Friday, April 6, 2012
Algebra I: Still Hazy After All These Years
This isn't good. One homework problem took me 32 minutes and two entire sheets of paper. As there were about thirty problems in the entire homework assignment, it should only take me...um...sixteen hours to do my homework. Did I do that right? 32 times 30, then divide that by 60? Good lord, I hope that's right, because if I can't figure that out, I am dead in the water in Algebra I. The scan above is the cleaned-up version of the problem, the version I re-copied so I could actually how the heck I got to a final answer.
I knew I would struggle in Algebra I, when I returned to class in order to get over my math anxiety, and not just because I have a lot of trouble visualizing how numbers work. The bigger problem is that due to my overloaded teaching schedule (I teach two sections of composition 8, one of composition 7, English 8, English 7, Latin 6, Latin 7, and Latin 8), I can only attend two of the four Algebra I classes held in a week. I do my best to keep up, and as I have mentioned, my students fill me in on the important lessons I miss.
The biggest hurdle I face at the moment is the lack of continuity. I jumped into Alison Gorman's Algebra I class halfway through the year, and missed all of the lessons that inform our current chapter (11). When Alison says, "Don't forget to use the discriminate factorability test! You will have to keep it in mind when you do tonight's homework!" I have to quickly and surreptitiously flip to the index in the back of the book to understand what she's talking about. D...D...Directly proportional...Disappearing variable...Discriminant...ah - Discriminant, test for factorability, 436.
"A quadratic [oh, crap, look that up, too] trinomial can be factored if an only if the discriminant [...and that, too] is a perfect square."
Lovely. As clear as swamp effluvia.
My biggest worry at the moment is that I am going to need the quadratic formula to do some of the work in this chapter. I remember learning it once, long ago...something squared over something else with b and 4ac and...
Q....Q...Quadratic degree...Quadratic equations...solving by factoring - here we are. Formula, 214. Way the heck back in chapter six.
What has been fun is the opportunity to see my students in a new context. Alison witnesses different aspects of these kids in her math class than I see in English and Latin. I am getting an education in my own students, and that alone has been worth the effort I've put into Algebra. This new knowledge has really paid off this trimester. One of my students was having trouble in math, and when I met with Alison to discuss what was going on, she was able to show me in the students' math notebook exactly what mistakes she was making. I never would have understood the nature of her mistakes before, and it allowed me to sit down with my advisee and offer up more than general advice about diligence and "doing your best." We were able to untangle her specific issues with the unit and devise a game plan. We laughed together over her misunderstandings and I empathized over the time spent working through the more confusing problems on her last test.
But she's still in better shape than I am. She had never spent 32 minutes on one problem.
This weekend's homework: catch up on relative rates problems. Alison calls them "sitcom problems" because whenever a sitcom character wants to freak another sitcom character out with a complex math problem, they give a relative rate problem as an example.
"A kisses B goodbye and leaves home on his bicycle, going 30 km/h. Half an hour later, B realizes that A left her briefcase at home and so he starts from the same house, going after A in his car, at 50 km/h. How long does it take B to catch up with A?"
Alison insists that these problems only sound complex, but are really just a matter of common sense. Alison's reassurances make one huge assumption, however. The small detail of common sense, which I fear I lack. As there are around thirty problems assigned for this weekend's homework, I'd better get to work. Monday is only 72 hours away.