This year I'm teaching proof much more the way I have taught writing in previous years in English programs, and I have to say that the scaffolding and assessment techniques I learned as a part of a very high-performing ELA/Writing program are helping me (and benefiting my Geo students) a lot this year.
I should qualify that my school places an extremely high value on proof skills in our math sequence. Geometry is only the first place where our students are required to use the techniques of formal proof in our math courses. So I feel a strong duty to help my regular mortal Geometry students to leverage their strengths wherever possible in my classes. Since a huge number of my students are outstanding writers, it has made a world of difference to use techniques that they "get" about learning and growing as writers and apply them to learning and growing as mathematicians.
We are still in the very early stages of doing proofs, but the very first thing I have upped is the frequency of proof. We now do at least one proof a day in my Geometry classes; however, because of the increased frequency, we are doing them in ways that are scaffolded to promote fluency.
Here's the thing: the hardest thing about teaching proof in Geometry, in my opinion, is to constantly make sure that it is the STUDENTS who are doing the proving of essential theorems.
Most of the textbooks I have seen tend to scaffold proof by giving students the sequence of "Statements" and asking them to provide the "Reasons."
While this seems necessary to me at times and for many students (especially during the early stages), it also seems dramatically insufficient because it removes the burden of sequencing and identifying logical dependencies and interdependencies between and among "Statements."
So my new daily scaffolding technique for October takes a page from Malcolm Swan and Guershon Harel (by way of Dan Meyer).
I give them the diagram, the Givens, the Prove statement, and a batch of unsorted, tiny Statement cards to cut out.
Every day they have to discuss and sequence the statements, and then justify each statement as a step in their proof.
This has led to some amazing discussions of argumentation and logical dependencies.
An example of what I give them (copied 2-UP to be chopped into two handouts, one per student) can be found here:
-Sample proof to be sequenced & justified
Now students are starting to understand why congruent triangles are so useful and how they enable us to make use of their corresponding parts! The conversations about intellectual need have been spectacular.
I am grateful to Dan Meyer for being so darned persistent and for pounding away on the notion of developing intellectual need in his work!
cheesemonkey wonders
Showing posts with label intrinsic motivation. Show all posts
Showing posts with label intrinsic motivation. Show all posts
Wednesday, October 19, 2016
Friday, August 22, 2014
WEEK 1 - PROJECT 'MAD MEN' -- Classroom Rules PSA Skits
Leonard Bernstein once said, "To achieve great things, two things are needed — a plan and not quite enough time." I decided to put that principle to the test this first week at my new school by assigning a project on Day 1 that thew together strangers with an absurd but achievable goal: given a particular classroom rule or guideline, create a Public Service Announcement (i.e., a 30-second "TV commercial" in the form of a skit) whose purpose was to motivate viewers to follow the rules/guidelines for the good of the group.
I created a set-up, instructions, and a rubric for the group project. And my students did not disappoint.
The idea was to get students to think about the consequences of their actions and choices, but their ideas for implementation exceeded even my wildest dreams. Most skits followed a "slice of life" strategy, but the ones that really blew us all away were the ones that parodied existing campaigns.
Two brilliant PSAs started from already-iconic Geico insurance commercials, but the one that left me with tears running down my cheeks was a take-off on Sarah McLachlan's ASPCA spots. The song, "In the arms of the angels..." began playing, and student "Sarah" appears onstage making the exact same kind of appeal she makes in those ads. They had the tone, cadence, and music exactly right, and they clearly understood the emotionally manipulative rhetorical strategy — the seemingly endless list of forms of ignorance designed to eventually provoke self-recognition in almost everyone. Their "mathematical justification" was as follows: the narrator enters and says, "In the past year alone, texting in class tragically cost 5 of Doctor X's students their lives. Remember, think twice before texting in class — there may be fatal consequences for your grade, and for you!
It was pure and inspired genius.
I also loved the spot-on impressions of my teacher persona. One student gave a pitch-perfect parody of my "Function Basics" talk that made me both cringe and laugh my ass off simultaneously.
The best thing about this assignment was that it really pushed the voice of authority downward, into the student community itself. Whatever they made of the experience, they owned it.
I am going to try and remember this for later in the semester, when we've become too routinized.
This is definitely going to be an ongoing part of my repertoire of Day 1 activities. I got through what I neded to, then gave them the rest of the abbreviated period to collaborate. The time pressure was a thing of art.
It was perfectly imperfect — exactly the way first days ought to be.
-----------
UPDATE:
Here is the link to a generified Word document that you can customize for your own class:
PROJECT MAD MEN- classroom rules PSA generic.doc
And here are the three sample 30-second PSAs I showed my classes to give them ideas:
I created a set-up, instructions, and a rubric for the group project. And my students did not disappoint.
Two brilliant PSAs started from already-iconic Geico insurance commercials, but the one that left me with tears running down my cheeks was a take-off on Sarah McLachlan's ASPCA spots. The song, "In the arms of the angels..." began playing, and student "Sarah" appears onstage making the exact same kind of appeal she makes in those ads. They had the tone, cadence, and music exactly right, and they clearly understood the emotionally manipulative rhetorical strategy — the seemingly endless list of forms of ignorance designed to eventually provoke self-recognition in almost everyone. Their "mathematical justification" was as follows: the narrator enters and says, "In the past year alone, texting in class tragically cost 5 of Doctor X's students their lives. Remember, think twice before texting in class — there may be fatal consequences for your grade, and for you!
It was pure and inspired genius.
I also loved the spot-on impressions of my teacher persona. One student gave a pitch-perfect parody of my "Function Basics" talk that made me both cringe and laugh my ass off simultaneously.
The best thing about this assignment was that it really pushed the voice of authority downward, into the student community itself. Whatever they made of the experience, they owned it.
I am going to try and remember this for later in the semester, when we've become too routinized.
This is definitely going to be an ongoing part of my repertoire of Day 1 activities. I got through what I neded to, then gave them the rest of the abbreviated period to collaborate. The time pressure was a thing of art.
It was perfectly imperfect — exactly the way first days ought to be.
