Connecting Process Problem Solving to Children's Literature
Leitze, Annette Ricks, Teaching Children Mathematics
Since the publication of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), many mathematics teachers and educators have become especially interested in making mathematical connections, such as that found between mathematics and children's literature. See, for example, Galley (1993); Kliman (1993): Lewis, Long, and Mackay (1993); Thiessen and Matthias (1992); and Welchman-Tischler (1992). This mathematics-literature connection is a natural way for teachers to allow students to see mathematics in everyday society, to give meaning to mathematics, and to make it come alive. It allows students "to observe the interaction of mathematics with other school subjects and with everyday society. . . . This integration of mathematics into contexts that give its symbols and processes practical meaning is an overarching goal of all the standards" (NCTM 1989, 84).
The NCTM advocates that "[p]roblem solving should be the central focus of the mathematics curriculum" (1989, 23), a way to think, a way to solve the problems that occur as a result of daily living, and a way to see the mathematics involved in daily life. "Children tend to think of mathematics as computation" (NCTM 1989, 33), and many college students view mathematics as plugging numbers into equations and computing the answer (Leitze 1992). In fact, from my experience, most people, including those with advanced degrees in fields other than mathematics, restrict their view of mathematics only to those situations involving numbers. A quick look at several graduate-level mathematics textbooks supplies convincing evidence that the study of mathematics need not involve numbers. Rather, mathematics is a way of thinking about problem solutions, which may or may not involve numbers. In the same way, solutions to many of life's problems that call for a mathematical solution may or may not involve numbers.
According to the NCTM, "[o]ne way to dispel this incorrect notion [of mathematics as just computation] is to offer [children] more experiences with other topics" (1989, 33). Moreover, the NCTM contends that "implementation of the standards should be organized in such a way that several goals will be addressed simultaneously" (1989, 84). I believe that connecting problem solving and literature is one way to achieve simultaneously several of the NCTM's standards. This connection incorporates problem solving into the curriculum, permits children to gain experience with mathematics other than computation, and integrates mathematics with other school subjects. Moreover, in classrooms where teachers use a literature-based language-arts program, the literature and process problem-solving connection can be further strengthened by connecting literature, problem solving, and language arts.
Charles and Lester (1982) believe that a problem must have three characteristics: the solver must (1) want to solve it, (2) have no readily available method, and (3) make an attempt to solve it. Process problems have solutions that "require the use of thinking processes" (Charles and Lester 1982, 8). Typically, these problems are solved by using one or more problem-solving strategies, such as making an organized list, drawing a picture, making a model, acting it out, making a table, using logical reasoning, looking for a pattern, solving a simpler problem, working backward, or guessing and checking.
Methods for Connecting Process Problem Solving and Literature
My preservice elementary school teachers and I have successfully connected process problem solving and literature using two approaches. The first approach focuses on the problem-solving portion of the lesson and a particular strategy and seeks problems and a book with which to coordinate the two. The second approach uses a storybook, usually an old standby or a class favorite, and rewrites process problems to target a particular problem-solving strategy to coordinate with the story. In each approach the literature serves as a springboard for the problem-solving portion of the lesson. …