Adversarial and friendly interactions: Progress in 17^th century mathematics

Many agencies, including the National Council of Teachers of Mathematics (NCTM, 2000) and mathematics standards boards (e.g., the Common Core State Standards (CCSS, 2010) and state teacher certification agencies, for example, suggest that it is very important that future teachers of mathematics be familiar with the history of mathematics. Krussel (2000), Sfard (1991), and others have noted that students benefit from an understanding of how mathematicians over the centuries have grappled with and solved significant mathematical problems. Ball and Bass (2000) have recognized that mathematics teachers not only need to know mathematics content and mathematics pedagogy but they also need to know how these ideas are integrated.