Monday, May 23, 2005

Teaching Probability with Tree Diagrams (Reflection)

Tree Diagram
Originally uploaded by Misterteacher.
We're finishing a two week unit on probability in my 7th grade classes. This year students had to make the jump from finding simple probabilities to computing compound probabilities (two tosses of a coin instead of one). Students were to use a list or tree diagram to find the sample space (total outcomes) and all favorable combinations (such as the number of times 2 heads and a tail occurs when tossing three coins).

Making tree diagrams has been extremely difficult for most of my students. They are having trouble even knowing where to begin with the diagrams. For instance, when calculating the sample space for tossing three coins, instead of branching out from a head and tail on the first toss, they might begin with three outcomes (two heads and a tail) and add three branches to each of those (to designate three coins being tossed).

To eliminate confusion next year, I am definitely going to create tree diagrams with blank spaces (see example) for each problem they solve and just have them fill in the blanks. This seems like the proper amount of scaffolding they will need to eventually create their own.


Unknown said...

A good idea.

Many texts nowadays do the same thing.

Another tack they take is to tell students that they are flipping, say, three coins, but just show them one at first. Ask students what the number of possible results of one flip are; then write down each result (heads and tails).

Then you ask them to deal with each possibility: Suppose I flipped a heads on the first coin, and now I'm flipping the second coin. What are the possible results on the second coin? (Obviously, it's just heads and tails again.)

And so on.

Dealing with one event at a time can help simplify the task.

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