Monday, January 19, 2015

Nonviolent Teaching

Martin Luther King, Jr. Day. Seems harder to pretend things are all better this year.

Some of my favorite recent posts around the web that fit with this #MLK day...

The Principles of Nonviolence, gathered at the King Center
  1. PRINCIPLE ONE: Nonviolence is a way of life for courageous people. It is active nonviolent resistance to evil. It is aggressive spiritually, mentally and emotionally. 
  2. PRINCIPLE TWO: Nonviolence seeks to win friendship and understanding. The end result of nonviolence is redemption and reconciliation. The purpose of nonviolence is the creation of the Beloved Community.
  3. PRINCIPLE THREE: Nonviolence seeks to defeat injustice not people. Nonviolence recognizes that evildoers are also victims and are not evil people. The nonviolent resister seeks to defeat evil not people.
  4. PRINCIPLE FOUR: Nonviolence holds that suffering can educate and transform. Nonviolence accepts suffering without retaliation. Unearned suffering is redemptive and has tremendous educational and transforming possibilities. 
  5. PRINCIPLE FIVE: Nonviolence chooses love instead of hate. Nonviolence resists violence of the spirit as well as the body. Nonviolent love is spontaneous, unmotivated, unselfish and creative.  
  6. PRINCIPLE SIX: Nonviolence believes that the universe is on the side of justice. The nonviolent resister has deep faith that justice will eventually win.
I see these as connected to how I want to teach. My nonviolence training came from Sr. Liz Walters, IHM, when I was an undergrad at Michigan State. (Short bio of Liz from an award she received.) At that age, I was (so typically) filled with idea of competition and winning masquerading as justice. When I think back on the transition to peacefully campaigning for justice, and that the means matter as much or more than the ends, the training from Liz was of profound impact. Found this post with some current organizations that do nonviolence training.

So how is teaching related to these principles?

Active resistance to evil. Nonviolence is in no way nonaction. Instead, it is active pursuit of justice. Teaching is often inherently nonviolent because it is a career built on constructing relationships. Not that teaching automatically moves in this direction, because we can bring confrontational relationship strategies to the job.  Most teachers are capable of careers that earn more or are essentially easier. Even teachers that leave the field I think have sometimes just finished what they had to give. Some vocations are for a season and some are for a lifetime. (When we lose the lifetime teachers because of school injustices, though, this is a serious loss. Personally and societally.)

Redemption may be strange language for education, but when we think about caring for all our students, it is going to include those wronged by the system or suffering from circumstance. When we work to create a safe learning space, it is naturally redemptive work. When we get to really know our students, it is constructive.

Defeat injustice, not people. This can be difficult, as students act out routines and responses to which which they have been subjected. But the classroom culture building to which I respond does an excellent job of separating the student from behavior.

How does suffering relate? One of the things I try to share with my preservice teachers is to be ready for this, what I often call the heartbreak of teaching.  By caring for our students, we are volunteering to share their burdens. There are going to be students that have difficult, messy and painful lives, and we are signing up to walk part of the way with them. We are opposing the dehumanizing forces in our society that want to use them up or pass them over or sell their share for a profit.

Doesn't "spontaneous, unmotivated, unselfish and creative" describe a lot of the teachers you admire?

I also believe that teaching is inherently hopeful. We are siding with the universe on the side of justice, or our higher power, or whatever gives you faith.

So on this Martin Luther King, Jr. Day, I've taken some time to pray for teachers, pray for their students and pray for my students. I'm going to look for opportunities to stay in the struggle, and support those resisting injustice.  And know that it isn't just for this day.

Friday, January 16, 2015

Moving Negative

Preamble
Wow - I missed a blogging month. And I had so much to say about it... we did Math in Your Feet, some excellent student projects, lots of new lessons, assessment thoughts... So I was thinking about resolving to blog less big, more frequently. Then Sue Van Hattum blogs her #edustory, and I think challenges me and a few others...

I've been thinking about doing more microblogging - and maybe I'll try it. I get stopped by "nobody wants to read that" which makes me forget that I'm writing out my own understanding, so that shouldn't matter. I'm not an author who's trying to please a fan base, I'm a teacher trying to work my way to understanding.

Actual Post
But what's really on my mind is embodied cognition. Last summer I got to try a session with Malke Rosenfeld and Christopher Danielson at TMC14 on Embodied Cognition.  (My account.) Outside of their session, Malke worked with Michael Pershan and Max Ray and others on doing a life size complex plane and number line. I wasn't even a part of that but it got me wondering. Malke and Max have continued to work on the idea, and there is an MTMS article in the works. They were willing to share their writing on that so I could try things in class.

The course is for preservice middle school teachers. I start off with negative numbers (and probably end with negative numbers too if you know what I mean. Where's my Dangerfield font?) because it is a good setting for talking about operations as story and action (exposing them to the CGI structures), and rolling in some content from our preservice elementary classes on fact families and operation strategies, models and landscapes of learning.


For the Cognitively Guided Instruction stories we watched the Kindergartener uses Direct Modeling video from the Heinemann site. Then sorted these stories.  Usually students sort them by operation needed to solve them, but the video was a great focus, because they really did a great job discerning actions. The idea is that young students encountering stories before direct operation instruction classify stories by what's happening in them. Are amounts increasing or decreasing? Are we comparing separate amounts or looking at static groups of different types? They then model and invent strategies that fit the contexts. For example, students who are taught addition first but then have to use it in a decreasing context often have difficulty solving the story problems. (James gave away 3 pencils but still had 5 left. With how many did he start?)

We followed that by brainstorming contexts  for negative numbers: money, debt, bills, weights/balloons, depth/sea level, golf, football yardage, temperature… the usual suspects but a good variety. When we tried writing stories for them, it was challenging to ask the questions in a way that the answer was negative. I nudged them towards the idea that one of the strongest contexts for negative numbers is when the numbers are describing change rather than direct quantities.


Some of the questions from Max and Malke:
  • where she was compared to where she started
  • tell us how far away from someone they were, and in what direction
  • a plan for how everyone could, in a coordinated way, get from their home position to their spot that was the same distance away but in the opposite direction
  • identify if there was someone who was the same distance away from Shane, but in the opposite direction
  • give students a target result and ask them to come up with a series of moves that resulted in the given displacement



We just used stickies to make the numberline. I marked a square as 0 and asked the PSTs to place stickies for 5, 10, 15, -5, 10, -15. First discussion: are we using the squares or the edges in between? (Squares, because of placement of zero.)

Students moved to various numbers on the line, called out by the teacher. Discussion: left right, direction big part of idea of negative. Distance talk, however, is naturally positive.

Then we started modeling change. If a student C walks from A to B: how far did they go? (Positive.) What is the change in their position? (Signed.) We did several iterations of moving in both directions. Discussion: PSTs started noticing how zero figures into the strategies. Frequently found change by b to 0, 0 to c.

PSTs challenged in groups to come up with a question that could be modeled on the line.
  • 1st group: stood at 8, 5 and -3. Class brought up person at 8 could be change: how big a change when walking from -3 to 5. Another said -3 could be how big a change from 8 to 5? Discussion: no way for 5 to be the change in that situation. 
  • Next group of 2 stood at 14 and -7. Their story was: Samantha climbed a 14 foot hill and jumped in the water, sinking to 7 feet below the surface. How far did she dive? Someone brought up 14, and dove 21 feet, where is she? (“Dead”)
Shared Max and Malke’s challenge to come up with a combination that resulted in a net difference. Students proposed 3, 4 and 5 move challenges to get the goal, took the challenge to mean literally standing on the line. Brought up how the challenge could lead to better strategies than counting one space at a time.

End of day 1, informal assessment: was this worth their time? All 4s and 5s on a 0 to 5 finger scale.

Homework: asked them to read one or more of the following: 
Day 2 we set the number line back up and started thinking about how to explicitly model addition and subtraction. The first group shared the idea to face positive: if addition of positive move forward, if subtraction of positive turn back, if negative turn... I raised my opposition to things that just feel like more rules and not connected to ideas. In discussion, the idea was raised to face neutral by default, turn positive to add and negative to sutract, walk forward for positive, walk backward for negative. I brought up how the class deciding this idea for themselves is probably the most valuable part.

Once we had decided on the representation, we got to some exciting stuff. We had students do a walk on the number line. (Start, turn, walk, stop) and then we wrote it down. 5 + -4 = 1. We discussed how non-threatening it was to walk for something like this, and it was a place where you were really free to experiment. When someone brought up different options, 7 - 13 or 7 + -13, we talked about how you can tell and was there really a difference. Then we hit on the idea that you could walk out equivalences. Are these two things equal? Let's try them! Someone had the idea to try commutativity. What would associativity look like? (Hard to walk.) There was an interesting side effect: some common student errors are impossible to walk. They just don't make sense in embodied cognition land



I brought a game idea, of course. Take a deck of cards, remove everything but A to 7, red is negative and black is positive.  Shuffle, deal two decks, like for War. Both players start at zero, facing each other. Flip the top card of your deck. Player with the smaller magnitude number goes first. You can add your number to yourself or subtract it from your opponent. The first player's move decides whether they are going positive or negative, and the 2nd player is going the other way. The goal is to get off the number line. (Ours went to +15 and -15.)

Sample turn:
  • player Positive is at 2 and flips red 6. Negative is at -3 and flips red 2. 
  • Smaller magnitude goes first, so Negative adds -2 to their position. 
  • Faces positive and walks back two squares to -5. Positive player doesn't want to add -6, so makes Negative subtract. Negative faces negative, then walks backward 6 squares to 1.
In the picture there are two different games going on. Other students tried the game or modeling stories with a chip model. People liked the game pretty well with the numberline, and got them a lot of practice thinking about adding and subtracting positive and negative, as well as use on the numberline.

Day 3 involved no embodied cognition. We discussed fact families and addition and subtraction strategies, and then discussed how to show a variety of strategies for integer addition and subtraction in symbolic records and in number lines. The number lines really showed the benefit of the previous classes' movement as they felt the directions really made sense.







All in all, great start to the year. I've only become more convinced of the need for more opportunities to embody mathematics, and the value of the intuition that this helps build through experience. And, of course, I'm interested in your stories about this, or ideas for what else you might have tried.






Friday, November 14, 2014

Fall 14 - Book Club

In my senior capstone history of mathematics class, I had had good luck with having students choose books to read and then sharing and swapping. (Previous post.) I thought it might be worth trying with my preservice elementary teachers, who in the past would all read one book. Currently, if I was picking just one it would be Boaler's. No more than 5 per book; choices included:
  • Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement, Steven Leinwand, (Amazon) [Practical, pre-service teacher approved)] (3)
  • Intentional Talk: How to Structure and Lead Productive Mathematical Discussions, Kazemi & Hintz, (Amazon) [Applies to more than math; good support for helping students learn to converse productively] (2)
  • Making Sense: Teaching and Learning Mathematics with Understanding, Carpenter, Fennema, Fuson, Hiebert, Murray & Wearne (Amazon) [Writers and researchers of the best elementary math curricula around tell what they think is important.] (FULL)
  • Math Exchanges: Guiding Young Mathematicians in Small Group Meetings, Kassia Omohundro Wedekind, (Amazon) [Similar to intentional talk, more strongly based in literacy routines.]
  • Math for Smarty Pants, Marilyn Burns (Amazon) [Collection of entertaining problems across all kinds of math from a master math teacher.] (FULL)
  • A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form, Paul Lockhart (Amazon) [Not sure about putting this on. Many readers are disappointed in the 2nd part, but the 1st part people see as a powerful argument for why math teaching has to change.] (FULL)
  • Powerful Problem Solving, Max Ray (Amazon) [New book from a very deep thinker about how to teach math.]
  • What's Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject, Jo Boaler (Amazon) [If I was picking one book for everybody this would be it. Dr. Boaler is doing a lot to research and shares how to make math better.] (FULL)
I was disappointed no one chose Kassia's or Max's great books - there was a bit of a follow the leader effect in choosing books. 

What follows is a poor transcript of the group discussion. On book club day, I ask students to bring in enough snacks for four people. They start in small groups with people who read the same book, then we have a discussion circle where each group shares and fields questions and I try to keep my mouth shut unless asked a direct question. (Group questions in italics.)


What's Math Got to Do With It? Jo Boaler
Anyone else hear Tina Turner
when they see this book?
I rated this book as must read, because it talks about what we grew up with, and what we should do. Connected with this class really well, and I’ve never had a class like this. The other way separates you by ability, makes the kids feel dumb or come to hate math. So then in life later, they can’t even think about careers that use them. “I wasn’t good at it I didn’t like it.”
Any specific lessons? Talked about research on the effects of this.
Also had kid perspective.
Did it address grading? Not as much as they could have. Did talk about what doesn’t work with tests and encouraged smaller assessments that aren’t a big deal. 



From Mark Bennet's visual reading notes
A Mathematician's Lament, Paul Lockhart Our book talked about teaching styles, too. His big point was that math is an art. Example: triangle area and formula. By giving problem and answer in one you’re cheating the kids. 2nd part was all about how he loves math. Redundant or over my head.
Students need to get to play around with it. Example of art class, where students aren’t told how to do each brush stroke. I like that, but 
It wasn’t very practical. We don’t have time to have each kid discover the area of a triangle. It really connected with me how I was taught. My high school geometry… my face got red as I read. 
Any solution at all? Really, no.
Also not fair to teachers to blame them entirely. Brought up issues, just wish there was more solution. I liked the book but kinda hated it. 
Was he a teacher? Sort of… 

How is he teaching?
Lockhart says, 'I want to know what you think of this. If you’re a student I send my condolences. Ignore the absurdity you’re taught in your math class.' 
You can’t be a teacher and tell students to ignore their teachers. I hated math, ignored my teacher, and got switched to a slower class - it didn’t work.
Kind of puts himself on a pedestal. 
Talked about textbooks, and how math is stuck in the 19th century. We can’t get out of it because then schools adopt these books. You read that, get fired up, but then what do you want to do. 

Talking Heads
(obviously)
Making Sense, by Fennema, Carpenter,  Fuson, Hiebert, Murray, Wearne  
We want to teach all students so that they make sense of mathematics. 5 dimensions. How to communicate teacher to student.
The book was helpful, set up logically, good examples of classrooms, but then repetitive. Everyone should read the first chapter, and then read more about one dimension.
At the end, giving examples of classrooms in different modes. But just stories - a detailed description would be better. Got tedious, chapters 7-10 were repetitive. Nice, but can’t tell the difference between some of them. Did tell how each related to topics in chapters 2-6. 
It was good. 

Intentional Talk, Hintz and Kazemi

Sets up different strategies, open discussion, targeted, gave strategies to assess and fix discussions. The examples were actual dialogues. Then they looked back and identified, here she was identifying goals, here she was introducing math ideas. Good strategies on how to make the classroom safe for discussion. The ideas and participation of all students are valued. So even wrong answers, it gave you lots of ways to use that and build from it. 
The book showed how you plan discussions. Gave a template, helped you think about how to plan it before, going from what you think they are going to say. 
I gave it a 5 because it was really helpful, I want to reread before I student teach. You wanted to take notes as you were reading.
Open strategy sharing. Like kids giving different ways to multiply, we need to think about different strategies so everyone has a way to learn.
That’s like at Family Math, we have 5 pizzas with 4 pepperonis. What’s a math problem like that? “Well we have 5 groups of 4…” I never thought about it that way when I was kid.
They give you talk moves, so you have ways to move it forward. 

Smarty Pants, by Marilyn Burns
On Etsy.
Our book was not about how to teach. It was just problems. Different kind of problems.  Listening to other people talk - I didn’t get that much out of this one. It was interesting, and fun to read through, but you don’t get a lot out of it except different kind of problems. 
Each part has a ton of new problems and cartoons.
Parents could use it as a supplement. 
My sister doesn’t know my nephews math, he’s like 14. They call me… could parents use that to practice.
This is younger, but more about abstract thinking. They got me thinking, but it doesn’t explain why it works out.
How do they take into account kids who are not ready for abstract thinking. They have specifics to do in the problem, but then it abstracts…
It is literally just a book of problems. I liked it. It was interesting. I enjoyed reading it.
Would it show them how to teach, like addition? There was a section on tricks to multiply, but it was just hints and different strategies.
It reminds me of problems of the week. I used to get my family doing them.
Even the answers were hard - upside down and backward. 

Accessible Mathematics, by Steve Leinwand
We played his Ignite on
"It's Instruction, Stupid!"
afterwards, so they could read in his voice.
This gives what’s wrong with math and gives different positive approaches. 
I really liked it. So straightforward, 10 shifts to do. Emphasizes how to always be asking questions. I’d recommend reading it. So practical, check homework more effective, using problems of the day. 

(Not much discussion, but a lot of interest in reading it afterwards.)

Their Summary My questions for them for the summary.

What would you like to read?
I’d want to read Accessible Mathematics. Like music ed, know the beats as a pattern… that’s doing math.
I’d want to read intentional Talk, because of good ways to get you to get students thinking. For teachers that are just starting out, it has very practical.
What’s Math Got to Do With It - practical, actual ways to teach.
Smarty Pants - I want to see the activities. How could you incorporate them into the classroom.
Variety or one book? Variety!  
Assigned or pick your own? 
Choice! Now we know multiple books, which one connects, time thing. 
We get to focus on one book, get more in depth, get to borrow.

My Summary
This worked out well.  I'm going to do it again, and try it in more classes. They did a nice job with this summary day, and I was convinced of their interest and investment.

I ask them to make a reading plan once books are chosen, with the end date in mind. I ask them to keep reading notes, for accountability and retention, that include a summary and a response to each session of reading. I don't grade those, but just check when done. I emphasize this as a rough draft of doing book studies as teachers, and like that we're arming them with some different book choices for those future book clubs. 

Thursday, November 13, 2014

Array Maker 9000

This is probably a stupid little post.

The other day I was making some math games, and I needed a rectangular array for a board. As one often does. So I made a quick GeoGebra sketch. And rather than make it so it only made one board, I made sliders so that it could make any rectangular board. Of course sometimes you'd have to zoom out to see the whole thing. A little clunky.

Then Tim Cieplowski (the BGU prof with the beautiful GeoGebra stuff) tweets:

Which makes me feel like I should do a proper job.

One of the things I love about GeoGebra is that you can make the window dynamic, so that it automatically fits what you want to show.

The problem with doing the array is that fitting it to the window will make it non-square and change the game board. So here's my workaround.



The array is just a ratio to compare a window of array plus a border of .5 to the actual graphics window. Corner[1] is the lower left corner around counter-clockwise to the upper left Corner[4]; those are helpful for making things that go right to the edge. Corner[5] gives the (width, height) in pixels of the graphics window. (You can even ask for Corner[2,5] if you have the second graphics window.) So these definitions make the window fit the height if that is taller than the width is wide, relative to the window.

Bonus: this is the closest I have come to doing the Border problem in real life. (Which is so well known that it comes up ahead of immigration stories, even.)

Here's the sketch on GeoGebraTube.

Can you think of a quicker or more elegant way to do this?


