Math Word Problem Solving

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.There is no reason that this should end in early childhood.

When tested, students have shown that they can be more successful with word or verbal problems than they are with equivalent problems that are purely symbolic (Nathan & Koedinger, 2000a, 2000b). The Journal of Mathematical Behavior, 18(2), 149–167.

Other research suggests that skill in algorithmic computation may not correspond to students' ability to conceptualize the relationship between numbers in word problems (Fuchs et al., 2006). https://doi.org/10.1016/S0732-3123(99)00026-7 Stern, E.

By situating mathematics in contexts that are understandable for students, word problems encourage students to pursue solution strategies that make sense to them and lead more often to correct answers (Koedinger & Nathan, 2004).

These strategies can then be made more formal and symbolic with additional instruction. In early mathematics, problems are almost always situated in realistic contexts that children can make sense of.

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 & Mac Gregor, 1999) that can interfere with the development of the algebraic thinking that is usually needed to solve word problems.

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.

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. 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).

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