The primary lesson of my experience thus far is that teaching requires a lot of time and effort. I work with students either as a class or individually almost non-stop from 7am until about 4pm on a daily basis (and later than that these last few weeks). I go home, eat, try to catch up on my personal life for a few hours, and then spend the remainder of my evening planning for the next day. The daily grind makes it a bit difficult to think big about the best way to teach any individual concept.

In my curriculum class we have been working on a lesson plan for factoring trinomials with leading coefficients greater than 1. Our group of four has spent a few months thinking about the standards, placing the lesson in context, and developing the best way to approach it. We still don't have a lesson ready. A few days ago I had to send some materials to the other members of my department, so I cooked up a power-point lesson on the subject in a few hours and sent it along. The thing is, factoring trinomials is an algorithm. Almost everything we do in Algebra 2 seems like an algorithm. Will our intensive investigation into the lesson planning process yield any significantly better way to teach this algorithm than my rushed powerpoint presentation?

I have been able to incorporate several experimental ideas into the geometry curriculum. I developed a triangle congruence unit based around my proof cards, and I think it has worked for a number of students. They aren't completely intimidated by proofs, in any case.

Although I joke about powerpoint presentations, they have become pretty useful. Creating a detailed presentation makes me think a bit more about the flow of my lesson, and it is nice to be able to display a problem for the students to work on and have the result already worked out to show after I have given them a chance to work on it.

The policy of making students keep all of their work in a binder has been working well so far. I think it streamlines grading and makes it possible for me to give them credit for participation in class (by checking whether they have filled in their notes). The students still don't really reference their notes, though.

I had my first evaluation (called a JPAS evaluation) this quarter. So far I haven't seen very much useful feedback. Maybe it is forthcoming.

All of my class materials are now available to students online. Some of them have made use of this feature during absences, but not enough to convince me that it is worthwhile. I am thinking of better ways to implement technology that will save me time.

I am rethinking my quiz system. Partly because I dread making up new quizzes every day. Partly because the students don't take them seriously enough when they are graded based on participation. But I am not exactly sure what to replace them with. I don't really want to implement something that would involve a lot of grading at this point because I don't have a lot of extra time. There really isn't enough time to be an effective lesson planner, lesson teacher, and evaluator for 200 students.

One of my focuses for this next quarter will be to try and develop stronger ties to those students in my classes who are struggling. Encourage them to come in for help. Make checking on their progress a higher priority during individual work time.

Most students prefer, and even need that algorithm to factor non-monic trinomials. The ironic thing is that students who learn to factor trinomials by feel rather than the algorithm gain a much stronger number sense than those who just memorize the steps and follow them. However, so many teachers penalize those who can do it intuitively, forcing them to memorize and regurgitate the algorithm.

ReplyDeleteI think the reason that these teachers force the algorithm is usually that it is easier to grade, and the teachers often don't understand the math as well as their best students. This is particularly true at the elementary level. So students are so used to just memorizing algorithms, that they know no other way of learning math by the time they get to middle and high school (and college).

I agree. In fact, in my class we used some of these ideas to design a revised lesson plan that focuses more on building number sense and giving a student an intuitive feel for the problems. Sometimes a little reflection does improve a lesson.

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