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Problems with “$n$"th-term problems. (English)
Math. Teach. Middle Sch. 16, No. 2, 88-94 (2010).
Summary: An nth-term problem involves a sequence. Students must determine which expression will allow them to calculate the nth position of the sequence. To solve such problems, students are to find “a rule that determines the number of elements in a step from the step number.” These types of problems help students develop concepts of functions, variables, and representations‒some of the “big ideas” of algebra. Students also learn to generalize relationships between sets of numbers while developing an understanding of the various components of algebraic expressions, such as the variable and constant, by reading and writing algebraic expressions. Van de Walle enumerated five different representational types used in pattern or sequence problems: (1) The pattern itself, which teachers can refer to as the “context"; (2) The chart or table; (3) The symbolic equation; (4) The graph; and (5) The language. According to the state middle school math curriculum documents, students should use symbolic, numerical, graphical, and verbal representations to describe algebraic thinking. This article explores the representational features of standardized assessment problems. (Contains 5 figures.) (ERIC)
Classification: H23 I33
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