Students have agonized over mathematics for decades, yet teachers continue to write two
example problems on the board and assign a set of similar ones for students to practice hoping
that this strategy will somehow breed deep understanding and appreciation of mathematics. With
this teaching technique present in schools across the nation, it is not difficult to reason why the
United States was so poorly represented in the Third International Mathematics and Science
Study (Goldsmith and Mark, 1999). Recognizing this detrimental trend, the National Council of
Teachers of Mathematics (NCTM) developed and revised a set of standards and curriculum in
1989, 1991, and 1995 called standards-based mathematics (Phillips, Lappan, and Grant, 2006).
The goal of standards-based mathematics is to remedy students’ fear, aversion, and
misunderstanding of mathematics by providing instruction which instills lasting comprehension
of concepts and processes; enhances students’ ability to make connections within the content,
other disciplines, and to everyday experiences; and finally generates students’ capability of
communicating mathematical ideas (Phillips et al. 2006)