Going International!

I’m excited to join the British Columbia Association of Math Teachers for their conference today, October 21, 2016! And I’m honored to present a session tackling improving student collaboration title “How are you smart in math?” This post will serve as a home for the slide deck we used to guide our time, and a few additional links and resources!

Session Description

How do we move from the ‘divide and conquer’ mentality of student collaboration to a place where student groups genuinely work together to create shared knowledge? One key lies in the way we view our students and how they view each other. During this session, we’ll build our vocabulary about the vital math abilities that are so powerful for students as they investigate and grapple with tough problems so we can dramatically shrink the deficit-based thinking of students and teachers alike.

Session-related Resources

Please feel free to comment here or to reach out via twitter @ReadySetBrette if you have additional questions or would like a thought partner about reducing status to improve collaboration.


Fostering True Math Learning

Some introductory brainstorming:

(One clarification first: When I use the words “our” or “we”, I mean “us” as math educators. Now the prompts!)

  1. What limitations from our own math learning are we bringing to our planning and the math experiences we provide our students?
  1. How can we model the skills and mindsets of a savvy problem solver for our students, and how can we model the learning of new skills and mindsets that we as adults don’t yet have ourselves?

Some context and elaboration:

In a recent visit to Cincinnati, Ohio to work with math teachers in the Winton Woods City School District, I pushed the room to take a step back. As a coach for the New Tech Network, it is common practice to push teachers, leaders, schools, and fellow coaches to articulate their purpose, to borrow from Simon Sinek and ask folks to state their “why”. In this case, we brainstormed how each of us might complete the following sentence:

“Math learning, true math learning, is essential because…”

One key phrase kept bubbling up in our sharing was that true math learning fosters and develops savvy problem solvers. So we pushed into what being a savvy problem solver really means and what indicators we might look for.

problem solver

While this is a great ideal, we all know that putting this ideal into practice is difficult. On my trip home from Cincinnati, I re-stumbled across a 2014 New York Times Magazine article titled “Why Do Americans Stinks at Math?” in which Elizabeth Green investigates why math education in the United States historically struggles to achieve this desired true math learning despite repeated, national initiatives (think: “new math” of the 1960s and the challenges of CCSS implementation now to name a few). Green interviews professor Magdalene Lampert who challenges us to assess our role in this struggle. While many of us, me included, were highly successful math students in school – so successful in fact that we became math teachers – Lampert notes that our math learning is likely the product of a traditional math classroom. I admit this line of thought brings up an uncomfortable sense of vulnerability for me. I think to myself: “Is she really saying that I am somehow ‘less than’ in my understanding of mathematics. This can’t be. I am a math teacher and a math coach after all, right?” I could get defensive. I could get defiant. I could foster learning environments that are comfortable for me because they are familiar. Instead, I take her words as a caution and as a nudge. A caution because I must admit that I may not have personally experienced what I try to foster in math classrooms now. And a nudge to be honest about where I can grow and improve.

Some closing brainstorming:

As you head into another school year and now will some additional context, I’ll again pose two questions for further brainstorming:

  1. What limitations from our own math learning are we bringing to our planning and the math experiences we provide our students?
  1. How can we model the skills and mindsets of a savvy problem solver for our students, and how can we model the learning of new mindsets and skills that we as adults don’t yet have ourselves?

Go ahead! Teach to the Test!

Teaching to the test. The four words that seems to simultaneously bring a sense of security to teachers and make them shudder at the same time. It’s a tempting option: prepare students for a standardized test by having them practice each piece of content that could be tested in the format it will be tested, primarily multiple choice. This should prepare students. This should improve test scores. This should keep teacher jobs secure. Repeatedly exposing students to content and test format should work, right?

Sadly we all know given both personal experience and national-level data that this doesn’t work. I would posit however that students do poorly on tests not because they haven’t been exposed to all of the content (or test format), but because they have only just been exposed to the content. The content has been covered, not learned. For example, picture the following two scenarios occurring while you proctor a test come May.