-----------
UPDATE:
Here is the link to a generified Word document that you can customize for your own class:
PROJECT MAD MEN- classroom rules PSA generic.doc
And here are the three sample 30-second PSAs I showed my classes to give them ideas:
'You Lost Your Life!' – game show hosted by the Crash Test Dummies (Since Vince & Larry, the Crash Test Dummies, were introduced to the American public in 1985, safety belt usage has increased from 14% to 79%, saving an estimated 85,000 lives, and $3.2 billion in costs to society)
'
What could you buy with the money you save?' - throwing things over a cliff (You could purchase TVs, bicycles, and computers with the money most families spend on wasted electricity)
'Five Seconds' – at highway speeds, the average text takes your eyes off the road for 5 seconds (Five seconds is the average time your eyes are off the road while texting. When traveling at 55mph, that's enough time to cover the length of a football field)
Monday, February 24, 2014
New strategy for introducing INBs: complex instruction approach
After months of not feeling like my best teacher self in the classroom, I got fed up and spent all weekend tearing stuff down and rebuilding from the ground up.
INBs are something I know well — something that work for students. So I decided to take what I had available and, as Sam would say, turn what I DON'T know into what I DO know. Love those Calculus mottos.
So I rebuilt my version of the exponential functions unit in terms of INBs. But that meant, I would have to introduce INBs.
As one girl said, "New marking period, new me!" The kids just went with it and really took to it.
Here is what I did.
ON EACH GROUP TABLE: I placed a sample INB that began with a single-sheet Table of Contents (p. 1), an Exponential Functions pocket page (p. 3), and had pages numbered through page 7. There were TOC sheets and glue sticks on the table.
SMART BOARD: on the projector, I put a countdown timer (set for 15 minutes) and an agenda slide that said,
As soon as the bell rang, I hit Start on the timer, which counted down like a bomb in a James Bond movie.
Alfred Hitchcock once said, if you want to create suspense, place a ticking time bomb under a card table at which four people are playing bridge. This seemed like good advice for introducing INBs to my students.
I think because it was a familiar, group work task approach to an unfamiliar problem, all the kids simply went went with it. "How did you make the pocket? Do you fold it this way? Where does the table of contents go? What does 'TOC' mean? What goes on page 5?" And so on and so on.
I circulated, taking attendance and making notes about participation. When students would ask me a question about how to do something, I would ask them first, "Is this a group question?" If not, they knew what was going to happen. If it was, I was happy to help them get unstuck.
Then came the acid test: the actual note-taking.
I was concerned, but they were riveted. They felt a lot more ownership over their own learning process.
There are still plenty of groupworthy tasks coming up, but at least now they have a container for their notes and reflection process.
I'm going to do a "Five Things" reflection (trace your hand on a RHS page and write down five important things from the day's lesson or group work) and notes for a "Four Summary Statements" poster, but I finally feel like I have a framework to help kids organize their learning.
I've even created a web site with links to photos of my master INB in case they miss class and need to copy the notes. Here's a link to the Box.com photo files, along with a picture of page 5:
We only got through half as much as I wanted us to get through, but they were amazed at how many notes we had in such a small and convenient space.
It feels good to be back!
INBs are something I know well — something that work for students. So I decided to take what I had available and, as Sam would say, turn what I DON'T know into what I DO know. Love those Calculus mottos.
So I rebuilt my version of the exponential functions unit in terms of INBs. But that meant, I would have to introduce INBs.
As one girl said, "New marking period, new me!" The kids just went with it and really took to it.
Here is what I did.
ON EACH GROUP TABLE: I placed a sample INB that began with a single-sheet Table of Contents (p. 1), an Exponential Functions pocket page (p. 3), and had pages numbered through page 7. There were TOC sheets and glue sticks on the table.
SMART BOARD: on the projector, I put a countdown timer (set for 15 minutes) and an agenda slide that said,
- New seats!
- Choose a notebook! Good colors still available!
- Make your notebook look like the sample notebook on your table
As soon as the bell rang, I hit Start on the timer, which counted down like a bomb in a James Bond movie.
Alfred Hitchcock once said, if you want to create suspense, place a ticking time bomb under a card table at which four people are playing bridge. This seemed like good advice for introducing INBs to my students.
I think because it was a familiar, group work task approach to an unfamiliar problem, all the kids simply went went with it. "How did you make the pocket? Do you fold it this way? Where does the table of contents go? What does 'TOC' mean? What goes on page 5?" And so on and so on.
I circulated, taking attendance and making notes about participation. When students would ask me a question about how to do something, I would ask them first, "Is this a group question?" If not, they knew what was going to happen. If it was, I was happy to help them get unstuck.
Then came the acid test: the actual note-taking.
I was concerned, but they were riveted. They felt a lot more ownership over their own learning process.
There are still plenty of groupworthy tasks coming up, but at least now they have a container for their notes and reflection process.
I'm going to do a "Five Things" reflection (trace your hand on a RHS page and write down five important things from the day's lesson or group work) and notes for a "Four Summary Statements" poster, but I finally feel like I have a framework to help kids organize their learning.
I've even created a web site with links to photos of my master INB in case they miss class and need to copy the notes. Here's a link to the Box.com photo files, along with a picture of page 5:
We only got through half as much as I wanted us to get through, but they were amazed at how many notes we had in such a small and convenient space.
It feels good to be back!
Tuesday, February 4, 2014
Building concept maps is harder than it looks
I'm having students create a concept map as a summative assessment for our Complex Numbers unit and... w o w — there is all kinds of learning going on.
Students are working in groups and can use all their notes and assignments from the unit. Some kids jumped right in and started hacking away. Others whined and asked why we couldn't just have a normal test.
We are using Post-Its, scissors, pencils, and paper to do our constructions.
In-process projects range from amazing to struggling, but what impresses me most is how much the work reveals about what students are figuring out and how each student is understanding and constructing meaning in their learning. It also demands that learners own their own learning.
Because this is so revealing, I am probably going to use concept maps both as formative assessments before and during the unit as well as using them as a 'ways of understanding' tool to help them consolidate their learning.
BREAKING: OK, this activity is definitely a keeper. Students are really digesting their learning, talking about it, debating how to represent it, and clarifying areas of confusion for themselves. Here is an outstanding example from today:
.jpg)
Students are working in groups and can use all their notes and assignments from the unit. Some kids jumped right in and started hacking away. Others whined and asked why we couldn't just have a normal test.
We are using Post-Its, scissors, pencils, and paper to do our constructions.
In-process projects range from amazing to struggling, but what impresses me most is how much the work reveals about what students are figuring out and how each student is understanding and constructing meaning in their learning. It also demands that learners own their own learning.
Because this is so revealing, I am probably going to use concept maps both as formative assessments before and during the unit as well as using them as a 'ways of understanding' tool to help them consolidate their learning.
BREAKING: OK, this activity is definitely a keeper. Students are really digesting their learning, talking about it, debating how to represent it, and clarifying areas of confusion for themselves. Here is an outstanding example from today:
Sunday, October 27, 2013
Noticing and Wondering as a practice with my 6th graders
When I'm using MARS tasks with my 6th graders, I have found no structure to be more effective in aligning their attentions and energies to the task than the Math Forum's Noticing and Wondering structure.
We kind of go into a "noticing and wondering" mode, in which we are choosing to limit our our monkey mind attention to just plain noticing and we let go of any other kind of attention that comes up during that cycle.
Noticing, in particular, is a quiet and nurturing structure for kids to simply be present with what they notice. We are not privileging noticings or knocking down noticings, we are simply welcoming them as valued and arriving guests.
6th graders love having a structure, so they loved the structure of noticing. Then once we'd heard from everybody,we did a round of noticing. It's powerful when space is allowed to sit with this first round of work.
Look at all these amazing insights they had:
We kind of go into a "noticing and wondering" mode, in which we are choosing to limit our our monkey mind attention to just plain noticing and we let go of any other kind of attention that comes up during that cycle.
Noticing, in particular, is a quiet and nurturing structure for kids to simply be present with what they notice. We are not privileging noticings or knocking down noticings, we are simply welcoming them as valued and arriving guests.
6th graders love having a structure, so they loved the structure of noticing. Then once we'd heard from everybody,we did a round of noticing. It's powerful when space is allowed to sit with this first round of work.
Look at all these amazing insights they had:
We took a little time to admire this collection. It's a great list!
They even did great a great job of thinking about the value of doing noticing and wondering at the start. The first item from the link is from @fnoschese, whose wisdom even my middle schoolers can grasp.
Doing this task together and then talking about it made students reflect in deep ways about what kinds of growth processes were going on for them.
I just wanted to share this one implementation for anybody who is interested in ways you can use this.
Monday, October 7, 2013
Teaching Mathalicious' "Harmony of Numbers" lesson on ratios, part 1 (grade 6, CCSSM 6.RP anchor lesson)
I started teaching Mathalicious' Harmony of Numbers lesson in my 6th grade classes today, and I wanted to capture some of my thoughts before I pass out for the night.
The Good — Engagement & Inclusion
First of all, let's talk engagement. This made a fabulous anchor lesson for introducing ratios. The lesson opens with a highly unusual video of a musical number that every middle school student in America knows — One Direction's "What Makes You Beautiful."
You'll just have to watch the video for yourself to see how the surprise of this song gets revealed.
What I wish I could capture — but I can only describe — was the excitement in the room as my 6th graders realized what song was being played. It took about eight measures for the realization to kick in. Imagine a room full of South Park characters all clapping their hands to their cheeks and turning around with delight to see whether or not I really understood the religious experience I was sharing with them.
Every kid in the room was mesmerized. Even my most challenging, least engaged, most bored "I hate math" kids were riveted to the idea that music might be connected to math. It passed the Dan Pink Drive test because suddenly even the reluctant learners were choosing to be curious about something in math class. My assessment: A+
We started with a deliberately inclusive activity to kick things off — one whole-class round of Noticing and Wondering (h/t to the Math Forum). Sorry for the blurry photography of my white board notes. They noticed all kinds of really interesting things and everybody participated:
From noticing and wondering, we began to circle in on length of piano strings and pitch of notes. This was a very natural and easy transition, perhaps since so many of the students (and I) are also musicians of different sorts. Five guys, one piano, dozens of different sounds, what's not to like?
The Not Actually 'Bad,' But Somehow Slightly Less Good
One thing I noticed right away was that, while the scale of the drawings on the worksheet worked out very neatly, it was kinda small for 6th graders to work with. The range of fine motor skills in any classroom of 6th graders is incredibly wide. At one end of the spectrum, you have students who can draw the most elaborate dragons or mermaids, complete with highly refined textures and details of the scales on either creature. At the other end of the spectrum, you have the students I've come to think of as the "mashers," "stompers," and "pluckers." These are the kids who haven't yet connected with the fine motor skills and tend to mash, crush, or stomp on things accidentally. Some will pluck out the erasers from the pencils in frustration ("Damn you, pointy pencil tip!!!").
This made me want to rethink the tools and scales of the modeling. It might be good to have an actual manipulative with bigger units (still to scale). Cutting things out is a good way for students this age to experience the idea of units and compatible units. Simply measuring and mentally parceling out segments is a little tough for this age group. Ironically, within a year or so, this difficulty seems to disappear. I'm sure there are a lot of great suggestions for ways to make this process of connecting the measurements to the ratios through a more physically accessible manipulative or model. But then again, I'm just one teacher, so what do I really know? My assessment: B
The Not Ugly, But Still Challenging Truth
The most difficult thing about this lesson is that 6th graders go S L O W L Y. Really slowly. My students' fastest pace was still about three times longer than the initial plan.
I am fortunate that this pacing is OK for me and my students. They need to wallow in this stuff, so I will simply take more time to let them marinate. We'll try to invent some new manipulatives for this, and I'll blog about them in a follow-up.
But the reality is that this lesson is going to take us three full periods to get through. They will be three awesome, deeply engaging learning episodes filled with deep connections as well as begging to have me play the video again (Seriously? Three times is not enough for you people???).
Even though this is a much bigger time requirement, I still give this aspect of the lesson an A+. Getting reluctant learners to be curious about something they're very well defended against is a big victory.
I'm excited to see what happens tomorrow! Thanks, Mathalicious!
The Good — Engagement & Inclusion
First of all, let's talk engagement. This made a fabulous anchor lesson for introducing ratios. The lesson opens with a highly unusual video of a musical number that every middle school student in America knows — One Direction's "What Makes You Beautiful."
You'll just have to watch the video for yourself to see how the surprise of this song gets revealed.
What I wish I could capture — but I can only describe — was the excitement in the room as my 6th graders realized what song was being played. It took about eight measures for the realization to kick in. Imagine a room full of South Park characters all clapping their hands to their cheeks and turning around with delight to see whether or not I really understood the religious experience I was sharing with them.
Every kid in the room was mesmerized. Even my most challenging, least engaged, most bored "I hate math" kids were riveted to the idea that music might be connected to math. It passed the Dan Pink Drive test because suddenly even the reluctant learners were choosing to be curious about something in math class. My assessment: A+
We started with a deliberately inclusive activity to kick things off — one whole-class round of Noticing and Wondering (h/t to the Math Forum). Sorry for the blurry photography of my white board notes. They noticed all kinds of really interesting things and everybody participated:
From noticing and wondering, we began to circle in on length of piano strings and pitch of notes. This was a very natural and easy transition, perhaps since so many of the students (and I) are also musicians of different sorts. Five guys, one piano, dozens of different sounds, what's not to like?
The Not Actually 'Bad,' But Somehow Slightly Less Good
One thing I noticed right away was that, while the scale of the drawings on the worksheet worked out very neatly, it was kinda small for 6th graders to work with. The range of fine motor skills in any classroom of 6th graders is incredibly wide. At one end of the spectrum, you have students who can draw the most elaborate dragons or mermaids, complete with highly refined textures and details of the scales on either creature. At the other end of the spectrum, you have the students I've come to think of as the "mashers," "stompers," and "pluckers." These are the kids who haven't yet connected with the fine motor skills and tend to mash, crush, or stomp on things accidentally. Some will pluck out the erasers from the pencils in frustration ("Damn you, pointy pencil tip!!!").
This made me want to rethink the tools and scales of the modeling. It might be good to have an actual manipulative with bigger units (still to scale). Cutting things out is a good way for students this age to experience the idea of units and compatible units. Simply measuring and mentally parceling out segments is a little tough for this age group. Ironically, within a year or so, this difficulty seems to disappear. I'm sure there are a lot of great suggestions for ways to make this process of connecting the measurements to the ratios through a more physically accessible manipulative or model. But then again, I'm just one teacher, so what do I really know? My assessment: B
The Not Ugly, But Still Challenging Truth
The most difficult thing about this lesson is that 6th graders go S L O W L Y. Really slowly. My students' fastest pace was still about three times longer than the initial plan.
I am fortunate that this pacing is OK for me and my students. They need to wallow in this stuff, so I will simply take more time to let them marinate. We'll try to invent some new manipulatives for this, and I'll blog about them in a follow-up.
But the reality is that this lesson is going to take us three full periods to get through. They will be three awesome, deeply engaging learning episodes filled with deep connections as well as begging to have me play the video again (Seriously? Three times is not enough for you people???).
Even though this is a much bigger time requirement, I still give this aspect of the lesson an A+. Getting reluctant learners to be curious about something they're very well defended against is a big victory.
I'm excited to see what happens tomorrow! Thanks, Mathalicious!
Saturday, July 27, 2013
Twitter Math Camp 2013 — reflections on a sustainable model of hope
At Twitter Math Camp 2013 (#TMC13) this morning, I was both amused and inspired to read these two tweets — one by one of my math ed inspirations and another by a colleague I could not respect any more than I do and whom I can also call a friend:
But years of experience have taught me that that is the "hope" of an Indulging Baby — a person who looks like an adult on the outside, but who really walks around believing that my every problem, need, and desire in life should be solved by benevolent and invisible external forces. This is in harmony with my frequent conviction that my life really ought to operate like one of those behavioral experiments in which, each time I press the correct lever, the Universe promptly and consistently rewards me with a food pellet.
So I'm sure you can imagine my annoyance with the reality that life — and teaching — refuse to cooperate with my first-draft of things.
For the second year in a row, I have blown away by what I receive at Twitter Math Camp. The best, the most creative, the most resourceful, and the deepest-thinking math teacher I know in the English-speaking world show up and share with me their 'A' game. This is not so much a blessing to me as what I would describe as a complete fucking miracle. In sharing, in presenting, in participating, and in attending, every single person at this conference gives me a richer PD experience than many teachers ever get in an entire lifetime.
And in a sense, that is the point.
For me, this conference is about refilling the well at The Great Oasis of The Impeccable Warriors. There pretty much are no Indulging Babies here at TMC. If you want somebody to take care of you and make you feel better and wipe your butt, well, this is not going to be the place for you. Everybody here is truly impeccable. To me, that means that everybody does the very best they can in whatever situation they are in. It's a stone soup mindset. If everybody has crap, then we will be eating crap soup that night. But if everybody brings one small, precious ingredient to the soup, then we will be eating like royalty — or at least, like Silicon Valley-based organizations that are overfunded by the Bill and Melinda Gates Foundation (use your imagination, or consult @fnoschese's Twitter feed and/or blog).
That is not to say that everything is perfect. People are still people, which means we can all sometimes be thoughtless, stupid, impulsive, stubborn, rude, and a whole host of other things.
But what makes this work, I think, is that everybody here owns their own "stuff" and is willing to be accountable for what they put into the communal mystic cookpot.
The truth behind the truth is, I brought my 'A' game too. I worked for three months on my sessions, planning, preparing, reflecting. You guys are my tweeps. My tribe. Even though I had an almost totally crappy year, I did not want to let you down. And I have learned that I will get back in proportion to what I put in (cf. CCSSM 8.F.1 and 8.F.3, and passim).
So my challenge to everybody who is attending Twitter Math Camp for the first year this year is to reflect on this question:
You don't have to answer this question right now. But if you want this to be here next year — both for yourself and for others — it is important to hold this question in your heart as you process the experiences you've had these past several days.
I believe that hope is a process, not a destination, and I believe that what Steve Leinwand was responding to was the awesome force field of being in the presence of 125 impeccable warriors all being impeccable together — 125 math teachers who don't simply complain about what a mess things are, but rather who each grab a mop and say, oh, I see— I'll do it.
Ann and I having great time in Philly at Twitter Math Camp - amazing ideas and energy! Massive hope for what is possible.
— Steve Leinwand (@steve_leinwand) July 27, 2013
You guys, we gave @steve_leinwand hope. We can go home now.Like my spiritual and general life role model, Wile E. Coyote, I am invariably hopeful in a small sense that this will FINALLY be the moment — that perfect moment when all my best-laid "plans" will do the trick and I will, at long last, have the solid, effortlessly nourishing, and unshakable ground beneath my feet that I crave (and that I believe I so richly deserve).
— Kate Nowak (@k8nowak) July 27, 2013
But years of experience have taught me that that is the "hope" of an Indulging Baby — a person who looks like an adult on the outside, but who really walks around believing that my every problem, need, and desire in life should be solved by benevolent and invisible external forces. This is in harmony with my frequent conviction that my life really ought to operate like one of those behavioral experiments in which, each time I press the correct lever, the Universe promptly and consistently rewards me with a food pellet.
So I'm sure you can imagine my annoyance with the reality that life — and teaching — refuse to cooperate with my first-draft of things.
For the second year in a row, I have blown away by what I receive at Twitter Math Camp. The best, the most creative, the most resourceful, and the deepest-thinking math teacher I know in the English-speaking world show up and share with me their 'A' game. This is not so much a blessing to me as what I would describe as a complete fucking miracle. In sharing, in presenting, in participating, and in attending, every single person at this conference gives me a richer PD experience than many teachers ever get in an entire lifetime.
And in a sense, that is the point.
For me, this conference is about refilling the well at The Great Oasis of The Impeccable Warriors. There pretty much are no Indulging Babies here at TMC. If you want somebody to take care of you and make you feel better and wipe your butt, well, this is not going to be the place for you. Everybody here is truly impeccable. To me, that means that everybody does the very best they can in whatever situation they are in. It's a stone soup mindset. If everybody has crap, then we will be eating crap soup that night. But if everybody brings one small, precious ingredient to the soup, then we will be eating like royalty — or at least, like Silicon Valley-based organizations that are overfunded by the Bill and Melinda Gates Foundation (use your imagination, or consult @fnoschese's Twitter feed and/or blog).
That is not to say that everything is perfect. People are still people, which means we can all sometimes be thoughtless, stupid, impulsive, stubborn, rude, and a whole host of other things.
But what makes this work, I think, is that everybody here owns their own "stuff" and is willing to be accountable for what they put into the communal mystic cookpot.
The truth behind the truth is, I brought my 'A' game too. I worked for three months on my sessions, planning, preparing, reflecting. You guys are my tweeps. My tribe. Even though I had an almost totally crappy year, I did not want to let you down. And I have learned that I will get back in proportion to what I put in (cf. CCSSM 8.F.1 and 8.F.3, and passim).
So my challenge to everybody who is attending Twitter Math Camp for the first year this year is to reflect on this question:
Now that you have fifty percent as much experience with TMC as even the most experienced Twitter Math Campers among us, how are YOU going to help make Twitter Math Camp just as amazing next year?I strongly believe that the people who show up for something are exactly the right people. So, hey — welcome to the club of Impeccable Math Camp Warriors! You certainly have something important to contribute, or you would not be here reading this.
You don't have to answer this question right now. But if you want this to be here next year — both for yourself and for others — it is important to hold this question in your heart as you process the experiences you've had these past several days.
I believe that hope is a process, not a destination, and I believe that what Steve Leinwand was responding to was the awesome force field of being in the presence of 125 impeccable warriors all being impeccable together — 125 math teachers who don't simply complain about what a mess things are, but rather who each grab a mop and say, oh, I see— I'll do it.
Tuesday, April 9, 2013
Allegory, iambic pentameter, and 8th graders
In 8th grade English we have just started our poetry unit, which is probably my favorite literature unit, and today was probably my favorite lesson of my favorite literature unit.
I had to start by finishing up what I think of as the "poetry bootcamp" section. There are all the basic terms, the mandatory vocabulary, bleep, blorp, bleep, blorp, and a yada yada yada. BO-RING. That is no way to engage 8th graders.
So I took my opening when I got to allegory, which, as I explained to them, is what we call an "extended metaphor," or as I like to think of it, a "story-length metaphor."
Like the fable of The Ugly Duckling.
I am a believer in the power of storytelling and poetry to save lives. They've saved my life many, many times over, and I know many others who've been saved by them as well.
I told them a version of Clarissa Pinkola Estès' version of The Ugly Duckling. I wove the story from the perspective of the bewildered, misfit duckling who cannot belong but who tries so hard to belong until he JUST. CANNOT. EVEN. At which point, he gets driven out of the flock into the landscape of despair.
He wanders through the landscape of despair — through the forest of his fears — until he has reached the end of all that he knows.
Finally, exhausted and hungry, he paddles out on the lake in search of solace and food. As he is paddling around, lost and spent, a pair of magnificent swans paddle up alongside him and ask if they can swim with him.
He looks over his shoulder to see if there is somebody else behind to whom they must be talking. The water is empty.
After many backs and forths, he relents and allows himself to swim with them. And as the sun peeks through the thick cloud cover, the glassy surface of the water turns into a giant reflecting glass, into which he looks, expecting to see his familiar, unlovable image.
But instead, he sees quite another image looking back at him — the reflected image of a third, equally magnificent swan on the lake.
I told them, we all wander lost at some point in our lives, but if we hold on and remain clear about what we are searching for, we will all eventually find our flock, our tribe, our true pack. The people with whom we can be authentic and with whom we belong. Estès talks about "belonging as blessing" as a promise, and I have learned that this is true, even though I always find the needle on my gas gauge quivering around the "E" end of the spectrum by this point in my journey.
On my own path right now, I'm not "there" yet. I don't know where I'll be teaching this time next year, but I do know the shape of this journey, and I understand that now is the moment when I need to redouble my faith in the archetype — even though every fiber of my being is ready to just lie down and allow myself to be eaten by whatever hungry ghosts are passing my way.
I told my students that there are patterns to our experience, just as there are patterns in mathematics and the natural world and in human history. And I think that I told them what I needed to hear for myself, namely, that education and growing up is the process of discovering and learning to trust the patterns that are bigger and greater than our own, fidgety little monkey minds.
I had to start by finishing up what I think of as the "poetry bootcamp" section. There are all the basic terms, the mandatory vocabulary, bleep, blorp, bleep, blorp, and a yada yada yada. BO-RING. That is no way to engage 8th graders.
So I took my opening when I got to allegory, which, as I explained to them, is what we call an "extended metaphor," or as I like to think of it, a "story-length metaphor."
Like the fable of The Ugly Duckling.
I am a believer in the power of storytelling and poetry to save lives. They've saved my life many, many times over, and I know many others who've been saved by them as well.
I told them a version of Clarissa Pinkola Estès' version of The Ugly Duckling. I wove the story from the perspective of the bewildered, misfit duckling who cannot belong but who tries so hard to belong until he JUST. CANNOT. EVEN. At which point, he gets driven out of the flock into the landscape of despair.
He wanders through the landscape of despair — through the forest of his fears — until he has reached the end of all that he knows.
Finally, exhausted and hungry, he paddles out on the lake in search of solace and food. As he is paddling around, lost and spent, a pair of magnificent swans paddle up alongside him and ask if they can swim with him.
He looks over his shoulder to see if there is somebody else behind to whom they must be talking. The water is empty.
After many backs and forths, he relents and allows himself to swim with them. And as the sun peeks through the thick cloud cover, the glassy surface of the water turns into a giant reflecting glass, into which he looks, expecting to see his familiar, unlovable image.
But instead, he sees quite another image looking back at him — the reflected image of a third, equally magnificent swan on the lake.
I told them, we all wander lost at some point in our lives, but if we hold on and remain clear about what we are searching for, we will all eventually find our flock, our tribe, our true pack. The people with whom we can be authentic and with whom we belong. Estès talks about "belonging as blessing" as a promise, and I have learned that this is true, even though I always find the needle on my gas gauge quivering around the "E" end of the spectrum by this point in my journey.
On my own path right now, I'm not "there" yet. I don't know where I'll be teaching this time next year, but I do know the shape of this journey, and I understand that now is the moment when I need to redouble my faith in the archetype — even though every fiber of my being is ready to just lie down and allow myself to be eaten by whatever hungry ghosts are passing my way.
I told my students that there are patterns to our experience, just as there are patterns in mathematics and the natural world and in human history. And I think that I told them what I needed to hear for myself, namely, that education and growing up is the process of discovering and learning to trust the patterns that are bigger and greater than our own, fidgety little monkey minds.
Sunday, March 24, 2013
Thoughts On Making Math Tasks "Stickier"
Last year, the book that changed my teaching practice the most was definitely Dan Pink's Drive: The Surprising Truth About What Motivates Us. It helped me to think through how I wanted to structure classroom tasks in order to maximize intrinsic motivation and engagement.
This year, the book that is influencing my teaching practice the most would have to be Made To Stick: Why Some Ideas Survive and Others Die by Chip and Dan Heath. I bought it to read on my Kindle, and I kind of regret that now because it is one of those books (like Drive) that really needs to be waved around at meaningful PD events.
The Heath brothers' thesis is basically that any idea, task, or activity can be made "stickier" by applying six basic principles of stickiness. Their big six are:
This framework can also help us to understand — and hopefully to improve —a lot of so-so ideas that start with a seed of stickiness but haven't yet achieved their optimal sticky potential.
I wanted to write out some of what I mean here.
For example, I have often waxed poetic about Dan Meyer's Graphing Stories, which are a little jewel of stickiness when introducing the practice of graphing situations, yet I find a lot of the other Three-Act Tasks to be curiously flat for me and non-engaging. Some of this has to do with the fact that I am not a particularly visual learner, but I also think there is some value in analyzing my own experience as a formerly discouraged math learner. I have learned that if I can't get myself to be curious and engaged about something, I can't really manage to engage anybody else either.
Made To Stick has given me a vocabulary for analyzing some of what goes wrong for me and what goes right with certain math tasks. The six principles framework are very valuable for me in this regard, both descriptively and prescriptively. For example, Dan's original Graphing Stories lesson meets all of the Heath brothers' criteria. It is simple, unexpected, concrete, credible, emotional, and narrative. The lesson anchors the learning in students' own experience, then opens an unexpected "curiosity gap" in students' knowledge by pointing out some specific bits of knowledge they do not have but could actually reach for if they were simply to reach for it a little bit.
But I would argue that the place where this lesson succeeds most strongly is in its concreteness, which is implemented through Dan's cleverly designed and integrated handout. At first glance, this looks like just another boring student worksheet. But actually, through its clever design and tie-in to the videos, it becomes a concrete, tangible tool that students use to expose and investigate their own curiosity gaps for themselves.
Students discover their own knowledge gap through two distinct, but related physical, sensory moments: the first, when they anchor their own experiences of walking in the forest, crossing over a bridge, and peering out over the railing as they pass over (sorry, bad Passover pun), and the second, when they glance down at the physical worksheet and pencil in their own hands and are asked to connect what they saw with what they must now do.
This connection in the present moment to the students' own physical, tangible experience must not be underestimated.
Watching the video — even watching a worldclass piece of cinematography — is a relatively passive sensory experience for most of us.
But opening a gap between what I see as a viewer and what I hold in my hands — or what I taste (Double-Stuf Oreos!), smell, feel, or hear — and I'm yours forever.
This way of thinking has given me a much deeper understanding of why my lessons that integrate two or three sensory modalities always seem to be stickier than my lessons that rely on just one modality. Even when the manipulatives I introduce might seem contrived or artificial, there is value in introducing a second or third sensory dimension to my tasks. In so doing, they both (a) add another access point for students I have not yet reached and (b) expose the gap in students' knowledge by bringing in their present-moment sensory experiences. And these two dimensions can make an enormous different in students' emotional engagement in a math task.
This year, the book that is influencing my teaching practice the most would have to be Made To Stick: Why Some Ideas Survive and Others Die by Chip and Dan Heath. I bought it to read on my Kindle, and I kind of regret that now because it is one of those books (like Drive) that really needs to be waved around at meaningful PD events.
The Heath brothers' thesis is basically that any idea, task, or activity can be made "stickier" by applying six basic principles of stickiness. Their big six are:
- Simple
- Unexpected
- Concrete
- Credible
- Emotional
- Story
This framework can also help us to understand — and hopefully to improve —a lot of so-so ideas that start with a seed of stickiness but haven't yet achieved their optimal sticky potential.
