Using a Spiraling Curriculum to Teach Complex Material

In this section, Dr. Srivasatava and Dr. Greenspun explain how the course curriculum touched on the same topic over and over through different lenses.

TINA SRIVASTAVA: We present complex material by circling back to it repeatedly. For instance, we might start with the challenge of going from MIT to Bennington College in Vermont by flying from Hanscom Field to the Bennington airport. First we show the students how one would navigate there in the old days by marking up a chart with a pencil and finding landmarks that you could identify from the air en route. Then we introduce a technical innovation from the 1950s, a device called a VHF omnidirectional range (VOR) that can tell you exactly what radial you’re on from a given navigation beacon. So if you're directly west from Boston, for example, you can just have that displayed on your instrument panel.

Last, of course, we show how to perform the same navigational task with GPS. Because it's an MIT course, instead of just saying, “OK, the GPS tells you your position,” we explain the principle behind GPS, and how it calculates your position based on your distance from multiple satellites. If you have your distance from one satellite, you know you're somewhere on a big sphere. If you have your distance from two satellites, the two spheres intersect in a circle. If you have three, you keep getting a smaller and smaller area of where you can be. So we discuss those principles and also the history of GPS—when it was developed, when it was launched, and so on. These topics aren’t on the FAA test, but they’re good things for this audience to know.

So we just keep circling back to that original flight planning challenge. After showing the students how you'd use the E6B slide rule back in the 50s, we show them how you can use a free website like to perform the same task with a lot less pain and agony with just a few clicks of a mouse.

PHILIP GREENSPUN: Especially for flight planning, the students encounter the same material over and over. For instance, they might learn a little bit about calculating weight and balance to make sure you don't have too much stuff in your airplane for the flight, and then a few hours later, Tina might deliver a whole talk dedicated to weight and balance.

It’s not just an academic description of how to calculate weight and balance but truly a demonstration of how one would do that as a pilot preparing for a flight.

— Tina Srivastava

TINA SRIVASTAVA: Just to elaborate on that example of the weight and balance talk, what we're talking about is how you load the aircraft in terms of the fuel, the passengers, the baggage, and how that affects the flight. The physical model plane we mentioned before is useful for this, to really demonstrate what happens to your airplane when your center of gravity is too far forward or aft. We also solicit input from the students regarding their weight and weights of bags. We advise the students, when they're flying, not to necessarily trust what their passengers tell them they weigh, but to be safety conscious and apply a factor of safety. And we use a book to show how you can do those calculations. Next we go online to the websites of certain flight schools to show how you can find the exact gross weight and loading characteristics of different aircraft. Finally, we also show how to do those calculations on an iPad with ForeFlight software.

So again, we’re showing the students different ways of approaching the same information and concepts, so that it’s not just an academic description of how to calculate weight and balance but truly a demonstration of how one would do that as a pilot preparing for a flight.