The state tests are coming up next week, so I've spent the entire week cramming (er ... "re-accessing prior knowledge") with my juniors. To be honest, it's actually been a nice break from a jam-packed and rather tedious precalculus curriculum - HSPA, New Jersey's state exit exam, actually tests a lot of good math and my students have tackled some legitimately interesting open-ended problems (more on those to follow). But, in any case, the point of this post is not my juniors (who I'm really hoping rock the HSPA next week (not that I really believe in the validity of a single standardized test (but still ...) ) ), but my seniors. I had to find something to do with them during the two weeks (one for review and one for the test) devoted to junior testing. Since I've been griping (mostly to myself) all year about why these particular seniors are taking precalculus (which is essentially algebra for the THIRD time) and not, say, statistics or computer science, I decided on a two-week statistics unit.
Now, it's interesting for me to work at a place where having a two-week window open up in the curriculum is an extreme rarity, and it was made clear to me that this unit was to last two weeks, period. I knew I wanted my students to do some sort of mini-project the second week so I had to really hone in on a few specific topics for the first week, which we just wrapped up. I decided to introduce the bell curve (of course) and focus on teaching students to use the z-tables for the standard and non-standard normal distributions. What I really wanted to get to by the end of the week was calculating margin of error and constructing confidence intervals, because that's what they'll need for next week's project. The idea is similar to a project I did at my old school, but in about 25% of the time. Students will be designing an experiment (like a Pepsi challenge) or a survey, writing an analysis of their results, and making a presentation. In their analysis they need to do things like construct their own confidence intervals and determine whether there is a statistically significant difference between two subgroups of their choice, like males and females.
So, back to the content: margin of error and confidence intervals. While I had used the "guided practice" model to teach students about normal distributions and the z-tables - "guided practice" is just my school's nomenclature for showing students a new skill and then gradually loosening the reins until they are doing it on their own - I decided to go for a college lecture on confidence intervals. Again, "college lecture" means something very specific at my school, but in essence the point is to give students a taste of what a 300-person college class will actually feel like. The teacher takes on the role of "professor" (which, I'm not going to lie, is a lot of fun) and delivers a PowerPoint lecture, preferably at super-speed and without much, if any, audience interaction. Of course we scaffold good teaching strategies in to make sure that our students don't flounder, such as intermittent note checks during the lecture and a comprehension check exit ticket afterwards.
My favorite part about the college lecture format is what happens the next day: students work in study groups on a college-style problem set, interrupted only by a brief chance to ask "the professor" questions during "office hours" (okay, so maybe we take the analogy a little far...). This brings me to the actual point of my post - sorry you had to read all the other stuff - which is: giving my seniors this independence and responsibility turned them from slouchy, grouchy second-semester seniors into a spitting image of actual college students. The transformation was unreal. They were engaged with the material 100% of the time (which is not usually the case in this class), challenging each other's understanding and use of terminology, referring back to lecture notes and the text when they got stuck ... essentially, everything we'd want them to do as college students in just a few short months. I use another teacher's room for that class, and that teacher actually asked me in the middle of the class if she could commend the students at the end of class because she's seen so many classes where their performance has been ... less impressive.
As I write this, I'm realizing that it's not rocket science. There's not much in the way of "guided practice" in college. And not to glorify some rather shoddy teaching methods, but maybe there is actually one good reason (albeit many bad reasons) for that - when people get to be a certain age (like, say, 18?) they crave less hand-holding and more independence. Based on some previous classes with my seniors, it might seem that they get easily frustrated with difficult math and take every opportunity to zone out. Now, I'm not so sure. These statistics topics are probably the most conceptually challenging ones we've done all year, and not even the usual suspects could be found zoning out. So maybe doing more of the lecture/problem set/legitimately interesting project or discussion is what they need? In other words: If I keep treating them like college students, will they continue to act like college students?