A Troubling Problem

   Solving word problems has been a thorn in teachers' sides as long as I can remember. We've all attempted to remedy this issue by pointing out key words, saying key information with heavy emphasis and even making students redo the problems until they get it right. With all of these efforts, we still end up with students who cannot independently solve a word problem. Ugh!!

   SMP 1 tells us students should always be making sense of the mathematics. As I compare that standard to the practices even I have implemented in my classroom, I realize if this is happening students are not making sense of the mathematics. No wonder when students are working with word problems they just spend the wheel of computation and does what "feels" right. So how can you get students to the place were they are exhibiting SMP 1 when solving word problems?

(Sorry for the sideway images.)

    This problem was solved by a 4th grader. When I asked how confident he was with his answer, he felt pretty confident. 

   I rewrote the problem on another sheet of paper minus the question stem and we started anew. I first asked him to read the problem. 

Me: What's the context of the problem?  What's happening?

Student: They're ordering pizza and there's pizza left over. 

   We read the problem again. 

Me: What mathematical information is there?

   We read the problem a third time. 

Me: What mathematical questions could we ask about this problem? 

Student: Do you need to add or subtract?

Me: Think again about the context. 

  I asked the student to compare his answers. He pointed to the 3 wholes and said, "This one is correct.  The questions are different."

Me: What's different about them?

Student: This one says 'How much pizza was left over'. 

Me: Well what made this problem easier (referring to the problem without the question stem)?

Student: I was able to answer my own question. 

  This 3-Read strategy changed my perspective on solving word problems. This idea was flushed out in the document Instructional Toolkit for Mathematics shared on Dan Meyer's blog http://blog.mrmeyer.com/wp-content/uploads/OUSDMathInstructionalToolkit2013-14.pdf. When asked was this strategy just for the kids who can comprehend well, I swiftly replied, "No!"  Don't limit this strategy to just some kids, expose all students to this strategy, especially those we have trouble with solving problems. 

So Who's Failing

It's that time again, the end of the unit. You pass out your multiple choice assessment, confident in knowing you've taught your students everything they needed to know. You've shown them everything you could to make them understand the unit's concepts. You even supplied students with a study guide mirroring the unit assessment and went through every question on the study guide prior to the test. 

After taking the time to analyze the data from your assessment you're stunned by the results. 

How could this be?! More than half of your students are not proficient on the unit assessment. You think to yourself, "They failed.  These kids just don't get it.  I need to assign more homework.  They just don't listen to me!" All while you are denying any wrong doing on your part. 

As an effective teacher, you watch for pitfalls, wrong way turns and plain out misunderstanding along the way. This is hard to do when you are cruising through the pages of a textbook, covering the content superficially. It's hard to do when the only assessments you administer come at the beginning and end of the unit. It's also hard to do when you implement 20 question tests which take several days for you to grade. 

What's a better alternative to ensure at the end of the unit journey you haven't left half your class behind?  Observation rubrics.  As students are working through a task, the teacher circulates listening to math discussions, looking at student work and asking guiding questions.  The rubric has predetermined expectations based on the standards and related to the task. Once the teacher has checked on a student's thinking, the student's name is recorded next to the appropriate level of understanding. 

In this example you can clearly see which students are on target to master the standard and which are not quite ready. You can vary the task students will complete the next day or pull small groups to remediate and accelerate students. This process is continuous through the unit and provides a better idea of how you adjust your instructional strategies to meet students' needs. 

If you come to the end of a unit and half of your students still lack understanding, you haven't met their needs. The use of informal assessments such as an observation rubric is an extremely effective way to gauge where students are and what you need to change about your instructional practices.  Because my friends, if half of your students lack understanding at the end of the unit, they haven't failed, you have.