concave up and down all were natural notions
John's questions:
How did the advent of technology and the handheld calculator affect the way that people approached and thought about calculation? How does it affect us? John is interested to think about why some things are harder or just different to teach today without slide rules.
Interesting History:
First handheld calculator, the HP-35, cost $395 in 1972 (~$2000 today)
People used to carry around book of log and trig tables…had interpolation tips as well to increase accuracy by 1 digit or so.
The Regents exam provided log tables
Gauss complained about the time consuming annoyance of calculation, and he’s famously good at it.
John Napier’s 1614 invention of logs was revolutionary. Before every calculation was done by hand. Napier got a really good feel for what the log function looked like (do high school students know what it looks like?)
Log xy = log x + log y (converts mult into add)
Log x/y = log x – log y (converts div into sub)
This is what was revolutionary, since addition & subtraction are way easier than multiplying and dividing.
Reverend William Oughtred (www.oughtred.org) used this trick to manipulate logs:
- Label rulers with numbers 1-10 but at log distances
- Developed within a decade of Napier’s work, but took two centuries to catch on
- Need increased in 19th century with engineering and war (cannon aiming) and so got popular in 1850, with the addition of the middle slider.
Tricks with slide rules:
- easy to chain calculations
- squaring things just means double log
- geometrically, just double the scale
- reverse to find square roots! (sq on A scale, root on D scale)
- cube the number on the K scale (and cube root backwards!)
Problems:
1. Want to paint a large sphere with radius 12.5. Paint label says 1 gallon covers 450 sq ft. How many gallons do you need?
2. Cylindrical tank has radius .82’. How tall should it be to hold 65 gallons? (NB: 1 cubic ft = 7.48 gal)
3. Have a tank 5.2’ high. Want it to hold 63 gallons. What is the radius? (uses sq root)
My inspirations after this:
- Teach decimal addition with just regular sliding rulers, play with measurement and perimeter. Use as a way of building meta-cognition about the sense of answers.
- Do a calculator correction activity, e.g.: Fix the problem: 42/85 = 2.0238
- Adapt what John did and run a math circle style workshop in which we re-discover the concept of sliding rulers to do arithmetic, the amazing transformation that happens when the rulers have logs on them instead of our regular rulers (I’d be interested in constructing a log table for that matter), how to chain operations, etc. Apparently real engineering slide rules have log log scales, so play with those too.
This pdf is what John gave us (kindly already cut out, just not folded) to make our very own slide rules.
Monday, February 8, 2010
students are human?
One of my most promising 9th grade students made a C- in my class last semester, Ds in her other classes, including the 10th grade science class she was advanced into.
Today we had an intervention. Four teachers. One student. A little over an hour.
We shared her strengths as we saw them. We asked her what her obstacles to success were. She was candid and honest with us. I think she felt glad to have such attention paid to her. She described her history of being bullied (for whatever reason anyone is bullied) and ridiculed for being faster/more focused on her work. She explained what it was like for her to work in a group, both at school and at home, where people had already given up. She talked at length about all the reasons she can't work at home, her brother who takes her books and throws them across the room, her mother who is always asking her to help out, her grandparents who need her to run errands, the chaos of her family life. She explained why she couldn't work on the subway (she'd get so into the work she'd miss her train stop) and spoke almost dreamily about how "sweet" it would be to have just an hour a day to do her work without being distracted or distressed.
There was nothing in her reasons that seemed particularly surprising, but somehow I recognized the humanity in her. She was stuck in that thing we all get stuck in, where we accept that our lives are just difficult and we have to survive them, at best understand why they are crappy, but not change them. How many of us don't exercise more, eat better, fail at New Years resolutions, get stressed out on Sunday nights when we haven't done as much grading or planning as we mean to... Of course she does that. Of course she gets lost and overwhelmed. I don't know anyone who doesn't.
It was exciting to use concrete structural interventions to try to help empower her to make her life how she wants it: to realize that "sweet" feeling she has when she imagines having time to study.
Cool, huh?
Here I was thinking I was the one whose humanity gets overlooked. Amen for awakening.
Today we had an intervention. Four teachers. One student. A little over an hour.
We shared her strengths as we saw them. We asked her what her obstacles to success were. She was candid and honest with us. I think she felt glad to have such attention paid to her. She described her history of being bullied (for whatever reason anyone is bullied) and ridiculed for being faster/more focused on her work. She explained what it was like for her to work in a group, both at school and at home, where people had already given up. She talked at length about all the reasons she can't work at home, her brother who takes her books and throws them across the room, her mother who is always asking her to help out, her grandparents who need her to run errands, the chaos of her family life. She explained why she couldn't work on the subway (she'd get so into the work she'd miss her train stop) and spoke almost dreamily about how "sweet" it would be to have just an hour a day to do her work without being distracted or distressed.
There was nothing in her reasons that seemed particularly surprising, but somehow I recognized the humanity in her. She was stuck in that thing we all get stuck in, where we accept that our lives are just difficult and we have to survive them, at best understand why they are crappy, but not change them. How many of us don't exercise more, eat better, fail at New Years resolutions, get stressed out on Sunday nights when we haven't done as much grading or planning as we mean to... Of course she does that. Of course she gets lost and overwhelmed. I don't know anyone who doesn't.
It was exciting to use concrete structural interventions to try to help empower her to make her life how she wants it: to realize that "sweet" feeling she has when she imagines having time to study.
Cool, huh?
Here I was thinking I was the one whose humanity gets overlooked. Amen for awakening.
