Using Technology to Unify Geometric Theorems About the Power of a Point

dc.creator	José N. Contreras
dc.date	2011-01-01T00:00:00Z
dc.date.accessioned	2015-07-20T22:11:07Z
dc.date.available	2015-07-20T22:11:07Z
dc.identifier	1062-9017
dc.identifier	https://doaj.org/article/e183f12b43cb45cbacc3721a4067d72e
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/14167
dc.description	In this article, I describe a classroom investigation in which a group of prospective secondary mathematics teachers discovered theorems related to the power of a point using The Geometer’s Sketchpad (GSP). The power of a point is defines as follows: Let P be a fixed point coplanar with a circle. If line PA is a secant line that intersects the circle at points A and B, then PA*PB is a constant called the power of P with respect to the circle. In the investigation, the students discovered and unified the four theorems associated with the power of a point: the secant-secant theorem, the secant-tangent theorem, the tangent-tangent theorem, and the chord-chord theorem. In our journey the students and I also discovered two kinds of proofs that can be adapted to prove each of the four theorems. As teacher educators, we need to design learning tasks for future teachers that deepen their understanding of the content they are likely to teach. Having a profound understanding of a mathematical idea involves seeing the connectedness of mathematical ideas. By discovering and unifying the power-of-a-point theorems and proofs, these future teachers experienced what it means to understand a mathematical theorem deeply. GSP was an instrumental pedagogical tool that facilitated and supported the investigation in three main ways: as a management tool, motivational tool, and cognitive tool.
dc.publisher	University of Georgia
dc.relation	http://math.coe.uga.edu/TME/Issues/v21n1/v21n1_Contreras%20(Color).pdf
dc.relation	https://doaj.org/toc/1062-9017
dc.source	Mathematics Educator, Vol 21, Iss 1, Pp 11-21 (2011)
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Education
dc.subject	L
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Science
dc.subject	Q
dc.subject	Mathematics
dc.subject	QA1-939
dc.title	Using Technology to Unify Geometric Theorems About the Power of a Point
dc.type	article