This last section of the book focuses on topics that the NCTM standards recommended for increased attention. One of the objectives of the NCTM standards is to promote the transfer of knowledge learned in the classroom to problems outside the classroom. Therefore, it is not surprising that one of the recommended topics for increased attention is the use of real-world problems to motivate and apply theory ( NCTM, 1989). This issue is examined in this chapter. Chapter 11 looks at estimating answers to word problems and using estimates to measure students' understanding of functional relations between two variables. Chapter 12 discusses curriculum reform and examines how research and the NCTM recommendations are influencing the design of instruction.
At various times educators and cognitive scientists have criticized word problems as being too artificial to transfer to real-world situations. For instance, Brown, Collins, and Duguid ( 1989) stated the following in their influential article "Situated Cognition and the Culture of Learning":
Math word problems, for instance, are generally encoded in a syntax and diction that Is common only to other math problems. . . . By participating in such ersatz activites students are likely to misconceive entirely what practitioners actually do. As a result, students can easily be introduced to a formalistic, intimidating view of math that encourages a culture of math phobia rather than one of authentic math activity. (p. 34)
This chapter begins by examining their view of situated cognition and then looking at recent research studies that have investigated how students solve problems that represent real-world constraints.