Fix It

I appreciate Marilyn Burns’ presence on Twitter and her blog. She offers great contributions to the math education community.

Marilyn's recent blog post, entitled Fix It: An Activity for Ordering Fractions, is a well-written reflection of a lesson she taught to fifth graders. Marilyn describes how she used an engaging format and includes details of some masterful scaffolding for a student who needed help. It's worth reading the whole thing.

Fix It Fractions reminds me of the Clothesline Fractions activity Rebekah Thomas did with her summer school class. Before class, she’d hang a set of fractions (using clothespins) on a length of string in her classroom. A different student was in charge of “fixing” them each day (putting the fractions in order). The student presented his or her work to the class along with an explanation.

In Marilyn’s activity, students create their own Fix It Fractions sets for others to try.

There is something inherently compelling about fixing. It is different than doing math work that involves simply performing a calculation or solving a problem. Students look at the work of someone else that may be intentionally or unintentionally incorrect and perform an error analysis. There are lots of formats for doing this, including My Favorite No, or presenting two or more solutions and asking students which is correct and why.

I always appreciate when I see error analysis type tasks in Eureka Math lessons, Smarter Balanced Assessments (both of which we use in our district), and other materials. When I think back to different jobs I have held in my life, I think the majority of my time was spent interpreting, analyzing, adapting, correcting, and reimagining work that had been begun by others.

Let’s think about how to include more of this type of approach for students, and see if it improves their school experience.

If I Had a Hammer

Peter, Paul & Mary

I just read a great blog post by Tracy Zager. Her blog is called Becoming the Math Teacher You Wish You’d Had.

It is about getting students out of the normal (sometimes boring) routines they’ve become accustomed to in math class.

Tracy describes being in a workshop with Brian Hopkins and doing a bunch of math problems in groups. Her group solved a problem and then there was discussion and learning about the mathematics that best fit that problem. When Brian posed a seemingly similar problem, Tracy assumed they would be applying that same mathematical construct to the new problem. That was not the case, which surprised Tracy.

“...Brian disrupted the predictable, pitter-pat routine of math class...

What I see in schools is we cue kids to know what tool to use. If we’re two weeks into a unit on fractions and we give them a story problem, the kids figure fractions are involved. If the name of the chapter is “Multiplying Two-Digit Numbers” and it’s written on the bottom of the worksheet, the kids are going to assume they should multiply some 2-digit numbers. If we’ve written an objective about linear equations on the board, kids figure the answer is going to involve linear equations. If my new tool is the hammer that divides fractions, I’m going to use that hammer until my teacher tells me it’s time to switch hammers.”

As educators, we are often frustrated by our students’ lack of ability to make sense of and solve problems (the first Common Core math practice standard). Yet, are we giving students experiences in math class that help or hinder their ability to solve problems?