id: 06466670
dt: j
an: 2015e.00488
au: Benson, Christine C.; Wall, Jennifer J.; Malm, Cheryl
ti: The distributive property in grade 3?
so: Teach. Child. Math. 19, No. 8, 498-506 (2013).
py: 2013
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: F32 G42
ut: geometric concepts; concept formation; multiplication; arithmetic;
distributive property; geometric interpretation; area conservation
ci:
li: http://www.nctm.org/publications/article.aspx?id=35865
ab: Summary: The Common Core State Standards for Mathematics (CCSSM) call for
an in depth, integrated look at elementary school mathematical
concepts. Some topics have been realigned to support an integration of
topics leading to conceptual understanding. For example, the
third-grade standards call for relating the concept of area (geometry)
to multiplication and addition (arithmetic). The third-grade standards
also suggest that students use the commutative, associative, and
distributive properties of multiplication. Traditionally,
multiplication has been a major topic for third grade. Linked to
repeated addition of equal-size groups, multiplication logically
follows the study of addition. Introducing rectangular arrays to
represent groups (rows) of equal size illustrates both numeric and
geometric interpretations of multiplication and naturally introduces
the concept of area. Rotating the rectangular arrays illustrates the
commutative property of multiplication, and determining the number of
tiles needed to build a multicolor rectangle allows students to
demonstrate their understanding of conservation of area and to discover
a geometric interpretation of the distributive property. Although
multiplication is typically a focus of third-grade mathematics,
third-grade textbooks usually include few, if any, concepts of area or
distribution and no geometric interpretation of the distributive
property, which raises at least two questions: (1) Are third graders
ready for the reasoning needed to understand these concepts? And, if
they are, (2) how can integrated exploration of these topics help
students make connections that deepen their conceptual understanding of
these topics and others already in the curriculum? Helping students
make connections like those illustrated here allows them to deepen
their conceptual understanding that the distributive property is not an
algorithm but a property, a characteristic that holds throughout
mathematics ‒ arithmetic, geometry, algebra, and other branches as
well. (ERIC)
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