Math reading problems can be intimidating, especially for beginners. They differ from ordinary computational problems because with computation, the method is already laid out. Word problems require more logical reasoning and deduction, which garners more of a stigma and heightened wariness towards them. However, there are things you can do to lessen the anxiety, and make it more engaging. Follow these comprehension strategies to make math reading problems less frustrating to teach, and less daunting to learn.
Reading Out Loud
First of all, it's always a good idea to read the problem aloud. This ensures that nothing vital is skipped over, plus it helps keep focus. It's a communal way of getting over the jitters if the entire class is an active participant in some form or another. Allow the children to take turns, and try to make sure that no one is left out. If there are simply too many students in class to do the reading, then rotate responsibilities. Have someone responsible for writing discussion points on the chalkboard, or taking notes for the readers. Make them feel like they are part of the process, and not just a passive set of eyes and ears. Children who are shy or need more practice reading will also benefit. The more accustomed the students are to reading aloud in class, the more likely they'll participate in other areas as well.
Before you assign a reader, inform the class that there are certain words they should listen for such as more, less, fewer, equivalent, etc. Explain to them that those types of words will help guide them in solving the word problem. Have the students read the problem slowly at first. Then open the class up for discussion about what the word problem is about, and what it asks to be solved. Again, go around the room in some predetermined order. Picking students randomly tends get some children more attention than others. This also helps to make sure that everyone pays attention because virtually everyone will be called on. The word problem may have to be read several times over in the beginning, so you may hit a few snags at first, but they will fade once the children get acclimated to reading.
For instance:
Word Problem #1:Troy needs to pick 255 apples for his cider recipe. So far, he's picked 89 apples. How many more apples does Troy need to make his cider?
After a student has read the problem slowly and clearly, ask the class what the math word problem was about. What does it want an answer to? Did they notice any of those special words you warned them about? What facts do they already know? If there are gaps and long silences, then have the problem read again. Then ask the class how they would come up with the answer, and why did they choose that particular method?
Write It Out!
Writing out their thoughts is another tool to help with comprehension and problem-solving. In general, this is slightly more attuned with note-taking, but it is a valuable process that helps children organize their thoughts and be able to communicate them more succinctly. Writing reinforces the information and spurs critical thinking. But it is important to stress early on, that neatness is important. After all, you can't follow what you've written, let alone explain it to anyone if you can't read your own handwriting.
So, as in the previously stated word problem, once it's been read out loud, the class should write the following question: What needs to be solved?
Doing this sparks logical reasoning. The answer to the question should be written immediately after: How many more apples does Troy have to pick?
Now, have the class list the clues given in the problem, write out the clues provided in the word problem, what method(s) they think can solve it, and what special word hinted towards their answer.
Like so:
Clues:
- Troy needs 255 apples
- Troy already has 89 apples
- The special hint is how many more apples, so that means I need to subtract 89 from 255
- 255 – 89 = 166
- Troy needs to pick 166 more apples to get to 255
Engagement is crucial because it strips away the fear, and is a terrific confidence booster for the child. Once their thoughts and ideas have been written down, share some of them with the class. Put their ideas to the test on the chalkboard. Have them explain their methods and their reasoning based on their notes. This is why proper handwriting is key. They need to be able to retrace their steps and explain them to others. This helps with memory, plus the student will be able to recall much faster as they get used to more word problems. If the child believes they have a way to solve the problem based on everything they've written, let them try it. Put it to the board, and make sure that each step is followed through. Have children double-check their own work first. Make them feel more responsible and proud of their work. If the child feels they've made a mistake, congratulate them for being so vigilant, and have them try again, only go more slowly. Remember to tell them, it's okay to make mistakes. Even mistakes can be useful because they are a part of problem-solving too. Go through the steps one-at-a-time, at a pace that's comfortable for them, in order to determine the answer. Over time, he or she will develop a methodology that works for them, and it will become automatic. By having the child talk about what they did, you are also bolstering their communication skills and self-confidence. If this practice is carried over at home as well, you should see an increase in class participation and performance over the course of the term.
Creative Stimulation
Now say there are fractions in the word problem. This is an excellent opportunity to use drawing and visualization. Once students have determined what needs to be solved, and the clues are jotted down, have the children try drawing pictures to help find a solution. Drawing is a terrific way to engage, trigger creative thinking, and harness spatial reasoning.
Word Problem #2: Monica baked a tray of 24 double fudge brownies. She sold 2/3 of them. Robert baked a tray of 24 banana-nut fudge brownies, and sold 1/4 of his. Who sold the most brownies?
So here as before, write down what needs to be solved, and the clues provided. The next step is a bit more creative. Drawing charts or pictographs helps some students, who think better visually, formulate their ideas and come up with suggestions for problem-solving. Have students draw two trays divided equally into 24 brownies. Use one color to shade in 2/3 in one tray, and use another color to shade 1/4 in the other. So now the class has a visual representation of the method used to find the answer. Count how many brownies each person sold. They must write the answer, and explain how they got it.
Tackling Complexity
As the math word problems become complex, it may even prove useful to show the class how to work backwards. Taking the logical course from Point D to Point A, keeping track of each step, and neatly formulating your reasoning is an excellent way of solving more complex math word problems.
Word Problem #3: Sara had $30.00 to buy materials for her project. She bought a bag of clay for $4.38, a set of pottery paints that was $12.80, and a pottery shaping toolkit. Her change was $1.07. How much did the toolkit cost?
Here, instead of adding all the smaller numbers up, trying to get to $30.00, the logical course would be to start with the highest number, and work your way down to figure out the missing price. The more complicated the word problem, the more important is it to keep track of all the clues and information that's given. Beginners may tend to skip a step or two, so always stress being methodical, writing neatly, and checking their work.
What needs to be solved? What is the price of the toolkit?
Clues:
- Sara had $30.00 to spend
- The bag of clay costed $4.38
- The pottery paints were $12.80
- Sara's change was $1.07
- Need to subtract all the smaller amounts from $30.00
- $30.00 – $12.80 – $4.38 – $1.07 = $11.75
- The toolkit price is $11.75
It is also necessary to approach the more difficult problems in an inclusive manner. Encourage communication, and reinforce taking your time and thinking things through. And remember to tell your class that mistakes are inevitable, but they are not the end of the world. Diffuse the notion that a challenge is frightening and should be avoided.
Practice! Practice! Practice!
But no matter how simple or ambitious the word problem is, students must do them frequently and consistently. Practice makes perfect. It's a lame cliché, but it's true. Many teachers focus mainly on computational math problems, and neglect word problems. That's a guarantee for comprehension problems and high anxiety for both the teacher and the class. The dynamic needs to shift, so that math word problems are taught earlier and at a slightly higher percentage because they are so integral to developing critical thinking and comprehension skills. The more children are exposed to math word problems, the less likely they are perceived as a threat.
On top of that, help students realize just how prevalent mathematics is in their lives. Let them write their own word problems using props from home like measuring cups, recipes, coupons, or grocery receipts. Have them create their own You Can Solve It! poster, or desk wallpaper, for class or for home use, with helpful hints on how to tackle word problems. Perhaps they may come up with their own suggestions. Show students that a challenge isn't something to shy away from, but to relish. Have them create their own little notebook tags or bookmarks reminding them of math problem strategies even at home. Success is imminent, but it takes time, dedication, and a tremendous amount of patience, but the results will speak for themselves.
References
- Education World.com
- Raising Motivated Kids: Inspiring Enthusiasm For a Great Start in Life (School Savvy Kids) by Cheri Fuller
- NEA
- Strategies That Work: Teaching Comprehension For Understanding and Engagement by Stephanie Harvey and Ann Goudvis
- This article is based upon my childhood experiences, personal accounts of tutoring my niece, and researching the Internet and various books.
- Math Word Problems Demystified 2/E by Allan Bluman
- U.S. Department of Education