NCTM Workshop

The title of my 2014 NCTM talk was Further Beyond Sudoku: Using Logic Puzzles to Develop Mathematical Reasoning.

Da Slides. (this might make sense on its own)

Da Handout. (this will make zero sense on its own)

In my presentation I talked about the CCSS-Mathematical Practices and how they relate to the idea of mathematical reasoning and the writing of proofs. We looked at three examples of logic puzzles: Yajilin, Slitherlink, and a classic word-based logic puzzle. I  also developed and discussed a three-part framework for the stages of developing a mathematical argument:

  1. How do you know what to do?
  2. How do you record your thinking?
  3. How do you convince your peers?

I also laid this framework over Avery’s “The Life-Cycle of Mathematics” as a way of referencing the fact that each step was more complex than one question could contain. And, yes, I gave the full-disclaimer about using my husband’s work in my talk. Thank yew very much.

Overall, I think my talk went really smoothly. There is always a little balancing act you have to play in workshop-style talks with regard to pacing and I think I did okay with that. Most people probably would have liked more time to work on the puzzles, but I chose to move ahead so that I could finish my talk and get a little bit of time on all three puzzles. I think the variety of puzzles was pretty solid–though the first two were pretty similar to one another–giving participants a chance to try something new (or new-ish) and to do something a little more familiar as well.

I have discovered that getting participants to do more than just attempt to solve the puzzles is really challenging. This is something that, if I give a similar talk again (I may be pretty much done with this topic), I will focus on more. I was okay this time with just giving them the ideas and letting them have some fun figuring things out. As I said in my three-question framework, you need to “solve” the puzzle/proof before you can create an argument that will convince someone else. So, many people weren’t really “ready” to move on to the next step in the limited time allotted.

In other thoughts, the 8 am time slot on the first day of the conference is Capital-G Great! I loved getting in, giving my presentation, and then relaxing for the rest of the conference. I was much better able to focus on the presentations that I attended when I wasn’t stressed over tweaking my slides or worrying about what I was going to say/wear/do.

I’ve been thinking about ideas for next year’s conference in Boston–proposals are due on the 1st–and so far I’m drawing a blank. If there’s something you’d like to hear from me, let me know…


MSRI Talk, a.k.a. This Post Is Too Long

On March 27, 2014 I participated in a panel discussion at MSRI about how my math degree did or did not prepare me for teaching math. Some of you gave me some excellent responses to my earlier solicitations regarding this talk, and you will see your words in my slides.

Slides: MSRI

Video of the talk.

It was a really interesting presentation to be a part of. I enjoyed hearing the three other teachers share their own perspectives on this topic. And there were some great questions from the audience. I got to talk about my experiences in my pre-service program and my early years of teaching at two schools that provided truly inspirational professional development*–especially to a newly-formed teacher. [Ilana Horn coincidentally blogged about both of these schools recently (using pseudonyms for the schools). I was all like: “Hey, I taught there! … Yep, there too.”]

My “big lessons” learned from my college math major, which I outlined in an earlier post, were:

  1. I don’t hate math.
  2. Math is supposed to make sense–even when math doesn’t make sense, it makes sense.
  3. Seemingly different ideas in math are connected, often strongly & deeply.

So, here’s some meat on that skeleton:

I really didn’t like math when I was in high school. I have some horror stories to tell, let me just say. And some stories that aren’t horror-esque, but that aren’t rainbows and kittens either. As a teacher myself now, I am very hesitant to refer to others as “bad teachers.” I don’t believe that this type of language is useful; it doesn’t serve either the teacher, or the one judging the teacher–neither party can learn anything from this negative labeling. That being said, I do believe that several of my high school math teachers were ineffective and actively aided and abetted increasing my (already existing) dislike of mathematics. [I do want to point out that there were also some major stand-outs-in-a-good-way throughout my time in school–my 8th grade algebra teacher, my community college pre-calc instructor were two individuals who got me interested and (almost) excited about doing math.]

When I got to college, I had already decided that I would hold off on declaring my major but that it sure as heck wasn’t going to be math. The best thing that happened to me was that I failed my math placement exam, meaning I didn’t pass out of the general ed math requirement. I decided to “get it over with” and enrolled in the math course my first semester–another good thing, as I probably wouldn’t have been able to complete all the graduation requirements for my major if I’d started later. And I really liked it.

You probably saw that one coming, right?

I liked the class because of points 2) and 3)–It made sense, and I was able to see the connections between ideas. My professor was super-passionate about math and got me interested enough that I decided to take Calculus the following semester. I think it might have helped that I’d already taken the equivalent of this class (and calculus too, btw) in high school, so things were already familiar, which allowed me to focus more on the big picture. By the time I was in Calc II, I’d already figured out that I needed to double up on Calc III and Linear Algebra the following semester and take 2 math classes each semester thereafter in order to complete a major in mathematics. And still I resisted declaring myself a math major! These “I don’t like math” beliefs get dug down deep, folks. It takes a lot to weed them out and dismantle them.

So, I got to share my story with the college math folks at MSRI. And now with you… One idea though, that I felt was worthy of consideration, was that I didn’t–and still don’t–know how much college and university math departments should be concerned with preparing math teachers. Obviously, not every math major is going to become a teacher. I certainly didn’t plan on teaching when I graduated. [Unwitting theme of this post: Things that Bree didn’t plan on doing: They just keep happening…]

There needs to be consideration for preparing math teachers within math departments. It would be kind of foolish to not think about this at all. But they need to strike a balance between serving all of their different constituencies.

I think my college math department did an excellent job of helping me meet my goals when I was in school. I wanted to take math classes that interested me and that opened my eyes to new ideas. And I got that in spades. Later, when I decided to teach math, not all of those classes turned out to be useful in my day-to-day work. And that’s okay. If I’d known that I was preparing to be a math teacher, I likely would have taken different classes. But I’m really glad that I took the classes that I did.


*At some point, someone should bug me to blog about this. Totes awesome experiences.

Meh-ed Camp

On Saturday Avery & I drove down to San Mateo for the SFBay Ed Camp “un-conference” where we met up with Jason and met some other cool people who are motivated enough to get up early on a summer weekend day to go talk about random educational topics. I’ve heard a lot about edcamps over the past year or two, but this was the first one I attended.

So, I know I was supposed to fall head-over-heels for the whole un-conference ed camp ju-ju, but I must confess that I came away from the experience feeling a little meh.

However, for full context, I should probably make crystal clear the fact that I’ve been feeling this way more and more about pretty much every conference I’ve been to over the past several years. When I first started out teaching–lo, so many years ago–I loved going to conferences. I found them exciting and energizing and inspiring and awesomely wonderful. But lately, I think the whole thing is just getting a little old–a tiny bit stale. I still enjoy attending conferences, but the big draw for me now is reconnecting with former colleagues and going to tweet-ups. Oh, and giving the occasional talk myself–that is certainly exciting…in a “I want to puke all over my fancy teacher shoes” kind of way.

I joked with Avery on the drive down that I had low expectations, so I wouldn’t be disappointed if things weren’t great, but I think I lied. I guess I had a deep-down secret wish that the edcamp model would knock my socks off for being so cutting-edge and grass-roots and innovative and I don’t know what else… and I didn’t find my experience to be all that different from an un-un-conference (a.k.a. a normal conference).

From my exhaustive one-day experience I’ve concluded that edcamp is basically a good forum for talking with other teachers about interesting ideas that you want to start exploring. If you want to talk about something you’ve been thinking about for a while, you will very possibly be the most experienced/opinionated/knowledgeable person in the room about that topic. I don’t know if there are some topics that might be more “edcamp friendly” than others…but the conversations I participated in seemed more like we were developing a list of online resources than hashing out a big idea. In some conversations I feel that was intentional, in others it seemed more like the underlying culture of people wanting to share “here’s something I did in my classroom” bubbling to the forefront. Not that sharing isn’t a great and meaningful activity, but sometimes it can come across as sounding overly dogmatic. “I did it this way, and so should you.” And, y’know, sometimes your cool idea just doesn’t do it for me.

Also, another layer to the edcamp being so tech-focused and virtually everyone being on twitter was that in every session I went to between 80 and 90% of the attendees were on some sort of device. And while I know that tweeps were likely just tweeting out the conversation, or were scoping for a different conversation that better suited their needs, I found it irritating. I think that the format of edcamp is actually one that doesn’t work for simultaneous tweet streams. Since the purpose of the sessions is to join into a conversation with other educators, your presence in the room should ideally be an active one. If you are listening to a speaker give her speech and are tweeting out the best bits, that is very different from trying to do the same *and* also participate in a conversation with the other people in the room. In this context it doesn’t work so well…

Upshot: I certainly don’t feel like I wasted my time by going to edcamp, and I’m glad I got to see what the fuss was all about. Though I do feel that with maybe a bit more structure I could get more out of the experience. Maybe have the session board online for the week leading up to the un-conference, and then people would have a bit more time to think about things before discussing them. That could also lead to developing those lists of resources ahead of time, and then you could do something with them the day-of in order to deepen the discussion.

So, would I go to another edcamp? Maybe. But probably the reason I would go is because there were other people going that I wanted to connect or re-connect with and/or it was taking place closer to home.

Lessons Learned

One week and one nasty cold later, I think I’m ready to reflect on my talk at Asilomar.

Lesson One: You can never have too many copies! [except, of course, for when you do…] 

I wasn’t expecting very many people to show up at my presentation. Well, I was wrong–there were people sitting on the floor. So, I didn’t have enough copies for everyone, which was a bummer. But people were really nice about sharing with the people next to them, and that led to (in many cases) a good buzz of collaboration, which may or may not have happened otherwise. Of course, most people would have preferred to have 2 copies–one to work on and another clean copy to take home with them. As someone who regularly kills trees with all of the printing and copying I do, I try to avoid dumping a big pile of extra handouts into the recycling. If I had been better organized, I could have gotten my materials onto the Asilomar CD so that people could have had it electronically.  I usually wind up chucking the Asilomar CD, which may be part of the reason I didn’t get my materials submitted by the deadline. I put everything up on my blog, which is sort of the same thing, but it takes an extra step to get into teachers’ hands.

Lesson Two: Do More Puzzles! 

I was happy to hear from people that they wanted to do more puzzles. More math is always a good thing in my playbook. In an earlier quasi-presentation, I did three different puzzles in 90 minutes and wound up feeling rushed. Much of that was due to the particular puzzles I chose, and in retrospect, I probably didn’t actually have 90 minutes at the PDO session. I realized mid-way through my Asilomar presentation that I had started out my pacing wrong and I was going to wind up with a big chunk of unfilled time. I had a quick pow-wow with Avery and decided on a plan, but still wound up being done 15 minutes early. And the last bit kind of dragged. The hardest part about adding in another puzzle will be deciding which one to use…

Lesson Three: I need an extra power cord.

I remembered my dongle, but didn’t have a power cord for my laptop. Someone told me that I could borrow his power cord for my session. *Ahem* However, that didn’t work out. Which was bad, because my laptop will go to sleep, regardless of setting preferences to “don’t sleep,” when it doesn’t have a power source. This was a pain in the ass, and made me look totally unprofessional. I’m not a professional, and this was my first attempt at a conference presentation, so I was okay with this. And my audience was very forgiving. But I’m for sure bringing my own power cord to NCTM in April.

Lesson Four: Giving a presentation is kind of like the first day of school.

Having only gone up and facilitated stuff like this in front of people who I actually know (and who know each other) I sorta forgot that people–even teachers–get shy and don’t want to talk in front of a group of strangers. As one person mentioned in their comments, “whole group reporting can take away momentum/energy.” There was a great sub-set of teachers who said some really interesting and valuable things, but many people didn’t want to speak and the room sounded full of crickets to me on a few memorable moments. Funny thing was that I had participated in a session several years ago that used much of the same format for the last part of my talk (i.e. I shamelessly stole this section of my presentation from that workshop) and it worked really well with that group. One challenge was we couldn’t really do a gallery walk, since the room was on the small side and filled with lots of people.

Lesson Five: I had a really great time!

I was nervous before-hand, especially at lunch right before my session. But after it was all over, I was so glad that I had done this. This was an experience that I learned a lot from. And giving a presentation to my teacher-peers made me feel like I’d grown a lot professionally. There aren’t all that many steps in the teacher professional growth path. Student teaching, teaching for real, and then what? You can do coaching, or go into administration, both of which usually involve leaving the classroom at least in part. This was a great way for me to see external evidence of the fact that I have progressed beyond “beginning teacher.” Well worth the butterflies in my stomach.

