Word Problems
Word problems are described as "verbal descriptions of problem situations wherein one or more questions are raised the answer to which can be obtained by the application of mathematical operations to numerical data available in the problem statement" (Verschaffel, Greer, & De Corte, 2000). Solving word problems involves:
- The well-organized and flexible use of both conceptual and procedural knowledge
- Strategies and metacognition
- Positive affect and beliefs (De Corte, Greer, & Verschaffel, 1996; Schoenfeld, 1992)
Is Solving Word Problems the Same as Mathematical Modeling?
Solving word problems is not considered to be the same as mathematical modeling. Mathematical modeling tends to be a more complex process involving identifying questions to answer about the real world, making assumptions, identifying variables, translating a phenomenon into a mathematical model, assessing the solution, and iterating on the process to refine and extend the model (COMAP & SIAM, 2016). The process to solve a word problem isn't necessarily as complex, as the problem itself usually gives the reader the question to answer and the information necessary to answer it, and doesn’t require modeling's level of meaning-making and interpretation. These differences are relative, however, depending on the abilities of the student and the nature of the solution required to answer the problem.
Understanding the Challenge
What Makes Word Problems Difficult for Students?
Students' primary difficulty in solving word problems is attributed to their "suspension of sense-making" (Schoenfeld, 1991; Template:Verschaffel, Greer, & De Corte). Instead of thinking through the context of the word problem to understand it, many students simply seek a simple application of arithmetic needed to produce an answer, whether it makes sense or not. In the following video, Kaplinsky (2013) reproduces a result of early 1980s research conducted at the Institut de Recherche sur l'Enseignement des Mathématiques in France.
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Math teachers are often concerned about students' abilities to transfer classroom learning into the world beyond the classroom, but this "suspension of sense-making" shows that the reverse is also difficult – students struggle to apply their knowledge and understanding of the world back into a mathematics classroom. Having been conditioned with years of arithmetic, almost always involving obvious operations and the expectation that each problem has a correct answer, students develop a "compulsion to calculate" (Stacey & MacGregor, 1999) that can interfere with the development of the algebraic thinking that is usually needed to solve word problems. Some (but not all) research findings suggest that "compulsion to calculate" worsens as students age and develop beliefs that math is a collection of rules (Radatz, 1983; Stern, 1992, both as cited in Verschaffel, Greer, & De Corte, 2000, p. 5).
Students can also struggle with word problems because they have difficulty with academic vocabulary, mathematical vocabulary, or both. Due to these difficulties, English language learners and students of low socioeconomic status score lower on standardized assessment items than proficient speakers of English (Abedi & Lord, 2001).