4. The Idea that Changed the World

It is called the most important concept in mathematics. It birthed the scientific revolution. It enabled computer programming. And its latest incarnation, spreadsheets, has revolutionized business. Yet, few of us can name it; still fewer of us can define it; and it is unlikely that even a handful of us know its evolution. This idea, that changed the world will now enable every student to learn mathematics as a creative experience.

  1. Functional Thinking 
  2. Machines are Functions 
  3. Functions Instead of Fractions 
  4. The STEAM Subjects Require Functional Thinking 
  5. Science 
  6. Technology 
  7. Engineering 
  8. Art 
  9. Math 
  10. The Near Perfect Tool 
  11. Spreadsheets are Function Machines 
  12. Spreadsheets Copy Functions Intelligently. 
  13. Spreadsheets Make Functions and “What if…” Thinking Concrete 
  14. How the Failure to Think Functionally Distorted Reading Education 
  15. The Word Gap 
  16. The Learning Curve 
  17. Implications for our Schools 
  18. “Algebra before Acne”

 

Chapter 4. Explorations

Calculus for 5th Graders

“Calculus is the study of change” is a common description and all too common misunderstanding. For if calculus is the study of change then algebra… Read more

Spreadsheets and the Rule of Four

A little over 20 years ago the Harvard Calculus Consortium sought to remake the calculus curriculum. “We believe that the calculus curriculum needs to be… Read more

The First Graph

This picture was first published in 1638! It is from Galileo’s great work Two New Sciences, that he smuggled out of his home imprisonment in… Read more

This is Why I Love Graphs!

This graph appeared on one of my favorite websites – Statista. Given the “breaking news” of the day, that the President wants to impose new… Read more

Math as a Laboratory Science

Math is not only the last letter in STEM or STEAM, it is the only one that we do not picture as experimental. We don’t… Read more