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 layer this idea onto Cathy Fosnot and Maarten Dolk's observation above, 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 "Really doing mathematics involves working at the edge of your mathematical knowledge and enjoying the puzzlement." (Pg 4)
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.
Idea #3 "[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." (Pg 5)
In the video clip shared during tonight's broadcast, Cathy Fosnot 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 to the reflections that I've read. As I think about this, the thing that really stands out is that the students are able to describe the relationships and patterns that have impacted their thinking. In conversation, they agree, disagree and build on each others' answers. It seems like they really did believe they were mathematicians. Now, that's worth a smile.