id: 05945648
dt: j
an: 2011e.00542
au: Shaughnessy, Meghan M.
ti: Identify fractions and decimals on a number line.
so: Teach. Child. Math. 17, No. 7, 428-434 (2011).
py: 2011
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: F42 F43 D72 D73
ut: elementary school mathematics; numbers; number concepts; number
representations; visualization; mathematics skills; interviews; error
patterns; educational diagnosis; mathematical concepts
ci:
li: http://www.nctm.org/eresources/article_summary.asp?URI=TCM2011-03-428a&from=B
ab: Summary: Tasks that ask students to label rational number points on a
number line are common not only in curricula in the upper elementary
school grades but also on state assessments. Such tasks target
foundational rational number concepts: A fraction (or a decimal) is
more than a shaded part of an area, a part of a pizza, or a
representation using base-ten blocks; a fraction (or a decimal) is also
a number with a specific location on a number line. These concepts are
described as core content in "Curriculum Focal Points" (NCTM 2006) and
in the Common Core State Standards (2010). To explore the nature of
studentsâ€™ difficulties when labeling rational number points on a
number line, the author interviewed students in an urban school
district in Northern California. The protocol she designed included a
series of number line tasks asking students to label marked points on a
number line as fractions and decimals. More students appropriately
labeled points on the number line as decimals than as fractions, and
more students appropriately labeled points when the interval from zero
to one was equally partitioned than when the interval was unequally
partitioned. An analysis of studentsâ€™ incorrect answers and their
verbal reasoning revealed four common error types characterizingâ€™
incorrect answers: (1) Using unconventional notation; (2) Redefining
the unit; (3) A two-count strategy focusing on discrete tick marks (or
parts) rather than distances; and (4) A one-count strategy focusing on
discrete tick marks (or parts) rather than distances. Instructional
implications of this study are discussed. (Contains 13 figures.) (ERIC)
rv: