
06455342
j
2015e.00457
Berger, Lisa
Equivalence relations across the secondary school curriculum.
Math. Teach. (Reston) 106, No. 7, 508512 (2013).
2013
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
E60
F40
H20
G60
I40
equivalence relations
mathematical concepts
geometric concepts
trigonometry
algebra
arithmetic
analysis
ME 2008d.00311
http://www.nctm.org/publications/article.aspx?id=35607
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, 656663 (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.