Once students determine the problem type, they can apply a schema (i.e., diagram, equation, or plan) to assist in solving the word problem. Two distinct schemas can be used to solve the problems. Combining or totaling is different from finding a change in that the examples represent two distinct problem types. If students are asked, Five blue birds flew away, how many blue birds are left sitting in the tree?, the problem type is finding the change (in the number of blue birds). If, however, students are asked, How many birds are on the tree?, the problem type is combining or totaling (the birds). For example, students may be given the following information: There are 7 blue birds and 4 red birds sitting on a tree. The problem type is determined by what is happening in the word-problem narrative. Often, word problems can be differentiated into types of problems. Pictures or diagrams, as well as number sentences or equations, can be used to represent schemas. In mathematics, students can use schemas to organize information from a word problem in ways that represent the underlying structure of a problem type.

A schema is a framework, outline, or plan for solving a problem ( Marshall, 1995). Over the last two decades, a sizeable literature has begun to accumulate with an emphasis on helping students develop schemas to solve word problems in mathematics (e.g., Fuchs, Fuchs, Finelli, Courey, & Hamlett, 2004 Fuchs, Seethaler, et al., 2008 Griffin & Jitendra, 2009 Jitendra & Hoff, 1996 Willis & Fuson, 1988). Many researchers have investigated methods for teaching problem solving to general-education students ( Marshall, 1995 Schoenfeld, 1992 Shavelson, Webb, Stasz, & McArthur, 1988) and, in more recent years, to students with learning disabilities (LD) (e.g., Case, Harris, & Graham, 1992 Mastropieri, Scruggs, & Shiah, 1997 Miller & Mercer, 1993). High-stakes standardized tests like the National Assessment of Educational Progress (NAEP National Assessment Governing Board, 2009) place heavy emphasis on mathematics word problems and national educational organizations like the National Council of Teachers of Mathematics ( NCTM 2000) heavily value the teaching of problem solving across grades K through 12. Word-problem instruction has become vital for students. Since Pólya (1945) introduced four steps for solving word problems (understand the question, devise a plan, carry out the plan, and look back and check), teachers have been encouraged to provide more systematic instruction on problem solving in mathematics.

Finding x word problems