I lasted all of 4 minutes. My answer in part b was no good.
I tried again, but still I failed.
I didn’t give up.
Then I gave up. (Guess it wanted me to type in n = 3 from the beginning. I’m still not sure. But by then, all I wanted to type in was: Uh oh… you must be shitting me.)
But Dan’s post mainly reminds me that I want to share a little bit about EnCoMPASS.
The EnCoMPASS Project is developing an online professional teaching community of mathematics educators focused on understanding and improving mathematical thinking through work with formative assessment rubrics and feedback to student problem solving. In this community, members extend their content knowledge for teaching and seek to become more effective at supporting the mathematical development of each student.
As teachers, we should be very interested in providing kids feedback. But feedback that is both meaningful and timely are tough to give for those of us who see 100+ students. (I had 141 students last year.)
For some years now, teachers can give feedback to students on their PoW write-ups at the Math Forum. A student submits her solution online, then the teacher can give feedback, and the student-teacher exchange may continue from there.
On the second day of school (8/26) I assigned the PoW to my 8th graders. They have one week — until 9/02 — to submit their solution. I’m reserving next week as our reflection week, meaning I’ll log in and give them feedback and let them know when I’m done so they can respond to my feedback. My plan is one PoW every two weeks: 1 week for them to work on it, and 1 week of us to go back-and-forth. We’ll see. If that’s not enough time, then I’ll change it to one every 3 weeks, or one every 4 weeks. The point is: we are doing this.
My Math 8 kids got this PoW:
My Three Dogs [Problem #2752]
My neighbor has three pet dogs, named Fifi, Maxx, and Sparky. Last week he took his beloved pets to the vet for their annual health check-ups and shots. The doctor weighed them as part of the examination. Upon returning home, my friend told me the animals’ weights in an unusual way. He said:
- “Together Fifi and Maxx weigh 72 pounds.”
- “Maxx and Sparky have a combined weight of 86 pounds.”
- “Lastly, the sum of Sparky’s and Fifi’s weights is 35 pounds.”
How much does each dog weigh?
Extra: Suppose my neighbor had four dogs instead of three, and that when he told me about their weights each statement he made included the total weight of three of his dogs. What’s the smallest number of statements he could make that would let me figure out the weight of each dog? Why do you think so?
Here are some current submissions from students:
No, I don’t always get a full write-up. Here’s this:
And I’m looking forward to giving my students feedback in the form of I Notice I Wonder. I must be specific in my feedback. I must be constructive. I must be appreciative. I must be helpful and kind. If I do this correctly, then hopefully it means that the student will want to respond, want to revise, want to learn from this exchange.
I must not screw up!!
Well, EnCoMPASS is working on making this student-teacher exchange all of the above and more. Teachers can highlight any part of a student’s work and thus respond to it specifically. We may ask permission to see work from other teachers’ students. We can categorize our highlighted passages and put them into folders, perhaps of the strategies used. EnCoMPASS is also working on allowing students access to see other students’ submissions and respond to them. In a nutshell, EnCoMPASS is the fancier version of what they have now.
I started subscribing to the Math Forum’s PoW since 2007 — Suzanne confirmed this for me. Yet I still have a lot to learn about giving kids the best kind of feedback.
It’s a teaching endeavor. A human one at that. Something a well-intentioned software can never achieve.