I’ve been learning from Cathy Fosnot for many years. I first started using her Context for Learning Math Units about 15 years ago. I’ve read her books, even the newest conferring book. I’ve attended in-person workshops with her. I listened to every episode, sometimes more than once, of her podcasts on VoicEd Radio. (Go here if you want to listen!)
You might think I didn’t need to go to a 2 day workshop to learn some more from her, but HOLY COW I learned so much in the last days.
Both days we focused on using Number Strings to promote the development of numeracy. I wrote in my notes: We do STRINGS to promote a development of NUMERACY – a deep understanding of number and operation. We want to eliminate as much working memory stress as possible. We want SO MANY things to become automatic and known so they (students) don’t have to work every piece out.
After spending a few days working through Number Strings with Cathy and many of my colleagues, I have come up with a few things for me to work on adding to or refining in my teaching practice.
- Cathy had all the problems in the string listed on the side of the board. She added her models and numeric representations on the side. Some of these were erased as they got messy or as she ran out of room, but the equations in the string stayed up during the whole conversation. This will help students have the answers from previous questions, and helps them see the patterns in the questions, which will hopefully help them see the patterns in the solutions that can help them learn how to solve equations.
- Cathy talked a lot about using multiple representations for a single strategy. This helps children who understand one begin to understand another. This is also because if they don’t understand the first they have a chance of understanding the second. Overtime they can develop some fluency and flexibility and choose for themselves which strategy or representation makes the most sense. In my notes I wrote: “DIFFERENT REPRESENTATIONS DEVELOP DIFFERENT THINKING! Choose the model carefully. Go back and forth between representations so that they can constantly see the connections.” This is also something Monica Neagoy really stressed in “Unpacking Fractions” (Summer book club, which I just realized I never blogged about!) Showing things with many different models helps kids understand the math instead of just understanding the model.
- I have been modelling decomposing using carrots, and Cathy was modelling them using parentheses/brackets. She admitted this is new thinking for her. I learned about the carrots from her! I’m going to use the brackets from now on. The carrots do make it messier. I also think that going straight to the brackets, using associative property and commutative property from the start, even in primary grades, is going to remove an attitudinal barrier that exists for students who think they are starting to learn algebra for the first time in grade 5 or 6. I think this makes it so obvious that algebra is taught all along!
Those are 3 pretty good goals, I think.
I am excited and mostly ready to go back to school. Workshops like this, at the end of August, help me get even more excited about starting with a group of children and helping them grow as mathematicians (and readers and writers, and humans.) I’m also looking forward to more podcasts with Cathy Fosnot on VoicEd starting at the end of September. I feel like I STILL have a lot to learn from her.