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Problems and Problem-solving

By Steve Draper,   Department of Psychology,   University of Glasgow.

This page is a brief note collecting points about the notion of problem-solving in education; and as a graduate attribute.

Everyday and school meanings of "problem"

  • Anything which the speaker doesn't immediately know how to solve.
  • A maths or science problem given in English, not in technical notation.

    A longer initial take on the meanings of "problem-solving"

    Problem solving 1: In STEM subjects (science, technology, engineering, maths) this means taking a question expressed in English with perhaps some numbers, translating it into equations, and calculating a mathematical solution. In medicine it now means taking a description of a patient with problems, drawing on technical knowledge, working out what treatment to recommend. In the Arts they don't talk about problem-solving, they talk increasingly of "problematisation" i.e. creating problems where others don't see one. In normal life problem-solving mostly means dealing with hitches that occur when a plan (or normal practice) goes wrong.

    There is thus no agreement about what it means. It has no natural place in the non-applied disciplines, which are not primarily concerned with making and executing plans. On the other hand, I imagine it is a prime requirement for employers to get staff who try to find solutions not problems, who get things done without being told how to do it. Most importantly, who recognise when they don't have the knowledge/skills required, and work around that: whereas most "problem-solving" in a discipline has the very loud implicit rule that the solution must use the techniques in the discipline and usually only those that were taught this week. This, then, may need to be taught outside the disciplines.

    Another vignette of "real" problem-solving, and its failure, is sketched by Dorothy Sayers in Murder must advertise, ch.10.

    Himself a precise and efficient man, he was nevertheless perennially irritated by the precision and effciency of Mr. Copley. He suspected, what was quite true, that Mr. Copley criticised the conduct of the department and would have liked to be given a measure of authority. Mr. Copley had a way of coming to him with suggestions: "Would it not be better, Mr. Hankin, if ..." "If you will excuse my making a suggestion, Mr. Hankin, could not a stricter control be kept ..?" ... Excellent suggestions, always, and having only the one drawback that they threatened either to annoy Mr. Armstrong, or to involve a quantity of tedious and time-wasting supervision, or to embroil the whole temperamental department and put it off its stroke. Mr. Hankin grew weary of saying "Quite so Mr. Copley, but Mr. Armstrong and I find it works better, on the whole, to have as few restrictions as possible".
    Mr. Copley wants promotion, and tries to get it by making suggestions about improved management. He fails because, while he identifies problems, he only considers the technical issues and fails to see the slightly wider, mostly tacit, human constraints that are also part of the problem. He has been there years, and his failure to perceive them even when explained or stated by Mr. Hankin, by itself marks him out as unsuitable for a managerial post, however right he may be "technically". This illustrates some of the complexity in even small problems in the real world, which HE teaching generally fails to teach in any discipline. And that the complexity is not so much about quantity of detail, but in the variety of types of constraint which must be satisfied.

    Or to put it another way, real problems in the wider world are often, even usually, not about mechanical reasoning and technical specialities. Almost all the discussion in the literature of "problem-solving", and especially claims about its general applicability, seems narrow, blinkered, and oblivious of what would be involved in a general approach to it.

    A pessimistic inference from this would be that employers shouldn't hire Arts/SocSci graduates; and should filter out science graduates who are stumped when a problem doesn't yield to any method they have already practised.

    Problem-solving 2: Dealing with ill-defined and novel problems (as opposed to an expert pulling a standard solution method from memory, as a physician diagnoses a known disease). History graduates are trained to do this in exams: take the question asked, and strongly re-define it in a way that is defensible, soluble, but generally unique to that individual.

    Problem-solving 3: the three phases: In reality, for practical purposes, there are three skills, and disciplines each emphasise only one, so all graduates probably need remedial equipping with the other two.

    1. Problematising: taking what others are letting slide by as OK, and flagging it up as something that needs treating as a problem. Every time a big fraud in a firm emerges, it is because people (auditors, ...) let it by. In fact employers need problem-spotters, although not all realise this.
    2. Redefining an identified but ill-specified problem into something specific that can be addressed. [e.g. anxiety; Malaria] (This is largely what I'm attempting in this memo.)
    3. Solving it: pushing through to an actionable decision and conclusion. Generally speaking, the Sciences drill their graduates on this all the time (because the store of solution methods is a large part of disciplinary knowledge), and the Humanities do not; (or perhaps the applied disciplines do but the pure ones do not.)

    Actually it is worse than that. "Problematising" as taught in social sciences and humanities is theoretical only. In real world problems, it requires work (too often neglected) to discover empirically what all the important constraints are. In computing, software engineers are supposed to gather requirements, but frequently fail to identify all the stakeholders and/or to get them to articulate them ... rather as in the Dorothy Sayers vignette above.

    Other related pages

    PBL: problem-based learning

    (See also this page.)

    PBL is teaching not by didactic exposition, but by setting "problems" whose solution the learners must discover, given resources to read. Generally involves:

    Here "problem" is, from a pedagogical viewpoint, a student assignment designed to focus learning for a week; but which also from the envisaged professional (and also the academic disciplinary) viewpoints is usually a task or case for which knowing the solution (and/or how to discover it from available reference sources) is required.

    Problems: Three categories of hard problems

    A critique of using black-box testing as a measure of problem-solving ability

    Some have used, as a measure of proficiency at "problem solving", a test that asks students to discover what the electrical circuit is inside a black box, using external measurements. This showed that compSci students do better at it than any other subject (Arts and STEM).

    A result. But I don't know who should be more embarrassed:

    CompSci people: because the task is actually systematic trial and error investigations NOT reasoning about code execution (although also, at least it is not just googling and copy/pasting code the learner doesn't understand). This is not "problem-solving" as the term is used by anyone else: not most physics teachers, mathematicians, business people and managers. It is what programmers call "debugging". It is what medics call "diagnosis" if that term includes not only collecting patients' report of symptoms, but measures (e.g. blood pressure) and lab results. It is what an electronics technician calls "fault-finding".

    Authors who show no awareness of what anyone else means by "problem-solving"; no awareness about how the biggest part in the process / "problem" in their test is the statement that this is a circuit which can be solved using only Ohms law, and disallowing other electrical components such as miniature neon lights (highly non-Ohm's law behaviours), electrical detonators (in daily use in demolition) which you don't want to risk finding out the hard way is there i.e. it effectively tells you it is safe to do trial and error when in many real situations this is false.

    Physicists: whose approach to undergraduate education is devoid of such empirical work in favour of analysis using maths. On the other hand, this exercise is about debugging physical equipment — a huge part of the life of experimental physicists. So it is testing what physics students should be good at, but aren't because it is usually omitted from physics degree programmes.

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