An Ode to Elementary Teachers

“The problem is that most of the middle school teachers don’t have a specialty in math.”

When I heard that statement, I knew it bothered me.  But at the time, I was unable to articulate exactly why.  There are a lot of problems with education, many more with math specifically.  But I know that pointing the finger squarely at the grades below is both unproductive and damaging.  Not only that, but when we are convince ourselves that groups of teachers lack certain “necessary” content knowledge, we close our minds to anything else they can teach us.

I’ve had a busy couple of weeks at AFT Thinking Mathematics training for 9 days and then straight on to Twitter Math Camp for another 5.  Both of those experiences will change my teaching for the better, and I found a common theme throughout:  Listen to what elementary and middle school teachers can teach you about mathematics pedagogy.

We talk about connecting representations of mathematics like graphs, tables, and equations.  But how often do we connect what kids do in elementary grades to what they experience in high school?  We lament in high school about kids lacking number sense, but how do our classroom routines support and build on the number sense kids have created through the primary grades?

Notice the similarities between the Ten Principles of Thinking Mathematics and the NCTM Math Teaching Practices:


Credit: AFT


Credit: NCTM

I know those are dense, but they are the foundation of what we need to do in order to improve mathematics education.  Every shift we make needs to be based in these principles/practices.  And the ideas need to connect from counting to arithmetic to algebra to calculus and all the places in between.  We can no longer be complacent in teaching as we were taught.  Doing so means committing negligence toward a generation of students who need a deeper understanding of mathematics in order to use it successfully in the world they create.

Tracy Zager brought it all home for me with her keynote at Twitter Math Camp.  Here is her blog post with the link to the slides and the video.  I heard the same things the research had been telling me over and over in Baltimore:  We need to listen to each other.  There isn’t a hierarchy of teaching from elementary through post-secondary.  The conversations between vertical groups of teachers are important – even necessary – to helping our students develop as mathematicians.

Here are some pictures from the AFT Thinking Mathematics Training (credit:  AFT)

0722162104-1.jpg0722162104a-1.jpg0722162105-1.jpg0722162107-1.jpgDay 5 - Diamond Dot Pattern ExamplesDay 5 - Pool BorderDay 5 - Seeing Dots

Tough Cartoon Conversations

My sweet little angel came back from grandma and grandpa’s house proclaiming her love for Powerpuff girls. In the last 6 years I’ve watched my share of mind-numbing cartoons, most with female characters that make me want to shove a pencil in my eye and swirl it around in my brain.  Powerpuff girls has 3 female superheros, so I thought, what could be so bad?

In case you aren’t familiar, here is a classic depiction of the three little world-saving wonders:

Credit:  Cartoon Network

Credit: Cartoon Network

Notice anything? …   I’ll give you a moment.

I try to run all of the media Maria is exposed to through the same scrutiny:  Does it include a diversity of characters, including diversity of race and family structure? How are the female characters depicted?  I’d like to say I’m looking for shows with a good message, but to be honest, I’m content with something that isn’t psychologically damaging at this point.

Hopefully you were as uncomfortable by the lack of diversity in the trio of pro-feminist ass-kickers as I was.  And if you don’t think that matters, consider this conversation I had with my daughter recently.

Me:  Maria, is it important to have all kinds of superheros?

M:  yes.

Me:  Boy superheros and girl superheros?

M:  Of course, mommy.

Me:  What about superheros with dark skin and superheros with light skin?

M:  No.  Superheros should only have light skin.

This stopped me in my tracks.  But I can’t fix it unless I’m willing to own my part in it.  I’ve worked very hard to make sure Maria is exposed to a variety of races, religions, sexual orientations, and family structures.  But the world the media has built for her is one in which superheros are white.  It’s my responsibility to disrupt this.   I’ve got much more work to do.

On Which I Pat Myself on the Back

Warning:  Some of you are going to find this really dumb.  You’ve probably been doing this with your STEM-fueled 5th graders for years and are wondering why a 35 year old secondary math teacher is so excited about.  Four words: This. Isn’t, About. You.

So in April, I went with two great #MTBoS friends, Julie Wright and Danielle Reycer to the Exploratorium in San Francisco after NCTM.  To be honest, I was awed by the place, but my motion sickness unexpectedly overcame me, and I spent most of my time at the exhibits that didn’t require visual attention.  But in the back, there was a “maker-space” (or whatever you edu-folks call it) where they were making Scribbling Machines.  I took a look at it and thought “I want to do that this summer.  Maria will get a kick out of it.”

Step one:  get a 1.5 – 3.0 volt motor.  [Crap. Something with wires and electricity.  I can’t do wires and electricity.  Cuz I’m math, not science.

Tip:  Don’t purchase a new one.  Re-purpose one from a child’s toy.  [Sweet!  Look out, loud spinning, jump contraption from Hell’s fifth circle, I’m taking your motor!]

What I thought was the motor was not, but when I attached the battery, it became magnetic, which was neat.  I loosened about 8 more tiny screws and finally extracted the actual motor.  Now the game was on.  I was like a mad scientist, tongue to the side, laser focused on getting this scribble machine to function.  No, darling spouse, I won’t tell you what I’m doing, but you can see when I’m done.  Now go away.  

Here are a couple of videos of the Scribble Machine in action after a lot of adjusting and reconfiguring.  Yes, I know, I listen to great music:  Listen to the Music Radio on Google Play Music.

Here are the instructions if you are interested in making your own Scribble Machine.  Now if I could just get it to spiral…

You might be thinking, Ok, Beagle.  What’s the point?  You made a thing and now you want us to be excited for you?  Well, no.  Yes, I’m excited I repurposed a motor from Lucifer’s Leaping  Musical Spin Toy of Satan.  But confession:  I was one of those women who was convinced that robot, electrical, and computerized toys were designed with boys in mind.  These Lego robots weren’t exactly screaming my name:


But this girl looks genuinely excited, right?


Until I saw something I wanted to make, I was convinced I couldn’t.  My daughter is growing up in a country where for the first time a woman is running for president and a woman will adorn the $20 bill.  But what’s more important than those major accomplishments for me and my daughter is for her to see her mom try stuff and fail.  And try again, and fail again.  And then try one more time, and fail repeatedly until I have a working Scribble Machine that doesn’t do much but prove that I wanted to, so I did, tripping over myself along the way.  Maria wants to learn to ride a bike this summer.  And while I won’t be the one out there helping her, I want her to believe that she can and she will.

I see my own mother do this with her sewing.  I’ve seen her tinker and toil over stitches and fabrics and techniques until she creates something so unique, beautiful and truly one-of-a-kind. Like this (oops, stained) Doc McStuffin’s jacket:


Note:  Maria’s analysis of the Scribble Machine is still pending.  Will update with reactions and artwork.


Beagle Blockade

Last weekend we took the beagles to the dog park.  Although they are small, and somewhat unassuming, Herbie seems to be able to hold his own when it comes to keeping up with the bigger dogs.  Here’s a 15 second snippet of the adventure:

Needless to say, the beagles were thirsty by the end of the trail.  Of  course the park was equipped with water at dog level, but for some reason, Herbie refused to partake.  This little hound had just ran his tail off, howling all the way but would not drink any of the water overflowing the canine-sized bowl available to him.

You can bring a beagle to water, but you can't make him drink.

You can bring a beagle to water, but you can’t make him drink.

I made the joke on Facebook, “You can bring a beagle to water but you can’t make him drink.”  We use this phrase often as high school teachers (with “horses” obviously), but the sentiment is the same.  “I can’t teach a student who isn’t willing to learn.”  Now before we get defensive, I want to break this down a little.  I’m guilty as any of buying into this mantra at one time or another.

One of the best things to happen in my district is the adoption of a PLC model which requires that we not only reflect on how we teach but on what kids actually learned.  Simply bringing the horse (or beagle) to water is not sufficient (nor was it ever), but we now have a district-wide culture that supports students who reject the water the first time.  In my beagle example, Herbie was afraid of the giant yellow pump that was pouring water into the bowl.  When he got home, he was still thirsty and proceeded to slurp down the entire contents of his regular bowl on the floor in the kitchen.  I owe my dog another opportunity to drink water because, well, he’s a dog.  High school students, no matter how much we desire the contrary, are not adults.  They are children.  And sometimes they will reject learning the first time, and the second time (and sometimes repeatedly just to spite us).  But as educators, we owe them continuous opportunities for learning.

Well, it’s the first weekend of summer, and I’m coloring spirals and making beagle metaphors on my blog.  The next three months promise to be pretty fun.


Spiraling Out of Control

I wanted to collect all of my spiral art on my blog.

Here is the document I used (spiralled numbers 1 – 1024)


Here’s the google doc:

And here is what I’ve created so far.  Enjoy!

Link to Google Photos Album:

0601161833e 0601161833d 0601161833c 0601161833b 0601161833a 0601161833 0601161833(1) 0601161832a 0601161832 0601161831g 0601161831f 0601161831e 0601161831d 0601161831c 0601161831b 0601161831a 0601161831 0601161829c 0601161829b 0601161829a 0601161829 0601161828b 0601161828a 0601161828 0601161827e 0601161827d 0601161827b 0601161827b(1) 0601161827a 0601161827 0601161826g 0601161826f 0601161826e 0601161826d 0601161826c 0601161826b 0601161826a 0601161826 0601161825g 0601161825f 0601161825e 0601161825e(1)

Next up:  Hexagon grid spirals.


