Wednesday, April 18, 2012

Rational Expressions Treasure Hunt (or, Intrinsic Motivation for the Intrinsically Unmotivat-able Bits)

We are coming up on our state testing window (STAR testing in California, ugh), which means it's time to finish "covering" all the so-called key standards material in preparation for the last-minute test prep and hand-wringing.

In our Algebra 1 curriculum, the last unit before state testing is the Rational Expressions unit, which I find to be one of those inherently frustrating and procedural sections.

The good news of the rational expressions unit is that it gives Algebra 1 students an opportunity to see how some of the foundational skills and concepts they've been learning can come together to provide some very sophisticated conceptual and computational tools.

The bad news is, students are tired -- tired of the routine of observation - guided practice - independent practice - followed by a chapter test. And they're just plain tired in the sense that they've absorbed a lot in every class they're in and basically their brains are kind of full.

So I reviewed my notes on Dan Pink's book Drive to see how I could weave together his ideas of autonomy, mastery, and purpose. And that gave me the following ideas:

• AUTONOMY - students needed a unit which relies more on self-checking than on getting a teacher seal of approval (or a rubber stamp);
• MASTERY - students seemed to need a unit which would emphasize tracking their mastery of skills and concepts, which meant giving them lots of opportunities both to do and to spot patterns in their doing;
• PURPOSE - students needed a sense of purpose to the overall activity, rather than the "bigger picture" sense of Dan Meyer's WCYDWT (What Can You Do With This?) -  to provide some light-hearted gratification or, as some might put it, a cheap thrill. :-)
As these ideas whirled around, I felt envious of Kate Nowak's wonderful circumcenters lesson (from Geometry) that harnessed fun clues with the need to draw circumcenters on a map of the school as a motivation for hunting down numbered markers which she had tucked around the school.

It occurred to me that I could use a treasure hunt idea (organized more as a geocaching or letterboxing hunt) as an intrinsically self-motivating reward system -- coupled with a series of self-check-able problem sets/worksheets -- to give students a little break from routine and a reason to work together purposefully to practice simplifying rational expressions and finding the excluded values.

So here are the components I created:

1. a set of graduated worksheets (one for each day) for them to use as practice problems
2. a handwritten Answer Key that I slipped into sheet protectors and tacked up on the front bulletin board for students to check their work against
3. a "rubber-stamping station" where I or they would stamp their completed AND checked worksheets to place in their...
4. group folder
5. a Ziploc bag or sheet protector stapled to the inside of the group folder where they could store their treasure tokens
6. a set of "clue" cards, one for each worksheet's treasure token, that students would take together with a...
7. Hall Passes (which clearly states that I have given them permission to snuffle around in the designated area to find their treasure tokens and come back to my classroom)
8. one weatherproof plastic Gladware container PER treasure box/worksheet to contain the treasure tokens for each worksheet/level (I used Woodsies stars that I bought at Michael's and labeled them 11-2a or 11-2b to correspond to their worksheets, but you could also use punched-out paper or cardboard shapes of any type); treasure boxes were labeled with masking tape and also contained a marker and an index card on which students would write their group's initials when they removed a token

A couple of observations. First of all, your "clue cards" will be different from mine based on your school and where you wish to send your students on their searching. Being a California indoor-outdoor type of school that is built into a hillside, we have a lot of beautifully xeriscaped/landscaped pocket gardens that made for good treasure box hiding places. So my clues said stuff like, "Facing room ELEVEN, TWO TIMES TEN paces or so to your right, you'll find a bathtub fit for a bird. Look below the bushes behind..." Or "Head toward LUCKY 13 and look for the LAVENDER HEDGE. The treasure box is tucked behind..."

Students responded positively to this shift toward autonomy. They delight in completing a practice task that grants them permission to snuffle around a little outside in the fresh air. And they seem to love unraveling the clues, maybe because they love reading and thinking about themselves and their own environment. The Hall Pass requirement gave them a clear set of expectations and accountability, and even my least accountable students have been taking it seriously, which is a refreshing change of pace for all of us.

Their assessment will come from my review of their group project folder -- its tokens, its completed and corrected worksheets, and the presence or absence of worksheets for each student in the group.

The worksheets and sample hall passes and clues are up on Box.net

1. So, is the requirement that everyone in the group finish and check their worksheet before they can go look for the treasure?

2. Yes, that is correct. The whole group needs to complete and check their

3. Interesting approach.
How did it work?

4. It ended up working really well!

The reality of California's standards is that students need a LOT of practice with rational expressions to succeed. So the treasure hunt idea lowered students' resistance to "wallowing" in working with rational expression. In fact, it gave them a secret excuse to enjoy the time they needed to wallow in the structure of expressions.

The nicest side benefit from my perspective was that it gave all students the time they needed to see structure in expressions. For many math teachers as math learners, noticing that structure was something that came naturally and without conscious effort. But a lot of people just need more time wallowing before that light bulb moment happens. Setting the stage for students to experience both intrinsic motivation and authentic discovery of the patterns was something that proved to be very effective. I will definitely be experimenting with this idea more and blogging about it.

5. What did you do so that you didnt have multiple groups going out at once? Or did you let them all go? What did you have groups do who finished early?

1. Good questions. There was a fixed number of "search passes," so if all passes were out with two groups, the next group had to wait until a group came back.

There were so many more worksheets to solve before they could get approval to go searching that they were motivated to search quickly.

I didn't have any groups finish early. I tried to have more work for them to do than was possible to finish before the end of each class period.