There is the classic misalignment of what they think math is and what I want them to be able to do. The makeup of the class is almost entirely people who are done with math after this course. In our department, we're trying to separate this from precalc, making a new course for people moving on in math and this course will be for people finishing their math. The goal is to make this course more conceptual, and prepare students for use of mathematics in other subjects. Previously this course had so many skill objectives that teachers were put into coverage mode. Tenure track faculty teach it occasionally, full time affiliate instructors sometimes and most frequently adjuncts.
The course started off on the wrong foot. Two problems that have been a smash in the past went awry. On the house painter problem they were unable to convince themselves of the answer. And on the fair pay problem a misconception was shared and caught on so that it became insoluble. When they came back, one student had a nice intuitive solution that he could not convince the class - even with my help - that it was correct. Finally someone asked me point blank if his answer was right. "Yes, but one of our goals is that you are able to decide for yourself."
Ay ay ay.
By nature, they are reticent to talk to each other. Despite my urging repeatedly, and sharing how math is best learned through discussion. Many don't engage in activities, they're waiting for me to tell them how, many are not doing the homework, and absenteeism is about 20%. Standards based grading has been a tougher sell than usual because this class, as a group, wants the math that was.
I've removed a lot of choice, I've been doing more demonstrations and spending time on the teacher half of gradual release of responsibility, and I'm super explicit about what problems show which standards on assessments. They still won't talk, and many won't engage in in-class inquiry. They will make up something rather than ask about a question they don't understand on an assessment.
Ay ay ay.
The other day I saw this image on Twitter, but stupidly didn't catch the source. Simon Gregg remembered - it was David Wees!)
Our College Algebra picks up with quadratics, but a lot of the work I do with students visualizing patterns is for linear content. (We did do the growth problems, though.) Doing some other work I realized that the students were not understanding symbolic representations as generalizing number patterns. (There are even such quadratic examples on my own blog!) They had been getting by on regression rather than representation. I though this problem would be a great introduction to this kind of generalizing. It did seems to be helping connections form. I wanted to extend this to cubic or higher, so I built this pattern.
First we discussed what was going on, what they noticed and what they wondered about. Very few students wondered about how many cubes for the next building. More assumed that the next building was to be built with exactly that many orange blocks. That's very different than my thinking, and emblematic of how difficult it is for me to anticipate how this class will respond to prompts.
I built a very scaffolded worksheet. I used to make stuff like this all the time, but have been moving away from it. But sometimes students need supports.
Another adjustment I'm trying to make is, instead of roaming the room to eavesdrop and do formative assessment, to roam and ask questions, try to encourage table conversation, and hover over students doing work for other classes or just sitting. I feel a little awkward promoting engagement by (what feels like) intimidation, but students need supports sometimes.
One of the more successful areas of class so far has been the math writing. They have six assignments over the course of the semester, they can count towards SBARs, they can revise for their final exemplars. Several people are writing about this problem for their current writing. That tells me this was at a good place for them, and I'm happy to see some of the sense making.
The strength of the temptation to give in, to teach them how they think they'd like to be taught is way stronger than I would have guessed. But so is my stubbornness to not give in. What I am trying to be wary of is to keep my stubbornness from stopping me giving the support that students need and teaching the students in front of me, rather than some fantasy class.