The Flaw of Legalism in Society and Education
Richard Garlikov

A kind of legalism, or formalism, is increasingly pervading society in general and education in particular, to the detriment of both. There is a serious problem with governance by formal rules or laws alone. Following the letter of the law without regard for its spirit, and without general understanding of its intent, does not normally produce the most desirable result.  Formal systems do not recognize a “spirit” of the rules apart from their explicit wording, and yet the underlying general understanding and significance of rules cannot itself be expressed within the system as a formal law or rule. Legalism has always been a problem because it creates loopholes on the one hand and too narrowly restricted behaviors on the other, and because it often impedes pursuit of discovering and doing what is actually right.[1] It even, on occasion, when rules are bad or simply misstated, prevents people from being able to recognize or adhere to the truth or the right behavior because that will result in their ostracism or punishment.  This is becoming increasingly important and problematic today as more and more education and corporate policies mistakenly claim, without argument, that:

Claim 1 (the moral version): Rules of conduct need to be thoroughly and explicitly stated in order for people to know what they are expected to do and in order to legitimately be able to hold people accountable if they do not do it. 

Corollary to Claim 1: If a person can state explicitly the behavior that is expected of him/her, then s/he knows what is expected.

Claim 2 (the educational version): What is to be learned needs to be thoroughly and explicitly stated in order for students to know what they are to learn and in order to be able to hold them accountable if they have not learned it.

Corollary to Claim 2: If a person learns and knows how to state explicitly the information s/he is expected to know, then s/he has learned it and knows it.

I believe these claims and corollaries are false.  They are bad psychology, bad educational policy, and mistaken ethics and legal theory.  I contend they lead to an unacceptable adherence to “letters of the law” rather than its spirit, and that over time, application of this fashionable conventional assumption embodied in these claims and corollaries fosters an endemic erosion of good work and meaningful effort by the better part of a generation of people who otherwise would have done much better, but who instead do no more than is minimally prescriptively required of them, and who, for the most part, even worse, do not even realize there is more they could be and should be doing.  The principle that all knowledge and understanding can be made explicit and can be transmitted to students by the teacher’s saying, and the students’ learning, the right words is simply false, as is the claim that this is the way teaching and learning needs to be done and to be demonstrated.

There are at least two ways in which these claim and corollaries are false:
(1) We often have comprehension without precise verbal descriptions.
(2) We often have verbal descriptions without comprehension.

Regarding (1), the human mind is able to extrapolate general ideas and principles from specific examples, even if those general ideas or principles are not themselves described in words, and even in many cases when those general ideas or principles are not even (yet) able to be described in words.  For example, when we teach children color terms, such as red, we may point to a tomato, to a mark made by a red crayon, to the red crayon itself, to a ripe red apple, and to picture of a red fire truck, and say “these are all red”. We may need to point to non-red things of the same sort and say they are not red. Normally, at some point, most children will get the concept we are trying to teach and they will then be able to identify many other red things even though the shades may be different.  They may not do it perfectly; they may, for instance, have trouble knowing whether or not to call magenta things red or not, or seeing why “magenta” crayons have their own name. They may not know quite when red shades into pink.  They may not be sure whether strawberry blond hair is red or not.  In short, certain cases, particularly borderline cases may be difficult for them at least at first.

There may be other kinds of cases or concepts/behaviors that are difficult for children to understand.  When I was young and we visited someone who gave me a kind of food I didn’t like, I immediately said it didn’t taste good.  My father told me later that was wrong and that you should eat what people serve you and not say it tastes terrible.  The next time that happened we were visiting my aunt and uncle at their farm, and they gave me a glass of milk that tasted terrible.  But I drank it and just figured it was the kind of milk they had or that “country milk” on a farm tasted different from city milk.  A bit later that afternoon, one of my cousins complained that the milk tasted bad (which I knew was wrong of him to do), but my father who was next to him took it and smelled it and said “Don’t drink it; it has spoiled.” And they opened up a fresh bottle for him.  Then my father realized I had drunk my glass, and he demanded to know why I had drunk a whole glass of rotten milk.  I, of course, pointed out that he had told me not to say anything bad about the way food tasted and to just accept it and eat it.  He said “Not when it has spoiled!” and, of course, I didn’t know what that meant or that there was some sort of exception to the rule he had given me.  But even today in a restaurant, for example, if I try a new food for the first time and it tastes terrible, I then have a problem because I don’t know whether it has an ingredient that has turned “bad” or whether it was accidentally incorrectly prepared or whether it is perfectly okay but just something I do not enjoy the taste of.  So I have to decide whether to ignore it or whether to call the waiter over to find out whether something is wrong or whether it is “just me”.  That becomes very embarrassing sometimes because they may not understand I am not complaining or wanting a replacement but just trying to find out whether there is something wrong or not with what I was served – and, if so, then of course I want a replacement, but if not, then that is my fault not theirs and I will simply pay for my mistake and know not to order that again for myself because it is simply a taste I do not care for.  I do not wish to be given special treatment but just reasonable treatment depending on whether it is a matter of an objective problem with the food or just an issue of my subjective taste, which is not a problem for which they or anyone is at fault, and for which they should not be penalized.

Many concepts, which might be called “ultimately simple” concepts that are not themselves verbal, such as color terms, cannot be defined in terms simpler than themselves.  The way we teach or define these terms is by pointing to examples, as with colors.  But we do this with regard to other terms or concepts too, particularly with basic sensory concepts, such as bright, dark, dim, smooth, rough, loud, inaudible, soft (sounding or feeling), acrid, sweet, sour, fragrant, etc.  It is impossible to define or describe these terms or concepts to anyone who would be devoid of the senses to experience them because they are terms that refer to those experiences. 

But there are non-sensory, intangible, or abstract concepts that resemble each other in ways which are difficult or impossible to correctly express or define merely in words without reference to examples from which the learner has to extrapolate for him or herself the idea intended: good, bad, right, wrong, beautiful, ugly, happy, sad, depressing, exciting, boring, logically valid, invalid, sexual, desirable, undesirable, pleasant, unpleasant, etc.  Many of these concepts we have trouble defining, but not particularly recognizing or using, such as Justice Potter Stewart’s claim about pornography, concepts such as frustration, death (in some cases[2]), health, anger, love, other emotions, hunger, balance in a painting, being humorous, etc. There are often disagreements or confusions in borderline or complex cases, but even in some simple cases it is difficult to define the concepts in words that really capture all and only what one has in mind.  Yet we use and discuss these concepts all the time with, for the most part, a basic understanding of each other, even when we disagree about an application – as, for example, about whether a particular joke is funny or not, even though we both know what it means for a joke to be funny.  The concept may be clear even though difficult to express in words.

And the main point of the above is that we can know and teach and learn these concepts, and be accountable for knowing them under reasonable conditions, even if they cannot be formally described or defined in some way.  We can discover, and we can learn to understand, concepts that transcend the examples we used to discover or teach them.

Moreover, a student who truly wants to learn difficult concepts, and a teacher who truly wants to teach them, will work hard to overcome the limitations of words, and will seek ways to convey and to understand the concepts apart from the words used in the process.  And that effort will, or should, normally be apparent, as will its lack.  In short, having the right words to directly convey in a formal way what one is trying to teach is not always necessary for teaching or learning it, as long as some reasonable and reasonably effective means of teaching it is employed.  For it to be fair for students to be held accountable for learning or for people to be held accountable for doing what is right, they have to be exposed to the kind of teaching or experience from which it would be reasonably expected they could and should learn it.  And, of course, they have to have the abilities or faculties to learn if they try, and the ability to try.  Good teaching will, of course also try to give incentive to the learning and make it more interesting and enjoyable to work on whenever possible, but that is not always able to be done or even necessary in some cases. And it does not mean precise, prescriptive verbal descriptions are necessary.

Moreover, precise, prescriptive verbal descriptions are also not always sufficient. Regarding point 2 on p.2, that we often have verbal descriptions without comprehension, one can state words without realizing their full meaning or range of application. For example, to be able to state Newton’s Laws of motion does not mean one can do classical mechanics problems in physics, even when one has been taught to analyze motion in terms of forces and vectors, etc.  Stating someone else’s understanding is not the same thing as understanding something oneself (see www.garlikov.com/Interpretation.html) or, as it is sometimes put “internalizing the understanding” or in a modern phrase that I think is particularly meaningless, “taking ownership of that knowledge”.  There are thousands of concepts that have been developed that students can state without really comprehending: moles in chemistry, place-value in math, other numerical relationships or theorems in math, Archimedes’ buoyancy principle, validity in logic, terms of a contract, legal concepts in general, traffic rules, driving instructions, airplane flying instructions, instruction manuals for assembling things or using software, the national anthem of one’s country or the “Lord’s Prayer” or “Pledge of Allegiance”[3].  In other words, being able to read words out loud (in the sense merely of pronouncing them correctly), or recite what one has been told, does not by itself mean one understands it or that one can apply it in a useful or meaningful way. This often becomes obvious not only in classrooms but in situations where, for example, people well-versed in some body of moral pronouncements do not see that they apply at work in behavior toward their employees or customers or in behavior toward other drivers on the road.

