The Day I Taught A Lesson (Gasp)

My students have become so comfortable with exploring problems in math that they think having me teach them is absurd.  In all honesty, it sort of is.  I really do believe that for the most part, having the students work through problems and then consolidating the major problems is the best way for them to learn.  Now that it is their culture, it is the norm and they are on-task.

Last week, I gave them a paper with some questions about fractions.  We've done a couple of weeks worth of problems surrounding fractions, but I couldn't really tell yet where their understanding was.  They have been comfortable the whole way through, but the idea of equivalent fractions seemed to evade them.  Even when the question suggested that they use equivalent fractions, they would still be able to find loop holes and solve the problems without even touching them.  That is wonderful, and I embrace this kind of open ended problem solving ... but at the end of the day, I need to have them be able to find equivalent fractions and understand how it works.  I asked them the following questions:

1) What is a fraction?
2) How can you change a fraction?
3) How could you turn a fraction into a decimal or percentage?

#2 blew my mind.  They drew the fraction in different ways.  They discussed the fraction in different ways.  Some even wrote the rest of the whole as a fraction (1/3, 2/3).  FANTASTIC!  But wait.  They hardly touched on equivalent fractions.

So today, I did a "lesson."  (Gasp! Shock!)

As I was getting into some demonstrations (and do note, I approach my lessons in a discover sort of way - there were a lot of aha! moments for the kids, especially those who had pieces of understanding yet weren't yet bringing it all together), one of the kids piped up (with attitude):

"Uh, Mr. Patrick?  When are going to get to work?"

I was flabberghasted.  THIS IS WORK! DUH!

But I realized as I was about to react ... this isn't work as they know it anymore.  This is weird.  This is Mr. Patrick blabbing away.  Yes, many of them had misconceptions repaired and some loose ends tied up in their understanding, but it was still me delivering data.

If I had more time with them, I would have happily continued to let them explore the fraction business and work more one-on-one with them.  But, with only a half day to deliver math, language and science, and time closing in on me as we reach the final 2 months, I can't justify (at this point) another two weeks of problem discovery.  There is still a lot left to cover, and a lot of it won't layer together.

The moral of the story?
1) The kids are comfortable in a problem based setting.  The culture is strong and they LIKE to work.
2) Explicit teaching is still okay, but only when it comes after some discovery.  Otherwise they'd have had nothing to tether it to, and my hot air would have been far less effective.
3) Perhaps I need a better balance - it always seems to come back to balance - and should "talk" just 1% more.  They seemed extremely uncomfortable.  Or maybe I'm just being paranoid - maybe it is a good thing.  But they will be moving on to someone else in September, and that person or those people (who knows who they will be?!) likely will not be quite as comfortable as I am being quiet.  I know it's taken me 3 years of hard, HARD work to learn how to shut up, and I still struggle with it!  So what's the right balance?  I don't know.