April 27th, 2016
Today we have a guest blog post from Christine Moynihan, author of the recent math books Common Core Sense and Math Sense. Christine takes a close look at the often-used “key word strategy” and explains why it might not be the best way to help your students get to the right answer.
Taking apart the “key word” strategy
By Christine Moynihan
“Does your answer make sense?” Can you estimate how many times you have asked your students this question in regard to word problems? Even if you are a beginning teacher, I am willing to bet that it has been, on a daily basis, several times a day, five days a week, 180 days a year! Do the math and you will find that you have asked that question of your students a staggering number of times.
Even if your students answer in the affirmative — “Yup, my answer makes sense”!— what may pass for their answers making sense is that they’ve checked to see if their computation is correct; if it is, they assume they are good to go. Tucking their answers back into the context of the problem after they have completed the computation still may not come naturally to them, even though you and their previous teachers have tried to build it into your practice, their practice, and the practice of mathematics in general.
In my pre-service math methods classes, I was told that when I was helping students learn to solve word problems, I had to support them first in making sense of the problem so that they could then determine which operation they had to perform. One way to do this, considered good teaching practice, was to tell them to search for key words. The next step was to get them to underline those key words, underline the numbers in the problem, and then to use the key words to write a number sentence to solve the problem. My guess is that many of you may have had the same experience in pre-service as well as having been taught that way when you were in elementary school yourselves. A few of the key words/phrases you most likely learned are: for addition – in all, altogether, total, increase, combined; for subtraction – difference, left, fewer, decrease, gave away, take away; for multiplication – of, times groups, twice, double; for division – per, groups, share, out of.
So what’s wrong with the key word strategy? I have had to answer that question countless times in my previous roles of mathematics curriculum specialist and building principal, as well as in my current role of educational consultant. The short answer is that using the key word strategy has limited scope and value. Further, it can be incredibly misleading and steer students to wrong answers that make no sense at all within the context of the problem. Additionally, it sends students the wrong message in terms of them thinking that solving problems can be done routinely, formulaically, and without much deep thought.
Let me share a recent experience I had with one of the fourth grade students with whom I have worked for two years. We were going over a sheet of problems he had done in class, as he had to make corrections to the ones he had gotten wrong. Now Jared is a very bright fourth grader who excels in reading, is highly engaging, and knows a great deal of information about a wide variety of subjects. He likes to work fast, think fast, move fast, and complete his work fast. Mathematics is not always his favorite subject and he often shuts down his thinking if he cannot see a solution path quickly. Here is one of the problems he had done:
Mr. Smith bought 14 new globes that his students could
use in class as they studied Earth. Each globe cost $76.
How much did the new globes cost in all?
Jared’s answer? I bet many of you can predict what his answer was. If you thought that he had written $90, you would be correct. I had him read the problem aloud and asked why he thought his answer made sense. His response was, “I did the right thing because 14 plus 76 equals 90. I did it in my head, but I know it’s right and I even put a dollar sign in front!”
I asked him to draw a picture that represented the problem. He drew 14 circles to show the globes. When I asked what the cost was for the globes, he wrote 76 under the first one and then did the same under the others. He then said, “This won’t work. Look at the problem – it says ‘in all’ and that means you have to add, so the real answer has to be $90.”
My next question was, “How much did two globes cost?” He immediately replied, “Well, it could be $152 but that can’t be right! They told me to add!” I had him continue to work and after he had successfully solved the problem, he looked at me and said with utter conviction and even a bit of indignation, “It’s not my fault! They put in ‘in all’ so how I am supposed to know I shouldn’t add?”
I know for certain that there isn’t anyone who teaches key words as the only and/or best problem-solving strategy. But the rigidity with which Jared applied the strategy reinforced for me just how limiting and misleading it can be. I continue to work with him with one of my goals being that he understands that the responsibility for making sense of a problem rests with him and that he needs to add to his repertoire of problem-solving strategies to ensure his answers make sense.
Entry Filed under: math