Taking apart the “key word” strategy

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

Christine Moynihan

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.

1 comment April 27th, 2016

Blogstitute: Got Common Core?

Today’s Blogstitute post comes from Christine Moynihan, whose latest book is Common Core Sense: Tapping the Power of Mathematical Practices. In this post Christine introduces the GOLD framework that helps make the Standards for Mathematical Practice more accessible to elementary teachers. Be sure to leave a comment or ask a question for a chance to win 12 Stenhouse books! On Twitter you can follow along using #blogstitute15.

Got Common Core?
By Christine Moynihan

FC FINAL CommonCoreSense.inddSomething I hear from many teachers is that it is challenging to be up-to-date on everything that teachers should and must know in order to be effective practitioners. This is especially true for elementary teachers, who are asked to be content experts in reading, writing, grammar, spelling, science, social studies, and, of course, mathematics. Not only do they need to have expertise in these curriculum areas in terms of content, but they must also be experts in the best instructional practices that will support their students in learning in each of these areas. (I’m not even going to go into how they also have responsibility for social and emotional growth, health and wellness, behavior management, and the list goes on. . . . )

So, as a former classroom teacher, I get it. As a former curriculum specialist, I also get it. As a former principal, I most certainly get it. As a current educational consultant, not only do I get it, I hear it all the time—there is just so much to know, so much to learn, so much to do. As a result, when I ask a variation of the “Got Common Core?” question, many teachers respond that although they “get” the basics of the Common Core in terms of the standards for mathematical content for their specific grade levels, they believe that they have a somewhat light understanding of the standards for mathematical practice. Most teachers report that what they know about the MPs has been by way of an introductory look at them at a professional development session and/or staff meeting, with little or no follow-up.

My major purpose in writing Common Core Sense: Tapping the Power of the Mathematical Practices emanates from my desire to help teachers gain a foothold in understanding the MPs and how they can affect their practice. The book is meant to be a vehicle for making the eight Standards for Mathematical Practice more accessible to elementary teachers, for I see them as the core of mathematical proficiency. As I wrestled with how to do that, I defaulted to something that has always worked for me as a learner—to devise some kind of a framework, a mnemonic of sorts, to aid in understanding and then activating that understanding. Because I had been saying over and over again that “the gold of the Common Core really lies within the mathematical practices,” I constructed the GOLD framework to help teachers see some of the major components of each MP and then think about what they may look and sound like in classrooms, and what might need to be done to support the incorporation and implementation of the MPs into daily practice.

The Framework:
Go for the goals—What are the major purposes of the practice?
Open your eyes & observe—what should you see students doing as they utilize the practice? What should you see yourself doing?
Listen—What should you hear students saying as they utilize the practice? What should you hear yourself saying?
Decide—What do you need to do as a teacher to mine the gold?

I identified three major goals for each mathematical practice, fully aware that there are many more goals to be found within each. In the link you will find what I have identified as the second goal of Mathematical Practice #3: Construct viable arguments and critique the reasoning of others. What’s not to love about MP3? When you can analyze your thinking enough that you can clarify it, defend it, justify it, and represent it, you have learned something that will be valuable in all areas of life. In terms of mathematics, that ability leads you straight to the path of being mathematically proficient—a goal we all have for our students. I hope that the chart for the second goal I identified for MP3 can help in your work to make this MP come alive for the students in your classrooms.

Accept that viable explanations of mathematical thinking must be organized, reasonable, and justifiable/laden with proof.

8 comments July 6th, 2015


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