I continue to try and get a handle on the Discrete Math class I inherited mid August. One of the highlights has been the conversational nature of the class. Each section has 8 students and they all sit at one large conference style table. We have been wrestling with probability and there were three questions I asked on their latest HW assignment that I was happy with as I wrote. What I realized during class today was that I will be much happier next year when I rearrange them. The first question was in four parts. The context was that I had tossed a coin four times and I asked the following questions:

- What is the probability that all four are heads?
- What is the probability that all four are heads if I tell you that at least one is heads?
- What is the probability that all four are heads if I tell you that at least two of the tosses are heads?
- What is the probability that all four are heads if I tell you that at least three are heads?

A number of my students struggled to see why the changing information changed the probability. In my first class they dutifully followed my path of reasoning as I drew the outcomes and talked about the answer. It was not until we reached questions three and four that I saw light bulbs go off. In question three I told them that a friend of theirs reported having tossed a coin ten times and seeing a head each time. Their friend tells them that he KNOWS that the next toss will be tails. Their job was to convince their friend otherwise. In question four the conversation continues with their friend arguing that there is only a 1/2048 chance of eleven heads in a row. No way that will happen! Again, they were asked to address their friend’s misconception. While we discussed these two questions a number of students popped up and said that the first question now made sense. So in my afternoon class I swapped the order of the conversation and question one fell into place so much more easily. I am definitely changing this order for next year to help support my kids as they develop their understanding of probability.

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