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Functions

Our grade 8 team has been working together for about 4 years.  We have a pretty good system in place, and by all measures, our kids have been doing just fine.  Our district has always provided time for us to collaborate and to learn; through lesson study, data teams, or just by giving us time to work together. With all of the opportunities we have for serious conversations about learning and teaching, we started asking questions.  It was when we started asking questions that “got under the kids’ thinking” that we began to see things differently, and we realized that we had some serious work to do.  (The quotation refers to Cathy Fosnot’s eloquent description of what happens when you ask kids to talk about their thinking.  She shared this during her presentations at the 2013 CMC-South Math Conference in Palm Springs, CA.)

Based on what we learned by asking our kids questions about their mathematical thinking, we decided this year we would focus explicitly on our own learning.  We began the year by reading the Standards for Mathematical Content and the Standards for Mathematical Practice.  Then, we selected Functions as our first unit of study.  Our first few conversations were centered around an idea we read about on blogs and tweets shared via the MTBoS (grantwiggins.wordpress.com)–what are the 4 big ideas of functions?  Our first draft list looks like this:

The Big Ideas of Function (take one)

  • Functions describe a situation in which 1 quantity is determined by another
  • How are 2 quantities related
  • Use Functions to model relationships between quantities
  • Interpreting graphs and relationships

Our first draft list was based on reading the content standards, side-by-side, with the Progressions Documents from The Institute of Mathematics and Education.  We also used documents and resources from the functions class organized by Christopher Danielson, at Overthinking My Teaching.  We are slowly making our way through some of the resources he shared–an article written by Shlomo Vinner entitled The Function Concept as a Prototype for Problems in Mathematics Learning, the work of the School Mathematics Study Group on functions, and tasks from Mathalicious and Connected Mathematics.  Each time we meet, we bring other resources and documents into the conversation.

We want to give a shout out to Fawn Nguyen for creating the site visual patterns.org.  It has been a great resource for us as we investigate the big ideas of functions.

It’s an interesting and crazy journey.  We are learning about and deepening our understanding of the same ideas, at about the same time our students are investigating the ideas.  Makes for some challenging and frustrating days, and for some really fabulous days–all of which are providing amazing aha moments for our kids and for us.

We meet tomorrow afternoon to do some more work.

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