Here is my response to yet another uninformed journalist/parent ranting about mathematics instruction:

Oh please. I am so tired of uninformed people posting stuff like this! We have all seen kids who create "another way" to solve a problem that is not as efficient as another way. Again the point of solving problems by decomposition is partly to become efficient at computing, but another reason to do it is to build a robust understanding of numbers. The only problem I have with this example is the judgement of the US Standard Algorithm as "old fashioned", as it communicates a negative attitude toward a pretty slick way of calculating. And, saying "new way" (these terms were probably introduced by a well-meaning teacher, but misguided) also seems mislabeled, since the goal is not to do something new, but something smart. Impressively (and probably not understood by the everyday person), the representation describes a strategy related to the number line, which can become more and more efficient over time.

One more thing: I have seen teachers (again, well-intentioned, but misguided) interpret "use a numberline", or "decompose numbers", or "use addition to solve subtraction", as an entry point for showing kids a specific way to solve problems rather than letting kids analyze the numbers and make computing decisions and then discuss those decisions as a mathematical activity.

Real World Photos and Counting Brownies with Second Graders

I have been fortunate to work with a bunch of really great second graders as a guest teacher this year. It has been super fun to see them grow in math. They love to be challenged with big numbers, and the number zero makes them giggle. The fact that you can start any counting sequence with zero groups of anything and get zero is a hoot for them. Last week, I decided to try out some of my photos I have posted under the Math in the World tab. I logged in on the classroom computer and pulled up the blog to show the photos through the projector.

I scrolled through all of them stopping for a moment to consider the math that was there in each one. The were intrigued by the children's classroom in Nicaragua, and overwhelmed by the crowd of people at the UT game.

We stopped on the photo on the cut brownies. I love this one because many fraction problems and array problems talk about a "tray of brownies". But let's face it nobody except a chef can cut a pan of brownies straight. My photo comes from a time my daughter made brownies and of course there is a chunk out of the middle too. She probably decided to take a taste!

When I asked how many brownies were there (they are just starting to talk about multiplication), they were excited. One student said he could count by ones and would have to double check that a few times. Then a couples of kids said they could count by twos (the 3 x 5 array was not immediately obvious to most of them--), and showed me how that would work. Then another child showed how he could group them by 5's, and make a ten, then 5 more. Next someone said, count by 5's! I kept probing for more and asking the children to show how each strategy would work.  By the end of the discussion, the children saw that 3 x 5 was the same as 5 x 3, and the whole array (pun intended) of strategies that could be used to solve the problem.

I think using an authentic photo like this kept the problem real and fun. The discussions were light, and kids felt free to offer all kinds of ideas.  I am not sure how this would work for fractions though, since the pieces are not cut evenly.

Zombie already?

Ugh sorry this blog is fast becoming a "zombie blog" ! I am working on a blog about counting games and shall post soon!