id: 06512796
dt: j
an: 2016a.00584
au: Alonso, Orlando B.; Malkevitch, Joseph
ti: Classifying triangles and quadrilaterals.
so: Math. Teach. (Reston) 106, No. 7, 541-548 (2013).
py: 2013
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: G40
ut: elementary geometry; triangles; quadrilaterals; classification; classes of
geometric shapes; definitions; properties; student activities;
partitions; side length; angles; partition pairs; conceptual schemes
for triangles; conceptual schemes for quadrilaterals; worksheets
ci:
li: http://www.nctm.org/Publications/mathematics-teacher/2013/Vol106/Issue7/Activities-for-Students_-Classifying-Triangles-and-Quadrilaterals/
ab: From the text: Classification of shapes in middle school and high school
geometry often seems mysterious to students, featuring strange terms
such as isosceles, trapezoid, and kite, which are defined by a mixture
of parallelism and metric ideas. The purpose of the following
activities is to introduce a more natural way to classify triangles and
quadrilaterals. The Common Core State Standards for Mathematics (CCSSM)
for middle school (seventh-grade geometry) states that students will
“draw, construct and describe geometrical figures and describe the
relationships between them". The standards later state: “During high
school, students begin to formalize their geometry experiences from
elementary and middle school, using more precise definitions and
developing careful proofs". The problem for students is that their
natural instinct is to associate a name with a particular shape or
prototype. This natural inclination provokes confusion in students’
understanding of geometric definitions, particularly widely accepted
classifications of two-dimensional figures in a hierarchy based on
properties. What we propose here addresses the problem by introducing a
new notation that enables a framework for the coexistence of two
conceptual perspectives that until now have competed with each other.
In this framework, students understand the integrating nature of the
inclusive conceptual approach (IA) (e.g., for which equilateral
triangles are isosceles) as a natural complement to an exclusive
classification approach (EA) (e.g., for which equilateral triangles are
not isosceles).
rv: