You Know What They Say About Assuming…

As a teacher, I have always known that connecting the curriculum to “the real world” is important, but I am just now beginning to understand what a HUGE difference it can make.  I have begun incorporating 3 Act Tasks and other similar activities in my classroom – and I have found that they not only reveal rather large gaps in student learning of the general content, but also in thinking.  Today fascinated me.  I chose to do Robert Kaplinsky’s task “How Much is a 1/3 a Cup of Butter.”  We had great discussion about how 1/4c could be right in the middle of the stick of butter. We modeled how you could take 2 sticks of butter and line them up, so that it would be easy to see that the 1/2c is at the end of one stick, we took time to point out 1/4c, we talked about what we knew about fractions, and we even took time to discuss what we noticed when we looked at the 2 sticks.

Let me stop here and tell you that I really thought I had blown the whole lesson.  I was thinking to myself that I taught them too much and now it would be way to easy.  After all, these kids are gifted…young, but gifted nonetheless.  So imagine my surprise when one student labelled 1/3 cup right after the 3 Tbsp. mark and then justified her answer by saying, “Well, I see 1/4 cup and if you take away one Tbsp. then you have 1/3 cup.  I  asked if anyone agreed with her answer and every kid raised their hand.  So next I had the student point to where 1/2 cup is.  (Remember, it’s labelled at the end and we already had a rather lengthy conversation about it.)  They agreed it should go after the 2Tbsp. mark.

I kept going with their line of reasoning, but I told them I was confused because we now had two different places labelled 1/2 cup.  I then asked which was bigger 1/2 or 1/4.  One girl immediately said 1/2 is bigger, then she drew 2 rectangles and showed 1/2 on one and 1/4 on the other.  When I asked her how she knew, she said her teacher told her last year.

That was a TREMENDOUS moment in our classroom.   I realized how students can know how to solve a problem on paper, but have no idea how it connects to real life.    See, I assumed that if they could determine what fraction was larger – that they would be able to solve this task.  Little did I realize, that their understanding had not progressed beyond solving naked math problems.  That’s a good place to be for a time, and there was even a time in my career when I would have thought that was perfect. But the reality is….they can solve our traditional problems while lacking understanding.  It’s our job to take them from doing math to understanding math.  It’s our job to provide rich opportunities, expose gaps and not merely assume they get it.  It’s an exciting time to be in education.