Saturday, February 6, 2010
hugging
I've been hugging all my students. Can I remind you that I teach high school students? The kind that are busy with their hair and their technology and being cool and impressing their peers. They have that haughty insistence on independence, sometimes even a resistance to connection.
But I tell you what: I hadn't seen them for real class in two weeks (Regents, Intersession) and when I opened my arms to hug them, one after another they came at me. No hesitation. Full on hugging. Like we love each other. Like we're in something together. It was amazing. I didn't know it was possible.
I've decided to love them more. I know, I know, this is what I'm saying in every blog post. Where is the math in my mathbebrave? I promise, it's there. I will talk about it more. But at the moment this just seems so important. Because I think I'm pretty damn loving, but each time I push myself just a little bit more into this job, that's the thing I learn. Not work more, or even more time: just love them more. Or rather, feel the love I have for them more freely, more purely.
This is softening my edges. I don't take the stuff they throw at me personally the way I used to, even two weeks ago. Things go badly in class and I practice loving them, seeing their humanity. I don't know how to extend their knowledge of Combining Like Terms tomorrow, but I know that I'm going to love them. Sunday night I was excited to go to work. I like my job, but I've never been excited on Sunday night before.
Here are the goals that I gave them for the week:
1. Have Fun
2. Do Tons of Math
3. Work in Groups
4. Do some problem solving
5. KIds talk more in class than teachers
6. Practice combining like terms
7. Quiz Friday
Then they checked the box that best fit how they fit about my goals: awesome, eh, or no way!
But I tell you what: I hadn't seen them for real class in two weeks (Regents, Intersession) and when I opened my arms to hug them, one after another they came at me. No hesitation. Full on hugging. Like we love each other. Like we're in something together. It was amazing. I didn't know it was possible.
I've decided to love them more. I know, I know, this is what I'm saying in every blog post. Where is the math in my mathbebrave? I promise, it's there. I will talk about it more. But at the moment this just seems so important. Because I think I'm pretty damn loving, but each time I push myself just a little bit more into this job, that's the thing I learn. Not work more, or even more time: just love them more. Or rather, feel the love I have for them more freely, more purely.
This is softening my edges. I don't take the stuff they throw at me personally the way I used to, even two weeks ago. Things go badly in class and I practice loving them, seeing their humanity. I don't know how to extend their knowledge of Combining Like Terms tomorrow, but I know that I'm going to love them. Sunday night I was excited to go to work. I like my job, but I've never been excited on Sunday night before.
Here are the goals that I gave them for the week:
1. Have Fun
2. Do Tons of Math
3. Work in Groups
4. Do some problem solving
5. KIds talk more in class than teachers
6. Practice combining like terms
7. Quiz Friday
Then they checked the box that best fit how they fit about my goals: awesome, eh, or no way!
Hyperbolic Space, Global Warming & Crochet
If you're thinking to do something with hyperbolic space or global warming, you might want to check this out:
http://www.ted.com/talks/margaret_wertheim_crochets_the_coral_reef.html
http://www.ted.com/talks/margaret_wertheim_crochets_the_coral_reef.html
Khan Academy
My stepmother sent me this today:
http://www.khanacademy.org/
I've only looked at half of one video, but I've already got ants in my pants to share it with you. The one I watched on linear equations was anti-climactic: procedural, superficial, kind of the opposite of what I want to do with my students. But I bet it's helping somebody, maybe lots of somebodies, and maybe it's of interest to you.
---
My friend Amy just clued me in to this:
"this dude was on NPR recently. i think it's pretty awesome, especially considering the whole thing was borne out of his distance-tutoring for his cousin."
for the NPR story:
http://www.npr.org/templates/story/story.php?storyId=121978193
http://www.khanacademy.org/
I've only looked at half of one video, but I've already got ants in my pants to share it with you. The one I watched on linear equations was anti-climactic: procedural, superficial, kind of the opposite of what I want to do with my students. But I bet it's helping somebody, maybe lots of somebodies, and maybe it's of interest to you.
---
My friend Amy just clued me in to this:
"this dude was on NPR recently. i think it's pretty awesome, especially considering the whole thing was borne out of his distance-tutoring for his cousin."
for the NPR story:
http://www.npr.org/templates/story/story.php?storyId=121978193
Friday, February 5, 2010
Love is...
After 3 days of making art with my students for our annual Intersession, I was delighted to return to classes today. New semester, new student teacher, new me. I felt rejuvenated by our art-making, and inspired by the PD with Jennifer Abrams I had on Monday, which I'll write about over the weekend.
Then someone emailed me this quote:
"Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres." 1st Corinthians 13
I don't know the Bible very well, nor have I looked to it before for guidance. But I am so happy to have received this today. It sums up exactly the kind of love that I want to have with my students, every day, every minute. When they are distracted, frustrated, discouraged, disrespectful, perfect. Protect them, trust them, hope for them, persevere on their behalf. Even when I'm disillusioned and discouraged, even when I'm tired and frustrated.
May you all experience this kind of love in yourself while you work. May you receive it from those around you too.
Happy Friday!
Then someone emailed me this quote:
"Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres." 1st Corinthians 13
I don't know the Bible very well, nor have I looked to it before for guidance. But I am so happy to have received this today. It sums up exactly the kind of love that I want to have with my students, every day, every minute. When they are distracted, frustrated, discouraged, disrespectful, perfect. Protect them, trust them, hope for them, persevere on their behalf. Even when I'm disillusioned and discouraged, even when I'm tired and frustrated.
May you all experience this kind of love in yourself while you work. May you receive it from those around you too.
Happy Friday!
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