id: 06035707
dt: j
an: 2012c.00513
au: Bucher, Christopher J.; Edwards, Michael Todd
ti: Deepening understanding of transformation through proof.
so: Math. Teach. (Reston) 104, No. 9, 716-722 (2011).
py: 2011
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: G50 E50 U70
ut: transformation geometry; proving; congruent transformations; elementary
geometry; line reflections; point reflections; rotations; translations;
polygons; rigid motions; geometry software; computer as educational
medium; problem posing
ci:
li:
ab: From the introduction: An algorithmic approach to transformational geometry
‒ one that omits rigorous proof ‒ misses opportunities to connect
the rigid motions to a host of other geometric topics. In this article,
we revisit several familiar transformational geometry constructions
with an eye to rigorous geometric proof. As we explore proofs of
familiar transformational results, we uncover a variety of mathematical
connections between the rigid motions and Euclidean geometry while
modeling an approach that teachers can use to explore transformations
in more depth with their own students. Moreover, we highlight the use
of interactive geometry software, specifically GeoGebra, to explore
questions that arise naturally from the study of transformational
proofs. Technology affords us the opportunity to answer “what if
not?” questions too often ignored in secondary school classrooms.
Conjectures generated by the “what if not?” process provide new
avenues for proof in our classroom.
rv: