id: 05878598
dt: j
an: 2011c.00643
au: Trinter, Christine P.; Garofalo, Joe
ti: Exploring nonroutine functions algebraically and graphically.
so: Math. Teach. (Reston) 104, No. 7, 508-513 (2011).
py: 2011
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: I23 I24
ut: functions; problem sets; mathematical applications; graphs; educational
strategies; middle school students; teaching methods; mathematical
concepts; mathematical formulas; mathematical models
ci:
li: http://www.nctm.org/eresources/article_summary.asp?URI=MT2011-03-508a&from=B
ab: Summary: Nonroutine function tasks are more challenging than most typical
high school mathematics tasks. Nonroutine tasks encourage students to
expand their thinking about functions and their approaches to problem
solving. As a result, they gain greater appreciation for the power of
multiple representations and a richer understanding of functions. This
article presents four tasks wherein students are asked to investigate
algebraic and graphical representations of several types of functions
and are thus provided opportunities to develop, use, and compare a
variety of solution strategies. Some of these solution methods take
advantage of less-used but nonetheless valuable features of graphing
calculators to generate representations for learners to analyze.
Appropriate use of these tasks challenges learnersâ€™ intuitions while
broadening and deepening their knowledge of functions through the
linking of multiple representations. Although these tasks have been
around for a while, most students find them to be novel, engaging, and
thought provoking. These tasks support NCTMâ€™s Algebra,
Representation, Connections, and Problem Solving Standards for grades
9-12 as well as the Learning and Technology Principles. In addition,
the tasks address topics assessed by the 2005 National Assessment of
Educational Progress, such as identifying and graphing exponential
functions, solving routine and nonroutine problems involving different
representations of functions, and performing operations on algebraic
expressions using appropriate tools. (Contains 5 figures.) (ERIC)
rv: