Gotta squeak this one in under the #MTBoSBlaugust wire. :)
In the world of meditation retreats, what I've come to think of as "Emotional Breakdown Day" of a five-to-seven-day sesshin is pretty much always on a Wednesday (or Day 3, if the retreat doesn't start on a Sunday). You can set your watch by this. There is something about getting psychologically and emotionally heated up that happens after you've been simmering for three days. I think this is true at all spiritual retreats around the world. At a three-day retreat like Twitter Math Camp, it comes at Day 1.5. All of a sudden, Twitter and blogs are flooded with snippets or full-on geysers of despair at how great everybody else seems to be doing and how totally crappy you [INSERT YOUR OWN NAME HERE] are as a teacher.
I have tried to learn not to take this seasonality personally, but it's hard not to. When you go deep, you get invested.
This cycle seems equally true for me during the school year. Week 3 is inevitably my emotional breakdown week. I can no longer keep up the pace (or the illusion of the pace) and the kids can no longer keep it up either. So things start to break. Students act out. Norms fall apart. I lose my shit.
This is just the nature of the cycle of practice. Like winter, or hurricane season, or the World Series, It. Happens. So the real test is how I am going to deal with it.
I changed the seating chart in 7th block and rolled out my best rethinking of katamari and speed demon problem-based learning practice (see "Lessons from 'Lessons from Bowen and Darryl'"). I put the speed demons with other speed demons so they would leave my katamari alone already. I want the katamari to learn how to trust their own minds, their own guts, their own hearts. They lack confidence. But put a bunch of them together, and they have no choice but to trust themselves and each other. Without the speed demons to carry them along, they have to think.
And I tell you, my friends, it was magical.
I revised the day's problem set to put the Important Stuff at the top (though I never label it as Important Stuff — that gives it too much weight for teenagers, plus too little weight for everything else), instructed them to get one table whiteboards, two markers, and a washcloth and I yelled, "GO!" I think the yelling is a particularly artful piece of instructional practice.
The room began to hum and glow in the late afternoon fog. This freed me to question and support the groups that felt particularly stuck — to help them get just unstuck enough to keep going.
They didn't even care when they worked beyond the time limit I had set for this work.
I especially loved the spontaneous alliances that formed across difference. After the first really juicy problem, two young men who hadn't said 'boo' to each other in the first two and a half weeks — a young black student and a Chinese-American student — gave each other a particularly complicated, multi-part handshake than made my heart smile. A table of girls cheered when they finished the same problem.
This is why I believe that getting students into a state of flow when they are doing mathematics is the most important thing. If you align yourself with everything we know is good and healthy and whole about doing math, then everything else will proceed smoothly.
Wednesday, August 31, 2016
Sunday, August 28, 2016
Week 3 — Talking Points — Desert Island Thinking #MTBoSBlaugust
When I arrived at Princeton, I had been placed with three other roommates in a Gothic dorm suite. I was proud of the things I had accomplished so far. I'd been tied for valedictorian at a huge and competitive public high school, I'd been a soloist at the All-State choral and orchestral concert, and I'd been president of and/or varsity lettered in all my extracurriculars.
So as I discovered that everybody I met had also been valedictorian, editor of the school newspaper, an All-State varsity athlete or musician, etc., I had quite an adjustment. I had to learn how to stay present with my own inner experience and on what was in front of me directly.
I've been thinking about that experience these past two weeks as I have been watched my incoming 9th graders at Lowell adjust to the shock of discovering what it means to arrive at the next level.
The classes are much, much more demanding than they are used to, even at the strongest middle schools. And in addition, as every visitor can see at the front entrance of our school, there is a board that celebrates accomplishments of many of our Lowell graduates since our founding in 1856. There are three Nobel laureates, Pulitzer Prize winners, Broadway and Hollywood stars, admirals and generals and and politicians and world leaders. There are sports legends and pop culture icons, civil rights heroes, the founder of The Gap, and friggin' Lemony Snicket, among others.
Every race, ethnic background, and gender seems to be well-represented.
No wonder my poor kids are freaking out.
Now I try to imagine what it must be like to be one of the very few African-American students in our school. Some of them appear to be doing just fine, but I imagine it is a very strange and disorienting experience to find yourself in what must seem like an endless ocean of whiteness.
We are trying to be intentional in how we are supporting these students and transforming our school culture. We are following best practices and reflecting critically on how we are doing and how we can support their experience. I wish that I could magically airlift in a larger number of faculty of color so that they felt more reflected in the adult community they see all around them. But that is not how public education works. And we have no time to indulge in magical thinking.
So this is the point at which I am introducing some Talking Points on what I like to call desert island thinking. It is the best way I have found to help students to cope with their own feelings of imposter syndrome and the need to be their own best supporters as they enter a completely new territory.
I call it desert island thinking because it is what helped me to cope when I felt overwhelmed and alone as a freshman at Princeton. I reminded myself over and over that, if I were stuck on a desert island, I would want to be with other smart and motivated and hopefully good-hearted people because that would give us our best chances to survive and thrive.
In my teaching life, I think of this as Otter Nation. Our motto is, Hold hands and stick together. When sea otters sleep, they hold hands so they don't drift apart from their tribe. The same is true of us math teachers. We hold hands through the #MTBoS and through #educolor , through Twitter and blogs, and through every social media-based method we can find.
We hold our students in our hearts and try to give them every possible support and advantage we can provide.
For me, a part of that involves helping them to become metacognitively aware and and self-reflective about what they are experiencing and how they can cope with it, how they are brave and well-equipped and the advantages of holding hands and sticking together.
Our Latin Club has hoodies with one of my favorite lines from Virgil's Aeneid emblazoned on the back: forsan et haec olim meminisse iuvabit, which I would loosely translate as, "Perhaps some day we will laugh about this." This is pretty much where many of my students — and especially my students of color — find themselves at the start of Week 3 too. At this point in Aeneid I, Aeneas and his troops have been driven from their homeland in Troy and find themselves on storm-tossed seas, wondering how they are going to survive.
A growth mindset, and some desert island thinking, along with Talking Points about it, are the best support I can offer them.
So as I discovered that everybody I met had also been valedictorian, editor of the school newspaper, an All-State varsity athlete or musician, etc., I had quite an adjustment. I had to learn how to stay present with my own inner experience and on what was in front of me directly.
I've been thinking about that experience these past two weeks as I have been watched my incoming 9th graders at Lowell adjust to the shock of discovering what it means to arrive at the next level.
The classes are much, much more demanding than they are used to, even at the strongest middle schools. And in addition, as every visitor can see at the front entrance of our school, there is a board that celebrates accomplishments of many of our Lowell graduates since our founding in 1856. There are three Nobel laureates, Pulitzer Prize winners, Broadway and Hollywood stars, admirals and generals and and politicians and world leaders. There are sports legends and pop culture icons, civil rights heroes, the founder of The Gap, and friggin' Lemony Snicket, among others.
Every race, ethnic background, and gender seems to be well-represented.
No wonder my poor kids are freaking out.
Now I try to imagine what it must be like to be one of the very few African-American students in our school. Some of them appear to be doing just fine, but I imagine it is a very strange and disorienting experience to find yourself in what must seem like an endless ocean of whiteness.
We are trying to be intentional in how we are supporting these students and transforming our school culture. We are following best practices and reflecting critically on how we are doing and how we can support their experience. I wish that I could magically airlift in a larger number of faculty of color so that they felt more reflected in the adult community they see all around them. But that is not how public education works. And we have no time to indulge in magical thinking.
So this is the point at which I am introducing some Talking Points on what I like to call desert island thinking. It is the best way I have found to help students to cope with their own feelings of imposter syndrome and the need to be their own best supporters as they enter a completely new territory.
I call it desert island thinking because it is what helped me to cope when I felt overwhelmed and alone as a freshman at Princeton. I reminded myself over and over that, if I were stuck on a desert island, I would want to be with other smart and motivated and hopefully good-hearted people because that would give us our best chances to survive and thrive.
In my teaching life, I think of this as Otter Nation. Our motto is, Hold hands and stick together. When sea otters sleep, they hold hands so they don't drift apart from their tribe. The same is true of us math teachers. We hold hands through the #MTBoS and through #educolor , through Twitter and blogs, and through every social media-based method we can find.
We hold our students in our hearts and try to give them every possible support and advantage we can provide.
For me, a part of that involves helping them to become metacognitively aware and and self-reflective about what they are experiencing and how they can cope with it, how they are brave and well-equipped and the advantages of holding hands and sticking together.
Our Latin Club has hoodies with one of my favorite lines from Virgil's Aeneid emblazoned on the back: forsan et haec olim meminisse iuvabit, which I would loosely translate as, "Perhaps some day we will laugh about this." This is pretty much where many of my students — and especially my students of color — find themselves at the start of Week 3 too. At this point in Aeneid I, Aeneas and his troops have been driven from their homeland in Troy and find themselves on storm-tossed seas, wondering how they are going to survive.
A growth mindset, and some desert island thinking, along with Talking Points about it, are the best support I can offer them.
Saturday, August 20, 2016
Week 1 - "very much like being shot out of a cannon" #MTBoSBlaugust
Week 1 is in the can and I wanted to blog one of my best ideas from my first week back.
I should start out by saying that Week 1 was very much like being shot out of a cannon — much more so than usual. My classes this year are huge — 36, 37, or 38 students per class — but my room is the smallest in the school. So it took a lot of clever angling and arranging to ensure that we could have enough desks in the room and that everybody could more or less see from their given position in the room. I always mark on the floor with a Sharpie so that it's easier to put the desk clusters back into their optimal positions. Once upon a time, I would have considered this a form of vandalism, but now...? Hey, that's just common sense.
SEATING CHART MANAGEMENTI had a major conceptual breakthrough with seating charts this August. I always use OmniGraffle to set up my basic seating chart/management chart template that I use on my clipboard to take attendance and make notes. This year, it occurred to me: instead of using those stupid little name card tags with names to make a wall chart (which takes up an unreasonable amount of time), why not just make a board with a sheet of vinyl across to hold blank copies of the week's seating charts?
The stapled blob of paper charts makes it super-easy to make notes about collaboration or mathematical successes during group work. It also makes it easy to enter attendance on the computer each class because I just look for the 0s or 1s. My scribbled comments make it easy to enter "Professionalism" scores or comments, or to send e-mails to students or families. My working copy of charts gets stapled together and placed on my clipboard. When the week is over, I archive it in a big binder.
There's a lot more to say about Week 1, but I'm still recuperating. More soon!
I should start out by saying that Week 1 was very much like being shot out of a cannon — much more so than usual. My classes this year are huge — 36, 37, or 38 students per class — but my room is the smallest in the school. So it took a lot of clever angling and arranging to ensure that we could have enough desks in the room and that everybody could more or less see from their given position in the room. I always mark on the floor with a Sharpie so that it's easier to put the desk clusters back into their optimal positions. Once upon a time, I would have considered this a form of vandalism, but now...? Hey, that's just common sense.
SEATING CHART MANAGEMENTI had a major conceptual breakthrough with seating charts this August. I always use OmniGraffle to set up my basic seating chart/management chart template that I use on my clipboard to take attendance and make notes. This year, it occurred to me: instead of using those stupid little name card tags with names to make a wall chart (which takes up an unreasonable amount of time), why not just make a board with a sheet of vinyl across to hold blank copies of the week's seating charts?
The stapled blob of paper charts makes it super-easy to make notes about collaboration or mathematical successes during group work. It also makes it easy to enter attendance on the computer each class because I just look for the 0s or 1s. My scribbled comments make it easy to enter "Professionalism" scores or comments, or to send e-mails to students or families. My working copy of charts gets stapled together and placed on my clipboard. When the week is over, I archive it in a big binder.
[visualize the dazzling photo of my wall chart that will be posted here on Monday]
There's a lot more to say about Week 1, but I'm still recuperating. More soon!
 |
| Hey, Megan, Here's my handouts hanger in situ! |
Friday, August 12, 2016
#MTBoSBlaugust 4 - Dear Pam (starting the year and Exeter Math 1)
Dear Pam,
The closer the start of school gets, the more I realize I need to be wise about how I choose to introduce Exeter problems. I want to set my students up for success. They are an extremely diverse group, coming from all over the city and all over the world. They are new to our huge school and to high school. And my classes are huge. There is still load-balancing to do, but right now my Algebra 1 rosters are topping out at 42. This is a special problem in my room because we can only fit 36 desk-chairs in the room. Literally. So I have to practice basic trust that this is all getting worked out through placement and class balancing and other dark arts of administration.
But all of this thinking has made me realize that I need to rely on my proven, first-two-weeks training plan to get them ready for my course and to help accomplish all of the transitions I am expecting them to manage. Bottom line: I need to start by training them with Talking Points to ensure equity and access for all.
Accordingly, I've created a set of Day 1 Talking Points about ratios, units, and rates (actually for us it's Day 2 because Day 1 is a loss), which are the topics of M1:1#1. I want to use this to train them on norms and practices in my class so that we can begin our problem-based learning together. For me, the first two weeks are critical. They are when I train my students intensively on my rules and norms, using Talking Points and other practices. With 36 students per class, this is a must. Everybody has to get bought in and skilled at the structures so we can proceed.
I also need to work this beginning-of-the-year routine into my four-stage How People Learn groove. Talking Points is my go-to beginning-of-the-year Stage 1 task structure (initial encounter with new concepts and activation of old). Our debrief and shift into doing notes/INB organization is Stage 2 (initial provision of a new expert model). We'll do some notes on ratios, units, and rates to review and organize our thinking, and then we'll do a little combo-plate Stage 3 / Stage 4 work (deliberate practice with metacognitive / transfer task) in the form of some opening Exeter problems.
I've changed my mind about ordering page 1. I'm going to have them do 1#1 first (easy application of ratios, units, and rates) as a "deliberate practice with metacognitive awareness" problem and then 1#5, the journey of a thousand miles problem (J-1000). What I like about this one as a first transfer task is that it pushes them to use their bodies and to involve their whole selves in the investigation. Once somebody in the class asks, "Hey, Dr. S — can we have a yardstick?" I know I've got them. ;)
From here we can move on to 1#2, which is really the heart of the intro to problem-based learning in my opinion.
But realistically, we won't get to this until Day 3 (which is my true Day 2). So I'm having to accept that this is the reality of where I can get them and when. I can tweak the rest of everything to make it fit the first two weeks, but this is my reality.
So Day 3 needs a new set of Talking Points to begin and then a handout for problem 1#2, the problem about counting non-stop by ones to one billion.
The closer the start of school gets, the more I realize I need to be wise about how I choose to introduce Exeter problems. I want to set my students up for success. They are an extremely diverse group, coming from all over the city and all over the world. They are new to our huge school and to high school. And my classes are huge. There is still load-balancing to do, but right now my Algebra 1 rosters are topping out at 42. This is a special problem in my room because we can only fit 36 desk-chairs in the room. Literally. So I have to practice basic trust that this is all getting worked out through placement and class balancing and other dark arts of administration.
But all of this thinking has made me realize that I need to rely on my proven, first-two-weeks training plan to get them ready for my course and to help accomplish all of the transitions I am expecting them to manage. Bottom line: I need to start by training them with Talking Points to ensure equity and access for all.
Accordingly, I've created a set of Day 1 Talking Points about ratios, units, and rates (actually for us it's Day 2 because Day 1 is a loss), which are the topics of M1:1#1. I want to use this to train them on norms and practices in my class so that we can begin our problem-based learning together. For me, the first two weeks are critical. They are when I train my students intensively on my rules and norms, using Talking Points and other practices. With 36 students per class, this is a must. Everybody has to get bought in and skilled at the structures so we can proceed.
I also need to work this beginning-of-the-year routine into my four-stage How People Learn groove. Talking Points is my go-to beginning-of-the-year Stage 1 task structure (initial encounter with new concepts and activation of old). Our debrief and shift into doing notes/INB organization is Stage 2 (initial provision of a new expert model). We'll do some notes on ratios, units, and rates to review and organize our thinking, and then we'll do a little combo-plate Stage 3 / Stage 4 work (deliberate practice with metacognitive / transfer task) in the form of some opening Exeter problems.
I've changed my mind about ordering page 1. I'm going to have them do 1#1 first (easy application of ratios, units, and rates) as a "deliberate practice with metacognitive awareness" problem and then 1#5, the journey of a thousand miles problem (J-1000). What I like about this one as a first transfer task is that it pushes them to use their bodies and to involve their whole selves in the investigation. Once somebody in the class asks, "Hey, Dr. S — can we have a yardstick?" I know I've got them. ;)
From here we can move on to 1#2, which is really the heart of the intro to problem-based learning in my opinion.
But realistically, we won't get to this until Day 3 (which is my true Day 2). So I'm having to accept that this is the reality of where I can get them and when. I can tweak the rest of everything to make it fit the first two weeks, but this is my reality.
So Day 3 needs a new set of Talking Points to begin and then a handout for problem 1#2, the problem about counting non-stop by ones to one billion.
Friday, August 5, 2016
#MTBoSBlaugust 3 - The Bumper Car Theory of Anti-Racist Training for Teachers and Staff
This one is challenging to write because I want to honor all appropriate boundaries while inquiring into my own personal experience of the process.
This next week, during our whole-school PD on Wednesday, we are embarking on our first year of a multi-year program of anti-racist training for teachers and staff. Earlier this summer, I was one of 25 teachers and staff from our school who attended the initial training, and naturally, nothing went as planned. Does it ever? Heavy Sigh. So this morning, we did our reset and met about our plan to do this training with our whole school.
The enterprise of confronting privilege to teach and learn about privilege is daunting, and it is unavoidable that many people who encounter this work will quickly get rubbed raw. In some ways, that is by design. You can't remain comfortable while digging into uncomfortable territory. But at the same time, conceiving the work merely as a project of "disruption" dishonors the good will and long-term focus of individuals who have come together on their own out of their own deep-rooted belief that we need to do better, both for our students and for ourselves.
So you can see how it's a complicated and messy process to get started.
What I am coming to understand about it all is this: in order to have courageous conversations about race, we need to learn how to see our own personal invisible beliefs. These are hard to see because they are by nature invisible. They are blind spots. For example, as a high-status, highly educated white teacher, I tend to feel confident in sharing my views publicly; but at the same time, I struggle to keep my passion and confidence from appearing as arrogance to those with different patterns of privilege. And I'm just one individual teacher in a very large faculty. I'm sure that other teachers struggle to notice their own patterns of privilege. Plus the nature of the dominant culture in our school is unusual and complex. So all in all, learning to see the individual and collective belief systems and blind spots is going to be a real challenge. We are going to need to spend a lot of time in a space of collective and individual not-knowing, together. And I fully expect that process to be uncomfortable.
What strikes me most is that this whole process is like being in racial identity bumper cars. Like at a carnival. We need to expect to be disturbed and surprised and confused as we discover how other drivers in their own identity bumper cars interpret and experience life from their own points of view, because everybody is so certain that their own personal bumper car point of view is clear-seeing and constructive and intentional. But every time the ride starts up, whenever you try to steer your own bumper car, you cannot help but crash into other people's bumper cars. So the process of investigation is complicated because there is no way to step outside of the bumper car bumping arena while the inquiry is ongoing.
From the 30,000-foot perspective, I can see that the bumper car system is designed to thwart objectivity. In their own bumper car ride, nobody is 100% in control of their own bumper car. We all have our own projections and privilege and beliefs that we project onto every other driver who crashes into us. If you consider how the bumper cars are designed, you may understand logically that the bumping is unavoidable. But after you've been in the arena for a little while, trying to steer your own car for a bit, it becomes hard not to take things personally. It becomes impossible to avoid lapsing into the belief that other drivers are intentionally crashing into you to push you off course.
I think this model is especially true when you've got a large room full of public school educators — smart, highly educated, open-hearted people who do what they do out of dedication to learning and to contributing to the common good. The moment you start to prod individual teachers into seeing how they benefit from various networks of privilege, things get painful. People shut down or break down. And I've never yet seen it handled well. In our culture, teaching is already pre-constructed as a "Wretched of the Earth"-level of profession. Poorly paid, micro-managed, and bullied by corporate reformers and unelected politicians. What could possibly go wrong when you try to confront public school teachers about privilege?
So I think it is going to take a certain gentleness, determination, and persistence to help a whole faculty to see how we as individuals benefit from different forms and degrees of privilege, both in our school culture and in our society. It is also going to take chocolate and a whole lot of radically appropriate self-care. I am hopeful in the long term that we will make progress, but I suspect that in the near term, things could get messy. Still, I remain optimistic and curious to see how things unfold.
This next week, during our whole-school PD on Wednesday, we are embarking on our first year of a multi-year program of anti-racist training for teachers and staff. Earlier this summer, I was one of 25 teachers and staff from our school who attended the initial training, and naturally, nothing went as planned. Does it ever? Heavy Sigh. So this morning, we did our reset and met about our plan to do this training with our whole school.
The enterprise of confronting privilege to teach and learn about privilege is daunting, and it is unavoidable that many people who encounter this work will quickly get rubbed raw. In some ways, that is by design. You can't remain comfortable while digging into uncomfortable territory. But at the same time, conceiving the work merely as a project of "disruption" dishonors the good will and long-term focus of individuals who have come together on their own out of their own deep-rooted belief that we need to do better, both for our students and for ourselves.
So you can see how it's a complicated and messy process to get started.
 |
| Your face here |
What strikes me most is that this whole process is like being in racial identity bumper cars. Like at a carnival. We need to expect to be disturbed and surprised and confused as we discover how other drivers in their own identity bumper cars interpret and experience life from their own points of view, because everybody is so certain that their own personal bumper car point of view is clear-seeing and constructive and intentional. But every time the ride starts up, whenever you try to steer your own bumper car, you cannot help but crash into other people's bumper cars. So the process of investigation is complicated because there is no way to step outside of the bumper car bumping arena while the inquiry is ongoing.I think this model is especially true when you've got a large room full of public school educators — smart, highly educated, open-hearted people who do what they do out of dedication to learning and to contributing to the common good. The moment you start to prod individual teachers into seeing how they benefit from various networks of privilege, things get painful. People shut down or break down. And I've never yet seen it handled well. In our culture, teaching is already pre-constructed as a "Wretched of the Earth"-level of profession. Poorly paid, micro-managed, and bullied by corporate reformers and unelected politicians. What could possibly go wrong when you try to confront public school teachers about privilege?
So I think it is going to take a certain gentleness, determination, and persistence to help a whole faculty to see how we as individuals benefit from different forms and degrees of privilege, both in our school culture and in our society. It is also going to take chocolate and a whole lot of radically appropriate self-care. I am hopeful in the long term that we will make progress, but I suspect that in the near term, things could get messy. Still, I remain optimistic and curious to see how things unfold.
Wednesday, August 3, 2016
#MTBoSBlaugust Post #2: Using Exeter Math 1 — down to brass tacks
I am shamelessly using the #MTBoSBlaugust challenge as a prod to organize my thinking about how to use Exeter Math 1 this year in Algebra 1.
Last year's Algebra 1 implementation was a mess. Not even a hot mess, just a mess. The materials from our district were inadequate and even with my enrichments, I found that the whole was not coherent enough or challenging enough for my students. It also started waaaaaaayyyy too slow out of the gate. And it didn't provide nearly as much work on modeling and sense-making as I wanted.
Other than that, it was fine.
So this year, to start with, here's my game plan for reordering units for the fall semester.
Sequence of Units
Begin At The Beginning: Unit 1
This is going to work because M1:1 – 8 cover all of the things I want to deal with as review topics anyway, but in a novel and challenging way: rates and units; "micro-" modeling (going from words to mathematics) and functional thinking; using the number line; modeling with non-standard rates, fractions, ratios, and proportions; distributive property and order of operations; "like" terms; and modeling with area and volume.
Meanwhile, the most important thing about the first two weeks is to really drive home my routines and norms and structures. That creates space to get to know students and do some formative assessment so I can make intentional groupings and establish the tone for the course.
This year, the material for the first 9 days will be the first eight pages of lightly adapted Exeter problems, i.e., replacing "Exeter" with my school's name and replacing all the kid names with character names of my own choosing (I tend to favor Batman and the character names from Sesame Street and Harry Potter).
Day 1 is a complete loss because (a) it's a ridiculously short period and (b) we are required to go over our syllabus (don't ask). But I think I will put M1:1#5, which I refer to as J-1000 (the "journey of a thousand miles" problem) on the opening slide as the intro task for students to do once they've found their seats. It's a little bit of math, but it sets the tone I want, which is that we get down to mathematical business in my classroom.
Day 2 is my true Day 1, so that will be my M1:1 day.
Background: Organizing Principles
For any day that I am using a page of Exeter problems, I want to organize the problems according to Bowen and Darryl's PCMI-based framework of Important Stuff / Interesting Stuff / Tough Stuff.
That way, I can also use their twin strategies of (a) intentional groupings (keep the speed demons away from the katamari) and (b) deliberately featuring katamari solutions and insights during whole-class discussion segments. For background on all of this, including PCMI, Bowen, and Darryl's group work strategies, first read Ben Blum-Smith's Lessons from Bowen and Darryl and then my post on Lessons from Lessons from Bowen and Darryl.
Any remaining problems left over from the day's classwork can be done as homework problems that night, and those can then be discussed during the next day's Home Enjoyment/Burning Questions segment. A beautiful thing.
Day 1: M1:1#2
Problem 1:#2 is a perfect rich task for starting off an Algebra 1 course. You can demand that students let go of their habits of learned helplessness and use whatever they know. You can encourage them with problem-solving process hints and without robbing them of the opportunity to do the thinking for themselves.
Everything else on page 1 is just review and activation of prior knowledge.
OK, that's all I've got for page 1.
Last year's Algebra 1 implementation was a mess. Not even a hot mess, just a mess. The materials from our district were inadequate and even with my enrichments, I found that the whole was not coherent enough or challenging enough for my students. It also started waaaaaaayyyy too slow out of the gate. And it didn't provide nearly as much work on modeling and sense-making as I wanted.
Other than that, it was fine.
So this year, to start with, here's my game plan for reordering units for the fall semester.
Sequence of Units
- Mathematical Modeling and Problem-Solving (EQ: How can we use mathematics and logic to make sense of real-world situations?)
- Equations, Proportions, and Number Lines (EQ: How can we use our existing algebra toolkit to solve equations involving proportions, variables, and absolute value?)
- Lines and Linear Functions (EQ: How do lines and linear functions enable us to analyze and predict real-world phenomena?)
- Functions and Functional Thinking (EQ: How can functions and functional thinking help us in our modeling work?)
- Systems of Linear Equations (EQ: How can we use multiple equations to model real-world situations?)
- Working With Exponents (EQ: What makes exponents such powerful tools?)
Begin At The Beginning: Unit 1
This is going to work because M1:1 – 8 cover all of the things I want to deal with as review topics anyway, but in a novel and challenging way: rates and units; "micro-" modeling (going from words to mathematics) and functional thinking; using the number line; modeling with non-standard rates, fractions, ratios, and proportions; distributive property and order of operations; "like" terms; and modeling with area and volume.
Meanwhile, the most important thing about the first two weeks is to really drive home my routines and norms and structures. That creates space to get to know students and do some formative assessment so I can make intentional groupings and establish the tone for the course.
This year, the material for the first 9 days will be the first eight pages of lightly adapted Exeter problems, i.e., replacing "Exeter" with my school's name and replacing all the kid names with character names of my own choosing (I tend to favor Batman and the character names from Sesame Street and Harry Potter).
Day 1 is a complete loss because (a) it's a ridiculously short period and (b) we are required to go over our syllabus (don't ask). But I think I will put M1:1#5, which I refer to as J-1000 (the "journey of a thousand miles" problem) on the opening slide as the intro task for students to do once they've found their seats. It's a little bit of math, but it sets the tone I want, which is that we get down to mathematical business in my classroom.
Day 2 is my true Day 1, so that will be my M1:1 day.
Background: Organizing Principles
For any day that I am using a page of Exeter problems, I want to organize the problems according to Bowen and Darryl's PCMI-based framework of Important Stuff / Interesting Stuff / Tough Stuff.
That way, I can also use their twin strategies of (a) intentional groupings (keep the speed demons away from the katamari) and (b) deliberately featuring katamari solutions and insights during whole-class discussion segments. For background on all of this, including PCMI, Bowen, and Darryl's group work strategies, first read Ben Blum-Smith's Lessons from Bowen and Darryl and then my post on Lessons from Lessons from Bowen and Darryl.
Any remaining problems left over from the day's classwork can be done as homework problems that night, and those can then be discussed during the next day's Home Enjoyment/Burning Questions segment. A beautiful thing.
Day 1: M1:1#2
Problem 1:#2 is a perfect rich task for starting off an Algebra 1 course. You can demand that students let go of their habits of learned helplessness and use whatever they know. You can encourage them with problem-solving process hints and without robbing them of the opportunity to do the thinking for themselves.
Everything else on page 1 is just review and activation of prior knowledge.
OK, that's all I've got for page 1.
Monday, August 1, 2016
Scan in your best worked examples #MTBoSBlaugust
This is going to be a short post because I am trying to take my own best advice:
And if you are just joining us... today's advice is: scan in your best worked examples.
I spent about 2 months working through every problem on every page of Exeter Math 1. All 91 pages of problem sets. And finally, today is ScanFest 2016.
I first learned this advice from Sam Shah (of course), and it bears repeating. Your frazzled, middle-of-the-year self will thank you for it.
And now, back to scanning.
Scan in your best worked examples.Let me repeat that: Scan in your best worked examples. Scan in your best worked examples.
And if you are just joining us... today's advice is: scan in your best worked examples.
I spent about 2 months working through every problem on every page of Exeter Math 1. All 91 pages of problem sets. And finally, today is ScanFest 2016.
I first learned this advice from Sam Shah (of course), and it bears repeating. Your frazzled, middle-of-the-year self will thank you for it.
And now, back to scanning.