Throw a graphing calculator into a classroom, and chances are that you'll hit a student who has struggled desperately to make sense out of math and science curricula.
Too often, technical topics are presented in a way that feels remote from everyday thinking...abstruse, arbitrary, and cryptic. The phrase from Shakespeare, "It's Greek to me," is both literally and figuratively apt to describe the bewildering way that technical material is forced upon students without sufficient grounding or intuition. The next generation of educators are taken from those who could somehow succeed anyway, and who may thus simply not know how others need to hear the subject matter. Worse, they may have gotten admiration for their unusual gifts, and may have an unconscious incentive to protect the mystery.
As a doctoral student, I contributed to a pilot program at the University of Chicago in integrated science and mathematics education for undergraduates. The idea was to make science and math more clear and intuitive for the student, to make learning easy rather than hard.
We grounded each semester's curriculum with story-telling in the form of a model system...perhaps a jet airplane, a frog egg, a chloroplast, or plans to build a bridge. A good model system is compact, intuitive, concrete, and situated within a narrative that potentially involves people and problems to solve. The jet airplane story, for example, offers opportunities to talk about materials science, fluid dynamics, reaction chemistry, thermodynamics, Newtonian mechanics, remote sensing and electromagnetism, control systems, and economics...to name just a few math-heavy subjects. By contrast, \word problems\" tend to be introduced after abstract ideas, and can have the opposite effect, confusing students with a barrage of fleeting scenarios.
Through model systems, our students learned and used a variety of mathematical techniques with surprising ease, because the concepts made sense.
The author's affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions or viewpoints expressed by the author.