id: 06514379
dt: j
an: 2016a.00463
au: Morin, Joe; Samelson, Vicki M.
ti: Count on it: congruent manipulative displays.
so: Teach. Child. Math. 21, No. 6, 362-370 (2015).
py: 2015
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: F20 F30 U60
ut: mathematical concepts; manipulative materials; concept formation; number
concepts; visual representation; hands-on representation; number sense
ci:
li: http://www.nctm.org/Publications/teaching-children-mathematics/2015/Vol21/Issue6/Count-On-It_-Congruent-Manipulative-Displays/
ab: Summary: Representations that create informative visual displays are
powerful tools for communicating mathematical concepts. The National
Council of Teachers of Mathematics encourages the use of manipulatives.
Manipulative materials are often used to present initial
representations of basic numerical principles to young children, and it
is through these early developmental experiences that children
frequently receive their first introduction to formal mathematics.
Manipulative displays are well suited to serve as proxies for
real-world problems, taking on the role of representing quantities.
Teachers intuitively assemble manipulative displays to construct such
representations, often attaching language to scaffold the real-world
connections they are trying to portray. Many children prosper from the
interaction; however, others do not. For the latter, confusion can
result when the arrangement of the display is not clearly connected to
the concept being taught. The aims of this article are to: (1) identify
the rationale for using manipulative displays as tools for
communicating concepts; (2) describe the desired attributes teachers
should consider when selecting and implementing manipulatives; (3)
define conceptual congruence; and (4) offer some suggestions for
helping teachers achieve greater congruence between the numerical
concepts and procedures they are teaching and the manipulative displays
they are using to represent them. The authors also present an example
of a $1 \times 10$ ten-frame display to use as a tool to facilitate
conceptual congruence. (ERIC)
rv: