I have also been quite surprised to see that it's often students who are struggling who give pushback to teaching methods that emphasize choice, group work, student-constructed knowledge, and open problems. They feel unsuccessful with these teaching styles and crave direct instruction, structure, and concrete, repetitive problems. These students (and their families) have been asking for textbooks, lecture, and an explicit curricular progression in which students are walked through algorithms and given lots of practice. In teaching these students, when I see how much more scaffolding they need to successfully mediate their relationship with mathematics, I understand their perspective and needs much better than I did before. Their gaps are often not in prior knowledge (although that's there too), but in how to learn Math. As a department, I think that we've done a great job of building a rigorous and interesting curriculum that works well for successful Math students who jump into open problems, ask questions, tinker and test, iterate, confer with peers, look for connections and patterns, reflect on their understanding, and figure out what they do and don't know independently. When they lack some of these skills, they are receptive to feedback and observation of peers who model them. We have not yet, however, figured out how to teach all of these skills while simultaneously asking students who don't yet have them to grapple with difficult mathematics in an environment that requires these skills to be successful in that work.

One solution to this issue is to give the students what they want: a choice between a track of open/challenging/problem-based math and a track of traditional/lecture-based math. For many reasons, this is not a solution that I can get behind. Perhaps I'm wrong, but I have not seen incontrovertible evidence that there are some students who just can't learn Math without lecture and repeated drill. If we really think this, we are basically saying that these students can't learn Math and let's just teach them how to regurgitate some procedures so they can get by on their standardized tests. I would have a very hard time supporting a bifurcated system like this.

Other ideas I have had that might help this issue are:

- Provide an extra Math class for struggling students that would focus on just content or just mathematical practices/habits; either make this optional or required
- Provide a summer bridge program for students who we worry might struggle in our program, focusing on building up their ability to learn and mathematical practices
- Start the year with work on mathematical habits and ways of learning Math with little to no focus on content for all classes.
- Work on improving our curriculum so that it incorporates more of the principles of Complex Instruction and can highlight students' strengths.

I would love to hear from others who have grappled with this issue and ways that they and their schools have approached it, either successful or not.

It sounds like your department has done some pretty ambitious work that shouldn't be overlooked. If you've worried to make a curriculum that works for the majority of students, it might be good to assume that your efforts are a baby that shouldn't be thrown out with the bath water. Our school, which is certainly no exemplar, has had success looking tally hard at our curriculum and adding lots of scaffolding. It might mean making choices between what "math" things are important some days and what "non-math" will take center stage other days. Also, really stressing writing, collaboration, and sharing may help to pull everybody together as the high flyers are IMO often the kids who struggle with putting lots of thoughts on paper clearly.

ReplyDeleteHey Carl - really good points here, thanks. I agree especially with the idea that some days, non-content should take center stage and that stressing practices and habits of mind helps with differentiation as it creates more areas to be potentially improved. A big part of this will be to have the community accept these less traditional components of doing mathematics as equally valid as the content with which they are familiar. I think that it's not a dichotomy between content and practices, but it is definitely not possible to keep all the traditional content and simply add on practices. Choices have to be made.

DeleteI would love to hear more about the ways that your school has added scaffolding and in what places. Thanks for the reminder that we're doing a lot of things right :)