I wish you could have been a “fly on the wall” during a recent SAT and ACT class. We were working on ACT word problems of average and slightly above average difficulty levels.
Math Word Problem Reactions
One of the students suddenly exclaimed with dismay, “Why are these questions so easy after you explain how to approach them?” A second student responded with, “Yeah, they are so confusing when I first see them, but they are sure easy when you show me the trap.” The third one added, “I always seem to know the math for doing the problems, but just don’t see how to use it when I need it. Why do they get so easy after you show us how to attack the questions?” Their comments and questions led to an exciting, motivating discussion about the best approach for ACT, SAT, and other standardized test math questions.
Word Problem Test Strategy
How does a standardized approach make math questions so much easier? I am not a math (or reading) teacher. Rather, I teach my students critical thinking skills that have consistently led to much-improved reading and math scores on a variety of tests. Better thinking leads to becoming test savvy which, in turn, improves test performance.
Back to my students. For over 25 years, I’ve taught an analytical way for attacking word problems. I don’t teach students how to “do” math. I leave that to qualified math teachers. Rather, I teach how to think about math in the context of word problems.
A gap that a large majority of high school students have in their math instruction is how to approach word problems. They are taught how to do particular, individual problems but they lack a comprehensive, unifying model that applies to substantially every word problem on standardized tests. Consequently, students start every word problem trying to figure out how to solve the problem based on its uniqueness rather than recognize what it has in common with other word problems.. When they get stuck on a problem, failing to do so is what keeps them from making progress on that problem. Instead of focusing on the specifics of the problem, they need to use the process that they’ve successfully used on other word problems and apply it to this “seemingly difficult” one.
Learn a Test-taking Strategy
When I recognized this gap was an issue for my students, I sat down and developed a “Word Problem Strategy.” It applies to all word problems that I’ve seen for SAT and ACT questions in addition to other standardized tests. Before introducing it to students, I ask them to each do a simple, age-appropriate word problem. (I also use it with elementary and middle school students.) Then we discuss what logical steps they used to analyze the information they were given in their word problem and how they used it to arrive at their answers. As we talk, I draw a flow chart that diagrams the pathway to arriving at the correct answer.
Then I give them a word problem from an actual ACT or SAT (or other standardized) test that is difficult for almost every student. It isn’t mathematically difficult. The complexity of the problem I choose is what creates the challenge. Somehow the wording or described situation or puzzling structure of the problem causes confusion for the students. Then the magic occurs. I use the diagram of the strategy they just developed for the “easy” math question and we begin to apply it to the “difficult” problem. That’s when the light bulbs go on and they see they knew the math for the second problem but didn’t know how to use it. They see how they just hadn’t seen how to systematically use a logical process for thinking their way through the problem to the correct answer. Now the “complex” problem is much easier.
Of course, over the years I’ve developed a step-by-step flow chart of the process for effectively attacking word problems and I give it to my students. They are then required to pick a few word problems and walk through the steps for tackling them using the diagram. In future classes, when a student is stuck on a problem, I have them walk through the process, applying the strategy to that particular problem. Usually, the students soon recognize why they were stuck on the problem. They learn that it wasn’t the math itself that caused their difficulty. It was their failure to use a particular step in the word problem strategy.
An interesting benefit of teaching how to solve word problems this way is that students soon realize it isn’t the math that causes them to be stuck. They know the math. They get bogged down in the process of systematically analyzing the situation described in the problem and working their way to the right answer. Ultimately, the students and I identify a pattern of how they are getting blocked from being able to do the problem. Sometimes, the student doesn’t recognize the math topic (overlapping geometric figures, proportions, algebra inequality, etc.). Sometimes, it is not recognizing what information is needed to answer the question. Other times, it is not knowing that they need to calculate missing but necessary information based on the given information. Once patterns are identified, it is a matter of working on the student’s faulty word problem strategy rather than reteaching math content that they already know. Teaching and learning become much more time efficient.
That was the breakthrough that my three students came to recognize during class. They knew the math, but they simply were having trouble applying the word problem attack strategy in certain situations. Once they figured that out, all the problems became “easy.”
If you would like a copy of the “Word Problem Strategy” flow chart, sign up for the free membership on www.betestsavvy.com and download it from the “Activity Sheets” page.
You can also take a look at the information about my latest book, “Becoming Test Savvy,” on my website: www.betestsavvy.com.
Please introduce your friends who are interested in standardized testing to my blog. As always, I look forward to your comments, experiences, and questions.