The cause of the "I can't do word problems" syndrome is the absence of instruction in using the mathematics as a language in problem solving in the K-12 curriculum.
Curing the "I can't do word problems" syndrome requires explicit instruction and exercise in the use of the language of mathematics in the problem solving process instead of an ever growing assortment of strategies designed to avoid coherent use of mathematics in problem solving.
This type of problem integrates developing mathematical skills and problem solving in early grades. Doing so has substantial future value. Developing mathematical skills within a problem solving environment bring real life meaning to the use of mathematics.
This step is the first stumbling block students encounter in problem solving and the use of mathematics. The cause of this is failure to develop the methodology in early grades. The more involved students do it in their heads and resist recording their thinking. Thus they do not develop skills that will be needed in more involved problems. The less involved student are left dangling. Students do not learn to use mathematics as a langauge quite simply because they are never provided the opportunity to do so.
These two steps are responses to the requests made by the starting equation. It is an opportunity to help the student become aware of the fact that the information needed is frequently in the problem statement. It is a systematic approach to gathering the essential information needed to effect solution of the problem. In problems encountered in early grades this can be done in the head by some students. These will resist recording the steps, or even being consciously aware of the steps, and lose the opportunity to develop skills of value in later work. The majority of the students are denied the opportunity to use mathematics as a language and develop mathematical skills of permanent value if these steps are glossed over.
Substitution is a process extensively used in mathematics. Follow the process here. The first equation is a response to what is asked for. The next two equations respond to requests by the starting equation. The responses are then substituted in the starting equation. Simplification of the result of substitution provides the final answer.
The resulting presentation of the solution is a complete story of the process of the solving this problem. It provides a model for more involved problems.
The organization of the solution follows the basic rules of communication, opening-body-close, that are used in writing an essay, business letter, computer program or any other form of effective communication. Teachers of mathematics could learn from teachers of written composition and of publics speaking. The same basics grammar applies. The tools differ.
The book's presentation is shown below.
Curing the "I can't do word problems" syndrome requires no more than providing the students the opportunity to see and exercise with the thinking process that precedes the generation of the result.
The circling of the word altogether stimulates a sequence of thought processes. These processes are typically hidden in textbooks and teaching materials. Curing the "I can't do word problems" syndrome requires making these processes visible. This must be done in early grades in order that organized thinking processes for problem solving will be available to students in later studies. Request-Response-Result provides a means of organizing the thinking part of the solution to word problems.
Propagation of the "I can't do word problems" syndrome is a result of the fact that in dealing with problems encountered in early grades students carry the thinking part, the algebra, in there minds. The thinking part of the more involved problems encountered in later grades cannot be carried in the mind. The working memory is simply not adequate for this task. When the working memory is overwhelmed confusion results producing the "I can't do word problems" syndrome. The cure is to reduce the burden on the working memory by training in the earlier grades directed at emphasizing the Request-Response part of the problem solving process by making this part of the problem solving process visual. This is in contrast to existing instructional material which emphasizes the Result part of the process.
Teachers do emphasize the thinking, the Request-Response, part of problem solving in their direct contact with students. However, the Result part is emphasized in much of the teaching material available. To optimize the use of the generally excellent problem material available it is necessary to supplement it by applying the Request-Response-Result problem solving process to that material.
Request-Response-Result provides a process for systematically applying the concept of backwards problem solving.For more on curing the "I can't do word problems" syndrome click in this line.Working backwards is a common-sense procedure within the reach of everybody and we can hardly doubt it was practiced by mathematicians and non-mathematicians before Plato.
p202 How to Solve It. G. Polya. Princeton University Press. 1945
The activities book from which the example was adapted (Math Topics, Grades 3-4, Instructional Fair) provides an excellent environment for beginning the transition from arithmetic to algebra.
Copyright: Howard C. McAllister, 1997.