I’ve already started thinking about what to propose for next year…I guess I’m hooked


Most of my feedback highlighted the lessons I wrote about above. But there were a few that I’m still mulling over [included here so I don’t forget ’em]:

  • expand the idea of a proof to other classes and proof types [emphasis added by me ’cause this idea is great].
  • want info about where to find materials.
  • more focus on [how to?] transfer [from] puzzle to 2-column proof.
  • more explanation of proofs in context of standards. basic proofs?
  • would like some discussion on how to scaffold the “proof posters” for students.

I’m not sure what (if anything) I’ll do to address these comments when I give my talk again. As with all critique, some of it you use, some of it you don’t–but it all informs your process. The fact that I’m not sure yet where to go with these comments speaks to the value in getting feedback like this. These people got me thinking about my presentation and how I can make it better, and I’m still thinking about it a week later. Thank you for that!

Tales From The Front

…of the room.

First time being on stage (so to speak) at a math conference. I’m not ready to give the full post mortem, but I wanted to get my stuff up online for anyone who wants copies, or just to take a peek at what I did. Without further ado:

You can look at my prezi (and swoop through the slides as often as you want). You can even create & edit your own copy should you so desire.

Here are the two puzzles we worked on:

And a link to, one of my favorite puzzle sites. 


Asilomar is Here

Howdy, folks. Just making a quick announcement:

Tomorrow is the start of the CMC-North conference at Asilomar. If you’re going to be there, I hope to see you around. My talk, Beyond Sudoku, will be at Pacific Grove Middle School from 1:30 to 3:00 this Saturday. I am excited, but also a little nervous about my debut math conference performance. It should be fun.

A Mathematics Manifesto

This post is for the Virtual Conference on Core Values (

I believe all students people are good at math.

I believe all students people struggle with math.


Going back into my ancient history, I don’t think I ever really “did math” until I was in eighth grade. I followed directions. I obeyed the rules. I applied procedures correctly, and often quickly. I was a successful math student.

And…I was bored out of my mind. I hated math.

But the thing is, I didn’t really know what math was. I thought it was memorizing all of the rules and remembering when to use each one, then going through the algorithm and arriving at an answer. Problem solving was nowhere in my definition of “doing math.” Up until eighth grade—when we did factoring—I hadn’t ever had a problem to solve. Not any that I can remember at least. I knew how to do all of the “problems”; hence I didn’t have any problems with doing the “math” that was presented to me.

But factoring, now that was a problem. The way my teacher taught factoring didn’t have a clear cut formula that I could use, or a special algorithm that I could follow to get the right answer. Sometimes there was even more than one right answer. What was the world coming to? No, this whole factoring business was different from all the math I had previously done.

My eighth grade teacher let me grapple with the idea and told me that I would understand factoring eventually. He let me get frustrated, but didn’t let me give up. And he was right. Eventually a light bulb flashed on over my head. I got it! I was able to handle any factoring problem anyone threw my way. I was so happy that I’d figured it out and that it finally made sense to me.

Time and time again I have seen this same moment happen with my own students. I have witnessed the excitement they feel when they figure something out on their own. When something that didn’t make sense yesterday makes sense today. I believe that the most important aspect of my job is protecting my students’ right to experience these moments.

It’s a fine line to walk between letting students struggle too much and not enough. Between giving them too much support or not enough. As their teacher it is a struggle to figure out where that line is for each student and to make sure that they don’t stray too far from it. I don’t want any of my students to become the good—but bored—student that I was; the student who knows how to do everything and therefore learns next to nothing. I also don’t want my students to become so frustrated, so enmeshed in constant struggle, that they feel unsuccessful at math; that they become one of those people who says they “aren’t good at math.” I truly believe that anyone can be is good at math, so long as they are working on problems at the right level of difficulty. Teaching is like walking a tightrope. One that is strung up between two skyscrapers. Falling off of either side is bad news.

It is damn hard though, to let students get frustrated. To let them be confused for a while, to let them struggle with the ideas. Confusion is a sort of conflict, and most teachers don’t really like conflict. But without problems to struggle with, we’re not really doing math. And shouldn’t math be at the center of a good math classroom? Shouldn’t every student get to feel the sense of accomplishment of working hard on something and then succeeding at it? In my classroom, that is always the goal.