Many students have little understanding or appreciation for the process of science.
I like to get my students involved in doing science, taking measurements, collecting data at the very beginning of the school year. Eratosthenes, a Greek mathematician, was the first to measure the circumference of the earth. He knew that at noon on the day of the summer solstice in Alexandria, Egypt, a vertical post cats a shadow. At the same time in Syene, a town directly to the south, a vertical post casts no shadow. Eratosthenes used Euclidean geometry to determine that the angle formed by the post and an imaginary line from the end of the shadow to the top of the post equals an angle at the earth's center formed by imaginary lines from the two towns.