#MakeoverMonday – Penny Circles

This is my first official blog post.  I’ve always lived and preached the idea that you need to start somewhere, so why not with Makeover Monday’s final task.

The irony of this task is that in my early years of teaching, I thought graphing calculator “investigations” like this were stellar. In fact, I found it buried in my files:  4.10 Investigation I know a lot of Algebra 2 teachers that completely skip this section, so I’ll give my younger self a pat on the back for including it in my curriculum.  Thank goodness I’ve evolved as a teacher, however.

Here are my thoughts/suggestions:

1.  I’ll start with the goal of the lesson:  To fit a quadratic function to a set of data.   I wouldn’t expect students to have read that goal or understand what it means if they had read it.  However, giving that much away at the beginning destroys most of the creativity that can happen with modeling data.  Not giving students a specific model with which to work lets them explore with different possible models in the investigation.

Or even better, stick with the pennies and the circles and have students create a set of data based on an estimate of how many pennies they THINK will fit into the circles.  Then they can create a model first with their estimates.  After they’ve completed the investigation, they can compare their estimated model with their experimental model.

2.  I’m not sure if this came from an Algebra 1 or Algebra 2 textbook, but nevertheless, a teacher cannot just handout compasses and expect perfect circles with diameters of 1 – 5 inches.  And what’s more, why circles and pennies?  I think we could be a little more creative here with our investigative devices. Nevertheless, if we stuck with pennies and circles, we could create discussion between students about how our data and model are affected by the fact that the pennies do not fit perfectly together.

3.  Having a datum for a diameter of 0 is unnecessary and unhelpful in achieving the goal of the task.  Adding that in just compounds the confusion of this messy task.

4.  A power function?  Really?  Again, unnecessary confusion added here.  It’s reasonable to have students play around with their data and try to fit a model to it. But adding the power function jargon in there is not helpful.  Especially when in the next question, the students are told that this is a quadratic function specifically.

5.  “Describe how well the model fits the data.”  These types of questions have to go.  They just BEG for answers like “it fits good.” or “bad.”  The “draw conclusions” section needs to totally be reworked.  It’s almost like the author is saying, “here are the conclusions you SHOULD have drawn.  Now, tell me how well your penny experiment fits those conclusions.”

Overall, the problem with this task, as with most traditional textbook tasks of this sort, is that there is SO much in here by way of directions, the learning objectives get lost.  What happens then, as did with my classroom, is all the students are doing is playing around with circles and pennies.  They aren’t able to generalize the results of their experiment on their own because the book tells them exactly what the results should be.

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