## Monday, July 17, 2017

### How Do You Get to School?

"The standards do encourage that students have access to multiple methods as they learn to add, subtract, multiply, and divide.  But this does not mean that you have to solve every problem in multiple ways.  Having different methods available is like having different means of transportation available to get to work; flexibility is good, but it doesn't mean you have to go to school by car, then by bus, then walk, then bike--every single day!"
Bill McCallum

Last month I stopped by a second grade classroom where the teacher was administering an end-of-year math assessment.  I paused by the desk of a student who, with a look of frustration on her face, was puzzling over this question:

"I forgot how to use an open number line," she responded, head down, staring at the blank page.
"Do you know another way to solve the problem?"
She looked up at me.  "Partial sums?"
"Could you show me how you would do that?"
Here's what she produced on a piece of scrap paper:

 And wrote the answer, 79, in the space provided.
Question: Do you mark this wrong because she couldn't show her thinking on an open number line?

Continuing to make my way around the room, I came upon this response:

"Tell me what happened here," I asked.
"I got confused about using the number line."
"Do you know another way to solve the problem?"
"I could draw base-10 blocks."
"Could you show me how you would do that?"

Question: Do you mark this wrong because he couldn't show his thinking on an open number line?

I spent the next several days looking through other end-of-year assessments for examples of questions where students were being commanded to solve problems using specific representations and methods.  Here's a sample from grades 1-4:
• Use the break-apart strategy to solve each problem.
• Use the turn-around rule to solve.
• Explain two different ways you could use doubling to solve 6 x 8.
• Explain how you can think addition to solve 14-7.
• How can you find the sum using a number grid?
• Explain how you can use the near-doubles strategy to find the answer.
• Use base-10 shorthand.
• Use an open number line.