I wanted to write out some of what I mean here.
For example, I have often waxed poetic about Dan Meyer's Graphing Stories, which are a little jewel of stickiness when introducing the practice of graphing situations, yet I find a lot of the other Three-Act Tasks to be curiously flat for me and non-engaging. Some of this has to do with the fact that I am not a particularly visual learner, but I also think there is some value in analyzing my own experience as a formerly discouraged math learner. I have learned that if I can't get myself to be curious and engaged about something, I can't really manage to engage anybody else either.
Made To Stick has given me a vocabulary for analyzing some of what goes wrong for me and what goes right with certain math tasks. The six principles framework are very valuable for me in this regard, both descriptively and prescriptively. For example, Dan's original Graphing Stories lesson meets all of the Heath brothers' criteria. It is simple, unexpected, concrete, credible, emotional, and narrative. The lesson anchors the learning in students' own experience, then opens an unexpected "curiosity gap" in students' knowledge by pointing out some specific bits of knowledge they do not have but could actually reach for if they were simply to reach for it a little bit.
But I would argue that the place where this lesson succeeds most strongly is in its concreteness, which is implemented through Dan's cleverly designed and integrated handout. At first glance, this looks like just another boring student worksheet. But actually, through its clever design and tie-in to the videos, it becomes a concrete, tangible tool that students use to expose and investigate their own curiosity gaps for themselves.
Students discover their own knowledge gap through two distinct, but related physical, sensory moments: the first, when they anchor their own experiences of walking in the forest, crossing over a bridge, and peering out over the railing as they pass over (sorry, bad Passover pun), and the second, when they glance down at the physical worksheet and pencil in their own hands and are asked to connect what they saw with what they must now do.
This connection in the present moment to the students' own physical, tangible experience must not be underestimated.
Watching the video — even watching a worldclass piece of cinematography — is a relatively passive sensory experience for most of us.
But opening a gap between what I see as a viewer and what I hold in my hands — or what I taste (Double-Stuf Oreos!), smell, feel, or hear — and I'm yours forever.
 |
| "My work here is done." |
Tuesday, October 30, 2012
What We Actively Value, Versus What We Tell Students We Value
Lately I've become acutely aware of what I actively value in my classroom, which has entailed an uncomfortable amount of noticing the conditioned habits of my teacher personality. I don't collect and stamp homework assignments. I don't have each day's agenda and objective for the day neatly written on the whiteboard by the time the first bell rings. My classroom is pretty messy most of the time. I don't have a good system for filing away those last three copies of every handout for future use. I took great permission from @mgolding's system of daily handouts using her Container Store hanging file system: basically, the handouts migrate downward one pocket until there are no pockets left, at which point they go into the recycling bin.
I've made my peace with these tradeoffs because I discovered early on that if I was allotting attention to those things, then that was attention I wasn't allotting to the things I actually do value.
I adopted an SBG assessment system because it aligns my grading/scoring system with the things I actually value: mastery, effort, and perseverance. And also presence — being fully present with the activity we are doing that I actually care about. And as I've noticed that, I have noticed something else I feel good about in my classroom: my kids know that those are the things I value. Which that means they don't waste valuable life-energy bullshitting me about the small stuff we all know I don't really care about.
This has led to a lot of interesting progress with students I didn't expect to make progress with. Less successful students who don't feel shamed stick around to ask questions and engage in meaningful academic inquiry. They come to my room during their study hall periods to follow up, get help on missed or misunderstood assignments, or ask for additional work they can do to improve their understanding.
Not their grade -- their understanding. Their performance.
I am not used to this, and it causes me a lot of inconvenience.
Students who have a reputation for giving up and giving in ask me if they can write another draft, reassess their missed algebra skills/concepts questions, and take greater ownership of their learning in my classroom. My ego would like to think this is because I'm such a highly effective teacher, but in actuality, I think it's more that my walk is becoming more aligned with my talk. I care about mastery and effort and perseverance, which means that those are the things I respond to.
What I did not realize until this afternoon is that this also means that I don't respond to things that are NOT those things. Which means that my kids are not expending any effort pretending to care about things around me that they really don't care about either. There is a focus on the work, and there is not a focus on things that are not the work. This may sound obvious, but actually it's not -- or at least, it wasn't for me. It took me years to discover that I'd been walking around in a consensual trance all my life.
This kind of awareness is challenging, to be sure, but it is also incredibly freeing. Students spend a huge part of every school day pretending to care about things that don't actually matter to them. Fitting in, pleasing teachers, winning points. Some of it is necessary but much of it they know to be complete and utter crap.
Ten, fifteen, forty, or fifty minutes of being authentically engaged in something that matters to somebody is a huge thing. Ten, fifteen, forty, or fifty minutes of authentic interaction with someone who is trying to focus as sincerely as possible on what actually matters in this life is even bigger.
I learned this lesson from years of experience with my mentor and teacher, Dr. Fred Joseph Orr — mind to mind, and heart to heart, though it took years to digest, and quite frankly, I'm still digesting. I'll probably be digesting for the rest of my life. No one had ever paid that kind of focused, intensive, thoughtful, and bounded attention and awareness in my presence before. And it made me discover how it feels to feel alive. I only discovered how precious that kind of awareness was -- and still is -- once that chapter of my life ended and a new chapter had begun.
I was noticing all this today during a test in which some of my lowest-performing students were asking for "help" with certain problems. I noticed that each time I came over in response to their request, they were not so much asking for assistance as asking for a kind of authentic engagement and support that was neither judging nor doing for them but simply witnessing their effort with presence. What I noticed today inside myself — and what distinguished this from mere adolescent attention-seekig behavior — was my own felt sense of a embodied memory of seeking out this kind of authentic connection in my own work with Fred. And this felt sense gave me the motivation to allow that connection and that presence. I trusted something inside my own inherent, intelligent functioning that told me to allow the connection rather than to pull back and resist. It was a subtle and quiet movement inside me, and I'm still figuring out what exactly was going on.
How many times have I mistaken noise for the signal? Do discouraged students ask because they hang on to the sane and healthy hope that they can learn and connect and make progress? Fred always told me, "The organism moves toward health," and I grew to believe him. I wonder if this is what my discouraged students are really asking for when they ostensibly make a seemingly attention-seeking request for something called "help."
