I've had the luxury of teaching the same courses for the past five years. I'm the only teacher in the building who has taught one of them throughout that time, which means I've been able to adjust the curriculum to meet the needs of the individual students from year to year. Today, I thought of an idea that may make the course much more interesting for my current crowd: I think I'm going to let them create their own math problems.
Now, they're not going to create meaningless problems, with random numbers and variables that have no context. I want them to live their normal lives, but when they see or hear something that captures their interest I want them to turn it into a problem. Their job will be to take pictures, videos, recordings, etc. of something the interact with and come of with a question that they (or someone else) can solve. They will have to be able to describe the scenario in words and visually, come up with a question or multiple questions, and also gather the information that would be needed to come up with an answer. I don't care what math topics they choose; it could be any high school level math. If it involved something they haven't learned, then we'll go through it as a class. If it uses information they already have, then they'll come up with an answer. Either way, its math in the real world.
Since I've started my career as a math educator this is something that I've spent a lot of time thinking about. Every student always wants to know why the topics they are learning are relevant. They don't settle for an answer of, "You're learning it because its on the test," anymore. They want substance and meaning. If I want my students to see math in the world (which everyone should want this), why not let them explore it themselves? I think if I organize this project correctly, some of their eyes might be opened to how much math is used.
I'm at the point where I see situations or objects and my mind jumps to 'How did they do that?' or 'What if it looked like this...' I want my students to become that way too. This will lead to them being life-long learners and it will exercise the creativity of their minds. If I can get them to analyze any situation and expand upon it or just wonder about it in a new way, I think I've achieved something.
Let's hope this goes well!