Reasoning and justifying is natural

So I took a class this summer called Making Mathematics Reasoning Explicit (MMRE).  The main idea behind the course is that students should be actively involved in learning math and in explaining (justifying) the things that they learn.  Shortly after the class ended I was with my 5-year  old son Ethan.  We were getting tires put on my car, and while we waited he asked to play the “plus game.”  Basically the plus game means that I give him a simple addition problem and he tells me the answer.  Now I just want to say that I had nothing to do with inventing the plus game.  Ethan and his older brother Connor came up with it and for some reason they love to play it whenever we need to pass some time.  But playing the game with them has given me some fascinating insight into how young kids begin to develop math concepts.  It has also made me realize that it is totally natural for kids to justify and give explanations for what they know.  Here is how the game played out that day at the tire shop:

Me:  What is 9 + 5?

Ethan: 14.  You know how I knew that?

Me: How?

Ethan:  Well, I know that 10 + 5 is 15.  So 9 + 5 would have to be 14 because 9 comes right before 10.

Maybe I’m just a proud parent that likes to brag about my kids, but I was impressed that he was able to demonstrate that level of reasoning with addition (I might mention that Ethan has not even started kindergarten yet).  But what really stuck me was the fact that he wanted to explain to me how he knew the answer.  I have seen similar situations with Connor also.  It seems like they just naturally want to explain and make sense of what they are learning.  Contrast that with the typical high school student who just wants their teacher to tell them the answer so they can get their work done.  Somewhere along the line they have lost that sense of excitement that comes from learning and figuring things out on their own.  Somehow I would like to try to get them back to that place.  I’m hoping that some of the ideas from the MMRE Institute will help me accomplish that.

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One thought on “Reasoning and justifying is natural

  1. That course sounds very interesting, I hope you’ll find more occasions to share what you learned through it!
    I also find it unfortunate that students somehow lose that natural desire to share their thinking. For me, hearing someone’s thinking is the most interesting part of talking with people!

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