With great power comes great responsibility.
Budding mathematicians and scientists would be best to remember this. Simply because one can understand complex theories, does not preclude one from making common errors.
The Ten Things All Future Mathematicians and Scientists Must Know (But are Rarely Taught), by Edward Zaccaro, lays out ten concepts to guide students to more critical and honest thinking. Students don't need to become mathematicians or scientists to benefit from these ideas.
By discussing actual events that were affected by the misunderstanding or delibrate disregard of facts and calculations, Mr. Zaccaro brings home the importance of understanding and accepting what numbers mean.
We adults can probably think of tragedies in our lifetime that ultimately came down to math or science: the Challenger explosion, the Kansas City Hyatt Regency walkway collapse, the death of Aaliyah. The Ten Things explores how these events could have ended differently, had the numbers and facts been taken seriously.
Fortunately, not just tragedies are covered. Mr. Zaccaro uses the strange world of average speed, cold fusion, the Mars Climate Orbiter, ulcers, psychic surgery, doctors who were fooled, the Bermuda Triangle, how ethical decision-making saved a company, knee surgery, and more to discuss why mathematicians and scientists (and, arguably, all of us) need to move beyond the cold facts and figures, instead utilizing them to make better decisions, safer choices, and strongly-founded conclusions.
Each chapter supplies several examples of incidents which support the topic. Each example is reviewed, the mistakes laid out, and then followed by discussion questions. The questions range from specific (why was something done) to open-ended (what do you think). Along the way, mathematic and scientific concepts are introduced and explained, never assuming the reader is an expert, but always teaching. Additional questions are given at the end of each chapter, ranging in difficulty from "Level 1" to "Einstein." Answers and explanations are in the back.
Lest all this sound overwhelming, rest assured that the book is appropriate for middle-school and higher. Of course, don't hold back the book if a younger child is interested in reading it. (My eldest son first read it when he was seven.) I would also encourage parents to read it, as we could all use a refresher course in critical thinking, especially when we're inundated with "facts" and "truths" through media, the Internet, and "friends of friends."
The Ten Things All Future Mathematicians and Scientists Must Know (But are Rarely Taught) is an excellent companion to any math or science program. It also works as a stand-alone book for inviting family discussions, a part of family life-long learning.
 This quote, in various forms, is attributed to Jesus of Nazareth, Voltaire, Rudyard Kipling, Karl Marx, FDR, Stan Lee, among others. (http://www.newsfromme.com/archives/2005_10_06.html; http://en.wikipedia.org/wiki/Uncle_Ben#.22With_great_power_comes_great_responsibility.22)
Article by Sarah J. Wilson