# Work forward in solving problems, not backward

The National Academies Press recently published another of their reports—Discipline-Based Education Research: Understanding and Improving Learning in Undergraduate Science and Engineering (downloadable here).

Chapter 5 of that publication is dedicated to problem solving; it advocates working forward:

“[E]xpert problem solvers typically begin by describing problem information qualitatively and using that information to decide on a solution strategy before writing down equations.” (p.82)

The report continues:

“To illustrate the working forward/backward contrast, consider a problem for which the goal is to determine the final velocity of a block when it reaches the bottom of an inclined plane. As discussed by Larking, (1981b), expert physicists begin by noting that the motion of the block on the inclined plane depends on gravitational and frictional forces, [which leads them to Newton’s second law, which], in turn, leads to retrieval of an equation relating final velocity, the goal of the problem, to acceleration.

Novices, in contrast, begin by focusing on the goal of determining the final velocity. This focus leads them to first find an equation that involves that unknown quantity, in this case the equation relating final velocity to acceleration. Acceleration is an unknown in that equation, so novices then look for a new equation that relates acceleration to information given in the problem, in this case [Newton’s second law].” (pp.82-83)

So let’s assume that what works for solving a physics problem will also work for other types of problems (and this assumption isn’t necessarily safe, as pointed out in the report, because physics problems are usually well-defined ones whereas we are interested in ill-defined problems, but indulge me for now).

## Don’t work backward

I can think of at least two ways of working backwards. The first is to start with data. Recently I was speaking with s friend who wanted to apply a satisfaction survey to hundreds of their clients. She wanted to do so because a previous such survey had been applied several years before and, surely, it would be interesting to compare them. The idea was to uncover potential changes but not to answer a specific key question. As a result, she would soon be boiling the ocean: going through large amounts of data to try and find something useful. This might work, sure, but it’s not efficient because she would probably have a very low signal-to-noise ratio.

The second way of working backwards is to start with straight with a hypothesis. If your problem is to increase profitability, you might decide that you’ll want to look at ways to increase revenues. Because increasing revenues can lead to higher profitability. Fine. But what about decreasing costs? Shouldn’t you understand the various ways that you can achieve your goal before deciding on the way to do so?