Solving Problematic Addition and Subtraction Word Problems

Word problems are used in school when teaching mathematics in order to help students connect math to real-life circumstances while strengthening their critical, problem-solving abilities. Contreras and Martinez-Cruz chalk the failure of word problems up to the unrealistic approach of children are expected to follow to solve them by applying a single arithmetic operation. Students simply memorize the needed arithmetic operation and fail to connect school mathematics to their life outside the school building. This article discusses the study of students, elementary teachers, and both of their approaches to solving additive world problems for which the solution is ± 1 than the answer produced by adding or subtracting two numbers. The study of the students, conducted by Verschaffel, DeCorte, and Vierstraete, and the study of the teachers, conducted by the authors of the article, Contreras and Martinez-Cruz, are both examined throughout the article which is divided in to three sections: strategies used by students, strategies used by prospective teachers, and implications and recommendations for instruction.

The results regarding the study of the fifth and sixth grade students showed that after giving the students a written test consisting of three nonproblematic problems and six problematic (problems that can not be solved by a straightforward arithmetic operation) whose solution was ± 1 than the answer produced by adding or subtracting two numbers, the students answered 24% of the problematic items correctly and 83% of the errors on the problematic items were caused by ± 1. Of the strategies used to solve the problems, 78% of them were formal, 6% were informal, and 16% percent were unclear. The conclusion drawn here is the students whom used formal strategies show an understanding of the problem and necessary operation but those whom used counting based strategies show a better understanding of the mathematical situation but were unable to use the necessary operation. As for the teachers, the study called for them to complete a written test consisting on nine experimental items (3 solved by straightforward addition/subtraction, 6 problematic) and seven buffer items. Focusing on their strategies, solutions, and interpretations of solutions, teachers performed well on the nonproblematic items with 92% correct responses, however, they only scored 9% correct responses regarding the problematic items. Similar to the students, a large percent of the errors were due to ± 1 mistakes.

The results of these two studies can mean several things. Teachers and students may approach word problems in a superficial way because they are used to solving problems using a straightforward operation. Another explanation could be the lack of understanding with heuristic strategies or an enumeration process involving ordinal numbers. Overall, it seems both teachers and students need more practice in solving whole-number addition and subtraction word problems in which the solution is ± 1 than the sum/difference of the two numbers. The article suggests different strategies to improve on this weakness. The strategies consist of using a variety of instructional approaches, modeling problematic problems, presenting the problems first to students so in return they have the opportunity to develop their own strategies and providing students with mathematical tasks that require making connections between math and real-world knowledge.

After reading this article, I was surprised to read some of the results I did from the two studies regarding teachers and students. This article interested me before I even read it because of the topic of word problems. As a child and still to this day, I am far more capable of solving a mathematical operation by itself than one that needs to be drawn from a word problem. Often, it was just easier to take any two numbers within the problem and put them in the learned formula, but I never made the connection to why I was doing what I was doing. I enjoyed being able to read just how many people that affects and that students were not the only ones having difficulty, but the teachers too. I agree with the article when they stress the importance of showing students and teachers the relation math has to real-world knowledge and the reason they carry out certain operations. I believe students and teachers would be better off and have a better understanding of math and strong problem solving skills.