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.
Hello, world! A new blog; a new school year; a new beginning!
Today here in Maryland, students begin a new year of school. Teachers (like me) started last week, and have had a week full of meetings: department meetings, academy meetings, district-wide meetings across town in an empty school. Plus one day to set up our classrooms for the new school year!
As I write to you, I am beginning my fourth year teaching here in Baltimore, where I teach math and engineering at a large public high school. Although I have greatly enjoyed learning and then teaching engineering each year, my first love is mathematics, and it is math and math education that I wish to be the main foci of this blog.
As my inaugural post, I wish to meet Sam Shah’s challenge and declare a triplet of New Year’s Resolutions that I have set myself:
- In the coming school year, I shall strive to be nearly paperless as a teacher. Inspired by another Maryland blogger, I wish both to reduce my environmental impact* and to encourage use of the tools of technology my students will draw upon as they enter the 21st century world beyond school. While I plan on providing a paper syllabus the first day of class (together with a whole host of forms that must be signed by students and parents), from that point on I shall post all materials, quizzes, projects, homeworks, and grading criteria online on the course website. I shall encourage but not require that my students likewise manipulate and submit their work by computer instead of in hard copy. The only things I shall print out are color copies of students’ technical reports and project presentations, so that these may go in the students’ portfolios. I am lucky enough to teach in a computer laboratory, which makes a goal such as this one possible.
- In the coming school year, I wish to implement a more structured homework regimen. In the past, I gave homework every night, but it was haphazard: p.238 #1-3,5,8-10 one night, a worksheet I developed the next; practice with calculating bridge efficiencies, alternating with completing the introduction of a technical report so that it may be proofread the next day. With more structure and pattern to the homework assignments, I hope students will fall into a rhythm with the week’s assignments and have greater rates of homework participation and completion. As part of this goal, every daily practice home assignment should be designed by me and consist of sections involving basic, moderate, and advanced application of a skill. Moreover, these daily practice homeworks will alternate with a weekly homework structure as follows (for engineering classes):
- Vocabulary weeks will alternate with engineering article weeks.
- In a vocabulary week, the vocabulary will be assigned Mondays. Definitions must be provided in hand written form by Tuesday. On Thursdays, students will study for a vocabulary test that will take place the first ten minutes on Fridays. Tuesday night and Wednesday night will include daily practice style homework.
- In an article week, students will be assigned an article to read, either on engineering current events, or on a subfield of the engineering profession. By Wednesday, students should have posted answers to both factual and opinion questions in an online discussion forum. By Friday, students should have responded to two others’ posts to create an interactive article discussion. On Monday and Wednesday nights, daily practice style homework will be assigned.
- As my third and final resolution, in the coming school year I hope to make and post videos. This resolution is my most vague. I might post videos of me explaining a math concept or procedure, so that students have access to this explanation at home while they work on homework. Perhaps I could videotape students explaining a procedure too. And/or I might post videos of student work. Toward this goal, I welcome advice from those who have worked with video before (I have not).
Thanks for reading! And please let me know your thoughts, especially on how best to implement videos in class.
* I can remember getting into school at 6:30am, the first teacher there, turning on the copier and making thick, many-paged packets for my engineering classes.