When I was in school, we were taught a process of problem solving called GRASP, an acronym for:
At the time it drove me nuts, because it was the least helpful technique for problem solving imaginable. Analyze and Solve. Right. How? GRASP provides no insight whatsoever on how to solve problems, it is just a format for making answers look pretty, and to provide formatting a teacher can grade using a checklist. It is not a problem solving technique, it’s an answer presentation format.
To my great consternation, I find that GRASP is still used as a “problem solving technique” in today’s textbooks. My goal here is to provide an alternative that is actually useful.
Many problems in science require steps that are not immediately apparent to people learning the material for the first time. With experience to draw on, students can relate problems to ones they have seen before, but the first time a problem is encountered there should be a procedure they can use to solve it without relying on previous experience. Experienced practitioners can solve novel problems, so how do they do it? Many people would say that they develop an “intuition” for problem solving, but this simply means they are unaware of the steps they are performing. From careful analysis of my own problem solving “intuition” and that of colleagues, I have pieced together a series of steps that can be used to solve novel problems that mimics that “intuition”.
I call this approach the Bridge Method, or the GAP Analysis Process (where GAP recursively stands for GAP Analysis Process…). With this method, the concept is to lay a framework for the problem, starting from the answer and working backward towards the question. Once the framework is complete, the solution can be worked out sequentially.
The process begins, as with the GRASP method, by jotting down the given information and the type of information required for the answer. The difference is that these pieces of information are written on opposite sides of the paper (or screen or whiteboard). This forms the gap we will span:
The next step is to identify what is required to solve for the answer. If sufficient information is available in the question, then the problem can be solved immediately. Otherwise, we must identify what is required to solve for the requirements for the solution, and so on. Repeat until a requirement can be fulfilled using the givens in the question:
By working backwards toward the question, we now have a trail of breadcrumbs we can use to guide us, step by step, back to the answer:
If you are an experienced problem solver, you probably perform the first steps in your head. By working backwards from the answer, you build a mental framework of how to get to the answer from the given variables. But that skill comes with practice and experience. It is human nature to want to start at the beginning – we are very linear creatures that way. Students seeing a problem for the first time, don’t have that reverse-engineered mental framework; they want to start at the beginning, so the first step is not intuitively obvious. Therefore, it is important to teach effective problem solving explicitly, and model the steps frequently to show them how to build those skills.
I am not so immodest as to think that this is the only method to solve problems – I am sure there are countless others, as well as many riffs and variations on each. But this is a method I use, one I teach to my students, and one that seems effective. And it can work equally for almost any type of complex problem – it need not be numeric. Questions in physiology and ecology can also be solved using this process, as long as there is some causal chain between the starting point and the conclusion.