I'm pretty sure that the response of most students would have been "Why am I being made to do this? What is the real world purpose of it?"
That's why it isn't trivially easy to be a mathematics teacher. The Russian tradition of mathematics teaching, which goes all the way back to the years when Leonhard Euler researched and taught in St. Petersburg,
does an especially good job of appreciating pure math for its delightful patterns and inherent beauty and elegance while at the same time being well informed by the many applications of math to science and engineering. One of my favorite textbooks for taking a balanced approached to making mathematics teaching interesting, rigorous, engaging, and practical is the late Israel Gelfand's and Alexander Shen's textbook Algebra published by Birkhäuser.
Many of the problems are HARD--the author is not afraid to pose research-level problems to first-time learners of algebra. On the other hand, some of the problems in some sections of the book are very approachable: "How to Explain the Square of the Sum Formula to Your Younger Brother or Sister." One section, "How to Confuse Students on an Exam," is laugh-out-loud funny. I love using this book in math classes that I teach as supplementary weekend classes for third-, fourth-, and fifth-grade-age pupils who like math and who want something more challenging than what is served up by the local school systems. I have clients from seven different counties in my sprawling metropolitan area. Pure math can be fun, and applied math can be fun, and both can be more enjoyable when they are taught hand in hand.
That's why it isn't trivially easy to be a mathematics teacher. The Russian tradition of mathematics teaching, which goes all the way back to the years when Leonhard Euler researched and taught in St. Petersburg,
http://mathsforeurope.digibel.be/Euler.html
does an especially good job of appreciating pure math for its delightful patterns and inherent beauty and elegance while at the same time being well informed by the many applications of math to science and engineering. One of my favorite textbooks for taking a balanced approached to making mathematics teaching interesting, rigorous, engaging, and practical is the late Israel Gelfand's and Alexander Shen's textbook Algebra published by Birkhäuser.
http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773
Many of the problems are HARD--the author is not afraid to pose research-level problems to first-time learners of algebra. On the other hand, some of the problems in some sections of the book are very approachable: "How to Explain the Square of the Sum Formula to Your Younger Brother or Sister." One section, "How to Confuse Students on an Exam," is laugh-out-loud funny. I love using this book in math classes that I teach as supplementary weekend classes for third-, fourth-, and fifth-grade-age pupils who like math and who want something more challenging than what is served up by the local school systems. I have clients from seven different counties in my sprawling metropolitan area. Pure math can be fun, and applied math can be fun, and both can be more enjoyable when they are taught hand in hand.