I had an amazing math lesson planned.  Engaging, linked to Friday’s work, kicking off a great classroom discussion.  And five minutes into class, I threw my plan out.

Why?  Because of a lesson that I already knew, but was retaught today – my student’s know what they need and will show me, through their actions if not their words, as long as I just pay attention.  

Class started with a few division questions –to get them thinking while I got other activities set up.  I had intended for this to last for about five minutes, but my students had other ideas.  Realizing that working independently wasn’t working, some went to classmates for help.  Others discovered their inner teacher and started running mini-lessons for friends.  I turned around to remind them all that they should be working quietly but stopped in my tracks when I overheard one student say, “Not quite.  Come to the easel and we can go step by step.”  I paused, trying to focus in on other conversations and heard, “I know you have that one wrong because the remainder can’t be bigger than the divisor.  Can you tell me why that’s true?”  

Fantastic lesson or not, they weren’t ready to move on.  They needed more time to explore… talk… work things through.  Instead of my lesson, I spent the next 40 minutes walking around my room, listening for my student’s voices telling me, in oh so many ways, just what it was that they needed to learn. 

Allison Smeltzer teaches grade four at Brentwood TLC

Tasha Roa-Yaremkowycz, Kathleen Shaver, Brianna Bolivar, Grade 4 Teachers at Andrew Sibbald School

Mathematics in our classroom takes on an experiential form where students explore their curiosity and interests through a variety of methods. We strive to create an environment where students feel safe to take risks and challenge their thinking. 

We realize that community is an essential part for students to develop a positive self-identity in mathematics. One way we support this is by engaging students in number talks where they are given the opportunity to think critically and challenge each other’s thinking in a respectful way. These types of rich mathematical tasks build community amongst students and encourage willingness to participate as well as confidence in self-efficacy.

When teaching is going well it takes on a life of its own. Students work in different groups, at their own pace, and explore concepts through a variety of conceptual approaches.  When working through fractions, students visualize concepts of ‘parts of a whole’ and are then encouraged to use whatever visual framework works best for them when solving problems, as long as they are efficient and effective. We overheard in our classroom today:  “If that is how you calculate the area for a rectangle, how you do calculate it for a triangle or a circle?”  This is when logic prevails in our room… As students grasp the meanings of the numbers, the formula, the fraction line or the reason for using a manipulative to reinforce a concept they are more likely to apply logic to solve problems. The result: passionate mathematicians. 

 
@TashaRoa Kathleen Shaver (@therealmomblog) & @bribolivar10 are grade 4 teachers seeking to instill curiosity, stewardship and collaboration amongst our students.  Join our journey: @grade4wonders

This story begins with a challenge: “Design a recreation centre for the youth of Tuscany.” This challenge came from a conversation with a visiting parent and set out to address a perceived need for this age group as there are currently few recreational opportunities for youth from 12-18 years of age in the community.

That’s it - that was the whole challenge. A simple sentence that led to weeks of survey construction, data collection and analysis, and careful architectural design.  A few teams felt unsure about how to proceed until one courageous and innovative group, with two students that did not view math as a personal strength, asked a simple question: “Can we use MinecraftEdu?”  

Suddenly, for some teams, everything changed. Using this tool they were able to create highly detailed plans for large and complex recreation centres. Instead of struggling with traditional procedures for creating scales and finding area/perimeter of large and unusually shaped areas, these teams could now show their ability to work through these challenges using a non-traditional method, one that is no less authentic or accurate in demonstrating their true understanding. Student leadership developed as these teams engaged in conversations around math concepts with ease and confidence, speaking clearly about the rigorous planning and careful calculations they were conducting in order to create their highly detailed designs, some of  which included functioning showers and food dispensers (and even a secret passage or two…)

So, what did WE learn? We learned that rigor takes many forms and that an understanding of math can be shown in many different ways.  We also learned that, sometimes, it takes a bit of ‘out of the box’ thinking (and your favourite video game) to create renewed passion and confidence.

Over the past several months, I’ve been conducting research into the role of visual-spatial reasoning in mathematics. Today, though, I had to step outside of my researcher role for a few moments, simply to bask in the glory of the math learning taking place in a grade three classroom at Fish Creek School.

The task was simple, but mathematically rich.  Students chose one of four challenges that required them to reason, proportionately, about the relative size of the zoo animals they had been working with at Open Minds School.  Students had strewn themselves around the room and were working on the challenge deemed most appropriate and most interesting.  They worked alone, with a partner or in small groups.  There were blocks and chart paper and counters and hundreds charts in use.  Students used their teachers as resources, but just as much they used one another.  Every single student was meaningfully engaged.  And the quality of their engagement wasn’t found in the buzz of activity throughout the room or in the kinds of manipulatives they chose to use – it was most evident in the nature of the questions the students were asking.  The questions showed both self-awareness and mathematical awareness - an understanding of what was making sense, what wasn’t, where they were stuck and what they needed to get unstuck – because the work they were doing mattered.  Learning mattered. 

What did I learn today? I learned, again, how mathematics, offered up to the hands and hearts and minds of young people in rigorous and generous ways, is just stunningly beautiful.  And I learned, again, that in the court of public opinion, intellectual engagement is worth fighting for. 

Alison Van Rosendaal (@boyd_Alison)is a Specialist with Learning Services.  She is passionately dedicated to public education, completely in love with mathematics, and profoundly grateful for the opportunities for learning that emerge through her work every single day.