Some wonderful people on twitter have made these into pretty neat computerized visuals.  Here are some of my favorites:

John Golden:

GHS Mathematics Department:

Dan Anderson:



Tales from the Nerdery

I think math is neat.   I like to play with math.  And sometimes I come up with something that supports my theory that math is neat.

First, I took the numbers 1 – 100 and spiralled them around some regular graph paper.  I wondered what would happen if I colored in the multiples of 4.  I examined my work and thought, “Huh.  Well that’s neat.”


Of course then I needed to spiral even more numbers and test out everything I could think of.  Multiples of 5, 6, 7 and so on.  Linear patterns, quadratic patterns, prime num…nope, nevermind.  I don’t do prime numbers.

Anyway, it’s that time of the school year where stress relief is necessary so I have been playing with these spirals for over a week. Today I came up with something worth sharing on my blog.  I took the positive y-values of y = x^2, y = x^2 + x, y = x^2 + 2x and so on, and colored those squares.  Then I put the images together and made a gif. Obviously, holding the camera at a steady angle is not a skill I have mastered.  But I still think it’s pretty darn neat.


Number Talks – Bumps in the Road

Today, I presented, with my colleague, Denise Anderson, a session on Number Talks at the Minnesota Department of Education.  The topic was ‘Where do we go from here:  Managing bumps in the road.’

Here are the slides if you are interested:

I’ll be presenting this session as a webinar on Tuesday, May 24th.  Details here:

My favorite slide:  0513161500



Heavy Armor


Here’s a picture. This happened in my classroom last week. This simple, beautiful moment is one I will cherish more than a million free burritos.

Look closely. It might not be apparent, but this student is behind my desk, fiddling with some of my chachkies. He’s telling me about a concert he got to go to this weekend.

It might not be obvious from the picture but this kid isn’t a huge fan of mathematics. In fact, he might be convinced that the whole discipline has it out for him.

There’s more to the story. This child walked into my room two months ago with his headphones in his ears and a chip on his shoulder. He made it completely clear he was there for one reason: to earn his credit.  Often he would refuse to complete any work and when he knew that wasn’t an option, he was quick to proclaim that he “didn’t get any of this.” He maintained his angry demeanor like a coat of armor.  Mathematics had let him down so many times before. Why would this trimester be any different? But what manifests as anger on the surface is perhaps pain, sadness, or fear underneath.
Every day I have this student for a “homeroom” of sorts. This means that after lunch, the class comes back to my room for 25 minutes. During this time, I saw this kid slowly open up.  Without the anxiety of the mathematics in play, I began to see underneath scars from an educational system that doesn’t help him thrive. He started taking off the headphones when he walks in the room at the beginning of class. Even though he usually responds with “sick” or “tired” when I ask how he is, at least there’s an acknowledgement of my greeting.

Then he begins to do math. Not just to “get his credit,” but he really wants to figure it out. His work becomes more than numbers on the page for his daily points. “Don’t look at my answer. You need to figure it out yourself,” he begins saying to his classmates. “My brain hurts. This class makes me feel like I’m growing a brain tumor.” And he keeps working. I know brain tumors aren’t joking matters, but I’ve never loved them more.

Consecutive Sum-mer

So May is a fun month.  In Minnesota, we can be reasonably certain the sub-40 day temperatures are behind us, the goslings have hatched, and the student countdown to the end of the year has begun.  In my classroom, they not only know that there are 18 days left, but that there are also only 3 Mondays remaining as well.

In John Stevens and Matt Vaudrey’s new book The Classroom Chef, they state that the opposite of bored is not entertained.  It’s curious.  While I agree, I needed some solid evidence to combat the never-ending question of “Can we go outside today?”   (For the record, I’m not totally opposed to taking them outside for math class.  It’s just not warm enough yet.)

Me:  Number your paper from 1 – 30.  (I’m off to an outstanding start, clearly.)  So and So, pick a number (hoping he/she doesn’t pick a power of 2).

Student:  Seven

Me:  Seven is interesting because it can be written as the sum of 2 consecutive numbers, 3 and 4.   What about 6?  Can you think of a way you could make 6 using the sum of consecutive numbers?

We talk about what consecutive numbers are, how many we should be able to sum, which kinds of numbers count as consecutive, whether addition is the only operation allowed, and so on.  Pretty soon, the entire class, (Yes, 100% of my juniors and seniors who have been beaten down by mathematics for 11+ years) is engaged, on task, and curious about the nature of these sums of numbers.

Student:  So you’re telling me that any number, except the powers of 2 which are few in number anyway, can be written as the sum of consecutive numbers?  

Me:  Nope.  I’m not saying that at all.  You discovered it.

Here is the Consecutive Sums problem poster from nrich: