Number Talks 4/28

Flopped today. Did

I was excited about it because there are so many different representations of fractions (see Hung-Hsi Wu for a discussion of fractions in the elementary grades), and my students lean pretty hard on procedures and calculators. I think this failed because the answer was instantly clear to everyone, and there was no value in representing it a different way.

Leads me to my first productive rule for conducting number talks:

The purpose of number talks is to give students opportunities to look for and make use of structure and think flexibly about relatively simple problems. However, if the problem presents a trivial solution using a traditional algorithm, the problem is unlikely to be successful in getting students to find structure and alternative approaches.

Number Talks 4/17

Asked students to count the squares on the border of this square:

Variety of methods and answers. One thing that went well in facilitating the number talk today was, in two classes, students early on clearly made mistakes in their calculation. No one called out and said “no, you’re wrong”, and we calmly moved on to the next person. Each student figured out their mistake, and one volunteered to correct it on his own.

One student realized that the border is 12×12 – 10×10. I was excited about that, but one student isn’t a big win. Gotta figure out how to facilitate that discussion so I can get a bunch of other students in on that conversation.

Number Talks

Look for and make use of structure

Did my first real number talk today. I’ve been thinking about doing them, and bringing elements of number talks to my daily grind, and mostly spinning my wheels wanting to do them but worrying they wouldn’t go well.

Anyway, I introduced them with the question 9% of 510. I did a think-aloud modeling two ways I might estimate the answer (10% of 510 or 9% of 500). Then, I gave them 41 x 196. They got about 40 seconds to think about it, and I took hands for strategies. At this point, I was pleasantly surprised by the quality of responses and student-to-student engagement.

After wrapping up the second example, I told them that the plan was to do a number talk every day after the warm-up at least for the next few weeks. I outlined expectations:

I’ll let you know approximately how much time you have
Everybody calculates–your answer need not be precise, you must have an answer. If I call on you and you don’t have an answer, I’ll come back to you in a minute.
Calculation is 100% silent, no pencils, no paper, no calculators
No hands, they’re distracting.
If you finish, try to find another way to do it.
When the time is up, I will start by cold-calling, then take hands for more methods.
I scribe methods to help the class understand your thinking.
We continue until all methods have been exhausted.

Then, students got the real number talk: 15×12.

I was really impressed with the variety of strategies students found. Among them:
12*12+12*3
12*5*3
15*4*3
15*10 +15*2
12*10 + 12*5
15+15+15+15+15+15+15+15+15+15+15+15
and several more I’m forgetting.

Challenges today:
Students making noises to indicate a student’s reasoning was off when someone’s explanation was faulty
Heads down/lethargy from a few kids while students are explaining their methods
I’m not a great scribe. Want to work on scribing in a way that reflects the mathematical reasoning
Students raising/waving hands

Things I may change:
I’m considering adding a timer to be more clear around how much time they have to calculate. Nervous that it will add unneeded pressure.
Fawn has her students scribe with her. I’m going to hold off on that for now, but may need a way to keep kids tuned in while other students are sharing
Asking students to summarize other students’ thinking. Not sure what this looks like, but I want to foster student-student discussion, and the way I did it today made it more like rotating tennis with the teacher.

All in all, a great start. I’m looking forward to digging into number talks over the next few weeks.