
06035707
j
2012c.00513
Bucher, Christopher J.
Edwards, Michael Todd
Deepening understanding of transformation through proof.
Math. Teach. (Reston) 104, No. 9, 716722 (2011).
2011
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
G50
E50
U70
transformation geometry
proving
congruent transformations
elementary geometry
line reflections
point reflections
rotations
translations
polygons
rigid motions
geometry software
computer as educational medium
problem posing
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.