Looking back on the Year of BTC

Here we are! Mid-April is slipping past and conversations are beginning to turn towards summer. At the same time, the weather in Kenya is heading in a direction opposite of what I am accustomed to experiencing. It’s getting cold! Will the change in season help me finish the year strong by tricking my mind to think that the year is still in full swing? We shall see…The school is asking a reflection of the year to happen now – I guess they want me to start packing my bags! – so here it goes.

A new school. A new home. A new group of students. And some new tweaks to the flow in my classroom. This year, I embraced many of the components of Peter Liljedahl’s Building Thinking Classrooms in Mathematics and my teaching journey centered around thinking about the changes and how they’ve played out with this group of students. I documented the year’s journey through a series of posts:

Students recently finished taking a standardized test in mathematics and I view results as an opportunity to pause and reflect. In my opinion, the test was offered about a month too early for a full measure of growth but that’s ok…this reflections seems a bit early as well! I wasn’t overly happy with the results and had expected more growth. Yes, there are a multitude of factors that I could attempt to analyze and describe but most will not aid in my own pursuit of growth. My response is centered around the question of What can I do better next time? That’s the joy of teaching! ‘Next time’ rolls around in a few months so get better.

1. Incorporate thin-slicing as a skill builder from the beginning of the year.

The standarized test is essentially a measure of skills. So, a tweak is to bring in skills-based aspects. During the second semester, I began to get a handle on ‘thin-slicing’ routines as described in BTC. I see these as powerful routines to build and reinforce skills. At the start of the year, I shied away from thin-slicing as I leaned towards a higher concentration of problem solving tasks.

2. Provide additional in-class time for individual practice.

I wrote about challenges in the flow of the classroom in this post and continued to tweak it throughout the year. I believe that one fix is external – more class time will become available next year. At the same time, more dedicated individual practice is needed. I leaned heavily on Exit Tickets at the beginning and am planning to balance the time with individual practice that lives in the notebooks of students. Even if exit tickets are given, more individual practice is needed.

Consolidation. Yes. This is an area where I struggled. In a few instances I felt good about how lessons were wrapped up but I was often left feeling like it could have been done better. This will be a great focus next year with the tips of keeping it to 5 minutes and ‘consolidating from the bottom’.

3. Notes to my Future Self

This ebbed and flowed throughout the year. I began the year using the OpenSciEd framework of posing a question and having students respond in text, picture/model and examples but when I hopped onto the BTC wagon I somehow dropped this format. What I like about it is that the response was open for students to reply as they see fit (i.e. notes to themselves, not me!). At the same time, there was a bit more guidance in what the students are writing about. Return to this.

The above are tweaks to delivery and flow in the classroom. I’ve also written about a few changes to sequence and also the need to incorporate more projects into class. The visual below is one from Robert Kaplinsky that I like and want to play around with more next year.

Combining Project Based Learning (Robert Kaplinsky)

The figure is not drawn to scale and is one that can continually change depending on the unit; however, the key question holds true. How can I weave procedural fluency, conceptual understanding and meaningful application through a unit? This is a balance to work with and one that I’m excited for next year. My year’s experience with BTC has provided a good framework for procedural fluency (thin-slicing), conceptual understanding (rich tasks and other problems on the whiteboards) and now I need to bring back projects.

Other items to do for next year (this is a list that will likely grow and grow and….)

  • ISK uses a framework of Habits of Learning. I need to be specific about the link between mathematics class and the “HOLs”. Peter Liljedahl’s research led to three competencies that rise to the top time after time: perseverance, willingness to take risks, ability to collaborate. What if I focused on these three, taught into them and regularly assessed / student self-assess these items?
  • Be more regular on biweekly parent reflection letters. This also needs to have continuous reflection on how students are learning skills. Are they confident and working or unsure but not putting in effort / seeking assistance?
  • Unit Projects: are there links to other departments for an ‘umbrella type project’?
  • Kick off the year! What are the great non-curricular tasks that I will use next year to hook students?

PLJ Goals: My How, Why and What

Note: this post was written at the beginning of the year on an internal platform. For some reason, I did not crosspost and the platform is being abandoned. So…close to the end of the year and posting from the start.

As the year gets going, teachers across the globe contemplate the direction that they will take as learners. What will guide our own personal inquiry as the students around us come into class each day, celebrate the ups and downs of their learning journey and finish the year reflecting on tons of learning? 

It is unprofessional to ask teachers to change more than 10% a year. It is also unprofessional to ask them to change less than 10% a year. Steve Leinwand

I first heard Steve say this during a math conference and try to come back to it each year. What is the 10%? How will I change? I think the Professional Learning Journey model here at ISK is a great way to realize the 10%. This year, I’m looking forward to continuing the journey of building a thinking classroom.

Thinking is messy. Getting into our own minds and sharing this out to our communities is both challenging and gets a bit crazy. Check out the thinking below when students were asked to share out What do people do that helps my thinking in math class? Students put out their ideas, agreed with others and additional classes added their own thoughts. Messy indeed! At the same time, it was as if out thinking was bringing the class together in a shared understanding of what might help us in class. I believe that this collectiveness happens when thinking is made visible and shared.


Why: So…that’s the why. I’m interested in continuing to build a thinking classroom because I strongly feel that students need to be actively engaged through productive thinking. It is through this process that students share their thinking, realize those parts that they feel secure with and begin to dig in and question the parts that might not make full sense. In order for this to take place, students need to be given the opportunity to think, make sense of problems and work with sharing their understanding.

How: Let’s do this! Build a Thinking Classroom!

It’s a new year for me in a new school with a new group of students. My first base need is to get through the year in a way that honors my aims and the learning of all the students who walk into my classroom. As I write this in September, I am aware of the different pulls on my time as I get settled into a new country and way of life: make sure that my family is set, pay bills (yikes, I just found out today about systems for trash, electricity and water), learn the culture of the school, don’t forget XC practice, get systems dialed in, and on and on and on. In spite of this tug o’ war, my daily emphasis as a teacher is to build the capacity of my students to be mathematicians. In order to do this, I need to continue to focus on the practices of making thinking visual and ways to up the thinking quota in the room. This journey will incorporate both new ideas (I hope) and practices that I feel nudge the burden of thinking on to students. 

Let’s get started with the old:

  •  Starting Class off with Mathematics – Students deserve to come in each day and get their thinking going. After all, these classes are short and only meet every other day! Key starts include: 
    • Graphing Stories, 
    • Visual Patterns, 
    • Which One Doesn’t Belong, 
    • What’s Going on with this Graph, 
    • Estimation180 and 
    • Reflection of the Cycle
  • Find Rich Tasks to get students working on math

The new – Peter Liljedahl has recently published a book titled Building Thinking Classrooms. His graphic (below) captures the 14 areas (also briefly discussed in this article) in which Mr. Liljedahl has determined to be conducive to thinking classrooms. My plan is to begin a book study of his book to dive deeper into my own practices and see where tweaks can be made. Returning to Leinwand, I believe that I have already incorporated some of the areas so the 10% rule will hopefully be realized by a few small changes to my practice. 


Where might this book study take place? I hope to find a variety of areas to push my understanding and to encourage discourse. One place is here at ISK. If other teachers engage, then it would be awesome to open classrooms and watch and talk about what happens. In addition, I hope to become more active on Twitter with the hashtag #ThinkingClassrooms and on the Building Thinking Classrooms Facebook group.

What: What do you hope to accomplish because of your learning? What will you do with the learning? What will you share from the learning?

In the end, I hope to develop stronger thinkers in my classroom. I hope to continue working on spreading the ideas of thinking classrooms to other mathematics (and other subjects!) classrooms at ISK. Already, a few more vertical whiteboard surfaces have popped up! I will share the areas to build on so that more can join in!

Exploring the tidal zone

Life in the tidal area is a rough one. Imagine the day in and day out disruption to your daily life. All is going smoothly and boom! the wave rushes in and suddenly you are buried under feet of water. We tend to call this a natural disaster. Or…the water that you rely on for life is swept out and you have to hold on to the little that you have until the water comes back. Another disaster. But, the animals of the tidal zone have adapted to this daily disruption of their lives. Early in the morning, I was out for a run and the tide was just starting to go out. This allowed me to make it along the shoreline and I returned later with the kiddos to explore. It seemed as if the tide was fully out a little after noon and we took opportunity to explore this ecosystem.

Some of the locals called this sea star a ‘Shakira Star’ They said they named it this because the star seems to dance.
Crabs everywhere!

A Watamu Beach kind of morning

I’m an early bird. There is something about waking up before the sun’s light reaches me that I fully enjoy. Maybe it’s the stillness of the day or the silence. Most days, I follow the same routine as I make my way to the hot water kettle and the coffee pot. Today, the difference was that after the beans were scooped into the French press and the water poured in, I went outside to usher in the new dawn in a beautiful and new setting. We are at the coast and the morning sounds are different with another set of birds and the marine air in the trees above. The avocado trees of our back yard have been replaced with palms and the fronds of other plants.

The light slowly began to brighten the sky as clouds swirled above. Would it be another scorcher or would clouds keep some of the heat at bay? Yesterday was low key as the need for a break hit everyone pretty hard. On one hand, it’s hard to believe that three-quarters of the school year has passed but on the other…seriously! It’s been a grind!

I loved how the light was playing around with the edges of this palm.

Today, our plan was to head out early before the heat came up and spend the morning in the ocean. A tuk-tuk was called and we were off to Turtle Bay. Surprisingly, the four of us fit quite comfortably into the back of this wee machine as we chugged along towards Watamu Town and the Kenyan Wildlife Marine Park – isn’t it cool that they have marine parks to go along with the elephant and lion parks?

I recently read how the tourism numbers in Kenya are quite low and a recent downgrade in the travel status will hopefully bring people in to help at the economy. At the same time, it’s March break and this beach down is empty! As a visitor it’s quite nice to be out and about without swarms of others. The ticketing process at Watamu Marine Park in Turtle Bay was as speedy as I’ve ever seen – five minutes tops! We then wandered about on the beach as we waited for our boat’s departure.

Beach Camel

Our boat was the mighty Millennium and we soon boarded for a morning of dolphin watching and snorkeling.

The shape of the rock in the distance is the namesake for Turtle Bay.

The boat slowly plowed its way out towards the reef with the hope of finding dolphins. They feed out the outside of the reef and rarely come inside. The tidal swing is a big one and it switches over fast so I guess the dolphins keep away from the shallows. In addition to dolphins, we were hoping to also see turtles. The nesting season begins in May though we were told that turtles can be found year round in the area. Unfortunately, turtles were not on the viewing menu for us today but soon after reaching deeper water we began spotting dolphins! I love seeing dolphins out in the ocean. The pod was quite large and we were lucky to watch them for a long time before they continued on down the coastline.

After the dolphins, we returned towards the shore and hopped into the water with masks and snorkels to explore the coral. Bright fish darted in and out as we floated above. The tide was dropping quickly and as we returned to our departure point, it was apparent that areas we had crossed prior in the boat were no longer passable.

Watamu’s beaches are a wonderful sight but the area is also know for its gelato. After a few hours in the sun, the girls’ minds turned towards ice cold yumminess and Watamu again did not disappoint!

Gulmohar Tree

The tree is just outside of the house where we are staying in Watamu. I thought that it was a tamarind tree but the seed pods were not quite right. A bit of searching around – Google Lens works pretty well – and it turns out that the tree is one of the oldest ornamental trees in cultivation.

The seed pod is incredibly woody and quite hard to crack into. Inside, the seeds are segregated into individual slots. It’s fun to find out that you’re completely wrong about something. (Ha! Maybe I’m still wrong so if you think the tree is something else, please let me know!)

The path through Tsavo East

When alarms went off at 5:30 am, no one minded getting up. The night had been miserable. Even though temperatures outside dropped into the low 20s (Celsius), the heat inside never seemed to budge. It must have been 35+ C all night long. I was happy to get the day moving – our hope was an early morning game drive to cross through Tsavo East National Park.

I love driving along the red soil roads

So far, each park in Kenya has had its own flavor and this one was no different. Unfortunately, it seemed as if there were few roads branching off of the main corridor through the park. The few that we did find led to beautiful sights. In our opinion, this park is all about the elephants. There were so many! At times where the views opened up, there may have been 50 to 75 dotting the landscape in small family groups.

Several giraffes, a few small herds of zebras and other 4-legged ungulates also kept us company along the way though there was a massive spell in the middle of the drive that felt like a ‘no-animals land’. We rattled down a highly corrugated road that was hot and dusty. We tried different sides of the road in the hope of a little less washboard effect and it felt like we were truly in the middle of nowhere. As we approached the Sala Gate (eastern entrance to the park) the view of greenery in the distance let us know that both water and animals were likely approaching again.

The comings and goings of the watering hole

After the gate, we were on a long, amazingly straight road that was absolutely beautiful. Fresh tarmac and no cars – this is something to get excited about in Kenya! We flew down the road passing some goats, cattle and a train of camels on our way to the final destination of the coast.

Our route through Tsavo East: Voi Gate to Sala Gate

On the road to Mombasa

One might think that the burned out and flipped semis scattered along the side of the road would provide ample warning of the dangers of the Mombasa Highway. One might think that cars would slow a bit. Or avoid overtaking in areas with the smallest of margins. One might think but it just isn’t so.

We left at daybreak to get a start on the traffic out of Nairobi and quickly passed from the west to east side. The fun began as the road dropped to a lane in each direction. This is not a low traffic road but the main corridor for transport and commerce between Mombasa (the primary port) and Nairobi. Trucks, laden with all sorts of items, plow their way along the steep uphills and descents. On the way up, they slow down as engines struggle to pull the load. I think I can…I think I can…at 10 kph. On the way down, brakes lock up and the smell is horrendous. In either case, cars continually play a game of leapfrog around these trucks. You have to, really. Otherwise the long drive will take forever.

As a driver, I don’t relax. Maybe I’m peeing around the edge of the truck in front of me to see if I can get by or I’m wondering if cars or semis heading in my direction will suddenly pop out. At the same time, an eye is kept in the rearview to make sure that I’m not getting overtaken just as I start to pass. 10 kph to 100 kph to 15 all in the space of a kilometer and repeated kilometer after kilometer. After six hours on the road, I was happy that we were only going part of the way to the coast.

A funny aside…A month or so ago, I got busted for overtaking in a no passing zone. Seriously, when you get the opportunity to pass a slow truck, take it! The policeman didn’t see it that way and a quick roadside payment was made. Today, we came along a nice stretch of road that surprisingly did not allow passing. I decided to play by the rules and sure enough saw a few police down the road. I was just saying to Krista that I was glad to have not passed when the cop signalled me over. What!?

After a polite greeting (our interactions have been so nice with the police so far) he says, “You were overtaking in a no passing area.”

“No, I did not pass,” I replied.

“Yes. I saw you with binoculars,” he responded as he patted his chest. There were no binoculars there – just the strap of the machine gun sling over his shoulder.”

“I did not pass,” I countered again. “I learned my lesson a few months ago. “

“Oh yes. How long have you been in Kenya?”

“Since August.”

He looked us over, reached in to give us a fist BP and wished us a good day. We were back on the road again!

The resting spot – promises of swim time kept the girls going in the car

Break is here (#SOL22 – Day 19)

The week began with an Airbnb fail – ‘Sorry, but the people who rented you their space have decided that they need it next coming.’

‘Wait. What? You mean that reservation that has been in the books for months?”

“Yes. That one. We apologize and are sure that you can find another place.”

It was not what we had hoped for a few days before the start of break and some scrambling ensued. In the end, we did find another place (not quite what we started with…) but also shifted our Nairobi departure by one day.

So, today has been an enjoyable first day of break. The pace has been slow. A late start (it must have been 6:30!), a mountain bike ride in the local forest and a lot of bread baking. We’ll take off early tomorrow morning but I’m kind of glad that today’s pace was so relaxed!


My only regret was that she was wearing a mask and I missed the full effect of her face lighting up. I would not have been surprised if a bit of her smile peeked out from the corners of her mask yet her eyes conveyed the thought. All of a sudden, she got it!

In class, we’ve been working towards a better understanding of the circle. Students have been drawing, measuring, describing and working on problems (Did you know that penny-farthing bikes are still being made and ridden?) . After a bit, we moved from thinking around the fact that pi is the ratio of the circumference to the diameter of circles and moved to area. Students began drawing circles on the vertical whiteboards and after a few set-up instructions (draw a radius, and then another that is perpendicular to the first) I put up the following image.

Students began making sketches and discussing their thinking. Yup, 1 circle definitely fits in. 2? Sure…3..hmmmm? Around the room, I saw that many students had gotten to ‘3-ish circles’ and given our materials this was about as good as it was going to get so I brought them all back together and asked them to think about what that ‘-ish’ might be…

Whew, that’s a lot of circular talk to get to the point where magic happened.

A couple of students had a good idea and wanted to volunteer but I asked them to please not shout out this time. Instead, I said statements along the lines of “so and so seems to have an idea”

It was great. Students were looking around thinking what connection they could make and exchanging glances with each other. Some made the connections and it was obvious in their eyes and then BOOM! I saw her face in the back of the room. She got it! Her entire face lit up and it seemed as if she would float up to the ceiling. I couldn’t resist. She had to share her thinking.

There are pi radius squares in the circle.

Baby steps forward

Reading is a series of skills that build on each other and teachers are always differentiating based on skill. Why don’t you teach math like that?

Dr. GQ

The quote above was said to me in a much more eloquent way, a bit tongue-in-cheek but also spot on. I’m constant amazed at the reading and writing classroom of my wife, Krista. So much is going on that is meeting students at their level. I’m a sounding board in the journey of unit development and I hear lots of talk about unit launch, connection to the world, big ideas and final exhibitions. At the same time, I know that she is constant building the skills of the readers in her room. All this is not going on in my classroom.

As I’ve mentioned before, I’ve worked a lot within the Building Thinking Classrooms for Mathematics framework this year and find that my unit approach is based on using rich tasks that ask students to critically think and problem solve while also leaning on ‘thin-slicing’ to build content-based skills. What I’m not doing is the bigger picture of connecting to the world, social issues or finding a way to exhibit learning at the end of a unit. My units are grouped around content topics while hers are grouped around big ideas. Hmmmm…..

‘But she has to do that! She’s a humanities teacher after all.’ True. The humanities bit (reading, writing and social studies) does bundle a lot together but the connection piece is really important.

‘In my ______(fill in the MS blank) math class, I have students who can’t yet add fractions.’ Yes, but I hear all the time how reading teachers have students at a 2nd grade reading level and a HS reading level sitting near each other.

Note to self – spend more time sitting in these humanities classes. How are these teachers managing the skill level of students and differentiating while moving forward on a project?

Yesterday, we had a math department meeting and some of these questions were brought up and kicked around. We also came back to the “Aims” of our school

Through the BTC lens…

  • Communicate – lots of discussion at the whiteboards as student interpret problems and express their thinking.
  • Solve – Critical Thinking for sure. We are solving problems!
  • Create – hmmmm
  • Learn – The growth of students this year has been quite impressive. I think the vertical whiteboard time has really assisted students in being self-directed and having a growth mindset.
  • Act – Lots of collaboration!

OK…we are engaging with the school’s aims, yet what is being missed?

  • Communicate: Empathize – This often comes from a design system thinking framework of the need to understand others to move forward. It also comes from understanding and connecting to social issues. Bringing in larger, relevant questions that ‘float’ above the unit as a target might help me focus on finding appropriate data sets.
  • Solve – Lots of critical thinking, but where is the Design & Systems thinking? This is an avenue of investigation for projects.
  • Create – This is lacking. I did a ‘Tiny Apartment Project’ in the first semester and students did design and create. In the end, I was not so happy with the project and time spent on it. This doesn’t mean that doing the project was wrong but that it was not the right project.
  • Learn – Inquiry is happening with the current flow of math class but it is not the sustained inquiry that I think I want to have. Again, I am leaning more into the idea of having projects that open up both choice and sustained thinking by students. I’m aware of so many project pitfalls and want to make sure that ‘sustained thinking’ does take place and that creation is authentic.
  • Act – I think that my classes are missing the power of mathematics. What can knowledge derived from understanding and presenting numbers do for us?

In the department meeting, thinking shifted to how might we do it differently next year? How can some aspects of what we do be streamlined to create space for bringing in some of the above? I really appreciated the talk as ideas were kicked around, insights shared and the willingness to look at different possibilities explored. A few things that we know are important: students must continue to develop in their skills as mathematicians. This is through the lens of concrete skills that match the progression of mathematics as well as problem solving strategies. Thinking back to the humanities classroom – for some students this does mean becoming more secure in previous skills or ‘catching up’ in order to be work at the Grade ___ level.

We also began to think about the idea of major clusters. We’ve been trying to do it all with maybe equal emphasis and…it just doesn’t work well. Here is a Grade 7 cluster focus:

The greens are the major clusters and are elevated to a priority. Let’s face the scenario at our school. There are a lot of great things happening but the amount of time given to the instruction of mathematics pales in consideration to many programs out there. So, let’s put ourselves in the context of our school and lean on its goals while also continuing our students progress in mathematics. Focus on proportional reasoning, equations and statistics. Build solid learning from here and work to bring in the additional clusters at the end if time.

From this point, the goal is to weave in skills, problem solving and projects. I feel that we are close to sorting things out but there is a bunch of work to be done. I know that this post has loose ends as it reflects my partial thinking. It will come together….I hope. Ha! I’m ready for March break.