id: 06455342
dt: j
an: 2015e.00457
au: Berger, Lisa
ti: Equivalence relations across the secondary school curriculum.
so: Math. Teach. (Reston) 106, No. 7, 508-512 (2013).
py: 2013
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: E60 F40 H20 G60 I40
ut: equivalence relations; mathematical concepts; geometric concepts;
trigonometry; algebra; arithmetic; analysis
ci: ME 2008d.00311
li: http://www.nctm.org/publications/article.aspx?id=35607
ab: From the text: Must two triangles with equal areas and equal perimeters
also be congruent? This question was introduced by {\it S. Rosenberg}
et al. in their article [Math. Teach. (Reston) 101, No. 9, 656‒663
(2008; ME 2008d.00311)], which also described the authors’ subsequent
investigation of a particular moduli space of triangles. {\it W.
McCallum} [“The essential unity of mathematics: from a problem in
high school mathematics to current research”, Presentation at the
Park City Mathematics Institute (2009)] suggested that this was likely
the only Mathematics Teacher article to address a moduli space, a
representation arising naturally across various branches of advanced
mathematics. His comment, along with the original article, inspired us
to explore the prerequisite topics of equivalence relations and
equivalence classes and their appearance in secondary school
mathematics. In particular, we describe an exploration of equivalence
relations in the high school curriculum that builds explicit
connections across various mathematical domains and provides teachers
with a greater depth of understanding of the mathematics they teach.
rv: