Saturday, July 30, 2011

NCTM Institute on Reasoning and Sense Making - Making Sense in Algebra 2 7/29

The last breakout workshop I attended on Friday was “Making Sense in Algebra 2” led by Henri Picciotto from The Urban School of San Francisco. All handouts are available on his website (

By the time I got to this session, I was hitting the mid-afternoon doldrums that you especially get when you have been at a conference all day and you’re not used to all that learning. This session was full and they did not have enough handouts. They were good and eventually got them to us all. I ended up at a seat on the side, so I wasn’t able to participate in the activities that used manipulatives.

His solution for Making Sense in Algebra 2:
  • Escape from the textbook!
  • Choose depth over breadth
  • Keep tweaking the course
  • Collaboration makes it possible - His department meets every week and continues to communicate.
Their Algebra 2 course is broken into two sections. He showed us the loose organization of the topics. I was not able to get all of it written down, but one of the key things they did in the organization of topics was split apart some topics that are traditionally put together (such as exponential and logarithmic functions). By separating exponentials and logs, parabolas and quadratics, it allows them to review and strengthen the grasp of their students.

We spent most of the rest of the session working through problems. Some of the activities involved using algebra tiles and other manipulatives. With each of the problems, he concluded with a point about making sense. Those points are:

Making Sense – Start with a Big Question:
 Starting with iteration…
 -levels the playing field
 -enhances calculator/Fathom/spreadsheet fluency
 -formulas encapsulate understanding, are not an obstacle to it, or a substitute for it
 -introduces convergence, divergence, limits
 -makes arithmetic and geometric sequences look easy!
 (starts with something more difficult and makes things look easier)

Making sense – use manipulatives as an exploration, reflection, and discussion environment

Making Sense – use real “real world” connections
-hands-on experiments motivate the concepts.

Making sense – concepts first (not notation, not terminology)
The activity involved finding the exponent in the expression 10 to a power (it’s called Super Scientific Notation). This activity gives meaning to logs, emphasizing that logs are exponents and helps to justify log rules. Henri did note that students do panic when intro notation and terminology – but remind them of this anchor activity and it eases their panic.

Making sense – reason about numbers
Connection to art
Application of geometry

At the end, Henri gave us his strategies for sense making:
  • Do fewer topics in more depth
  • Sequence them strategically
  • Start units with memorable anchor problems
  • Incorporate manipulative and electronic tools
  • Concepts first
  • Formulas, notation, terminology – handle with care!
  • Navigate between multiple representations
  • Do not skimp on visual, geometric, and hands-on approaches
These strategies make Algebra 2 accessible, but doesn’t make it easy. In conclusion, Henri touted the website, which is a community that offers suggestions on how to “escape the textbook” and if I understood him correctly, there is a forum with problems and a place to share information and strategies.

I struggled somewhat with this session. After having spent time looking at what Dan Meyer was presenting and working on incorporating media and a “wow!” factor to it all, this seemed somewhat duller to me. However, upon further reflection and discussion, I am seeing that one cannot do that type of thing all of the time. It loses its “shiny” nature to students. If you do the same thing all the time, even if it’s wonderful, it will lose some of its effectiveness. I think there is some merit with what Henri presented. I’m still trying to figure out how to make it all work for me.

1 comment:

cheesemonkeysf said...

I love Henri Picciotto! He is a legend here in San Francisco, because his students REALLY grasp the mathematics they are doing in a deep and durable way. He gets a higher percentage of students into -- and through -- Calculus than anybody I know. @woutgeo, @btwnthenumber, @suevanhattum, and I are all regulars at Escape from the Textbook!

His ideas are less glittery than Dan's video-based lesson ideas, but they are incredibly effective. I have so much admiration for his results.

And speaking as a learner who is not always helped by visual representations, I appreciate Henri's commitment to creating multiple entry points including kinesthetic and auditory approaches. It is hard to be passive in his classes.

The best thing I've learned from Henri's strategies is that no one approach works for every learner all the time, which is why it's so helpful to have a deep basket of approaches available to me. This is an area where Henri's creativity and generosity have been super-valuable.

- Elizabeth (aka @cheesemonkeysf on Twitter)