by Krista Sarmatiuk
Sitting here, listening to Cathy Fosnot talk about young mathematicians is creating quite the conversation in my kitchen. All manner of opinions about education have surfaced at our supper table, and I’ve really enjoyed listening to the impact of learning and teaching on my own kids. As the last of my children prepares to graduate, I am happy to say that all of our kids have strong opinions on what makes the difference in education.
Tonight, my 17-year old daughter and I have a conversation that revolves around the teacher’s learning stance. As always, I am reminded that when the teacher takes on the stance of learner, alongside the students, kids are much happier.
“Teachers don’t know everything and they haven’t run across all of the different types of learners. They never will.” This is a powerful statement from a student, and it connects to some key ideas presented in chapter 1.
After reading and listening to the podcast, three big ideas resonate with me.
Idea #1 Context Matters.
“Truly problematic contexts engage children in a way that keeps them grounded. They attempt to model the situation mathematically, as a way to make sense of it.”
This makes me think about those moments when we see a child really connect to the mathematics. Dr Lisa Lunney Borden talks about putting math into students’ hands. We are noticing the difference that this makes. When I braid these ideas together, I am reminded that the story is what draws us in. It can’t be just a story, it needs to be something we can connect to, in order to really engage us. The same can be said for a truly rich math problem. It’s not just about building a context around a computation or set of numbers, it’s about creating a logical, reasonable situation, which in turn leads students to be able to apply reasoning skills in an authentic way. Can your answer make sense? It can, if the situation is possible, or better yet, probable.
Idea #2 Challenge Matters.
“Really doing mathematics involves working at the edge of your mathematical knowledge and enjoying the puzzlement.”
When we watch Terry encouraging her students to try a variety of strategies to solve their problem, we listen in to the questions and prompts that direct the traffic of learning, rather than just leading students to their destination. This is what my daughter is looking for – she wants to be challenged to explore new ideas and build understanding, as Cathy describes in the podcast.
Idea #3 Connections Matter
“[Mathematicians] make meaning in their world by setting up quantifiable and spatial relationships, by noticing patterns and transformation, by proving them as generalizations, and by searching for elegant solutions.”
In the video clip shared during tonight’s broadcast, Cathy reminds us that all students are mathematicians and it’s our role to ensure that they see themselves in this way. I can’t underline enough the importance of this idea. At the end of the school year, I ask my students to write me a reflection called “My Math Learning Journey”, using some guiding questions to lead them to think about their strengths as mathematicians.
It’s interesting to compare this definition of a mathematician to the reflections that I’ve read. As I reflect on this, the thing that really stands out is that the students were keen to describe the relationships and patterns that had impacted their thinking. In conversation, they agreed, disagreed and built on each others’ answers. It seems like they really did believe they were mathematicians.
Now, that’s worth a smile.
Featured image by Caleb Frith on Unsplash