id: 05948969
dt: j
an: 2011f.00542
au: Matteson, Shirley M.
ti: Problems with “$n$"th-term problems.
so: Math. Teach. Middle Sch. 16, No. 2, 88-94 (2010).
py: 2010
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: H23 I33
ut: elementary algebra; number sequences; number patterns; teaching methods;
equations; graphs
ci:
li: http://www.nctm.org/eresources/article_summary.asp?URI=MTMS2010-09-88a&from=B
ab: 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)
rv: