I had the pleasure of attending the NCTM regional meeting in Nashville this week. I learned some cool stuff that I'm still processing, and I got to do a presentation. In the presentation I tried to explore whether the way I would rewrite and rework lessons when I was a high school teacher can be generalized and communicated to other people. I was, I think, marginally successful.

NCTM is trying this cool pilot where participants can engage with presenters after the conference. So instead of sharing stuff about my presentation here, I'm going to send you over to the presentation page on their site.

# f(t)

## Alert!

**Hello, reader! If you intend to post a link to this blog on Twitter, be aware that for utterly mysterious reasons, Twitter thinks this blog is spam, and will prevent you from linking to it. Here's a workaround: change the .com in the address to .ca. I call it the "Maple Leaf Loophole." And thanks for sharing!**## Saturday, November 21, 2015

## Friday, October 2, 2015

### Friday Favorites 7

Happy Friday! (It's really Saturday but I'm going to backdate this post and pretend it's Friday. Ha! Technology!) My reading and favoriting has slowed down because I have made the decision to limit my Twitter time, which is exceptionally mature of me, I think. (Using Stay Focusd, which is a chrome plugin that yells at you for not working. It's brilliant.) What I'm mostly doing these days is a zillion math problems, which is pretty fun, actually... You know how when professional chefs see a bag of onions, they get excited because they get to chop a bag of onions? That's how I feel about doing a bunch of math problems. It's a little bit drudgery, but satisfying. Still and all, when something gets a little mentally difficult it can't be too easy to distract myself. Twitter needs to not be an option in those moments.

This is not a favorite because I made it myself, but it's public, so I might as well share it. It's a place to stash mathematically interesting artifacts that I might turn into tasks or assessment questions or lessons. There's nothing worse than needing to write a question in a context and googling for hours. You're welcome, future Kate.

Now here are real favorites:

This is not a favorite because I made it myself, but it's public, so I might as well share it. It's a place to stash mathematically interesting artifacts that I might turn into tasks or assessment questions or lessons. There's nothing worse than needing to write a question in a context and googling for hours. You're welcome, future Kate.

Now here are real favorites:

#### Capture Recapture with Goldfish

I did this lab in an Algebra 1 class ages ago. It reminds me of that illustration of statistics vs probability: If you know what's in the bag, reach in and grab a handful, and want to predict what's in your hand, that's probability. If you*don't*know what's in the bag, reach in and grab a handful, and use the handful to predict what's in the bag, that's statistics. It's a good activity, but my first or second year teacher self probably didn't do such a great job with it. Because, obviously, I didn't have Elizabeth and Julie's helpful writeups. I like the way Elizabeth frames how it fits into a bigger Algebra 1 picture. I could also see using it in a stats lab in a way that emphasizes sampling and sample proportions just as easily as a 7th grade-ish solving proportions lab.#### Problematizing Geometry Constructions

I love everything about this. Using a popsicle stick as a straight edge: pro move.#### How Parents and Students and Teachers Can Work Better Together

...is a better headline than the clickbaitey one they gave this article. Which is empathetic and treats everyone involved as a professional and a human. Forward anonymously to those parents whose first move is calling the Principal.#### Michigan's Teaching and Learning Exploratory

Don't let the boring name fool you - Michigan has done an awesome thing here by posting hours and hours of unedited classroom footage. I learned in the last chapter of Why Don't Students Like School? that looking at video of yourself or someone you know is too scary a place to start, and it's easier to watch and practice constructively critiquing someone you don't know. This resource makes that a whole lot easier.## Thursday, October 1, 2015

### Every Bit of This

Link

High schools focus on elementary applications of advanced mathematics whereas most people really make more use of sophisticated applications of elementary mathematics. … Many who master high school mathematics cannot think clearly about percentages or ratios.

## Wednesday, September 30, 2015

### Exponential Functions and also Area of a Triangle

That title is confusing, right? I know! I just wanted to alert y'all to some tasks that recently went up on Illustrative Mathematics that might address some of your needs, if you are teaching these things.

