One of the best experiences about being a teacher is the opportunity to bear witness to student sense-making. I enjoy hearing learners help one another develop different ways of approaching problems because I know this is a skill that will transcend mathematics class into when-are-we-ever-going-to-use-this land.
I was first introduced to the idea of a Math Talk when I was taking Jo Boaler’s online course How to Learn Math. This one is simple enough that anyone able to count can do it. Seriously, take a second and give this one a go:
How many dots are on the card? How did you determine your answer?
The answer of ten is hopefully quite obvious to your students. But it’s the incredible number of ways in which they determined that answer that blows me away. Is it two rows of 3 and two rows of 2? Or is it 4 diagonals of 1, 2, 3, and 4? Maybe 5 in the top 2 rows and 5 in the bottom 2 rows? Perhaps 5 pairs of vertical dots catches their eye? THESE ARE JUST DOTS, PEOPLE! All of this awesome thinking over dots arranged strategically on a piece of paper. But these dots opened the door to my getting my students to explain their thinking to one another.
Fast forward to MCTM this past weekend. I was reminded of the power of the Math Talk at a session hosted by Christy Pettis and Terry Wyberg. I knew Fawn Nguyen had some wonderful examples on her website, so I jumped in.
The results have been lovely.
Monday: Which is greater 79×25 or 75×29?
Tuesday: Visual Pattern #10
How would you have determined that there were 85 puppies in step 43?
Wednesday: Which is greater 12/17 or 5/8?
There were many lovely responses to all of these questions in each of my classes. But the one that stands out as my favorite was Caytlin in my 5th period Algebra 2 class. For Wednesday’s problem, Caytlin says that it’s easier to compare the reciprocals of those fractions, so she flipped them over to compare 17/12 and 8/5. When converted into a mixed number, 1 and 5/12 is smaller than 1 and 3/5. The opposite would be true for the reciprocals of the numbers. Therefore, 12/17 is larger than 5/8 since its reciprocal is smaller.
Honestly, isn’t that golden!? What I love about math talks is that students are asked to make sense of the problem themselves. They aren’t shown an example or taught a rule. They develop their own method and then help their classmates by sharing it. There have been a lot of good experiences in my classroom this year, and math talks rank up there near the top.
(For additional information on math talks, I recommend the book Making Number Talks Matter by Cathy Humphreys and Ruth Parker)
Number Loving Beagle 
Megan – what level students do you do number talks with, and how frequently? I love the idea of these, but I’m hesitant with high school students and brief 42 minute periods.
I have hs students and 68 min periods. I am doing them every day with the goal of having each kid share at least once during the week.
Very very nice problems to get the kids discussing their thinking.
I plan to keep this in mind for later.
These seem like a really nice practice. And some of the sample questions seem like great elementary or perhaps middle school topics. For instance comparing fractions to see which is greater or counting dots. Somehow It seems like the topics should scale up to match their knowledge a bit more. by Algebra II. It would be interesting to brain storm more question sets.