Tell me more about THINKING CLASSROOMS….

Recently I found myself in my friend Lynn Maksymchak’s office to talk about something, I can’t even recall what.  Lynn had recently returned from a Math Coordinators event and before I was even able to get out my question, she asked if I knew of the research on ‘Thinking Classrooms.’  Although i had heard the term, I really wasn’t sure of the specifics and so she began to sketch out what she had learned.  Her excitement and passion for both instruction and of course mathematics was clearly evident.  I took a piece of blank paper and wrote ‘One91 Guest Writer’ and left it with her.  She gave me one of those looks that implied ‘good luck buddy’ so I really wasn’t sure that I would receive anything.  I was pleasantly surprised to receive this piece of guest writing a few days later.  Although this comes from a master math teacher, many of these concepts can be applied to many of our K – 12 classrooms.  Take some time to read through Lynn’s writing and click on the hyperlinks to explore and then take some time to respond to the blog with your thoughts below.  Providing some feedback to our guest writers is the least that the rest of us can do.

Thank you for sharing your learning Lynn….

On Monday September 28, 2015 I had the pleasure of attending the meeting of math coordinators from across the province.  The session was in North Vancouver and covered many topics (mostly the new curriculum) but it was the section on Thinking Classrooms that struck me the most.  This is what I learned.

Thinking classrooms are:

  • About the moving the learner from dependence on the teacher to being independent
  • Noisy, and collaborative and seem to look like learning chaos until you look closely
  • Where learners show positive affect (learning confidence) and engagement
  • Where knowledge moves through a class (porosity)
  • Where students have some autonomy (e.g. it is OK to check a cell phone or be off task for a quick break as long as they go back to the task)
  • Where teachers understand that the fear of failure has an effect on creativity
  • Where teachers don’t rescue too quickly or pile on too much

All of this can be summed up in the graphic below (credit to Michael Pruner, BCAMT president and Peter Liljedahl, SFU)

Screen Shot 2015-10-03 at 10.14.38 AM

The three gears work together and make each other move as a system.

The big gear has the following characteristics:


should be fun and engaging; should be based in questions that you have not already taught the learners to solve.  The first ones given should not be content based but rather show students that math is fun and build a culture of thinking in the classroom.  Then we should move to content tasks.

For example:

  • Once learners have explored fractions, and how to represent them in multiple ways, ask them to add two fractions and stand back.
  • Once learners have studied binomial multiplication, give them a trinomial to factor and stand back.
  • Once students have explored rational numbers in all their formats, give them a list of rational numbers to put in order and stand back.

So where are we going to find these tasks?math-problem

VNPS (vertical non-permanent surfaces)

All math work does not need to be done on paper or in work books.  In fact this stifles creativity for many students who are scared to make a mistake and then have to cross something out in their presentation of work.  (I have personally had these-test-questions-show-how-math-has-totally-changed-since-you-were-in-schoolexperience of students who would not fix a mistake they identified because their page would no longer be pretty.)  Also math work does not have to be done sitting down.

Instead have students use non-permanent markers on:

  • Whiteboards – the ones on the walls and smaller ones
  • Windows
  • Table tops – can be horizontal but think about standing them on end
  • Any surface where mistakes can be wiped off as they are identified
  • Share with your colleagues other ideas along this line
VRG (visibly random groups)

This is all about collaborative learning and exploring.  Change the group members each day.  Have groups of 3.  Be a member of any group that cannot be a “three”.  Do not worry if the learners working on one surface start scanning the room to see what other groups are doing.  This is not copying – it is porosity.

To make these random groups, some teachers use a smartphone app such as “Shuffle Names, Dice” while others use websites such as “Team Maker”.

The smaller gear moving with the large gear has the following characteristics:

De-front the room

Move away from the teacher having a set station in the room.  Call the class to a side window and teach or demonstrate from there.  Bring the class to the surface a group is working on and use this work to ask questions, show strategies.

Think about room layout – do you have individual desks, desks pushed together or tables?  Is there room for movement (can a learner walk over to another group to collaborate easily)?


How are the tasks linked to old learning?  Do the learners have enough basic knowledge to work on the given task?  What questions will we need to ask to move learners along?  What formative feedback are we giving to stimulate further, deeper work?

The final gear has the following characteristics:


Allow students multiple ways to show their learning; use formative and summative; use self and peer evaluation; think Damian CooperWebCooper and the content he delivered in our summer workshops.

Answer questions

Productive struggle is good when learning math but frustration is not.  Sometimes you will need to answer a question with a question to promote thinking.  Other times you will need to provide a content-specific answer if it is obvious the learner has missed a foundational piece.


Provide structures that help the learners access content so it is the content they are focused on and not the vehicle it is wrapped up in.  Be mindful of specialized language, mathematical notation, reading levels in word problems, etc.  And make sure that the content is age appropriate or community sensitive.


  1. Great article Lynn. When I thought of a classroom operating in how you are describing, it would be one that would ooze with interaction and engagement. No standing and delivering, instead teachers can focus on provoking thought and engagement. Creating a work/learning environment for students that allows for open discussion, risk taking and learning at times in a team mode. This is the type of learning students will be able to pack up and utilize in their every day lives after high school.

    When we assume all students are young and willing to take risks in everything including their learning, we are so wrong. As you point out, creating a learning environment that allows for a multitude of learning styles within it, will create the confidence within our students to take risks in the learning…especially in Math.

    Many students become paralyzed in their learning because of how they perceive Math as being either “right or wrong” world and cannot see the progress they are making in their thinking, even though they had made just a simple mistake in a complex problem. This method of instruction and inspired learning would definitely help to alleviate such problems.

    I will pass your writing on to our staff to stimulate some further discussion.


  2. Kindergarten classes tend to reflect this style of learning environment. They are very open to learning and taking chances at this age…

  3. I have heard some of these suggestions before in previous workshops, but thank you for putting it together in a model for the classroom. I think we often underestimate the power of the non-permanent surface or letting students try a skill without formally teaching it. We are, more often than not, stunned by the level of learning. I also think it is important to think of this model in a cross-disciplinary way and include some of the strategies into our our reading and writing groups as well.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s