Academic journal article American Annals of the Deaf

# Deaf and Hard of Hearing Students' Problem-Solving Strategies with Signed Arithmetic Story Problems

Academic journal article American Annals of the Deaf

# Deaf and Hard of Hearing Students' Problem-Solving Strategies with Signed Arithmetic Story Problems

## Article excerpt

THE USE OF problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e., modeling, counting, and fact-based strategies), they showed an overwhelming use of counting strategies for all types of problems and at all ages. This difference may have its roots in language or instruction (or in both), and calls attention to the need for conceptual rather than procedural mathematics instruction for deaf and hard of hearing students.

Problem solving, defined here as the solving of story problems or what have traditionally been called word problems, is a valuable mathematical activity through which mathematics is learned and created, and by which mathematics understanding can be examined and measured. More than the simple use of a procedure, problem solving can be further defined as a sense-making process whereby a synthesis of knowledge and procedures is used as a means to devise a meaningful interpretation of a problem situation - the "story" in the story problem (Carpenter, Ansell, Franke, Fennema, & Weisbeck, 1993). Successful problem solvers are inventive, practical, flexible, and reflective in their use of a variety of solution strategies (Baroody & Dowker, 2003; Franke & Carey, 1997; Hegarty, Mayer, & Monk, 1995; Schoenfeld, 1985). Problem solving thus becomes a "window" through which one can see not only what a solver knows about mathematics, but also, through its application, the depth and quality of that knowledge.

In the problem-solving process, the solver must first understand the problem situation. At the most basic level, this requires that the solver have full access to the problem - that is, that the problem be in a language and mode, and at a level of complexity, that match the skill and knowledge of the solver. The solver then devises a plan or solution strategy based on what she or he knows about the situation and about related mathematical concepts and procedures, and, finally, acts on that plan, thinking logically about its outcome. Skilled problem solvers, however, do more than simply translate the syntax of a problem (e.g., key words) directly into symbols and then operate on them - they analyze the semantics of a problem situation and, as part of the solution process, may decide to transform the problem situation into a form in which it will be easier to solve before they represent it mathematically A conceptual rather than procedural understanding of mathematics allows solvers to draw on all of their knowledge and skills as they address the present situation. By contrast, those who have learned a set procedure that is attached (mentally or instructionally) to a specific problem type are stymied by any situation that does not follow the learned structure. These solvers tend to be rigid and unable to succeed at "true problem solving" (Hegarty et al, 1995; Kelly Lang, & Pagliaro, 2003; Reed, 1999).

Researchers continue to find that many children have not been given the opportunity to develop the conceptual understanding of the mathematics one needs to be a successful problem solver. Instead, many have been taught and rely on rote procedures for solving story problems that are not based on sense making but on "surface-level analysis" (Kelly et al., 2003; Pagliaro, 1998b); such students scan the story problem for numbers and verbal cues (such as key words) that will "tell them what to do" (Garofalo, 1992; Hegarty et al, 1995; Wiest, 2003). Although these procedures may often result in a correct answer (and thus persist), they prevent the solver from making sense of the problem and from truly understanding the relationship between the situation and the mathematics that represents it (Parmar, Cawley & Frazita, 1996). …

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