id: 06597673
dt: j
an: 2016d.00633
au: Wickstrom, Megan H.; Nelson, Julie; Chumbley, Jean
ti: Area conceptions sprout on Earth day.
so: Teach. Child. Math. 21, No. 8, 466-474 (2015).
py: 2015
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: G30 M90
ut: area; concept formation; real-life problems; measuring; gardening
ci: ME 1987e.03737; ME 1996a.00328
li: http://www.nctm.org/Publications/teaching-children-mathematics/2015/Vol21/Issue8/Area-Conceptions-Sprout-on-Earth-Day/
ab: Summary: With the adoption of the Common Core State Standards for
Mathematics (CCSSM), many concepts related to area are covered in third
grade: (1) Recognizing area as an attribute of a plane figure; (2)
Understanding that a square with a side length of one is a unit square;
(3) Measuring area by tiling figures and counting the squares it takes
to cover without gaps or overlaps; and (4) Relating area to the
operations of multiplication and addition. Area concepts take time and
experience to work through and understand. Researchers have shown that
when students first encounter area, they often find difficulty
structuring square units in rows and columns. Students will overlap
area units or will leave gaps between them as well as create nonuniform
units. In response to these concerns, {\it K. Miller} [in: Origins of
cognitive skills. The eighteenth annual Carnegie symposium on
cognition. Hillsdale, NJ: Erlbaum. 193‒228 (1984; ME 1987e.03737)]
and {\it Y. Wolf} [J. Exp. Child Psychol. 59, No. 1, 49‒75 (1995; ME
1996a.00328)] have documented that when students are allowed to use
physical square units or tools, they are more likely to develop
strategies consistent with multiplicative rules and also develop mental
imagery. To build spatial awareness, students need to solve problems
through mathematical modeling, allowing interaction with and sense
making of their world. This article describes a measurement lesson
created by the authors to conceptualize the idea of area beyond the
formula. The lesson centered on gardening and plant growth. Students
investigated area and perimeter by constructing rectangular gardens
using the same perimeter of fencing to see if and how this affected the
area. Estimating, drawing, building, and checking were incorporated to
help students develop and refine their conceptions of area. The lesson
took approximately three days of instruction, one day for part 1 of the
lesson and two days for part 2. (ERIC)
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