## Tuesday, 11 March 2014

Lesson four - Problem solving

One of my primary goals is to change learners’ behaviour with mathematics and numeracy.  A big part of this is accomplished (I hope) by using problem solving activities.  My main challenge has been overcoming the learners’ absolute resistance to working together to solve problems.

Essentially, the learners in the tertiary sector treat all activities as individual tests rather than learning tools.  While they may talk to each other, they do not use each other as resources for solving problems and hence miss the learning opportunities that good problems provide.  Yesterday I included the fish tank problem in my lesson, below is a quick account of how it went.

The fish tank activity (Hat tip Dan Meyer)

Objectives:
• Develop group problem solving discourse patterns such as conjecture, clarification and justification;
• Develop trial, error and evaluation skills;
• Appreciate the need for dimensions of measurement such as milimeters, centimeters, area, volume and time.
• That answers can be expressed as tolerances (not just right or wrong)
I video recorded a fish tank being filled slowly and consistently from a hose.  I showed them the first quarter (roughly) being filled up and timed it.  I then stopped the video and the timer and asked them to work out how long it would take for the tank to fill.  I had the fish tank (empty) in the room with us and each group had measuring tapes.   The partly filled tank was up on the screen where all could see it.

My first question to them was to think about what information you needed to know to help solve the task.  The groups did not engage as I would have hoped.  All groups guessed based on the water taking 48.31 seconds to reach roughly a quarter to a third and used additive thinking to identify a number a little over 3 minutes.  Each group estimated between 3:10 minutes and 3:30 minutes.

Unfortunately these guesses came from individuals within the group working on their own.  There was very little collaboration and hence objective one was completely missed.  Yes, I did discuss the need for this before the activity began and have been trying to cultivate this in the class.  Those who were not sure simply let the others do the working.  I’m struggling to overcome this issue.

We wrote the estimates on the board and then watched the remainder of the video.  As the tank filled groups began to change their guess.  I had total engagement for a moment or two as they all watched the tank fill (a painfully long 3:48 seconds) and all wanted to know the final time.  So even the students who did not contribute to the estimates were still engaged.  That’s one good thing!

What I wanted was groups to use the measuring tape to at least measure the height of the water tank and then determine from the video the exact water level at the time given.  Then I wanted them to extrapolate this out.  Ultimately what they could have done was to find the volume of the tank and then use the video to determine the remaining volume and the exact time to fill it.

The positive of the activity was that all the learners cared!  Even that one student who is always sleepy.  They looked carefully at the video, they asked about how to add seconds given that every 60 is one minute.  One learner had one minute and 92 seconds which started a very good conversation. They stayed five minutes later than they had to.  I'm taking this one as a win!

In a few weeks I think I will redo the activity and actually model how to solve it.  We are going to be working on measurement from here on in so it will facilitate content around time, length, area and volume.  Perhaps even Pascal’s law?

Have you ever tried this activity?  Check out this TED Talk for an overview – the tank activity is toward the end.

A very good clip for tutors teaching numeracy.