Legal Education Digest
The Socratic Method and the Mathematical Heuristic of George Pólya
R J Rhee
 LegEdDig 37; (2007) 15(2) Legal Education Digest 51
81 St Johns’ L R, 2007, pp 1–14
Shortly into my law teaching career, I learned that most law students dislike math. Mathematics and legal analysis, however, share an important attribute — both are fundamentally problem solving branches of knowledge.
The difficulty of teaching how to solve problems is not unique to math. Law teachers strive to develop critical analysis, a skill not emphasised enough in college education. From the student’s perspective, the first shock of law school is that the process of lectures, memorisation and regurgitation is alien to law school. At some point in their experience, they realise that analysis is more important than learning ‘the right answer.’ The solutions to legal problems can be multivariate depending on the plausibility of the reasoning, and the problem solving process is the education and the practice of law.
To develop the problem solving skills, the traditional (idealised) law school class is devoted to a dialogue, an intellectual journey whose end is sometimes unclear. One questions, one reasons, one arrives at tentative conclusions, only to question again. This quicksand-like process is the source of befuddlement and stress, particularly for first-year students. In the intellectual quest for the law, the student rightfully shares a substantial burden of discovery. The Socratic method facilitates this process of learning.
The Socratic method emphasises repetitive tasking: derivation of issues, holdings, rules of law, policy and principles, and their limits tested through hypotheticals and professorial challenges. Through this repetition, students learn the first level of legal analysis — the critical analysis of legal authority, case by case and statute by statute. There is, then, the next level of legal analysis — the more complex task of weaving law and fact to form a persuasive theory of the case.
The assumption has been that once students learn to analyse legal authority, they can take the next step of disaggregating a complex fact pattern and reconstituting the facts to support a case theory built on logical or plausible interpretations of the legal structure. Of course, we test for this in the final exam. On this second level of analysis, I am less sanguine. Students need a framework, a heuristic that puts the classroom process into a larger structure of a problem solving process. The mechanical repetitions of the Socratic method, without more, may not always resonate with students, who may find it difficult to connect the abstraction of case and policy analyses to the real world of messy facts and uncertain law. If, however, the Socratic method is complemented with an understanding of a broader framework of the problem solving process, students may connect the dots that go from the Socratic method, to the analysis of legal authority, to the construction of case theory.
My concern is less with whether students can learn to analyse discrete legal authority, but with whether they can combine analysis of facts and law in the ultimate task of legal problem solving. I distinguish case analysis, which involves the formulation of legal rules from primary sources (on the scale of skills a rather ordinary task), from case theory synthesis, which involves the complex task of problem solving through the application of rules. My concern in this area arises from my experience. In past courses in Business Associations and Civil Procedure, I gave short answer questions in the final exam in addition to long essay questions with complex fact patterns. The short answer questions presented discrete problems that required the application of one or two rules of law, and they are used to test areas considered less important or miscellaneous. Students tended to perform very well on the short questions and the variance of the scores was low. Their performances suggest that as a class they studied hard. The distributions of performance in the long essays, however, were the more broader distribution of very good, average, and poor answers. The difference is that the long essay format required more sophisticated problem solving skills: sorting facts, organising them, handling multiple rules, picking their application, etc.
With these experiences behind me as a relatively new professor, I came across How to Solve It. There, Pólya dispelled the notion that the process of solving a problem was deductive. Contrary to the conventional wisdom, he showed that the process of solving problems was inductive, depending on educated guesses and messy intuitions that may or may not advance the problem. Legal problem solving too involves an inductive process, where experience, analogy, trial-and-error, and motivation are just as important as logic and ordered deduction. Lawyers, like engineers or mathematicians, solve problems that are constrained by rules. There are many views of legal analysis, of course, but one view is a scientific process of discovery: understanding the problem, discerning the knowns and unknowns, applying related theorems or principles, and conducting a trial-and-error process of experimentation. Pólya argued for the application of this scientific process to the practice of mathematics.
He set forth a four-step process, of which the first two are the focus here.
Understanding the Problem. A student must understand the problem before she can solve it. This thought seems obvious, but many students attempt to solve a problem without first understanding it. Understanding the problem means more than understanding the question. Pólya suggests that the teacher should guide the student with general questions: Can you restate the problem? What is the known? What is the unknown? What are the limiting conditions? These questions are meant not to lead the student towards the solution, something Pólya cautions against, but to provide a framework to understand the nature of the problem.
Devising a Plan. No problem can be solved without understanding its essential nature. Thereafter, the task is to devise a plan of execution. In solving a problem, the student may get a ‘bright idea’ and solve it. If not, he must go about the more difficult task of finding the solution. Pólya suggests reasoning by analogy: Do you know a related problem? What is the unknown? Is there a smaller problem that can be solved? These questions stimulate the creative, inductive process, eliciting a series of educated guesses and intuitions, some of which may end nowhere and some of which may advance the problem. This process constitutes the steady, if not methodical, ‘hunt’ for the solution.
Any help by the teacher must be ‘unobtrusive’ and facilitate ‘the ability of the student and not just a special technique.’ The teacher’s role should be to ‘indicate a general direction and leave plenty for the student to do.’
Pólya’s heuristic casts a different, albeit subtle, light on the Socratic method. Understanding the problem is the first, and arguably most important, part of the problem solving process. This is different from the traditional statement of the legal issue, which is a statement of the question that the court decided. While this statement is necessary, it also dresses the problem in legalism.
The traditional Socratic dialogue is specific and employs the common language of legal analysis: recitation of material facts, statement of the issue, derivation of holding and rule of rule, and analysis of reasoning and policy and their limits. The focus is on the distillation of rules and principles. The dialogue is familiar and thus routine. The alternative approach denudes the inquiry of legalism, and instead focuses on restating the problem to one of definitional ambiguity. Both approaches seek the same result, but come at the problem from slightly different angles. There may be times when the traditional Socratic dialogue can be supplemented by focusing on understanding the problem and restating it beyond simply a statement of the issue and legal policies surrounding the judicial decision.
Devising a plan is Pólya’s second step to solving a problem. Here, he asks the student a couple of basic questions. Do you know a related problem? Can you use the related problem? What is the unknown? Consider again a typical problem in torts. Virtually all students study Palsgraf v. Long Island Railroad, which set forth the classic debate on the scope of duty in negligence. This topic is rich in theory and philosophy, and discussion should be lively. Once it is covered, many classes proceed at some point to a discussion of negligent infliction of emotional distress as a special problem in the area of duty. The traditional approach is to assign cases showing how the common law has muddled through this issue: i.e., the physical impact, physical manifestation, zone of danger test, and bystander tests.
An alternative approach could apply Pólya’s heuristic of devising a plan. Before even assigning the case readings on emotional distress, we can provide the fact pattern from Waube v. Warrington without assigning the case: a mother witnessed from afar her daughter being struck and killed by a car, and the resulting shock led to severe emotional distress. The student is asked to solve this social problem by constructing the rule of law with the knowledge they have accumulated thus far. What is the problem here? After some discussion (lengthy perhaps), the student identifies the social ramification of unlimited liability based on a foreseeability of harm standard, the ever expanding ripple of liability. The problem is balancing the desire to provide remedy and limiting social liability to tolerable levels.
Since emotional distress cases have not been assigned, devising a plan to solve this problem requires the student to work with limited knowledge. Do you know a related problem that raised these social issues? After some discussion, perhaps the student hits upon a vague resemblance to Palsgraf. What is the unknown? What did Palsgraf answer and what did it not answer? The student notes the differences in the injuries. Mrs. Palsgraf suffered a physical injury, but the mother’s injury is emotional distress. We can ask the student to devise a legal standard that ‘solves’ the problem of emotional distress claims. The student guesses and intuits. One answer may be a blanket rule against liability. Another may be that only those who are especially close to the victim, like parents and siblings, should be allowed to recover. Still another solution may be that if Mrs. Palsgraf, who was a distance away from the brown package of explosives, cannot recover from her physical injuries, then certainly a mother who is standing afar from the accident should not recover either.
All of the above solutions to the problem were tried by nineteenth and twentieth century judges. By allowing students to create (to devise a plan for) the solution to a difficult legal problem, by allowing them to replicate the mental processes of an early twentieth century judge without the benefit of case law in this area, the teacher stimulates the legal problem solving skill more than a standard dialogue of case by case analysis. In some ways, the Socratic method of case analysis is a postmortem, which is fine for most occasions. Legal education encourages students to second guess judges who arrived at tentative solutions to social problems. But sometimes it may be fun and educational for students to put on their mathematical hats, if only in spirit, and solve the problem through intuition, guessing and analogy without the benefit of a judge’s wisdom. If the student attempts to solve the social problem without the benefit of case law, the subsequent readings in this area will stimulate far greater critical thinking.
Ultimately, Pólya advocated creativity — not of the fictional, fanciful or unreasonable variety, or the innate kind that produces the unexpected ‘bright idea,’ but the learned kind acquired through hard work and required to solve hard problems. His heuristic, while simple, is designed to stimulate the thought process in an ‘unobtrusive’ manner. What is the problem? Restate it in your own words? What is known? What is unknown? What are the conditions? Is there an analogous problem? Can you use that solution to this problem?
This problem-solving approach lends itself to the case method of teaching.
As a relatively new law teacher, I wrote this Article as a way to sort out my own understanding of how to teach legal problem solving skills within a Socratic dialogue. In my view, it is unfortunate that the teaching method is declining in popularity and use. The Socratic method, in whatever unique shape and personality given by the collaboration between teacher and student, is effective and it will be the mainstay of my teaching method for many years to come. But sometimes the dialogue can fall into a routine as method and frame of reference remain the same and predictable. Repetition is good for learning, but it can be stifling as well. By applying Pólya’s problem solving heuristic to legal teaching from time to time, we can vary the tone and cadence of the dialogue in subtle ways. We can change the language of the discussion, the frame of reference, and perhaps in due course the mental processes students use to analyse not only legal authority but the more complex legal problem of creating case theory. Moreover, a problem solving approach to the dialogue may better complement other pedagogical methods, and in particular the case study method. Writing this article has allowed me to better understand the problem of teaching effectively through the Socratic method. As Pólya observed, if you do not understand the problem, you cannot solve it.