The Power of NOT Giving the Answer

It was a busy week for me!  Report cards were due and we had two nights of conferences.  My son’s football team made it to the state championship game and WON!  Whew!
So, we are starting to get deeper into the content of fourth grade and we are beginning the first of many “mini units” on fraction concepts.  Although our series is good, I MISS my fraction unit that I wrote a year or so ago and still feel compelled to use a huge part of it.  Part of what I love is the deep thinking that the unit requires.  I love to watch my students grow as thinkers and “reasoners”. In fact, I have been using the phrase “Use your reasoning” a LOT lately…I want my students to get better at thinking about what they already know and what makes sense.
So, before I got into the fraction work from our series, I presented my students with this problem from MY unit and gave them some time to think about write about it.  
I was intrigued to walk around and see the “reasoning” my students were sharing…and it seemed to be clear that their understanding of fractions was really pretty unsophisticated.
I thought perhaps having a lively debate might help us clarify some understanding so I asked my students to commit to one or two sides of the issue and here is what we found…
Once the students committed to a side, we split into “teams” and practiced using math talk to try to convince students on the other “team” to come over to their side.  If students listed to the reasoning and changed their mind, they moved to the other side of the taped line.  I was a little disappointed that no students heard any compelling arguments…not enough to make them switch teams.
After only about 5 minutes. I could already see attention waning.  I couldn’t believe it!  I could tell I only had about half the students with me when one blurted out…
“When are you just going to tell us the right answer?”
It was right then when I made the decision that they were going to have to wait for this one.  I was NOT going to tell them.  I wanted them to think.  I wanted them to stew.  To make sure they did?  Their homework was to take the problem home and discuss it with someone.
The next day they came in and picked up our discussion where we left off–but a few students HAD changed their minds.  We continued our discussion and our debate but I still wasn’t really hearing deep enough thinking so after a few more minutes I heard the same request.
“NOW can you tell us the right answer?”
I decided to let them stew on it one more day…and I told them that I really wanted them to use their reasoning to be able to prove their thinking.  On Day 3 I finally had a student make an argument compelling enough (She got into the “half of a half” argument) that got a number of students to convert.  So why did I drag this out?  Math is not a right answer.  Math is not a fill in the blank.  Math is thinking.  Math is reasoning.  I want my students to know that not all answers come instantly or even after a day or two…and that’s ok.  It’s more important to really understand than to take short cuts.  Did they all understand the problem?  Time will tell–but I think it was worth the wait.
If you weren’t a follower of mine back when I did my series of 16 posts about fractions, you might want to click the “fractions” label on the right to see more.  The resource I made with all 16 lessons can be found here if you are interested.  Have a great week, everyone!