Thursday, October 23, 2014

Percy Jackson's Math Class

[I haven't written this post yet, and I know it's going to be more rambly than usual. Fair warning.]

My eldest child has been a big fan of Percy Jackson. Me, too, to be honest. I'm reading The Blood of Olympus now. The first Percy Jackson series is one of the few non-graphic novels my son read by choice. So this was a natural click for me: The Percy Jackson Problem at the New Yorker by Rebecca Mead.

It begins with a quote from Neil Gaiman (another family favorite):
“I don’t think there is such a thing as a bad book for children,” he argued, adding that it was “snobbery and … foolishness” to suggest that a certain author or particular genre might be a baleful influence upon young reading minds—be it comic books or the works of R. L. Stine. Fiction is a “gateway drug” to reading, Gaiman said. “Every child is different. They can find the stories they need to, and they bring themselves to stories. A hackneyed, worn-out idea isn’t hackneyed and worn out to them.” Well-meaning adults, he continued, can easily kill a child’s love of reading: “Stop them reading what they enjoy, or give them worthy-but-dull books that you like, the 21st-century equivalents of Victorian ‘improving’ literature. You’ll wind up with a generation convinced that reading is uncool and worse, unpleasant.”
If you're a math teacher, how can you read this and not connect? We've been feeding students, as a profession, "worthy-but-dull" math for ages. (Worthy when it was good, that is. When it was bad, we're talking Tartarus.)

The author's argument is the counter to this idea that all reading is good.
Riordan’s books prompt an uneasy interrogation of the premise underlying the “so long as they’re reading” side of the debate—at least among those of us who want to share Neil Gaiman’s optimistic view that all reading is good reading, and yet find ourselves by disposition closer to the Tim Parks end of the spectrum, worried that those books on our children’s shelves that offer easy gratification are crowding out the different pleasures that may be offered by less grabby volumes.
I don't like this argument for reading. But I have made similar arguments in math. After a steady diet of exercises, students have no interest in problems.

But I think what I mean is that students have no experience with problems. The engagement that comes from finding a really meaty one. The question is whether reading Percy Jackson is really reading. I would argue that spending time on Tumblr is not reading (a current teenager discussion), and wonder if graphic novels are reading. (Aforementioned comic-obsessed son.)

I think this is an issue K-12. In elementary, there is a danger that teachers don't believe that students can do real problems. In high school, a desire to have the students do the basics first. Working with preservice and inservice teachers I try to stress and give experience with contexts that are problematic, but accessible. If it's not a problem, it's not doing math, no matter how many numbers and operations are involved.

Just being letters and words doesn't make it reading?

The author isn't so concerned with the Percy Jackson books, as with the forthcoming book of Greek myths as told by Riordan, writing in Percy's voice.
While the D’Aulaires wrote that “Persephone grew up on Olympus and her gay laughter rang through the brilliant halls,” Percy’s introduction to the story of Demeter’s daughter reads, “I have to be honest. I never understood what made Persephone such a big deal. I mean, for a girl who almost destroyed the universe, she seems kind of meh.”
It seems to me that this is some of what the common core struggle is about. Parents don't recognize newer curricula as math. (Which, of course, really has nothing to do with the common core in most cases; the Common Core gave them something to be against.)

The author closes with this concern:
What if instead of urging them on to more challenging adventures on other, potentially perilous literary shores, it makes young readers hungry only for more of the palatable same? There’s a myth that could serve as an illustration here. I’m sure my son can remind me which one.
Ooh, clever. I'm sure she knows which myth. What if after doing Desmos and Three Acts investigations, students don't want to do hackneyed word problems from the end of the chapter? That's probably not fair. Will they not be interested in the real problems of calculus, geometry, analysis and algebra? I think if we had a Percy Jackson parallel in math, the greater numbers of young people interested in math would mean a boom in STEM fields. The Percy Jackson problem? We should all have such problems.

