#NCTMRegionals PHX

After school on Wednesday, I high-tailed it to the airport to fly to Phoenix for the National Council of Teachers of Mathematics Western Regional Conference.

When I took off, it was 50 degrees.  When I landed, it was 92 with 0% humidity.

Phoenix is gorgeous! The city itself is almost perfectly flat, but it's surrounded by mountains.

What sessions did you attend, Justin? What did you get from them?

What a great question, fiction reader!  Let me tell you.

When I opened my laptop, I was pleased to find a picture from my older daughter:

Those red marks on our faces are kisses.  Also, I assume that my daughter thinks that, under my beard, I have a butt-chin.

I began the conference with Karim Ani (@KarimKai) from Mathalicious talking about the differences between procedural, conceptual and applied understanding.  I have seen several presentations from Karim and Ginny Stuckey on the amazing programs, activities and applications that Mathalicious uses to make math real for students.  I always love how engaging they are, both in terms of the activities themselves and as presenters.  I am a firm believer in their vision and how it's executed.

My session went as expected.  I had 7 attendees, all of whom were engaged and asking questions, but it solidified in my mind that I need to stop presenting about blogging.  It just isn't a topic for which people are interested in attending a session.  It was suggested that I make it a workshop, where I help people sign up for Twitter, create a blog and get them started on the path, but I'm not sure how interested I am in that.

Rather than blogging, I've been thinking more and more about doing workshops on how to teach all levels of mathematics using the interlocking hexagonal building blocks that I've been collecting.  Workshops tend to draw more people and a considerable amount of interest has been expressed about this.

Looking around at the exhibitor hall, I noticed that there are tons of manipulatives for various grade levels, but not really any that are used from K-12.  I think this is an area that could use some exploration.  I was encouraged further on this point by a fairly important mathematician (whom I'll talk more about in a bit.)


Following my own session, I attended Megan Schmidt's (@VeganMathBeagle) session on teaching statistics and social justice.  The room was very well attended and the presentation was excellent.  We had a discussion afterwards about the kinds of people who would attend such a session.  Social Justice and Mathematics can be a fairly polarizing topic.  Either you understand the importance of it and feel the need to incorporate it into your lessons, or you feel that math class has no need to address these issues.

We encountered a few gentlemen in the presentation who felt the need to question the validity of the statistics that were used because they didn't conform to their worldview.  They felt the need to voice their concerns as though they had just attended a seminar entitled "Mansplaining is Like Nike: Just Do It!"

The first time this occurred was when Megan presented the raw data that showed the birth rates by gender paired up with the gender breakdown of elected law-makers in each state.  There was no analysis, simply a presentation of data.

"Well, actually, male babies have a higher birth rate than female babies," he interjected.

Later, when looking at breakdown of school performance by race, another gentleman called out that Asian students were not on the list and had been marking their race as "white" so that they could get into medical school.

At our morning session on Friday, this man sat with us and attempted to engage Megan in conversation. We were not having it.

A third gentleman questioned the bias of the raw data obtained by the national department of education.

Megan did an incredible job redirecting the conversation back to the presentation and it was, ultimately, an engaging, fascinating and important conversation for us to have.


That evening, I attended a cookout with Stephanie Bowyer (@Melomania) and several of her colleagues.  We spent the evening talking math, teaching, nerd culture and having generally a great time.  I FINALLY got to meet Daniel Schneider (@MathyMcMatherso) and we hit it off like gangbusters!  Dude is awesome and brilliant!

When I got back to the hotel, I opened the program book for Friday and promptly fell asleep in it.


I attended 3 sessions on Friday, all of which were AMAZING!

Lisa Bejarano (@lisabej_manitou) started us off by walking us through her warm-up procedures for the week.  We worked through several of the exercises ourselves and it gave me a considerable amount to think about in terms of my own warm-ups and how directed they are.

Monday: Which One Doesn't Belong
Tuesday: Visual Patterns
Wednesday: Estimation 180
Thursday: Number Talks
Friday: Find the Flub

I've been using Estimation 180 as my daily warm-ups, but the diversity of problem types here makes me want to switch it up.  She even had a sheet for students to fill out each week to provide them with guidance and direction.

I left her session feeling energized.  It only went up from there.

Next, I went to James Tanton's (@JamesTanton) session on Exploding Dots and a deep discussion of understanding place value.

Everything he said and showed us made me lean further forward in my chair and say "Holy crap!!"

Halfway through the presentation, I sent a text to my colleagues back home that said "ASK ME ABOUT DOTS WHEN I GET BACK!!!"

What really hit home for me was how simple his explanation was to understand and how I can smoothly it goes along with the work I've been doing with hexagons in my classes.

After the presentation, I went to speak to him, to show him the hexagons that I had and how I had been implementing his practices in my class without realizing it.  When I pulled my hexagons out of my bag, he asked me how many I had.
"About 6300 at this point."
"Fantastic! Keep collecting them!"

James Tanton told me to continue feeding my hexagonal addiction.  Be still, my beating heart!


Still running high from these two sessions, I went over the "big hall" to watch Robert Kaplinsky (@RobertKaplinsky) talk about Depth of Knowledge.

His talk was engaging and disturbing, the kind of disturbing that makes a teacher question if they just spent 10 years thinking that they were teaching when really they were just passing students through the classroom.

He spoke about 3 different levels of Depth of Knowledge and how we can determine whether students TRULY understand the concepts we are teaching.  He talked about the different types of questions that go with each level.

DoK 1: What is the perimeter of a rectangle that is 4 by 8?
DoK 2: What are the dimension of all of the rectangles with a perimeter of 24?
DoK 3: Of all the rectangles with perimeter of 24, which one has the largest area?

All of these questions assess an understanding of the definition and execution of perimeter, but they get more and more complex as you increase the depth of knowledge.

Another incredibly interesting thing that he said was about the difference between "complicated" and "complex."  He said that things which are are complicated are difficult, but easily to replicate, while things that are complex are difficult, but very hard to replicated.

This is the difference between rocket science and parenting.  Rocket science, while incredibly difficult, can follow a series of steps.  Building the FIRST rocket is infinitely more difficult than building the 1000th.  Raising a child, however, has no set of steps to follow.  Just because you've successfully raised your first child, or second, or fourth, doesn't mean that you will be any better at raising the next one.  There are simply too many variables.

"People think that cooking is complicated, that you can just follow the recipe, but in reality, it's complex. Just following the recipe isn't always enough."

I've followed Robert on Twitter for a while now and have talked with him a few times, but actually getting to meet him in person was fantastic.


The list of people that I was honored to spend time and speak with is WAY too long to mention and I'm afraid that I would miss someone vital.  It was a pleasure to speak with so many incredibly insightful educators and learn from them.  I have a few days to mull these things over before NCTM Eastern Regional Conference in Philadelphia on Monday and Tuesday and then back to work on Wednesday.


I'd love to talk further about my experiences to anyone who is interested and made it this far in my post.

Time to board a plane.  It's 94 degrees here. It will be 53 when I land.

Day 44: Hexagears

Every student who reassessed skills today showed improvement.  I am incredibly pleased.

While they were working, I put the finishing touches on my substitute plans until my return from NCTM Phoenix and NCTM Philly.

I also started playing around a bit with the hexagons to try to incorporate some movement into my creations.  I developed a rudimentary set of gears with some string I had around my classroom.

These are much more impressive when they turn

I will be bringing those, as well as 600 other hexagons, with me to Phoenix.  I would bring more, but that's all I can fit in my carry-on.

Knowing that I will be spending a considerable amount of time waiting for and sitting on airplanes over the next few days, I went over to Math Equals Love and got some pretty awesome puzzles to nerd out to next to strangers.

Man! Those strangers are going to be so lucky to be sitting next to me!

I'm so jealous of them.

Day 43: Poor Grade Prep

I want to avoid giving homework as much as I can, but the students do need practice.  To that end, I try to make time in class and today was that time.

While they were working, I went around the class to see who would be reassessing skills tomorrow before the end of the marking period.

For a week, the list of requirements has been on the board.  They've boiled down to:
1) Do corrections on your last test.
2) Get test and corrections signed.


Every student had this opportunity.

7 will be taking advantage of it.

Several students claimed that they didn't know they had to do test corrections in order to be eligible.  I pointed out where it had not only been written on the board, but where I had them copy it into their notes.

I am bracing myself for a barrage of angry emails and phone calls when students receive less than ideal grades on their report cards.  I have been considering my response:

Thank you very much for your concerns.   I believe in learning from mistakes and am more concerned with student improvement than perfection.  To this end, my grade book will remain open for the entirety of the school year and students may return to any skill to demonstrate mastery.  Students learn at different rates and I do not believe that students who take longer to learn a certain concept should be penalized for it.  As of this moment, your child has demonstrated mastery in several skills and has the opportunity to improve in several others. 

In regards to the grade on the current marking period, the percentage that you see may be lower than what your child has traditionally brought home.  This is partially due to the the increased level of rigor in the middle school and partially due to the difference in my grading system.  The percentage grades that are displayed on the report card are not set in stone, but rather are fluid and may change as your child demonstrates their mastery of the material.  The students have had three opportunities to demonstrate their understanding of the concepts.  As we progress through the year, they will be given more. 

While learning is a life-long process, and shouldn't be limited by calendars, the school year does have such a limit.  If your child is unsatisfied with their mastery of the material, we have discussed in the class the steps that need to be taken to improve their understanding.  For example, the reassessment that was offered on October 26th needed to be preceded by test corrections and a parent signature to keep parents and guardians informed of the process. 

I have explained to the students that their grades are only final when the year is over or when they choose to no longer reassess the skills.  The Report Card is merely a snapshot of their current demonstration of understanding and can be improved up until the end of the school year. 

Thank you very much for your time.  I know that this process is different from the norm and can be confusing.  If you have any further questions, please don't hesitate to ask.  

Thank you again,
Mr. Aion

Here's to hoping I won't have to send it out.

Day 42: What's Going Wrong

I don't want to go back to rows.  I don't want my classroom to look like the traditional class.

I want my class to be based in discussion and discovery.  I want my students building ideas together and working to understand the idea that other people built.

I just don't know how to get there from here.

I feel, in fact, as though we are moving in the wrong direction.



I'm not sure why is happening, but I do have several theories.

1) The novelty has worn off

The district is entirely under one roof and the graduating class is less that 80.  The majority of the students have been here for not only their whole lives, but for several generations.  A large portion of the teachers have children in the district, or are alumni themselves.  It's very tight-knit.

Being a new teacher in any district comes with benefits and drawbacks.  The major drawback is that you don't know the kids as well as you would like and it takes longer to build up the rapport that makes teaching what it is.

As a new teacher, however, you can do all sorts of new things in terms of pedagogy and the students will go with you.  Ideally, they see benefits from these new methods before they slide back into "school sucks" mode.

It takes 28 days to build up habits and some have taken root, but not all.

2) I am not familiar with the curriculum

I have taught multiple different subjects using different curricula over the years, so this really shouldn't be an issue.  I should just be able to follow the text that was chosen by the previous teachers and go through it.  I'm having a problem with timing and sequence.  In addition to this, I find myself having to teach or reteach concepts that would consider to be pre-requisite.

Since the curriculum is new, the pre-requisite skills are also in a very different order than the one with which I'm familiar and different from that which the students have covered.

3) I haven't adjusted to the maturity level

Part of the purpose of having a middle-school model for education is because the drastic change between elementary and high school.  7th and 8th grade are supposed to be used as transition years, helping students to develop the habits that they need to be successful.  Many of these skills and habits are social in nature and are designed to help students not only deal with the academic rigor of high school, but the social pressures of life.

It took me almost an entire year to adjust when I first started teaching 8th grade.  That age level suits me well.

The 7th grade is entirely a different animal.  The kids are goofy and high energy.  Many of them still have an elementary mentality and I haven't adjusted to that yet.

Since this is my first year teaching kids so young, I'm still not sure what is developmentally appropriate behavior and what should be addressed more seriously.

I've been dealing with "he's touching me!" more than I ever have before and I can't tell if it's the kids, or the age.

"Phillip, please cancel my 4:15. I made a boom-boom in my Armani."

Greg, we need to talk.

The reality is that it's clearly a combination of all three of these, as well as several others that I haven't thought of.  The cause is only important since it will help me to identify a solution more quickly.  I'm getting frustrated and that frustration is feeding into a cycle.

The first quarter ends on Wednesday, so I need to figure it out soon.

Day 41: I Made A Thing

For the last day or so, I've been fooling around with Geogebra in an effort to make a 3D geodesic dome to show my class.

I started with a polygon inscribed in a sphere.  At each vertex of the polygon, I added another sphere with a radius of the side of the polygon.

Then I marked the intersections of the smaller spheres with the larger one.

Where those projected circles intersected with each other, I dropped a point.

Finally, I connected the points into equilateral triangles!

I made one from a 10-sided polygon, but didn't love how it looked.  It was good, but basic.

After a few more attempts and several program crashes later, I managed to get the 16-sided base the way I wanted it.

Each triangle is created by using the intersection of small spheres with the large one, then finding the intersections of THOSE, marking a point and connecting them together.  And then doing that again.

And again.

And again.

I'm not super pleased with the top, but with the sheer number of objects on the screen, the program couldn't handle what I wanted to do.

The resulting dome looks pretty awesome.  It was my first time playing around with the 3D capabilities of Geogebra and it was fun.  Several of my pre-algebra students were fascinated by it so I'm going to use a computer lab day to have them play around with it a bit.

I maaaaay also have recreated a simple version of it in every class to show off my skill...I mean...to show off the math and simplicity of it...


I also think that I need to do a better job of structuring the greenhouse project.  The groups are deep into the design phase with several teams already building models.  This is before they've blueprints, calculations or budgets.  We will talk about it more on Monday, but I'm worried if they do those things AFTER the model and things need to be changed, they will be too frustrated with the effort they put in and either fudge the numbers, or give up altogether.


I'm glad it's the weekend.  This week has been trying.

Day 40: Half Day

Last night, while eating chips, I broke a molar.  Today, I took a half-day so I could get it fixed.

In Math 7, we worked more on area models for fractions.

In Pre-Algebra, since we are moving into transformations, I handed out geoboards and had the kids find congruent triangles.  They seemed to truly enjoy the activity and they only broke a few of the rubber bands.

This is one of the shortest posts I've written.  That's mostly because during my down time at school today, when I normally write, I was busy tinkering with Geogebra, constructing a geodesic dome for the integrated math class.

It's taking a while, but it's pretty awesome.

Day 39: It's Escaping!

After a nice long walk to get fresh air and catch a bunch of Pokemon yesterday, I'm feeling a bit better.  I'm still tired and was up, for some stupid reason, at 3 am.

In spite of the lack of sleep, I was feeling more engaged in my classes today.  In Math 7, we began talking about rational numbers and I'm VERY excited to talk to them about the area model of fraction operation.

I'm a pretty big fan of physical representations of abstract concepts, which is probably why I think, speak and teach through analogy.

In Pre-Algebra, since we are starting to talk about transformations, we used mirrors to examine what it looked like to reflect a point across the x- and y-axes.  I even build a small GeoGebra applet for quick and easy examination of the concept.

The Integrated Math class is really what has my attention at the moment.  This Greenhouse project is MUCH bigger than I had originally planned.  We have permission from the principal to build the thing and we scoped out a location.

I called the local borough office to find out what permits we would need to obtain.  I spoke with the shop teacher about the logistics of what we would be able to do in-house and what we would have to outsource.  He talked to me a bit about material selection and planning since he has a fairly large greenhouse of his own.  I asked if he would come and speak with my students at some point soon to talk about planning.

I went and spoke with the director of food services for our cafeteria.  The previous director had actually started the process of getting a grant to build a greenhouse, but never completed it.  The new director told me that she would help look into the requirements that need to be met if we want what we grow to be served in the cafeteria.

Things I need to do (A non-comprehensive list):

Look into fundraising from local businesses
Obtain necessary permits
Set up a time with the computer teacher to get a CAD tutorial for my students
Ask local gardening center to come speak to them/organize field trip to local garden center


The more people in the district that I tell about this project, the more excitement is growing. I'm really fascinated to see how this turns out.



On a totally separate note, the superintendent sent an email to the faculty today advertising EdCampPGH and encouraging everyone to go.  When I wrote back and told her that I have been involved in organizing it for the last 3 years, she asked me to organize one for the district.

While it is not without challenges, I'm so happy in this district.