Sunday, April 19, 2015

Digesting NCTM

Just had an amazing 4 days being steeped in the world of math education at NCTM. On the plane ride home last night, I went through my notes from each of the sessions I attended and my own (by the way, I think that the most learning that I had this week was from planning my session with the inimitable @fnoschese and @_mattowen_ - there's nothing like preparing a presentation with thoughtful colleagues for elevating your own understanding of your practice) to try to congeal and connect all the various thoughts that I had in my head this week. Here are my conclusions and to-do's, the big takeaways being:
  1. A curriculum is not a series of tasks, projects, and activities, no matter how open or interesting. It is a cohesive progression with clearly defined goals that needs to spiral within a given year and progress from one year to the next. Everything else will be piecemeal until we create a common understanding of our curriculum progression and look at it as a whole. On the other hand, it was nice to realize that we are already doing so many of the individual best practices I heard about at NCTM and just need to pull it all together.

  2. Real-time professional collaboration is where it's at. In several of the sessions, it was evident how powerful lesson study, teacher time-outs, and opportunities to team teach and reflect on each others' practice in a supportive, nonjudgemental way can be. We are already working on a mentor program for new math teachers, but this reminded me of the need for this for all teachers. As wonderful as Twitter is as a resource, it doesn't replace working with your colleagues to move your school forward.

Specific notes from my plane ride brain dump (please feel free to stop reading, this is just for my personal recording and accountability):

More scaffolding for big projects

  • Too low and too high guess to start
  • Make a plan
  • Work independently for 5 minutes
  • Share with others in class
  • Amend plan or make a new one, reflect on why the original one didn't work out
  • Some time outside of class
  • More time in class and check-ins through the process, not just following up with students after the deadline
  • Required revision for at least one project (will connect to portfolio project and end-of-year defense of work)

Integrate projects more into course structure

  • Follow up in class to share strategies and connections to content
  • Activity or project can serve as launching point for several other problems, can be lynchpin for entire unit or subunit - use it to build cohesion and add more continuity and coherence into the unit
  • Revisit same project or task at the end of the unit or do a similar one to reflect on progress

More frequent feedback on practices

  • Update homework spreadsheet every week
  • Students track own content scores (I can still use Active Grade to track it officially)
  • Track class discourse and participation (from Carmel Schettino's handout)
  • Individual meetings every 2 weeks for ongoing feedback and more back-and-forth rather than one direction for feedback
  • Have students explictly reflect on practices as part of biweekly reflection on progress in course
  • Have students rate themselves on practices and cite specific evidence for each (need to get a link to Carmel's handout for this)
  • Get more frequent feedback from students as to what is working and what needs to be tweaked from my end. Be more open and inviting of feedback, solicit negative as well as positive feedback.

Professional collaboration

  • Buddy up with a teacher to team teach one lesson per week in one person's class, switch off week to week; use teacher time outs during class
  • Organize department-wide lesson study to plan together and revise - could this be done with teachers from other schools?
  • Organize next year's schedule to have some same-level classes scheduled at the same time - can double up the two classes and two teachers once per week
  • Continue K-12 strand work through the summer and next year to build better cohesion between courses

Improve questions and conversations

  • Include "I learned..." and "I wonder..." either as exit ticket (digital) or as homework
  • Take more time for labs - white boarding and debriefing are crucial, have students reflect on each others' work, discuss meaning and context, summarize as a class, create a space where summaries from one day to the next can be saved and seen
  • Build on lab as a way to start a unit and investigate a new topic, should serve as launchpad for following activities (similar to opening project or task)
  • Make labs more open
    • Start by showing something and asking kids what is interesting, what we could measure 
    • Identify a relationship to measure, ask kids to define variables (creating a model is a key part of modeling in addition to manipulating a given model)
    • Have each student make their own data table and sketch in their notebook, each one answers questions in notebook before creating group whiteboard
    • Don't tell them how to figure out the relationship always; start with more scaffolds: telling them to graph by hand and find equation by hand first, then show them Desmos, Excel, graphing calculators, then show regression models and let them choose how to represent (can require at least two representations or whatever makes sense)

  • Work on including more open questions
    • Embed review content into applications or new contexts
    • Ask students how the problem might be changed to make it easier? Harder?
    • Ask questions in which students have choice a la Marian Small: "Make two quadratic functions with intercepts at -1 and 5" instead of, "find the intercepts of this function." Then you can discuss the characteristics of all the functions students generated.
    • Spiral up investigations and tasks to remove scaffolding as the year progresses, should end with investigation of their own design (progressively more complex from one year to the next)
    • Include "Would you rather..." and "Which one doesn't belong?" and all the other techniques mentioned by Geoff Krall to open up tasks

Next year plans

  • Summer math class for incoming 9th to fill in gaps in content and practices
  • Require graph notebook (binder? digital?) - decide as a discipline what we want for students; it could be different year to year, but should be a cohesive progression
    • This will tie into portfolio project - digital might make sense if kids are taking pictures and turning in all assignments digitally
  • Look at the progression of our math courses: how are we spiraling content and practices year to year? Can we build on projects/mathematical spaces as students develop a more sophisticated understanding of content?
  • Look for better projects and tasks to build more coherent progression within the year and between years (investigate Carmel's materials, 3 act tasks, IMP books, Geoff Krall's materials, Robert Kaplinsky's materials, list of labs from Casey Rutherford)
  • Coordinate more with other disciplines; goal is at least one collaborative project with each discipline per year
  • Look into a capstone project connected to grade trip; 9th grade Peru trip can connect to statistics and data analysis, 10th grade Costa Rica trip can connect to modeling

Books to read

  • Good Questions: Great Ways to Differentiate Mathematics Instruction, Marian Small
  • Art of Problem Solving series
  • How to Solve It, Polya
  • Fostering Geometric Thinking, Mark Driscoll
  • Mathematics Formative Assessment, Keeley
  • Investigate Geogebra, Python (may need online class), TI-Nspire, Sketch Explorer, Mathematica, Wolfram, new programming project from Bootstrap
  • Look through CME Project integrated series for possible adoption

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