I was thinking recently about how best to teach trigonometry, and especially how to teach the long and difficult processes of vector analysis and truss calculation. Now, it seems to me that these processes aren’t really going to sink in unless a student practices them a number of times. But that sort of independent practice is difficult to achieve for such complex, many-step processes.
Now, I can do guided practice of these processes by letting students lead me through a 20-minute example on the board. But then the student gets little individual time to work it out herself. If I try to have the students work a problem on their own too early, I’ll be called in fifteen directions at once as each student gets stuck in a different place and needs one-on-one help. To varying degrees of success, I may try to scaffold a problem by doing some parts for a student or asking him leading questions; or I may list the steps in the algorithm on the front screen while students work on applying it.
However, to get the students all the practice they need to get comfortable with these topics, they do need to work on them in homework too. And I cannot be there to scaffold the instruction; I can provide neither one-on-one assistance nor lead a classroom guided practice.
In an effort to help students with their homework in these areas, I decided to videotape myself working through a vectors example: that way they could see the process while working on a homework assignment, with the ability to pause to work on a similar part in their own example, and the ability to rewind to hear a step over again.
I’d appreciate any feedback, and especially constructive criticism, as I’d like to make videos a recurring part of my teaching this year. I intend to make a truss calculations video quite soon, to follow up on these ideas.