Friday, October 26, 2012
And this is why I teach...
It was another crappy Friday in an arithmetic series of crappy Fridays that were running together and threatening to define the limit of my patience for fall trimester as x approaches a mid-sized number that is nowhere near infinity. So I have no idea what possessed me to wake up even earlier than usual to pull together an extra day's practice activity for my right-after-lunch class of rumpled and discouraged algebra students — the ones who believe to their core that California's Algebra 1 requirement is God's own punishment for unremembered karmic crimes they must have committed in previous lifetimes.
But I did it.
The topic was solving and graphing compound inequalities — a skill set that must be mastered in order to have any hope of making sense of and mastering the next topic traditional algebra curricula force-feed to our students: the dreaded topic of absolute value inequalities.
There's really nothing I can say to convince a roomful of skeptical eighth graders that compound inequalities will prove not only useful in business planning (which, after all, is simply algebra writ large across the canvas of the economy) but also amusing and possibly even interesting little puzzles to delight the mind.
To this group of students, they're simply another hoop to be jumped through.
So something in me understood that I needed to reframe the task for them, and to do so using Dan Pink's ideas about intrinsic motivation from his book Drive.
Nothing unlocks the eighth grade mind like an authentic offer of autonomy. As I explained recently to a room of educators at a mindfulness meditation training, middle school students suffer emotionally as much as adults, but they have comparatively little autonomy. A little well-targeted compassion about this can carry you for miles with them, though I usually forget this in the heat of working with them.
For this reason, I like to save practice structures such as Kate Nowak's Solve—Crumple—Toss for a moment when they are desperately needed. I have learned to withhold my Tiny Tykes basketball hoop for moments like this, when students need a little burst of wonder in the math classroom. And so even though I was tired and very crabby about the ever-increasing darkness over these mornings, I pushed myself to pull together a graduated, differentiated set of "solve and graph" practice problems to get this group of students over the hump of their own resistance and into the flow experience of practicing computation and analysis.
And oh, was it worth it, in the end.
The boys who are my most discouraged and resistant learners came alive when they understood that a little athletic silliness was to be their reward for persevering through something they considered too boring to give in to. They suddenly came alive with cries of, "Dr. X— watch this shot!" from halfway across the room. One boy who can rarely be convinced to do the minimum amount of classwork completed every problem I provided, then started tutoring other students in how to graph the solution sets and perform a proper crumpled-paper jump shot.
The girls in the class got into it too, but they seemed more excited about the possibility of using my self-inking date stamp to stamp their score sheets. So I gladly handed over the date stamp to whoever wanted to stamp their own successfully solved and graphed inequalities.
I was far more interested in reviewing their mathematics with them. One of the things I love best about practice structures like this one is that they give me an excuse to engage one on one with discouraged students under a time crunch pressure that adds a different dimension to their motivation. Suddenly they not only want to understand what they have done, but they want to understand it quickly, dammit, so they can move on to another problem, another solution, another graph, another bonus point.
Ultimately, Solve—Crumple—Toss becomes an occasion for conceptual breakthroughs in understanding.
I can't tell you why this happens. I can only tell you that it does happen — often. It makes me feel lighter, more buoyant about teaching them algebra. And it makes them feel happier too.
I wanted to write this down so I could capture it and remember this for a few weeks from now, when it stays darker even longer in the mornings and when I feel crappier and crabbier and more forgetful.
But I did it.
The topic was solving and graphing compound inequalities — a skill set that must be mastered in order to have any hope of making sense of and mastering the next topic traditional algebra curricula force-feed to our students: the dreaded topic of absolute value inequalities.
There's really nothing I can say to convince a roomful of skeptical eighth graders that compound inequalities will prove not only useful in business planning (which, after all, is simply algebra writ large across the canvas of the economy) but also amusing and possibly even interesting little puzzles to delight the mind.
To this group of students, they're simply another hoop to be jumped through.
So something in me understood that I needed to reframe the task for them, and to do so using Dan Pink's ideas about intrinsic motivation from his book Drive.
Nothing unlocks the eighth grade mind like an authentic offer of autonomy. As I explained recently to a room of educators at a mindfulness meditation training, middle school students suffer emotionally as much as adults, but they have comparatively little autonomy. A little well-targeted compassion about this can carry you for miles with them, though I usually forget this in the heat of working with them.
For this reason, I like to save practice structures such as Kate Nowak's Solve—Crumple—Toss for a moment when they are desperately needed. I have learned to withhold my Tiny Tykes basketball hoop for moments like this, when students need a little burst of wonder in the math classroom. And so even though I was tired and very crabby about the ever-increasing darkness over these mornings, I pushed myself to pull together a graduated, differentiated set of "solve and graph" practice problems to get this group of students over the hump of their own resistance and into the flow experience of practicing computation and analysis.
And oh, was it worth it, in the end.
The boys who are my most discouraged and resistant learners came alive when they understood that a little athletic silliness was to be their reward for persevering through something they considered too boring to give in to. They suddenly came alive with cries of, "Dr. X— watch this shot!" from halfway across the room. One boy who can rarely be convinced to do the minimum amount of classwork completed every problem I provided, then started tutoring other students in how to graph the solution sets and perform a proper crumpled-paper jump shot.
The girls in the class got into it too, but they seemed more excited about the possibility of using my self-inking date stamp to stamp their score sheets. So I gladly handed over the date stamp to whoever wanted to stamp their own successfully solved and graphed inequalities.
I was far more interested in reviewing their mathematics with them. One of the things I love best about practice structures like this one is that they give me an excuse to engage one on one with discouraged students under a time crunch pressure that adds a different dimension to their motivation. Suddenly they not only want to understand what they have done, but they want to understand it quickly, dammit, so they can move on to another problem, another solution, another graph, another bonus point.
Ultimately, Solve—Crumple—Toss becomes an occasion for conceptual breakthroughs in understanding.
I can't tell you why this happens. I can only tell you that it does happen — often. It makes me feel lighter, more buoyant about teaching them algebra. And it makes them feel happier too.
I wanted to write this down so I could capture it and remember this for a few weeks from now, when it stays darker even longer in the mornings and when I feel crappier and crabbier and more forgetful.
Subscribe to:
Posts (Atom)