This post started when I discovered no way to comment on the article. Because I wanted to share my daughter's response. And I want to think of this in terms of math, too. Here's Ysabela:
If they were arguing against, like, Twilight, where the language use is bad because the author has no writing experience, AND the plot and ideas are unoriginal/problematic, then I would agree with them. When Twilight becomes people's standard for literature, they start accepting total crap without a second glance, which is bad.
But Riordan understands language? And his plots (at least in the original series) were good? I'm not saying it was Harry Potter, but Percy Jackson was quality, and saying it wasn't just because the language is accessible to people who aren't scholars is just... really elitist. Like I know a lot of people who find reading really, really hard, but were able to enjoy Percy Jackson because it actually made sense to them. Plus, the series was narrated by a teenage boy, it was realistic.
And don't even get me STARTED on the D'Aulaires, they're SO AWFUL. They watered down the myths so much they were almost unrecognizable, "for kids," and then wrote it at like a college reading level. Plus they organized it like total tools. I can't express in words how much I would have rather had a Riordan book of myths than the D'Aulaires when I was younger.
Hello Katie @ Society 6
As she steps out the door now, she's railing against having spent two weeks on factoring. Because the last day before the mini fall break they learned the quadratic formula. "And it always works!" Do you know why it works? "He showed us from \(ax^2+bx+c\). It's extra credit on the test." How much more dangerous is it that she believes math is that pointless and uninteresting?

So, I think I'll side with Neil Gaiman on this one.

Saturday, October 18, 2014

Such a Thing as Free


A friend found his new-to-him school in need of Algebra I and Geometry textbooks - for cheap or free. I took the Twitters, and people responded quickly and generously. Thought I should collect their suggestions.

Free Curricula
My first suggestion was Geoff Krall's (@emergentmath) Problem Based Learning maps. Amazing work. It's a worklife dream to develop a collaborative site like this where we could all link our best lessons and do some informal lesson study.

My second suggestion was Illustrative Mathematics, Algebra and Geometry (plus everything else).

Then #mtbos hit the gas:
  • David Coffey (@delta_dc) reminded me of the Georgia Common Core Materials.
    When he wasn't Khan-baiting.
    This is where I would start. Very complete, a lot of excellent lessons and compatible web resources, even including 3 Act structure stuff. 
  •  Bridget Dunbar (@BridgetDunbar)  ·  out of Utah: Mathematics Vision Project.  They follow integrated sequence...but good materials.
  • Engage NY, Algebra and Geometry (but complete K-12, math and ELA).
    Inconsistent quality to me, but a lot of good stuff and assessments are there, too.
    Lisa Bejarano (@lisabej_manitou) recommended one of these two.
    Dan Anderson (@dandersod) noted it, but does not love it.
  •  Macomb ISD Math (@MISDMath)  ·  have you looked at the EMATHS materials?
    That's the online materials for Michigan's virtual schools. New to me.  Looks thorough, with PD materials, lesson plans, activities-based and assessments.
  • @geonz  shared Algebra2go. Early, online algebra curriculum with videos and homework.
Other Ideas
  • Peg Cagle (@pegcagle)  suggested: Visit Abebooks for old Key Curriculum Press materials-brilliant rigorous & coherent-a bargain at full price, now available for a few bucks.
    I noticed some IMP stuff there. Love IMP.
  • Justin Lanier (@j_lanier)  ·  There are the Exeter and Park School problem sets, which are freely available.
    At Exeter they have been problem-based for a long time, in 12 student classes. Read more about their Harkness method.
    The Park School curriculum is available on request, but you may have to nag them.
  • Raymond Johnson (@MathEdnet)  ·  Not as cheap as they used to be, but College Prepatory Mathematics is worth considering.
    Samples here; those are good stuff.
I also let him know about the single serving sites:
That list lives on my Reading Recommendations page. I also put in a plug for GeoGebra (of course).

If you have experience with any of these things, or know of other resources, please list them in the comments. And thanks to everybody who responded or retweeted.