Some ideas on engagement & how to get it (from our students):
Dan Meyer says: mathematics is real if students can argue about it, and looks specifically at sorting tasks. I really like these as an investigative way to get students thinking about a concept before defining it.
Grant Wiggins says: a presence and commitment to engaging students is absent from too many students, and suggests learning from public speakers, TED talks, and fellow teachers.
Underwood Dudley says: we pretend mathematics is more relevant than it actually is. He argues articulately that we overstate the importance of mathematics in the real world (or at least the necessity of all students learning all of school math while they are in school). His solution is to be honest with students by presenting mathematics as intellectually invigorating challenges, not as you-have-to-know-this-or-you’ll-never-get-a-job.
Curmudgeon worries that prioritizing student engagement–that students must be engaged in order to learn–teaches the wrong lesson about the value of learning mathematics, and in the end turns students off to it.
My take: engagement is hard. There are wins and losses. Engagement can come from lots of places. I have a list on my computer–why my students work hard for me. It says:
They like to be challenged
They know what I’m teaching them is important
They’re scared of consequences
They like to be praised
They trust me
They respect me
They like me
They enjoy the feeling of learning
They want good grades
They want to please someone else
They want to do well on an assessment
They see everyone else working hard
I want my students to work hard. I won’t be successful if I wait for them all to think every task is worthwhile, but there are lots of levers to get kids working hard. Once they’re working, and they’re learning, I can think about what will push them in their skills, their knowledge, their mindset. But I think the habits of hard work come first, and I’ll take what I can get when I can get it.