Math Word Problems Study Skills
Classes in mathematics and the sciences have traditionally been the nemesis of students' attempts to maintain high grade point averages. While some of the difficulties students have with these disciplines may be ascribed to highly esoteric vocabulary and great quantities of factual material, these attributes are found in other non-science courses as well, and thus cannot form a sufficient explanation of the problem. However, the scientific disciplines are unique in their heavy reliance on problem-solving methods, and in testing strategies which use work problems as a major part of the test format.
The feature of word problems which makes them so difficult is that information is expressed in a form which is different than that used in obtaining a solution. Thus, before a student can attempt a solution, it is necessary that he/she isolate the major pieces of information the problem contains, relate them to a specific mathematical equation, and then perhaps modify the units of the given data to fit the conventions of the equation.
The difficulty is further increased because of the enormous number of situations which may be generated as the subject of a word problem, and the fact that verbal descriptions are inevitably much longer than symbolic statements. One might initially suppose that the extensive use of solved problems, both during lectures and in accompanying texts, might serve to alleviate some of the difficulty. While it is certainly true that these illustrative problems contribute to a student's mastery of a given solution method, the very fact that they are illustrative of a concept, and are identified as such, removes a crucial step in the problem solving process, i.e., the need to establish the general nature of the solution. Also, most of the illustrative problems given utilize a single concept for the solution, contrasting strongly with the types included in exams, where combinations of concepts are required.
Despite the fact that word problems are difficult for all students, it is still obvious that some students are much more successful in dealing with them than are others. One of the distinctions between these two groups is the ability of the successful students to simplify the information in the problem and identify the mathematical relationships necessary for its solution. A prerequisite of a person's ability to perform these steps is the establishment of a mental pattern which contains the central features of problems of different types. Such mental patterns are formed as a result of having compared many problems of the same type so that accidental specifics cancel out and what remains is an awareness of the types of information and the types of questions which may be asked about a given topic. These patterns cannot be taught - their development requires individual discovery. It is this discovery, this comparison, which is the feature lacking in the study pattern of the unsuccessful students.