# Calculus

The Economist November 9 2013, p45:

Bill Gates once said that if every child had mathematics teachers as good as those in the top quartile, the achievement gap between America and Asia would vanish in two years. (His lecture has been watched 1.5 m times online.)

In fact, listen to* “How do you make a teacher great ?”* TED 2009. It is quite a bold claim but there is some element of truth in it, while it helps to be so ambitious. While you are at it, perhaps also consider the Wall Street Journal interview and the TED 2013 lecture that teachers need coaches and feedback (other than from students).

The same November 9 2013, I had a presentation in workshop D5 of the annual Dutch Teachers of Mathematics Day. My presentation was on the algebraic approach to the derivative, see the slides, the YouTube lecture and the book *Conquest of the Plane*.

Some mathematicians are aware of an algebraic content in the derivative, see for example here, but they still stick to the use of limits. The new notion of “dynamic division” removes the need for limits and greatly simplifies and clarifies calculus.

The discussion on the derivative links up with my earlier blog on the mathematical constant Archi = Θ = 2 π. The derivative generally gives the slope of a function, but the slope is also the tangent given by the sine / cosine ratio that depends upon the angle.

Mathematical teaching requires re-engineering. Much in the highschool programme can be made more accessible to students. Society can advance when people have a bettter understanding of logic, finance, voting theory, and the distinction between model and reality.

My original presentation was in Dutch and was split up in two sections of 15 minutes, with 5 minutes inbetween for questions and 20 minutes afterwards for discussion. The reception was OK, with serious questions and discussion, and modest applause at closure. Don’t expect teachers of mathematics to jump and dance on tables. It will take a lot of time before the new algebraic approach will be used in the schools and make math clearer for students. A comment by one of the teachers: Holland cannot change by itself, we have to stick to the world standard. My suggestion is that when math teaching is improved, so that students better understand math, then it should not be too difficult to explain what the world standard is and why it is so crummy.

The video that I put on YouTube uses English and lasts 47 minutes. Thus it is not in the TED 20 minutes mold. The discussion in Dutch wasn’t recorded so I included an additional quarter of an hour to discuss some points from that discussion. The sound recording is bad, I should get a better microphone. I practiced in Dutch and not in English, so the presentation is not as fluent as it could be. I am already aware of this, so there is no need for *feedback* on these aspects …