The Zone

The Zone of Proximal Development is huge in education.  Basically, you can't learn if you have nothing for the learning to cling to, or if it's so dang easy that you could do it in your sleep.  I'm finding that this year more than ever, I'm hitting the zone for my students, evidenced by:

- on task behaviour
- thoughtful questioning
- perseverance
- success of their answers

When conducting Problem Based Math, it is absolutely necessary to pick your curriculum expectations before starting the questions, and look at the "long run" - I look at about 4-5 days at a time.  I ask myself:

1) What strands can go together based on this "inspiration expectation"?
The inspiration expectation should be your MAIN expectation: this is what you'll base everything else around.

2) How many expectations are manageable with my main inspiration expectation?
When starting, only 2 may be manageable.  I find that the basic number sense expectations go pretty much with everything, so those remain most weeks, or cycles as I call them, as my five day plans don't always land inside a perfect week.

3) What strategy/strategies do I want the kids to focus on/learn/build with this cycle?
If we're going to focus on building a table, then I know my expectations should fit into a question that requires a table.  This week, I'm focusing on finding different dimensions for a specific area and/or perimeter, so a table may come in handy, but we'll layer in Working Backwards, so that the students can focus on the relationship between multiplying and dividing.  (Example: The area is 36cm.  Since 36 divided by 9 is 4, I know that the dimensions of the rectangle are 9cm (length) and 4cm (width).  9x4=36 and 36 divided by 9 is 4.  I can work backwards from the answer of a=36cm.)

When I know this, I look for expectations from each strand that could fit nicely together.  I can usually layer in about 3 strands comfortably.

Then, I take the prompts directly from the curriculum to get started.  The example in #3 is from a prompt.  That prompt will be the focus of our learning for 3 out of 5 days of this cycle, worded in different ways, so that an understanding of area, perimeter, operations, organization, and patterning/algebra (missing numbers in an equation) is built.

I start day 1 of each cycle by introducing or revisiting a problem solving strategy.  The questions I ask are easy, but the students are regularly reminded that the numbers are easy so that they can focus on understanding the strategy.  This is how I access their zone for the strategy building part of the week.  Once that strategy has been practiced as a whole group, with peers, and independently on day 1 (each problem, which comes from different problem solving resources, including Problem Solver and Word Problems for The SmartBoard), we reflect on the strategy in our math journals, and call it a day.


As we progress through days 2-4, their zones are established by reminding them of the strategies they can use, the problem solving steps they can use, and by reading the problem together as a class.  Really, the kids do most of the work.  I rarely say anything other than their names so they can "teach."

During the problem solving period (about 30-40 minutes) on days 2-4, I am constantly circulating, to see where the kids are and how they're progressing.  Some need prompts, but I try to keep those rare, only when they're absolutely necessary.  This is how I stay on top of who is in the zone and who is lost.

Once I've figured that out, I can pull small groups for "Guided Math," and at the end of each problem solving period, the kids volunteer to show off their work.  I'm lucky enough to have a document camera with my Smart Board, so we can show their work on "the big screen."  The kids volunteer even when they know they've made a mistake, because they have something show off: maybe it's their organizing skills, or maybe it's their proof statement.  Regardless, they have something to share, so I encourage it.  It builds confidence and exposes students to possible errors, different thinking, and different correct answers.

On Day 5, I do a "check."  This is an independent assessment question that has nothing new to it.  It isn't a copy of the others, but it uses similar wording, numbers and expects the same from the students.  Otherwise, it would be an unfair assessment and a waste of time.

By constantly monitoring and going into curriculum documents on a weekly (sometimes daily!) basis, you'll hit their zones no problem.

The curriculum documents fully support problem based math, and are one of the few resources you really need.  Imagine clearing the bookshelves of old and tired copiable worksheets and text books, and placing manipulatives on the shelves instead.  It's possible.  I know, because I'm doing it!