The Rookery

We are currently in the midst of a math unit on probability.  It's a logical next step after our work on fractions since one application of fractions is probability.  Throughout the unit we stress the importance of trusting math more than one trusts one's "gut."  If I flip six heads in a row, it may seem unlikely that I'd flip a seventh — but in fact, it's still a fifty/fifth chance.  Even when students understand this intellectually, it can take a while to have them really believe it.  In education, this is called conceptual change.  When students (or adults) have a pre-conceived belief, it takes a lot of empirical evidence for them to change their minds.

I remember an example of conceptual change cited in one of my education books.  Students were shown two thermometers.  One was left out on the floor of the classroom and the other was placed on the classroom floor with a large pile of coats on top of it.  Students were asked to predict what would happen after thirty minutes.  Almost all of the students predicted the one under the coats would be hotter than the one in the classroom.  It was not until the class was shown the results and discussed them as a class, and addressed all the possible other explanations ("cold air got in,"  "we needed more time.") that they believed coats didn't make things hotter.

Conceptions of probability work the same way (even for adults – just ask my mother-in-law about her luck with Scrabble tiles!)  We've designed the probability unit to give a lot of concrete experience with probability so that students can successfully shift their understanding of how "luck" works.  Gabe, Cathy and I have each focused on a different kind of game situation – dice, spinners, or picking tiles – but in each of our lessons, we work with students to determine the theoretical probability and then test it using the experimental probability.  That is, we work out the math for how likely something is going to be and then run trials to see how close the reality is to what we expected.  

When students do just a few trials, the results often differ from what was expected (this is what causes a perception of good luck or bad luck) but when we combine all of the trials in the class we see that the experimental probability gets closer and closer to what we expected from the math.

This is a great time to play card games and dice games with your child.  They are ready to be more strategic in their play.  Push them to use math to make their decisions.  A game like "high/low" in which you flip a card and make a prediction about whether or not the next card will be higher or lower is a good place to start.  Students can make a chart to see how many cards are higher or lower than the card that's currently up and use that information to make the best guess.  Over time, students who always go with the mathematical probability will be more successful than those who go with a hunch.  Have your child play both ways to see!  It's only with repeated experience that your child will come to believe in the math (and, hopefully, decide that playing the lottery is not the best plan for retirement.)