When words confuse the numbers

Garima Goswami

Most of us have dreaded solving word problems in math. Word problems, arguably, are the prime reason why many children develop math phobia. As National Council of Teachers of Mathematics Standards advocates, problem solving is an integral part of all mathematics learning and therefore we cannot wish away word problems in math.

This article is all about my experience with training my third graders in how to attack word problems, and the results are encouraging.

When I started working with third graders of my school, I would notice a sudden halt in the pace of our class whenever we started with word problems. Most of the students were not able to make complete sense of the problem. Students, usually, went blank when it came to working with word problems. They were looking for someone who would tell them which operation to apply so that they could work out the answer. Or else, they would just make a guess, and when challenged to justify it, they would quickly change their mind. Surprisingly, any answer was acceptable to them. They just did not have the ability to validate or verify the answer.

I then started reading up on how I could help my students. I came across several researches on the topic. A set of researches was focused on the role of mathematical vocabulary in the ability of students to solve word problems (Amen, 2006; Blessman & Myszczak, 2001; Georgius, 2006; Brethouwer, 2008; Kranda, 2008; McConnell, 2008). These researches suggest direct instruction in mathematical vocabulary. Solomon (2009) showed that taking time to write words related to problems and discussing their meaning in the context of the problem provides students more opportunities to know what to do with problems. Research done by Maryam Sajid suggested the importance of representation (that is, translating the given problem into a pictorial representation) in solving word problems.

Overall, my readings led me to put down the following list of gaps which are coming in the way of a student’s ability to solve word problems:
• Poor teaching
• Lack of mathematical vocabulary
• Inability to represent the problem diagrammatically
• Not having a strategy to attack a given word problem

As I was going through my desk research, my mentor suggested training students on a 6-step process for solving any word problem, which, to my mind, took care of all the gaps mentioned above. The process went as follows:
1. Read the word problem to find out what is to be found out
2. Read the problem again, this time focus on what is given, and put all this down in a diagram
3. Read the problem, one more time, to see if it mentions any conditions
4. Now look at the diagram and figure out a strategy to get to the answer
5. Apply the strategy and solve the problem
6. Verify the answer

Let me demonstrate this process through a typical word problem at Grade 3 level: What number should be added to 57 to make it the largest two-digit number?
Step 1: Student reads the problem and thinks about the largest two-digit number and makes a mental note that it is 99, and then jots down – “number to be added to 57 to make it 99”.
Step 2: He reads the problem again and makes following representation of the problem: 57 plus ? equal to 99.
Step 3: He reads the problem one last time and concludes that there are no conditions given.
Step 4: He looks at the representation and thinks of what should be done to find out the number which when added to 57 will make it 99. He decides to subtract 57 from 99.
Step 5: He does the subtraction and gets the answer as 42.
Step 6: This step requires him to validate the answer. So he adds 42 to 57 and gets 99, and concludes that his answer is correct.

Supposing, in Step 4, instead of subtracting, the student decided to add. He would then get the answer as 156, and when he tried to verify this answer he would realize that his answer is wrong. Also, he would figure out that the answer cannot be more than 99! Therefore, the 6-step process actually creates a loop which forces the student to go back and make corrections if the answer is not correct.

Therefore, I decided to train my students in this 6-step process. However, before I embarked on this task, I also collected data on what part of the process students were able to do currently. I did that using two methods: one, by giving them a set of word problems to solve, and second by interviewing them one-on-one.

Data, so collected, revealed two important pieces of information: none of the students was able to represent the problem, or verify the answer, and the percentage of students who were able to get the correct answer was just 37.

I then started teaching my students the 6-step process for attacking any word problem. Students were taught to apply these 6-steps throughout their classes for almost four months. Before tackling any word problem, students were asked to follow the suggested steps. I made a poster of this process and hung it on the classroom wall. Students were immersed in the environment where problems were seen as logical and solved strategically following all the steps. I could see that students were now enjoying grappling with word problems.

At the end of four months, I again collected data using the same method. The results, as expected, were very encouraging. Now 48% of the students were able to represent the problem pictorially, and 38% were able to validate their answer, as against none earlier. Most importantly, now more than 67% were able to solve the problem correctly, against the 37% earlier.

Apart from what data shows, I could see the confidence with which students were approaching word problems now. Earlier they were all confused about how to get started. Now they knew what to do first, what to do next, and so on. Most importantly, my students also learned that the answer they get is not some arbitrary quantity but is always accompanied by some unit, for example, not just 4, but 4 apples. Verification helps them to see that the answer is reasonable.

To conclude, I am convinced that the 6-step process of solving word problems should be taught to students as they encounter their first word problem, which can be as early as Grade 1. This would help more of our students love math.

References

  • Florida Department of Education, Bureau of Exceptional Education and Student Services 2010. classroom cognitive and meta cognitive strategies for teachers.
  • Lurdes Lopez (1996). Helping at-risk students solve mathematical word problems through the use of direct instruction and problem solving strategies.
  • Eda Vula, Rajmonda Kurshumlia. Mathematics Word Problem Solving Through Collaborative Action Research.

The author teaches at DPSG School, NCR. She can be reached at [email protected].

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