Parameters in Problems (That's the Problem)

The problem with math is the wording of problems.

The longer I teach, the more I realize that I don't know what I'm doing.  No - wait.  That's not flattering, is it?

I do know what I'm doing when it comes to: planning and plotting, marking and giving feedback, building healthy, positive relationships with every student.

But, I don't know what I'm doing when it comes to: letting them find the way.

I think that the biggest problem we, as teachers, have created for ourselves is that we don't let them find their way.  In fact, we have created so many parameters that we have all but cornered ourselves into teaching.

Yes, there is a curriculum.

No, it doesn't need to be followed from expectation #1 to expectation #1million or whatever the last one is.

Parameters is something that clicked for me during a Hub.  I realized the problem with our questions was that we:

- assume that they know the parameters that we know, because we looked at the curriculum and "designed" the question in a brilliant way

- get upset when they build their own parameters and don't go the direction we were expecting

- get upset when we want them to build parameters and they don't because they don't know how or think that they're allowed, because we got upset when they did it before


Phew.  Take a moment to let that all soak in.


So what do we do?

I've started trying to design questions that have missing information.  I'm hoping that by allowing for - and discussing with the students - the parameters that are missing, that are present, and that are IMPORTANT, some of this silliness can be avoided.  Afterall, if I pose a question and the students solve it according to their parameters - they do the leg work, can prove their thinking, and are finished shortly thereafter ... what's the problem?  It didn't hit on the right curriculum expectations?  Not to be crass, but hey, shut up and be happy.  Make a note in your anecdotal records, where ever you keep them (mine are in my phone under the Memo app), identify what expectations they DID meet, and move on.

Here's an example of a problem I gave with little parameters.  I wanted to see where they went:

Create an equation to show how many days of school the students attended, if there are 194 days of school.

Note: We've been working on equations, symbols and missing values, constants and variables.  This was all highlighted before we got to the question.

I wanted to see where they would go.  I knew some would do this:
- how many days did ONE student go to school?
- how many days did OUR CLASS go to school by the end of the year?
- Where is the attendance?

None found the answer for the students in the entire school.  Most focused on the FINAL ANSWER and NOT the equation part, which was really the only concrete parameter I gave.  But that's okay, I took the info and incorporated it into the next day's problem, and identified it during our wrap-up.

Most students looked at attendance, made tables and charts, and found out how many days of school had been attended to date.  THAT is good, since we obviously don't know about future snow days or sick days.

One group identified this equation: 21 (students) x 194 - DM (days missed)  Perfection. Sorta. 

This question is WIDE OPEN.  On purpose.

Here is a LESS wide open question:

Build an equation to show how much Mr. Patrick makes, if he earns $10 an hour.  (Note: You can change it to challenge yourself.)  How much will he make in:
- a day's work?
- a week's work?
- a school year's work?

This was surprisingly difficult for the kids.  Not the finding the answer part, but the finding the equation part (which in this case, is the answer, actually).  Of course, I know I can say "If I make $10 an hour and work 7 hours a day, I will make $70/day.  So, take the days worked and multiply that by the amount I make: D (days) x $70 = answer.  But, different people set up different parameters.

They wanted to know:
- how long do you work?
- how long is the school day?
- does it include breaks?
- do you get paid if you do more?
- do you get paid if you stay late? come in early?
- do we count weekends?
- are holidays part of the 194 days at school? should I take them out? what about snow days?

And so on.  It was impressive.  They built rules for themselves, and found answers that suited their own set of rules.  I still got what I needed from them, even though many didn't quite make it to that FINAL ANSWER.  It's okay.  It was a positive experience, and I got to see (from the two days featuring these questions) that they have solid skills to find answers, even if it is not as quick and efficient as using an equation with constants and variables.

End of the world?  No way.

Let them eat cake! I say.  Oh, and let them build their own parameters, which are suitable and informed and make sense and are important to the problem, and then we'll all be happy ... and we can eat cake.  Who wants to split it into fractions for me?