"Problem" Based Questions
Problems have solutions; questions have answers
In the last newsletter, I focused on the idea that not everything is a problem and the associated idea of “problem attributes.” This is for good reason: So often in popular discourse, and even in academic writing, there is a lumping together of what can generally be considered as questions, with what can specifically be considered as problems. Questions basically invite a response, a reply, or a request for information, often a known answer. Problems can be described as a situation that need a solution.
As an example, one does not answer problems on my favorite game show, Jeopardy! One answers questions. Questions have answers. Problems have solutions. An answer to a question may be part of a solution to a problem, but an answer to a question is not a solution.
How these two words have become conjoined twins is interesting. Since problems are defined as “obstacles” for the most part, one could assume that since the answers to some questions are difficult, the “problem” aspect of that struggle has morphed into a substitute of questions as problems.
Of course, calling problems questions does no actual harm in the short term.
At a basic level, it is more of a terminology issue. Often, educators will use the term “problem-solving” (in having students answer questions with known answers) to inspire and train students to learn problem-solving techniques. But answering questions, and in fact, mastery of any subject, has little to do with real problem solving.
And to a degree, one can use problem-solving methods to answer certain kinds of questions posed as problems. Problems can be stated in the form of questions (problem-based questions [PBQ’s]), but problems have solutions that often need to be developed or discovered, not just answered.
Of course, this is not a deliberate misrepresentation among educators or anyone else for that matter. Nor do I think researchers in the field are unaware of the difference between questions and problems. Posing a question as a problem “jazzes up” the question.
I believe that in many cases the word “problem” has become a substitute or catchall word for any activity that requires a sequence of steps to complete. Therefore, teachers refer to students “solving problems.” In these cases, students are not solving problems - they are working, often procedurally, in deriving (in classes such as math, logic, physics, chemistry, etc.) already known answers to pre-selected questions, by applying a series of intermediary calculations to form what is then referred to as a “solution.” And there is completely nothing wrong in characterizing this as “problem solving” as long as it is understood that what is being “solved” are not problems, just answers to questions.
In most cases, the actual “problem” for the students is that they are trying to learn the problem-solving methods or calculations to produce correct answers, or they will not progress, get a bad grade, or fail to understand what is being taught. The best solution is that they learn how to solve real-world, unscripted problems. Practice problem solving on drill questions provides confidence. However, I would advocate for students being handed actual problems to solve, even if they cannot come up with a solution.
Learning real world problem-solving methodologies is a valuable skill for our rapidly changing technological world.
Therefore, it is my belief that the assumption by some that working through answers to already solved problems is going to somehow translate to skill in solving “real world problems” is highly debatable. For example, the standard drill problem sets in most entry level math classes (up to about the junior year of college mathematics instruction) have little to do with advanced mathematics, or for that matter, with teaching productive real problem-solving skills.
In fact, the argument could be made that it does not, at all. It may even hamper the development of those very same skills. Even extremely challenging and puzzling questions on one of the hardest math tests in the world (the annual Putnam Exam), while relying on some pretty advanced problem-solving techniques to answer those questions, are not unsolved problems, by definition. One could theoretically feed a computer the questions and have it spit out an answer quickly. Ingenuity of technique or cleverness of method to answer a “tough” question is not problem-solving either. When one “solves” a problem, one is not even sure a solution may exist…only that it might or could, but with no certainty.
Srinivasa Ramanujan (1887-1920), an Indian mathematician regarded as one of the greatest mathematical prodigies ever, though he did have schooling and was recognized early as a genius, learned most of traditional mathematics from one textbook on theorems. From “studying” these “results” he developed into a problem-solving machine, discovering some of the most interesting mathematics of the early 20th century, astounding professional, world-renowned mathematicians, such as G.H. Hardy (1877-1947), with his brilliance and inventiveness. Ramanujan’s problem-solving skills were phenomenal, with very little formal instruction and direction. He was inventing solutions to real world mathematical problems in unique ways. What he lacked in formal education others had at that level, he more than made up for in his problem-solving abilities.
Looking up answers to questions, or even working out answers to questions, is not problem solving in the strictest sense, even if the answers seem “unknowable” to that person; they know, or could find out, that somewhere out “there” there is an answer. As I wryly stated earlier, often the only real problem for some students is if they can “find” the right answer, by whatever means necessary (calculation, logic, creative thinking, cleverness, among other methods). The internet in general, and a lot of software in particular, has diminished true problem-solving ability…for any question, one can simply research the answer or plug in the question to a sophisticated software program which will then give the result. There are programs now that will give step-by-step “solutions” to sophisticated math problems.
But here’s the catch: Real problems (whether they are in science, technology, engineering, math, or personal, professional, business, social) do not come with pre-packaged solutions that one can look up, reference, or ask a program to derive.
Therefore, the basic differences between “questions” and a “problems” become important later when easy questions become intractable problems with no defined or known answers, just possible solutions. “How many people do not have access to the basic amount of food they need each day?” is a question that invites an important answer in response. “How do we adequately feed an ever expanding world population?” is a problem-based question with no easy solution.
Conclusion: Questions are not problems.
My next newsletter is going to cover the various definitions of a “problem” from both a historical and current perspective. I had originally intended to publish that newsletter first, but I thought that initially discussing the fact that questions are not problems would help to further cement the uniqueness of problems. In the next few newsletters I will also move forward to focus on problem-solving strategies in the real world, the “meat and potatoes” of what I would like to communicate. Since these newsletters are an introduction to problem solving, that is the direction we are moving towards.
I really want to stress that the value proposition to the reader is this:
By reading this newsletter and following the problem-solving techniques discussed, you can better understand the nature of problems and develop superior problem solving skills in your life, whatever that may encompass!
Happy Problem Solving!