One of the things I started my Algebra 1 Support classes off with on the first day of school was Fawn Nguyen’s Noah’s Ark problem.
Wait. Before I begin, I want to say this problem is REALLY HARD. I worked it myself a few times, couldn’t figure it out, and finally wound up needing Fawn herself walk me through the logic of it. (Of course, once you see the logic, it makes so much sense. Also, in my defense, I was on the right track, and then got distracted with something else and didn’t continue that train of thought.)
So my students were working this problem and a few of them just had no idea how to begin. We talked about the difference between asking questions and saying “I don’t get it” and then I asked them lots of questions. They didn’t seem to be big fans of this approach, but I didn’t care. Others could get started but got stuck after about 2 steps. I asked them lots of questions too. Others insisted they had an answer (it was 2 – seriously, every single group got 2 as their first answer) but then broke down in the middle of their explanations when I asked them to explain their reasoning. It was interesting to see how obvious it was that no one’s ever asked them to do that in a math class before.
The first day, I think they worked on it for about half an hour. The next day, I summarized the major findings that most groups had gathered from the day before on the board (with lots of input from the class) and set them to work again. They got another half hour, and only one class finished. (This would be the class that figured out the easiest method to solve it while we were doing our recap.)
Yesterday (3rd day of school), we had a discussion about what we do in this class (a school-wide topic for the day to build culture). They immediately started off with the usual “we do our work and you help us” crap, so I started asking them to think about the activity we’d been doing for the last couple of days. What did you do? What did I do?
They finally realized that they did lots of thinking. They did lots of talking. They did not do very much writing, and they did no calculation or plugging of numbers into formulas.
When asked what I did while they were working, this conversation happened in all my classes:
Some kid: “You helped us.”
Me: “Did I?”
Silence and confused looks
Me: “Did I tell you the answer?”
A bunch of kids, in rather sulky tones of voice: “No.
Me: “Did I even tell you if you were right or wrong?”
One kid yells YES but he’s the only one. I actually did tell him he was wrong at one point because that’s what he needed to hear to force him to try something different.
Me: “What did I actually do?”
Some other kid: “You asked us to explain how we got our answers.”
Me: “So I asked you lots of questions?” (write this on the board) “Ok…what else did I do?”
More silence and confused looks – you can see it suddenly dawning on them that this is pretty much all I did for two days: asked them questions. The look on their faces when they realize this is priceless.
We finally agreed that my job is to give them hard problems and make them think and explain their reasoning. Their job is to work on those problems, communicate their reasoning, and persevere.
I can assure you, they were not expecting that from their math teacher.
Misconceptions or Gaps That Noah’s Ark Uncovered:
- Lack of experience with explaining their thought process
- Little true grasp of the concept of equivalence, and even less understanding of how to use this concept to their advantage
- We’re going to need to do a lot of work on the whole concept of perseverance.