Scenario 1: A student sees content she is unsure of on the test, she doesn’t know how to start investigating the problem, anxiety spikes, and the question is skipped.

Scenario 2: A student sees content she is unsure of, she pauses, re-reads the instructions, tries a few things she feels like might help lead her to the answer, and ultimately works backwards from the answer choices thinking about which might be the most reasonable option given the context.

In the first scenario, the student is likely armed with a vast, breadth of surface-level content knowledge. In the second, the same student is likely armed with admittedly a smaller subset of content knowledge, as well as persistence, initiative, estimation, bravery, attention to givens, confidence, willingness to restart, and ingenuity. The difference is that one classroom experience is focused on covering content, and one classroom experience is focused on how to approach content. One classroom fosters problem knowers while the other fosters problems solvers.

So go ahead and teach to the test! But first make one critical shift in your test preparation mantra. Heading into testing season, I encourage you to actively shift your mindset from, students will do well if they know the content –> students will do well if they know how to approach the content.

When sports and education collide…

How would you define culture? Had you asked me this some time ago, I likely would’ve responded with something somewhat generic, or maybe I would have given some examples. At best, I would have said “trust, respect, and responsibility”, for those NTNers out there. That’s what I would’ve said. But then this happened…

Let me back up to say that I have a few passions in my life, two of which include sports (March Madness is a real illness for me and fall weekends are football-centric) and, of course, progressing and improving (math) education. And on occasion, these two passions collide in an awesome way.

As I often do, I spent a night in a hotel room recently prepping for a site visit the following day. With ESPN on in the background, I typed away on my laptop. Longtime SportsCenter host Steven van Pelt caught my attention with a story about this year’s 3rd NBA draft pick who got into some legal trouble. This young man almost immediately responded with a tweet of atonement.

While I can almost recite the commentary about young, entitled athletes that I expected to follow, that’s not where this sports journalist was headed. Instead, he asked viewers who else might be responsible for this behavior. And he brought up this player’s NBA team and (here it is!) the team culture that might subtly or even overtly condone negative behavior.

What’s more, the definition of culture used in this story was the following:

Culture (n): conditions suitable for growth

What if this definition was our guiding question framing culture conversations in education?

As you think about the various cultures at play at your school or in your classroom, what conditions are suitable for your growth or your students’ growth? And what conditions aren’t suitable for growth? We hope that students enter our classrooms each day with the intention to be fully dedicated to their peers and to learning. But we know intentions are often best laid, and then not followed. So how do we bolster the conditions for growth so as to support our students to achieve their intentions, and for us to learn and grow with colleagues?

I can’t say I have an answer to those questions. But as one of my passions collides with another, I’ve at least found my new answer to the question, “How would you define culture?”

I want to do PrBL, but where do I start?!

The Common Core State Standards (CCSS) for Math are a blend of content standards, the content of our courses, and practice standards, the manner with which students tackle that content. In an ideal world, our students would bring the mindset of these practice standards, their math disposition if you will, to class each day. But these, too, have to be developed, facilitated, and practiced, which admittedly adds to a teacher’s load. Many teachers, and I would be bold enough to say rightly so, feel that a problem-based learning experience (mini-projects essentially) is a great way to allow students to participate in experiences that will ask for a blend of these two types of standards. NCTM research, New Tech Network work with math facilitators, and my own experience in the classroom back this up. But that doesn’t make it any less daunting to take this on – to go against the way you yourself was taught (and were likely successful at) math and probably the way you were taught to teach math as well. So where do you start? I have an idea!

The CCSS math practice standards come with some guidance stating, “Expectations that begin with the word “understand” are often especially good opportunities to connect the practice to the content” (CCSS for Math, page 8). If you are looking for spots to help develop your students’ ability to engage with the content, I suggest starting here. As an example, below is the Geometry Overview taken from CCSS for Math with the appropriate “understand” expectations highlighted. If you view the full list of standards, there are a few smaller strands that also begin with the word “understand”, but I think the big picture perspective of the Overview is just the ticket if you as you think about curriculum planning for next year.

Geometry Overview


  • Experiment with transformations in the plane
  • Understand congruence in terms of rigid motions
  • Prove geometric theorems
  • Make geometric constructions

Similarity, Right Triangles, and Trigonometry

  • Understand similarity in terms of similarity transformations
  • Prove theorems involving similarity
  • Define trigonometric ratios and solve problems involving right triangles
  • Apply trigonometry to general triangles


  • Understand and apply theorems about circles
  • Find arc lengths and areas of sectors of circles

Expressing Geometric Properties with Equations

  • Translate between the geometric description and the equation for a conic section
  • Use coordinates to prove simple geometric theorems algebraically

Geometric Measurement and Dimension

  • Explain volume formulas and use them to solve problems
  • Visualize relationships between two-dimensional and three-dimensional objects

Modeling with Geometry

  • Apply geometric concepts in modeling situations

There are three critical places where you have key opportunities to dive into PrBL, places that the authors of the standards highlight as excellent crosswalks between the math content and the math practices. I do not mean to understate the importance of the others expectations that ask students to use, apply, describe, or explain; these are important to gain a well-rounded and thorough view of Geometry. But if you are looking for a spot to start your PrBL journey, here it is! The standards themselves narrow down the scope of expectations and hopefully guide you to standards/units where you can throw some energy into really creating PrBL experiences for your students. So grab a copy of your standards, bust out a highlighter, and dig in!

P.S. Once you’re done highlighting and know where to kick off your PrBL planning, I recommend stopping by emergentmath.com and checking out all of problem ideas Geoff Krall has gathered together under the “Curriculum Maps” tab.

Group Roles Aren’t Just for Students

Establishing and maintaining a department-wide culture of collaboration and learning is no small feat. But high level support, discourse, and planning are not only achievable at a department level, but is well worth the time and engagement.


As the first day of school looms, it is a great opportunity to think about your own department roles. We spend countless hours thinking about and monitoring the roles of our student groups, but then often find ourselves sitting in aimless department meetings that collaboratively fail because we don’t take the time to work through adult roles in the same way we do with student roles. By pausing now to focus on how a department of teachers collaborates and supports each other, we can simultaneously model collaboration and establish a department with the capacity to improve instruction and student learning.


Below I’m offering up two possible structures for department roles. The first is operationally-based; the second is advocate (or discourse)-based.


Operational Roles

Advocate-based Roles*

District Face: We chose not to have a typical department head as we felt that we were sharing many of the responsibilities, but we thought it was important to have a consistent communicator with the district office. This person attended the district meetings and relayed important information. 

Advocates: We had two academies at our school and we felt it important to have one person per academy that was the liaison to that academy’s administrator. This person needed to be forward thinking and willing to advocate for scheduling needs, funding, test scheduling, and also (and maybe most importantly) to get administrators into our classrooms to see and understand the work we were doing.

Momma Bear: Again, we had two momma bears, one per academy. This person was in charge of checking in the personal well-being of our department members. Whether it be a birthday, rough day with a student, success with a risky lesson, the momma bear was there to support and cheer.


Social Chair: We quickly realized that tough department conversations were far easier if we really knew each other outside of the classroom. When you know each other well enough to know outside interests and maybe even go on a run together, hit up a yoga class, or watch Monday Night Football, coming to a common understanding during a heated curriculum decision was far more feasible and far less personal. So, our social chair was in charge of scheduling a monthly (or every other monthly) happy hour so that we had some precious time outside of the school building to shoot the breeze and learn about each other.

District Advocate


Technology Advocate

PrBL Advocate

Equitable Groupwork Advocate

Peer Reciprocal

Observations Advocate

Systems Advocate

Family/Community Involvement Advocate

College & Career Advocate


*These roles gave us each the freedom to bring these realms to the forefront of conversation whenever they might be neglected. Without being a nag (it’s your advocate duty after all), each advocate gets to bring up something that he/she is passionate about and that is also vitally important to the work we hope to achieve.