Recently my math class was studying basic probability and I had one student who was really having a hard time wrapping her head around the topic. One evening I got an email from them, stating that they didn’t understand one of the practice problems:
Given that P(E) = 1/4 find the odds in favor of E.
P(E) means the probability of E happening. 1/4 means that there are four possible outcomes and that E (the one we want) is only one of them.
We figure our odds for something by comparing the number of possible things that we want (in this case just one) versus the number of possible things we don’t (in this case the other three).
So the odds are 1 to 3 that our event E will happen because out of four total, only one of them is E.
I hope this helps.
They responded that it didn’t help and that they had read the chapter multiple times and just weren’t getting it.
I gave this some more thought and decided on a different tactic:
Let me give it one more shot:
We’re having a dog race — four beagles: Evelyn, Sam, Henry and Charlie.
All four dogs are evenly matched – same age, physical condition, everything – so each of them is equally likely to win.
However, Evelyn is your favorite and you’d like to know the probability that she’ll win the race. There is a total of four dogs so she has one chance in four to win. In math-speak, this is known as :
P(E) = 1/4
What about the odds? Well, It’s Evelyn against the other three dogs so we say that the odds for Evelyn winning are 1 to 3 or 1:3
Once I had expressed it in the form of a story, it clicked. They replied that they now understood what the problem was about and had a better sense of the material.
In my experience, the mere mention of ‘story problems’ (sometimes known as ‘word problems’) is enough to send my students into fits. (Google ‘story problems suck’. This is not an isolated issue.)
But stories are the primary way we humans communicate with each other. I use stories in my classes all the time. Sometimes they’re personal anecdotes (usually of the ‘See what I did there? Don’t do that’ variety), historical references or just something I made up like the example above.
I think that the issue with traditional story problems is that they’re not very interactive. Most seem to be little more than a written statement of the math problem we’re trying to solve.
So maybe we need better stories.
One promising project is Oppia. This is a Google project described as a “Tool for creating interactive educational content”. In other words, you can create a story that guides your student through a topic, periodically asking them to apply what they’ve learned to solve a problem within the context of the story.
You can set up your own copy of Oppia on your own computer to test it, contribute to or browse through the lessons at the official hosted server or just use their test server to see how it works. I played with one of the tutorials and it was very engaging. So head on over there and give it a try, let me know what you think.