Should the history of math and science be taught in K-12?

Sometimes it seems as if schools deliberately teach math and science so as to make it as dull as possible. I think it would make these subjects much more interesting if, as part of a math or science course, some historical context was given. It should not take up a lot of time and it should not be included as part of the tests.

I am mostly familiar with math. Here is a list of some of the things that I would include in math courses. What else should be included? What should be included in a history of chemistry, physics and biology?

1. Brief introduction to math of Egyptians and Sumerians. Explain that since there was no algebra, math was taught by example.

2. Importance of Greek math. First development of formal proof and idea of axioms. Controversy of Euclid’s parallel axiom. Brief introduction to non-Euclidean geometry and explanation of its significance.

3. Development of so called Arabic numbers by mathematicians in northern India, including use of zero and negative numbers.

4. Work of Arab mathematicians in advancing algebra and disseminating work of Indian mathematicians .

5. Work of Italian Renaissance mathematicians in solving third and fourth degree polynomials. Demonstration of how these equations can be solved. Work of Abel and Galois in showing that there is no general solution for fifth degree and higher order polynomials. Very brief introduction to abstract algebra.

6. Discussion of the dramatic development of math in 17th century Europe. Napier’s logarithms (show how these relate to slide rule), work of Fermat and Pascal in number theory and probability, Descartes’ analytic geometry, and discussion of impact of the calculus of Leibniz and Newton.

After the 17th century, it is hard to keep track of all the things that happened. Perhaps a discussion of Euler’s development of topology and an introduction to the work of Gauss.