Student questions about probability

After yesterday’s realization that I was directly the flow of learning too much in my class, I asked my students today to generate some questions they were interested in regarding probability. Here are their responses (posted also on the class blog at mrgrasley.wordpress.com).

  1. What are the chances of winning the lottery?
  2. What are the chances of finding a shiny Pokémon?
  3. What are the chances of the earth being destroyed by an asteroid?
  4. What are the odds it will snow tomorrow?
  5. What are the chances of winning a car in Roll Up The Rim?
  6. What are the chances of being “caller number 5” on a radio contest?
  7. What are the chances of your seat being picked for the million-dollar shot at a basketball game?
  8. What are the chances of being struck by lightning?
  9. What are the chances of finding a $100 bill on the ground?
  10. What are the chances of getting all red lights on the way to work?
  11. What is the probability that a solar storm wipes out Earth’s electronics?
  12. What are the odds of an average poker hand winning?

I’m proud of their questions. I can see that some of them will be very difficult to answer, and others fairly easy. All of them will require some thinking about possible outcomes or statistical probability (which we haven’t studied yet, so that’s pretty awesome).

Tomorrow we’re going to start trying to solve these questions. I’ll give the students the list, and we’ll start drumming up solutions in groups using chart paper to record thinking. I’m pretty excited; I hope they are too. There is a ton of excellent learning that can come out of this.

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I made another mistake: missing out on inquiry and authenticity

I’m teaching MDM4U (Data Management) this semester and we’re starting to talk about probability. We’ve spent the last few weeks learning a bunch of counting techniques (permutations, anyone?) and soon we’ll be applying those techniques in this new context.

But I’m concerned about how teacher-directed everything has become, and how comfortable my students seem to be with that mode. When does their curiosity take control of our journey? How will their interests drive our learning?

On the first day of the probability section I was speaking with the entire class about the sorts of probabilities they would be familiar with: chance of rain, poker, winning a football game, etc. One student asked, “What are the chances of winning the lottery?”

And I made a big mistake.

I told him, “We’re going to look at that when we have a few more tools to work with.”

I should have said, “Let’s try to figure that out. Now.”

His curiosity would certainly have driven him and other students to pursue an answer to that question. No, they don’t necessarily have the skills to answer that yet (some would), but I also don’t need to teach a bunch of lessons before they can start.

I should have encouraged him to frame that question mathematically, identify the information that would be needed to solve it, and begin to do so.

Instead I put him off and went on with my boring talk about rolling dice and flipping coins. I missed a great opportunity for authentic learning in favour of simple, canned questions.

So, my deepest apologies to that young man and to the rest of the class. Tomorrow, I fix it. Tomorrow, you will decide what you want to learn, and then you’ll learn it, and I’ll be there to coach you along the way.