Wordy Word Problems

June 1, 2013 at 7:26 am | Posted in Content Area Literacy | 3 Comments

(Erin Weld)

When beginning the process of choosing a topic for this blog, I began by looking up the connection between literacy and mathematics. After reviewing multiple documents, it came to my attention that the main component connecting mathematics and literacy would be solving word problems. When thinking about this topic, may concerns come to mind: student’s ability to pull out pertinent information, understanding the actual question, and overall readability of the question? In an article by Swanson, she references the idea that in 1945 Polya devised a four step process to solving word problems. The four main steps that would be to gather the data and analyze it to understand the problem, devise a plan by making connections to previously solved problems, test the plan and finally look back to make sure the results effectively answer the questions.

A study was conducted and reported on by Nasarudin Abdullah1, Effandi Zakaria1 & Lilia Halim, where they assessed the effectiveness of a thinking strategy approach to solving mathematical word problems. This study focused on taking word problems and turning them into visual representations in order to gain insight into the question, and then subsequently solving the given problem. This study uses the following steps in order to picture the problem: visualization, arrangement, plan, calculate, check the solution.

There are obvious overlaps in these two different processes; do you believe that the similarities bring two methods together? Which method do you believe could be most effective? Which method do you believe your students will find most effective?

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  1. First of all, I wanted to say I liked your title. Since I now know alliteration is the repetition of sounds or words, I liked your use of that in the title.

    When I read your post, the first thing that came to mind for me was one of the articles we read in class called Teaching Reading in Mathematics and Science (the green one). The article discussed how text style in mathematics usually varies from what students are used to seeing in other subjects like ELA. One of the most important differences (to me) is that the main idea usually appears at the end of a word problem. The student reads about a ton of information and is then introduced to what they need to do. By the time they reached they end they may be confused by all of the needed or not needed information they were given. They may be thinking to themselves “Why do I care?” This article gives the reader a 6-step strategy called SQRQCQ-Survey, question, read, question, compute, question.

    Adding this third strategy to the mix, I think they are all very similar. if I were to pick a strategy, mine would involve all three. All of these strategies have steps that I would consider very important to solving word problems. If I could choose a strategy that I find most effective and incorporating strategies suggested by these scholars, here’s what it would be:

    Step 1: Read the problem to find out what it is asking you. Underline the question or main idea. Make sure you understand what you are asked to find.
    Step 2: Re-read the problem and circle the information given that you need to help solve the problem. (Steps 1 and 2 taken from all three strategies, but underlining has been added)
    Step 3: Draw a picture or visual representation if possible.(Nasarudin Abdullah, Effandi Zakaria & Lilia Halim)
    Step 4: Plan how you are going to solve. Write down any formulas or facts that will help you. I prefer students to write down everything to help them in the checking step. (Taken from all three)
    Step 3: Solve.(All three)
    Step 4: Check your work. In this step you must ask yourself “Does my answer make sense?” This step is very important to solving any mathematical problem. (All three with my own opinion added)
    Step 5: If the answer you found does not make sense, re-read the problem and make sure you understand what it is asking and re-work your plan to solve. (This step is obvious to some but not so much to others. Students may have trouble being able to decide if an answer makes sense which means we need to put a great emphasis on understanding what the question is asking)

    Obviously one strategy is not going to work the same for all students. The goal is to help the students figure out what does work best for them individually. Therefore I think what I have come up with will be effective, but there is room for modifications. Many of the steps can be done differently or with added pieces. I found this site which has other strategies and variations on strategies for solving word problems. This site discusses student differences and how we need to think about them when designing and teaching strategies. From Miller 1996 and Montague 1988 they quote “Recognize student characteristics (cognitive and behavioral) and preferences.”

    In conclusion, it is not easy to pick one strategy for solving word problems that will be most effective, that is, until you are in the classroom and have gotten to know your students. These “most effective” strategies will be individualized based on your students.

  2. I think word problems can be a huge challenge for kids at all levels of reading ability, so this is a great topic to research. The two processes that are referenced in the post almost seem to be common sense for someone who has experience with successfully solving word problems, but it would make sense to explicitly explain them to students. The main difference I see in the two methods is the visualization step in the second method, which I believe would be the most effective in my classes for my students.

    In my earliest physics classes, we were always taught to make a visual representation of the problem first, something that is easy to do with most physics problems, since they involve things we can easily represent visually, like inclined planes, trajectories, or even electric fields. There are many standard physics drawing representations that are easy to use, for example, the free body diagram , and ray diagrams . As we all know with word problems, sometimes the actual question gets lost in the words. But, once the visual representation is available to look at in a physics word problem, what the question asks for falls easily into place as the unknown quantity.

    As we talked about in class, and as Andrea discusses in her comment, sometimes word problems are written in completely contrary to what we usually think of as good writing. The main idea, or in this case the question, is at the end instead of the beginning, causing all sorts of confusion to the student. Using the visualization technique will help clarify what students are reading, and as a teacher, I definitely will be helping students decode word problems so they can more easily understand them. Using a visual representation of the problem will be a huge part of helping them understand and ultimately solve these problems.

  3. Mathematics is a very difficult field of study to integrate literacy. This is often due to the abstract nature of mathematics in general. As future teachers, it is important to step beyond this obstacle and connect every topic with students’ daily lives. Word problems are thus the gateway for connecting abstract math ideas to applications in the real world. Teaching effective word problem solving strategies in the classroom allows for students to understand the importance of math in a practical way.

    There are many different strategies that students can use to assist them when solving word problems. Your post references Swanson’s article and the four steps to problems solving. This method is very simple and straightforward when approaching word problems. Looking at the big picture and understanding the problem is the first step in Swanson’s method. It is imperative that students recognize what the problem is asking of them before they begin the physical problem solving process. Formulating a plan is also highly crucial to successfully answering the problem. How can ideas be expressed such that they lead to an answer? What tools are required to mathematically solve the problem? These are questions that fall under this planning step. The final two steps of this method (testing the plan and checking the answer for accuracy), are necessary steps that students must take when solving word problems. Swanson’s process is therefore a very effective technique for solving word problems. At its core, this method requires students to understand the problem, plan the necessary steps for finding an answer, and solve the problem once a result has been accepted. The online resource MathStories provides several strategies for solving word problems that all follow the basic outline. This simple procedure gives students the direction they need when solving complex word problems.

    The second method you describe is also a very effective tool for solving word problems. Visualization and representations can lead to greater understanding of what the problem is asking. An article entitled Habits of an Effective Problem Solver sheds light on the benefits of visualizing a word problem. It benefits students by helping them translate abstract ideas into practical diagrams or pictures in order for the students to better understand the parameters of the problem. Creating visual representations is therefore the basis of accurately solving a word problem! If a student fails to connect the abstract ideas to a workable/usable diagram, then the student’s level of comprehension is not maximized. Teachers must promote methods of problem solving that incorporate the use of visual representations. In turn, students will achieve a greater understanding of problem solving.

    These two methods of solving word problems are very similar in that they both follow the basic pattern that requires students to understand, plan, and solve. Since there are many strategies for solving these types of problems, and not all of them are beneficial to every student, it is impossible to say which method is more effective. However, the method of visualizing the problem can be easily integrated into Swanson’s four-step method (under the comprehension step in the process). Regardless of the method used for solving word problems, literacy is best incorporated into these types of problems through understanding the problem, planning and constructing a visual representation, and arriving at a valid answer that satisfies the conditions.


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