Wednesday, February 11, 2015

Day 104: Making Problems Better

Irrelevant, out of date, overly complicated, boring: These are just a few of the ways that I could describe the problems that are in our text book.  I found a great example today that I wanted to share:

The function c = 0.5m + 1 describes the cost c in dollars of a phone call that lasts m minutes made from a room at the Shady Tree Hotel. Graph the function. Use the graph to determine how much a 7-minute call will cost.


Dan Meyer talks about ways that teachers can take bad problems and make them good.

This problem is pretty bad.  Other than the incomprehensible wording, confusing presentation and forced premise, I can't figure out what skills or content this problem is supposed to be practicing.

Is the purpose to get students to see that functions are used in real life?  Is it supposed to imply that phone bills will arrive covered in algebra?  Does it want students to feel that world is a confusing and incomprehensible place?  Does it just want them to be able to graph a function with the basic direction of "Graph the function c = 0.5m + 1" cleverly disguised as a practical, real-world problem?

Does it want them to hate and fear mathematics, making them test averse, driving down scores on the standardized tests designed by those same companies, forcing districts to spend their scarce resources on quick-fix curricula designed by the companies that instigated and perpetuated the "downward spiral" of those scores in the firsts place?

I don't know. I'm just a humble math teacher.

What I DO know is that this problem is terrible.

So I used it as an opportunity for my students to practice the skills that I value.

"What in the world are they asking here?"
"Does Verizon put a formula like this in their commercials?  Have you ever seen it written that way?"

They had not.  We had a discussion about how we could reword the problem to make it more real and less absurd.  We came up with several ideas.

In order to call out from the hotel phone, the hotel will charge $1 to connect the call and $0.50 for each minute that you talk.  Create a graph that shows how cost and minutes on the phone are related.  What equation would describe that graph?

Not perfect, but much better.  I want my students analyzing situations that they will encounter, using wording they will see.

In geometry, I've been following the guided notes that they use at the high school to ensure that we cover the same content.

Today, the activity was one where the students explored the possibilities of sides that will or won't form a triangle.  The activity in their guided notes had them experimenting with strips of paper that were 2, 3, 4, and 5 inches long, asking them to form a hypothesis about necessary side lengths.  Picking 3 of these sides, there are 4 possible combinations.

I wanted something a bit more than this.  So I made more strips for them of lengths varying from 3 centimeters up to 24 centimeters.  There were 15,600 possible combinations, making the group work a bit more interesting.  It opened up the possibility for one person to get all combinations that made triangles and another to get none.

While they were working on that and discussing it, I build an applet in GeoGebra with sliders that let us input side lengths and see whether they made a triangle.

With the visuals, the conversation got much deeper into WHY the sum of the two smaller sides had to be larger than the third side.  The other upside is that my demonstration, along with a brief video from Pixar about how they use geometry to make their movies, has my kids champing at the bit to play around with GeoGebra.

With it loaded onto the student profiles, I hope I'll be able to get them into the lab in the next few days and let them play around with it.

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