Solving the Problem

Do you remember that feeling you had as a child or teen when you got to the problem solving part of a lesson or unit in your textbook? Perhaps you felt joy in finally getting to do something somewhat more challenging than completing the 50 number sentences you just solved. Or maybe you felt fear that someone might actually notice that you really have no idea what you are doing. Worse yet, indifference may have become your bland taste for math and none of it mattered to you anyway. For me, the word problems always seemed like an enigma. Often it was just for extra credit – a nonessential part of mathematics. Other times it was assigned and I prayed for the magical key words to guide my way to a solution. I always felt uncertain. Having just practiced a set of rules for a page of tedious equations, the word problems didn’t fall into the same category as the rote memorization of the lessons practiced. It was disjointed and out of sync. Even those memorized key words didn’t help most of the time. They didn’t match multi-step problems or ones not involving algorithms at all. We all know the joke about the train –  If a speeding train is heading towards Los Angeles at 84 mph….Who cares? I’m not on that train.

I often find students in the same quandry. Upon entering 2nd or 3rd grade, students mistakenly believe that to solve a word problem you take the numbers, throw in an addition or subtraction sign, and then find the answer. The answer doesn’t need to make sense since the problem may not have to begin with.

My feelings about problem solving changed drastically when I went through training and implemented Cognitively Guided Instruction (CGI). Problem solving became the basis for my lessons rather than the afterthought. It became both my tool for teaching and the students’ access for understanding. I could finally really see what my students understood, and determine precise next steps for instruction. It took time to cultivate a classroom (and a teacher) that values problem solving. Through conversation and strategic share outs, students had real access to the underlying complexities within math that had evaded them. I came to understand mathematics with much greater clarity than before. And you know what? My students don’t need 50 problems to develop that understanding too. As it turns out, problems solving is the key to understanding, not the afterthought.

This is a sample format for differentiating word problems for your students. The sample on the left is a subtraction problem (SRU: Separate Result Unknown). There are multiple number choices for students to choose from depending on their comfort with the problem. The box is for the plan. I expect students to try at least two plans before trying a new number set to solve. I don’t always use a formal paper, as students have math journals to work in. However, it is nice to have a sample to send home or collect to collaborate and examine with colleagues. I have a rubric attached to my Snowmen Subtraction Word Problems that can be used to grade word problems. Again, I don’t grade all of the student’s word problems, but I do keep anecdotal records that tell me how they thought about a problem and how I need to push them to the next level.