Category Archives: MTBoS Challenge

“I’m not good at math.”

I can’t tell you how many times I’ve heard this from students. I guess I was lucky. Growing up, nobody ever told me that I wasn’t good at math (or anything else, really). More importantly, nobody ever made it okay for me not to be good at math, or school, or whatever I was interested in learning about. But not all of my students have the family support that I did (and continue to have). So part of nurturing their talent falls to me. I’ve always told my students that I want them to be fearless problem solvers – to face life unafraid of what lies ahead. To nurture this I have to allow space within my classroom for some of the “messy stuff” like playing around with patterns and numbers, wondering about data and statistics, or building seemingly impossible 3D geometric structures. And then pointing out how they just did math – and they were good at it.

You see, when my students say, “I’m not good at math,” they really mean, “I’m not good at quickly recalling math facts when I think everyone is looking at me and waiting for me to respond in some brilliant way.” They equate math with arithmetic and math facts and speed. I try to point out the difference between math and arithmetic (math facts), which sometimes helps. I tell them how bad I am at subtracting numbers quickly in my head.

So what do I do to develop fearless problem solvers? I pose a problem for my students to solve. Then I step back. I observe. I listen. I ask questions. I make them all think before anyone is allowed to speak. I make them talk to me about what they’re thinking and I make them talk to each other, especially to each other. That way I get to listen more. I practice wait time, sometimes for awkwardly long, silent moments. Eventually, I no longer hear, “I’m not good at math.” Except when they want to compute something quickly, on the spot, in the moment, and it isn’t working. And then they turn and say, “Sorry, arithmetic.”


Filed under MTBoS Challenge, teaching

Fresh Blogging Opportunity

Welcome to the Explore the MTBoS 2017 Blogging Initiative! With the start of a new year, there is no better time to start a new blog! For those of you who have blogs, it is also the perfect time to get inspired to write again! Please join us to participate in this years blogging initiative! […]

via New Year, New Blog! — Exploring the MathTwitterBlogosphere

1 Comment

Filed under MTBoS Challenge

My Favorite Games

My advisory students are now seniors. We started together four years ago, along with the school. It’s a humbling journey to spend four years with the same group of students, helping them navigate through high school, getting them ready for whatever adventure follows.

We do a lot of work in advisory – research about “Life after Baxter,” prepping for student-led conferences, creating and maintaining digital portfolios, keeping track of academic progress, and completing any required paperwork, for starters. Even though we meet three times a week for about 35 minutes each time, we still have some “down” time.

We like to play games together. We play Set, Farkle, and Joe Name It along with various card games. Taking some time to play and laugh together is important to building those relationships.

1 Comment

Filed under Baxter, MTBoS Challenge

“That’s a Big Twinkie”

You know the quote. You can watch the clip.

Yesterday I brought a box of Twinkies to class so my students could check Egon’s math. They measured twinkie dimensions and borrowed scales from the science lab. They made the classic error of not paying attention to units. And they argued – consulted – with one another. They didn’t quite finish during class yesterday. I predict that they will be somewhat surprised by the results.

Leave a comment

Filed under MTBoS Challenge, problem solving

The Grant

So we got this grant. It’s big, for us anyway. And it’s a federal grant. We’ve tried for three years to get a federal grant and finally, we got one. We never had any start-up funds. We just jumped in and did it. What did we get this grant for? For everything that we’ve been trying to do and have to do anyway. Nice, right? It is. Really.

My part of the grant is to look at “Anytime, Anywhere” learning, streamline it, organize it, find ways to link our standards to it, and talk to the folks who are looking for ways to track it. This includes our snow day learning, Flex Friday, and alternative course work. And I get to work with a really awesome colleague to do this. Meanwhile, others will be working on dual-enrollment college courses, community service, and internships.

Because learning isn’t confined to the classroom. And learning math doesn’t have to happen in a math classroom from a math teacher. Learning how to write can happen in science class, because they are taught how to write in science class. We are working to be flexible because we are competency based. And that means that we look at evidence of what the student knows, not who the student learned from. Learning is organic and holistic.

So look for future posts about the progress of our Anytime, Anywhere learning curriculum development. It’s going to be quite a ride.


Filed under Baxter, MTBoS Challenge

What a day …

It was one of those days, like so many other days, when there wasn’t a moment to breathe and so much was pulling me in so many different directions. Today was the “official” Teacher Appreciation Day, according to the Google doodle, anyway. Yesterday was the day that we had bagels and I received some notes from kids and parents. Today was just hectic and crazy. Plus, we’re having a spirit week. You know, when kids (and teachers) are supposed to dress according to different themes every day and you pit classes against each other in “friendly” competition to earn meaningless “pride” points. Each morning my job is to record who is present in my Advisory and who dressed up. I predict that we come in tied for last. So far, we’ve earned 0 points, and I’m so okay with that. Can you tell I’m not a fan?

After all of this – the teaching, the lunch meeting, the guidance meeting (where I at least got to decompress a bit), the writing emails to parents, the updating RTI plans – today’s after school meeting is in content areas. That means that I get to talk about math & math teaching with a few really cool people. We’re trying to finalize our courses for next year so that we can have kids sign up. (I know, you probably did that at your school in February.) We’re still working out the kinks as we iron out issues with our proficiency-based, student-centered, balance between high demand and access for all. But that’s the good work, the work we not only need to do, but the work I signed up to do. And I am lucky that I get to do that work with good people.

So, happy Teacher Appreciation Day to all of you in the #MTBoS and beyond who keep doing this work for your students. And who every once in a while challenge me to connect with you. Thank you. I truly appreciate it.

Leave a comment

Filed under MTBoS Challenge

Classroom arguing

Today and last Thursday the same group of students was arguing with each other about the math they were learning. On Thursday, they stayed about 5 minutes into lunch to finish their argument. It was fun to listen to. They were so engaged and talking math and refining their understanding. Eventually, today, they called me over to hear their arguments and clarify any misunderstandings. Here’s the beginning of the exchange:

S1: “Let me ask you this, Pam …”

S2: “No don’t ask her that, you’ll just confuse her.”

S1: “Let me ask. She’s a teacher with a lot more experience with this stuff than we have. I bet she won’t get confused.”

My students make me smile.

Leave a comment

Filed under Baxter, MTBoS Challenge

More 3D Geometry


After my last post, Mike Lawler gave me all of these awesome ideas for my 3D geometry class. Considering that my class has been working on nets, I was most fascinated by the dodecahedron that folds into a cube, which came from Simon Gregg.

When I first watched the gif animation, I just couldn’t figure out what was going on. I thought, “I’ve got to show this to my students!” Thursday was that day. I tasked them with a build challenge. Of course 55 minutes wasn’t enough time to complete anything, but students had drawings (which gave us insight into the construction)

a CAD rendering (completed during a snow day)

and a previously constructed dodecahedron that had been re-purposed (completed during lunch).

So, thanks Mike, for the inspiration, and thanks #MTBoS for being there helping us to support each other.

1 Comment

Filed under MTBoS Challenge, teaching

“How Do We Know That?”


I’m teaching this 12 week geometry class focusing on 3-dimensional figures. It’s a brand new class, like many at Baxter Academy, so I get to make it up as I go. Since our focus is on 3-dimensional figures, I thought I would begin with some Platonic solids. So I found some nets of the solids that my students could cut and fold. Once they had them constructed, there was a lot of recognition of the different shapes and, even though I was calling them tetrahedron, octahedron, and so on, many of my students began referring to them as if they were dice: D4, D8, D12, D20. Anyway, I must have made some statement about there only being 5 Platonic solids, and they now had the complete set. One student asked, “How do we know that? How do we know that there are only 5?” Great question, right?

I really felt that before we could go down the road of answering that question, my students needed a bit more knowledge and exploration around these shapes, and maybe some thinking around tiling the plane would help, too. So we spent some time trying to draw them, counting faces, edges, and vertices, visualizing what they might look like with vertices cut off, unfolding them into nets, and wondering why regular hexagons tiled a plane, but regular pentagons did not. We played around with the sides – a lot – and even talked about this thing called vertex angle defect. Then we returned to the question of why only five. Students were able to connect the need for some defect (angles totaling less than 360 degrees) and the ability to create a 3-dimensional figure. Through the investigation, they were able to see that the only combinations of regular polygons that worked (by sharing a vertex) would be 3, 4, and 5 equilateral triangles, 3 squares, and 3 regular pentagons. They could give solid reasons why 6 triangles, 4 squares, 4 pentagons, and any number of other regular polygons could not be used to create a new Platonic solid.

I had not anticipated this question, and had not included it in my plans. But, because it was asked, thankfully, by a student, it pushed us into thinking more deeply about these shapes (and their definition). And, ultimately, my students were able to answer the “why only five” question for themselves.


Filed under MTBoS Challenge, problem solving, teaching

Stacking Pennies


There are lots of things I love about my classes – my students are at the top, but I also am enjoying teaching a course for the 2nd or 3rd time. This activity is for a statistics course called “Designing Experiments and Studies.” It’s a course that lasts for one trimester (about 12 weeks) and we have just completed week 4. The Penny Stacking activity is an introduction to experiments. I ran this lesson last week (Jan 12 & 13).

The rules of penny stacking are simple:

  • You can only touch one penny at a time.
  • Once the penny is placed on the stack, you cannot move it.
  • Stack as many pennies as you can without having the stack fall over.
  • Each student stacks pennies once, with either their dominant hand or their non-dominant hand.
  • Students are randomly selected to stack pennies with either their dominant or non-dominant hand.

Before embarking on the experiment, we made the following predictions:

  • More pennies would be stacked with the dominant hand (although a few students disagreed and thought the results would be the same for both hands).
  • A few students thought the ratio of pennies stacked with dominant hand to non-dominant hand would be 3 to 1.
  • The range of pennies stacked with dominant hand would be 15-45 pennies, while the penny stacks from the non-dominant hand would range from 10-35 pennies.

Then it’s off to conduct the experiment. This is pretty tricky given that up to four students sit at a table and our building is so old that if someone walks across the floor upstairs, our floor will shake. Here are the results:

penny stacksHow would you interpret these results?

We calculated the means: dominant -> 30.9 pennies; non-dominant -> 26.25 pennies. It’s clear that, on average, the number of pennies stacked with the dominant hand is greater than the number of pennies stacked with the non-dominant hand. But is that difference in the means (of 4.65 pennies) significant? Is it unusually large? Is it more than what we might expect from randomizing the results?

To check this out, we randomize the results. Each pair of students received a stack of cards. Each card had a result. The partners shuffled up the cards and dealt them out in a stack of 10 (for the dominant hand) and a stack of 8 (for the non-dominant hand), calculated the means, and then subtracted (dominant – non-dominant). They each did this a couple of times and we made a histogram from the results of the randomization test.


(It’s a Google Sheets histogram – I don’t know how to get rid of the space between the bars)

If you look at our difference of 4.65 compared to these randomized results, it looks pretty common – not at all unusual – to get such a result. If you think that our randomization test was too small (with only 24 randomizations), then you can use the Randomization Distribution tool from Core Math Tools, a free suite of tools available from NCTM. And it’s the only tool that I know that runs this test effectively. Here are the results from 1000 runs, just like the card shuffling but faster.

more pennies

penny summaryAnd you can even get summary statistics that show that our result was within 1 standard deviation of the mean of the results that we got from randomizing the data. Not a very unusual result at all.

We followed this up on Thursday with an experiment inspired by an example from NCTM’s Focus in High School Mathematics: Reasoning and Sense Making – memorizing three letter “words.” Based on the experiment described in the book, I created random lists of three letter words and three letter “words.” The lists of words were meaningful, like cat, dog, act, tap, while the lists of “words” were nonsense, like nbg, rji, pxe, ghl. Students were randomly assigned to receive either a list of meaningful words or a list of nonsense words. They were then given 60 seconds to memorize as many words as possible. Like with the penny stacking, I made them predict what they thought the results might be. What would your predictions be?


1 Comment

Filed under MTBoS Challenge, teaching