**Exponential Functions**: These tasks involve negative exponents in a functional relationship in a context and are aligned with F-LE.

- Decaying Dice (It's like the penny lab for modeling half-life that kids often do in Earth Science... except with dice.)
- Predicting the Past (Making sense of negative integers in the domain of a simple exponential growth function.)
- All Your Base are Belong to Us (Exponential decay and negative exponents, together at last. Bonus points if you get the reference.)
- DDT-Cay (Interpreting the exponent in a half-life equation.)

**Area**: These are meant to be used to build understanding as you're working toward a formula for area of a triangle in sixth grade (6-G.1). But they could be useful to reactivate knowledge at the beginning of a study of area in a later Geometry course.

- 24 Unit Squares (To remind kids what area means and stymie their attempts to use formulas they don't understand.)
- Areas of Right Triangles (Depending on how you approach area of any triangle, this might be a necessary precursor.)
- Areas of Special Quadrilaterals (Emphasizes decomposition into familiar figures.)

And, hey, it is non-trivial for me to test stuff out with kids these days, so if YOU try them out and you notice stuff or have suggestions, you can comment here or better yet, right on the task on the IM site. (Please let me know if you do that - I don't think I get a notification. And thanks!)

I did draft the initial versions but I can't take credit for these. Tasks published on IM are very much a team effort. Many thanks to Ashli Black who is an ace reviewer and helped me make these a ton better.

## Friday, August 28, 2015

### Friday Favorites 6

Happy Friday! I am elbows deep in Trello, of all things, but the cat is good company. Here we go...

I took a stab at Activity Builder with an activity that deals with discovering pi and thinking of circumference vs diameter as a proportional relationship. And wow, it's so much better because of their Twitter interaction. I don't know if my favorite part is setting a table to make points draggable only vertically, or their suggestion to share Teacher Notes in a linked google document.

In case you haven't heard, there's also a repository of user-created Desmos activities here. Mileage may vary.

In case you haven't heard, there's also a repository of user-created Desmos activities here. Mileage may vary.

#### All the Math Talking Points

Are in this shared google folder. If you haven't grokked the magic of Talking Points yet, go read you some cheesemonkey wonders.

#### OER Curricula and Curricular Outlines

In case I haven't talked your ear off about it yet, I'm of the strong opinion that a school's math department should Decide on a Coherent Curriculum and riff off of that, rather than expecting their teachers to create a curriculum on the fly using random resources they find on the Internet. Some textbook series are good, and there are also decent OER (Open Educational Resource) ones are already out there, and too many people don't know about them.

- New Visions for Public Schools (High School)
- Carnegie Learning (Middle School)
- BMGF Mathematics Design Collaborative (Middle and High School)

#### This Coaching Model

Where your team gets a Teacher Partner - someone who teaches a few classes but also coordinates your collaborative teacher learning. I love this.

I might be a little obsessed with other people's planning documents.

I might be a little obsessed with other people's planning documents.

#### Icebreakers That Won't Make you Cringe

#### John's Exhaustive Tour of the Good Stuff

Where do I start? Here.

## Wednesday, August 19, 2015

### And Then There Was Not Teaching Some More

Waddup, nerds. Just a quick note about what is going on around here, which is that I've joined forces with Illustrative Mathematics to do some very exciting curriculum work. I'll keep y'all posted here as I am able.

Practically that means it's not a new school year for me, which sucks, because I love the first day of school. There's something so inspiring about a fresh start. And also because there won't be as much to report here.

But it also means I work at home, which, I'm not going to lie, is pretty boss. I can get all the work done with a cat in my lap and also throw in a load of laundry and also prepare real food for dinner.

My rig. I realize the television is dominant in this photo, but I haven't actually turned it on yet. It's just extra. That fridge is full of fizzy water. |

I'm around, on the Internet, of course, and I want to keep doing the Friday Favorite thing. You are welcome to yell at me when I slack off.

## Friday, July 24, 2015

### Friday Favorites 5

Happy TMC, everybody! I know all the TMC-ers are busy TMC-ing right now, but it's Friday! Here we go...

#### John's MTBOS search engine

What a good idea. I don't know how I missed this.#### Tracy's Proof Games

Here at camp there's a "Games and Strategies" class running this week, and kids keep running up to staff proposing games like "We start at zero, take turns adding 1, 2, or 3, first one to 19 loses." These are kind of addicting, is what I'm saying, and motivate and "Support Generalizing, Conjecturing, Strategy, and Proof-Like Reasoning," as the title suggests. And here are a zillion of them in one document!

#### I Am Not Tom Brady

Just putting this out as a public service announcement that schools that pull shit like this exist, so you can walk away quickly if you get a whiff of it in an interview. h/t Lani for the share.

#### Cathy's Write-up of a 17-Armed Spiral

Here's some recreational math for you, in the spirit of math camp.

#### Shelli's Teacher Binder

Back in the days of student-ing, my life was all about my paper organizer. I had very specific requirements and shopped and shopped until I found it. These days I'm a more scattered leaving-digital-detritus-in-my-wake kind of organizer, but this makes me think maybe it's not too late.

#### Look How Pretty

The #mathphoto15 Flickr stream.

## Friday, July 17, 2015

### Summer Problem-Solving Course

This summer I have the privilege of teaching a problem solving class to mathematically-inclined rising eighth graders. The course is called Math Team Strategies because a big goal is to get kids more ready for contests like MATHCOUNTS and the AMC contests. But we are also looking to highlight problem solving strategies that are broadly useful, whether kids decide to participate in contests or not.

I'm going to make this post pretty nuts and bolts just the facts ma'am - it's the nitty gritty details for people who want the ideas.

I lovingly plucked from the work of, and want to give tons of credit to:

All the students worked on the same problem at the same time, standing at chalkboards. I had anywhere from 6 to 12 students in a class, so this was manageable. I also had a TA who was a math-major undergrad. Nirvana. Before I left home I grabbed a handful of fridge magnets, thinking they might be useful for something, and we used them so students could stick the current problem to the chalkboard.

Also, of course, some students finished more quickly than the group. I also tend to always make the same suggestions when students say they are "done," so I made this poster for them, too.

Questions, feel free to throw them in the comments.

I'm going to make this post pretty nuts and bolts just the facts ma'am - it's the nitty gritty details for people who want the ideas.

I lovingly plucked from the work of, and want to give tons of credit to:

- Matt Weber, who is teaching this same course at this program's other site
*Crossing the River with Dogs*by Johnson, Herr and Kysh [Amazon Google Books]- MATHCOUNTS Past Competitions and School Handbook

## Pacing

Eight days, two hours a day, one focus strategy per day. On the final day, instead of a new strategy, students experience a somewhat-complete MATHCOUNTS contest.## The Strategies

(Most of these are chapter titles in*Crossing the River with Dogs*- but that book has many, many more chapters. It's awesome. You should check it out.)## The Lesson Flow

For each day, I selected problems that lent themselves to that day's strategy. Some problems are from*Crossing the River*, some are from old MATHCOUNTS contests, and some I made up. Additionally, we developed a few mathematical shortcuts over the course of a few days, like counting permutations with repetition and the length of a diagonal of a square. I cut the problems up onto slips, so students would only have one problem at a time. (For a longer course, or perhaps for older students, I'd probably elect to use*Crossing the River*as a text.)All the students worked on the same problem at the same time, standing at chalkboards. I had anywhere from 6 to 12 students in a class, so this was manageable. I also had a TA who was a math-major undergrad. Nirvana. Before I left home I grabbed a handful of fridge magnets, thinking they might be useful for something, and we used them so students could stick the current problem to the chalkboard.

## The Posters

The intention was for the whole class to go over each problem before everyone started the next one. (See this post about group discussions.) Of course, some students took longer and needed support. When I am helping, I tend to make the same suggestions and ask the same questions over and over. This poster was for students to refer to if both the TA and I were busy when they got stuck.Also, of course, some students finished more quickly than the group. I also tend to always make the same suggestions when students say they are "done," so I made this poster for them, too.

## The Self-Assessment

Before we went over each problem, I asked the students to turn in their problem slip with their name and a rating of the problem from 1 through 4. I did compile this data in a spreadsheet, but I'm not sure what to do with it. But I thought the self-assessment couldn't hurt.

## The Resources

Will be here until someone holding a copyright yells at me to take them down. Or maybe this is fair use. I dunno. I hope it's good advertising for the publications cited above. Some of the problems turned out to be too easy, and I'll be changing them if I'm back next year. Some were too hard, but I thought it was okay to give kids at most one problem a day that was a big stretch for them. When that happened, I invited the TA to share their solution.## And That's about That

This was a really rewarding course. The kids loved it, I loved it, we all just had a grand old time talking about math for two hours a day! It was refreshing to not feel pressure to cover content at a breakneck speed, or sell kids on math (these kids already like math), or have to assign grades. (This morning when we did a sample MATHCOUNTS Sprint, a girl asked "Does this count? Oh, wait. We don't have grades." And she worked hard on it anyway.)Questions, feel free to throw them in the comments.

### Friday Favorites 4

It's the second week of Math Camp... that means I have a little time to post. Yay! Things are still a tad chaotic here - long days, tween drama, field trips, little sleep, etc etc, but I finally have the class I'm teaching all planned out through the end of this week. Phew! Time to write and reflect and observe some great teachers in action.

Also I taught some 13 year old boys how to juggle yesterday. Before I signed up for that duty, I did not consider how many times I would have to say the word "balls." The first time was awkward, but then we naturally took it to a ridiculous extreme. "MALACHI! CONTROL YOUR BALLS!" (Normally I wouldn't post photos of student faces, but this one is on the program's website.)

And now for some fresh faves...

Also I taught some 13 year old boys how to juggle yesterday. Before I signed up for that duty, I did not consider how many times I would have to say the word "balls." The first time was awkward, but then we naturally took it to a ridiculous extreme. "MALACHI! CONTROL YOUR BALLS!" (Normally I wouldn't post photos of student faces, but this one is on the program's website.)

And now for some fresh faves...

#### Megan's Easy Way to Start Blogging

Although it's really valuable professional learning for lots of people, keeping up a blog during the school year can be a daunting proposition. An on-ramp can be a 180 blog - just take and publish one photo a day from your classroom. This practice has less overhead in terms of time, but gets you in the habit of noticing things to share. This recent post by Megan Hayes-Golding suggests one way to set this up using Instagram, IFTTT, and Wordpress to make it low friction so that you are more likely to stick with it. If you're unfamiliar with those platforms, don't worry - they are all pretty easy to get started. You could have this up and running in a few hours if you're new to it (a few minutes if you're not). Also, IFTTT works with lots of different services.#### Dylan Builds His Intuition

Dylan Kane has been chronicling his growth as an early-career teacher. If you haven't been following along, you should plug into that. I really enjoyed his post about the ways he has to be attentive to avoiding pitfalls of bias and developing intuition that will be productive in his practice, because they paralleled some of the things I realized along the way (although he has articulated them much better).#### Meg Encourages MTBoS Users to Make It Work for Them

Much as I love our spirited army of awesome, folks can get a tad dogmatic and judgey from time to time. It can be a turn-off, when you come across some strident prose that makes you feel like you're doing everything wrong. Meg Craig's post speaks to two audiences: seekers of resources and conversations, who are reminded to stick with it and make it work for them. Also sharers of resources and initiators of conversations, who she gently offers ways to phrase your sharing so that it's a bit more inviting and inclusive.#### Dan Meyer is going to fix NCTM for Us

Here's how. Thanks, Dan. (Adding some clarification here because I'm afraid this sounded snarky - I'm totally sincere. I'm really excited about the prospect of NCTM taking up the recommendations of the ShadowCon organizers. I think we all of us NCTM members realize that NCTM is not working well for many members and prospective members, and I wholly support these concrete proposals.)#### Please Review Our Book

Have you read Playing with Math? Are you going to? (You should! It's so awesome.) It's on Amazon now, and it would be great to get some more reviews. (Since I wrote one of the essays I'm ambivalent about writing one myself.)## Wednesday, July 15, 2015

### A Magical Incantation

So this week I'm basically the luckiest girl in the world, because Ben Blum-Smith is on staff at SPMPS, and he observed me teach and then we had a conversation about it. (I know. Be jealous.)

He offered a concrete suggestion enabling student dialog which I want to share. I am pretty good at getting kids to talk to each other about math in pairs or triples...

but I've always struggled with conducting good conversations with the whole group -- getting kids to talk to each other about math

What we have been doing in this class is having everyone work out solutions to a task on the board. (Classes are small enough (7-11 for my classes), I've partaken of the vertical-non-permanent-surfaces kool aid, and kids at camp are exhausted because it's a three week slumber party, so keeping them on their feet helps with the awakeness.)

When everyone is done-ish, we gather around someone's solution and they walk us through it.

So let's say that a student presents her solution or approach to a task to the whole group. Generally they speak too fast, and gloss over important bits. When they are finished, I have uncovered many, many unproductive questions to ask the rest of the class:

But here is the magical incantation that can pick this lock:

This is a lovely question. I tried it out at every available opportunity today. Interpreting another student's written and verbal solution requires all kinds of nice cognitive work. I imagine that as kids come to expect that they might be asked this question, they're more likely to be more attentive to others' explanations. And, it offers a nonthreatening invitation into the conversation where a student is immediately clear on what she's expected to say.

Ben mentioned that he didn't really grok the power of this move until well into his classroom experience, and I think I'm kind of in the same boat. I'm sure I've heard of it before, but now I'm in a place where I can really deploy it surgically. Well I mean today I deployed it in kind of carpet bomb fashion. It's like a new toy I can't put down. But I'm going to enjoy the process of integrating it.

He offered a concrete suggestion enabling student dialog which I want to share. I am pretty good at getting kids to talk to each other about math in pairs or triples...

but I've always struggled with conducting good conversations with the whole group -- getting kids to talk to each other about math

*in front of everybody*. (Aside from the two kids in every class who always raise their hand for everything.)What we have been doing in this class is having everyone work out solutions to a task on the board. (Classes are small enough (7-11 for my classes), I've partaken of the vertical-non-permanent-surfaces kool aid, and kids at camp are exhausted because it's a three week slumber party, so keeping them on their feet helps with the awakeness.)

When everyone is done-ish, we gather around someone's solution and they walk us through it.

So let's say that a student presents her solution or approach to a task to the whole group. Generally they speak too fast, and gloss over important bits. When they are finished, I have uncovered many, many unproductive questions to ask the rest of the class:

- Does anyone have any questions for Bianca? (crickets)
- Miguel, what do you think of Bianca's solution? ("I don't know. It's fine.")
- Does anyone have anything to add? (more crickets)
- Did anyone approach it a different way? (Actually I never ask this anymore, because I pick usually two students with different approaches to present.)

But here is the magical incantation that can pick this lock:

*Hey, so-and-so, would you explain your understanding of Bianca's solution?*

This is a lovely question. I tried it out at every available opportunity today. Interpreting another student's written and verbal solution requires all kinds of nice cognitive work. I imagine that as kids come to expect that they might be asked this question, they're more likely to be more attentive to others' explanations. And, it offers a nonthreatening invitation into the conversation where a student is immediately clear on what she's expected to say.

Ben mentioned that he didn't really grok the power of this move until well into his classroom experience, and I think I'm kind of in the same boat. I'm sure I've heard of it before, but now I'm in a place where I can really deploy it surgically. Well I mean today I deployed it in kind of carpet bomb fashion. It's like a new toy I can't put down. But I'm going to enjoy the process of integrating it.

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