Now I want to begin consideration of Claim 1 by examining a point made by George Washington in his Farewell Address, though he stated it in a way that I think needs some further analysis in order not to be misleading:

Let it simply be asked: Where is the security for property, for reputation, for life, if the sense of religious obligation desert the oaths which are the instruments of investigation in courts of justice? And let us with caution indulge the supposition that morality can be maintained without religion. Whatever may be conceded to the influence of refined education on minds of peculiar structure, reason and experience both forbid us to expect that national morality can prevail in exclusion of religious principle.[i]

Since I believe that in some important sense morality can be learned and perfectly well-practiced without religion, because there are plenty of morally good atheists and agnostics, and because many people are morally good in situations not addressed by their religions, I want to first offer an interpretation of his claim that supposition should be indulged with caution. I believe that his next sentence means that it cannot be expected that the general population will be moral without religious convictions, not that no one can be moral without religious convictions or principles.  And I suspect, but cannot prove, that what Washington had in mind here is that there needs to be some role involving belief in punishment (by God), or else some people at least will not do what is right.

But whether we are talking about religion or secular law, when a system of behavioral governance is established that is based solely or primarily on what the least respectful, least conscientious, and least responsible people need in order be controlled or held accountable, that system bodes ill for the rest of the population for two reasons.  The first is that it is extremely difficult, if not impossible to state explicitly how people ought to behave in every conceivable situation.  Second, any system designed to prevent amoral and immoral people from doing harm will normally not allow those who are scrupulous and conscientious the full range of freedoms they need to flourish and contribute. Such a system will neither help unconscionable persons understand their full responsibilities nor prevent behaviors they will believe they can get away with doing because those behaviors are not explicitly forbidden, even if they know those behaviors are wrong.  And such a system will also not provide any incentive for irresponsible people to become conscientious.

This has importance for more than just criminal behavior.  We are seeing the fruits of legalistic policies in education in college, graduate level, and post graduate work today, as the so-called “Y generation” shows interest only in minimally meeting requirements, and does even that in a legalistic way that argues if they have not violated any specific rule or law, they are not culpable for any of their actions, no matter how bad those actions are.  The view among students  frequently is that if they “show up” for class and turn in assignments, they should pass or get an “A” regardless of the quality of their work, because quality is not explicitly described.  If a teacher does not tell them exactly how to make their work be good, it is the teacher’s fault if the work is poor.  Basically many students think that if they are not given the exact answer to fit the way the question is asked, they are not responsible for not knowing it.

The exaggerated humorous example of this was given in an episode of the Damon Wayans television situation comedy My Wife and Kids when the teenage son was reminded he continuously made poor behavioral choices and his response was “You are still talking about that one situation, but, as I said then, “no one ever told me not to pee out of my (upstairs) bedroom window … and I didn’t know you and mom were outside below it”.

A more realistic but still often perversely humorous manifestation of it is the behavior of high school students who scour the student handbook of rules in search of loopholes that will allow them to perform acts they know will aggravate the administration – that is, acts they know are wrong-- but which will allow them to escape punishment since the act will not be proscribed by the rules. And when the administration mistakenly believes there can be no punishable transgressions without a breach of prior stated rules, the only administrative recourse is to add that rule to next year’s handbook.  This is a repetitious process that basically only serves to fatten the handbook of student rules, but does little to alter student behavior.  However in this case students do know better, but are simply exploiting their knowledge in light of a weak and silly administrative policy.  These sorts of acts tend to occur in cases where administrators generally unreasonably enforce unreasonable rules and earn the disrespect of students who wish to retaliate by playing the rules game, meaning that if administrators or teachers are going to make students live by rules strictly as they are written, students are going to make them suffer for rules not written or not properly written.  It is students’ way of saying it should be obviously false to administrators that an act is wrong if and only if there is a specific rule against it

It is my contention that administrations could prevent this kind of behavior whether it is malicious or in jest by, instead of invoking endless, often petty rules, having a policy something to the effect that students are expected to behave ethically, including, but not limited to respecting others and the rights of others, and that any student who willfully does anything wrong that s/he ought to know is wrong, will face consequences commensurate with the seriousness of their offense.  More about this form of policy momentarily, but it should be clear that when students do this sort of thing, they understand the difference between what is right or wrong on the one hand and what the rules state on the other.  It is only the administration that believes one cannot know what is right or wrong, and be held accountable for doing what is wrong, without reference to previously established rules printed in a handbook.[4] Just as the ninth amendment to the United States Constitution points out there are rights beyond those enumerated in the Bill of Rights, it would be wise, I believe, for any list of rules to point out there are bad behaviors besides those enumerated which will be punished if there is good reason to believe the person should have known better than to do them.

More serious is the individual, corporate, or governmental use of legal loopholes to get away with behaviors known to be wrong but which are not specifically illegal and thereby punishable under the law.  In some cases, in civil suits, juries will often recognize this type of behavior for what it is, and if possible under even the slightest pretense or interpretation of the law, will award huge damage awards against a corporation that they believe seriously, knowingly and intentionally, mistreated and took advantage of someone who purchased their product or services, particularly under cover of a technical aspect of the law or in expectation of low customary previous damage awards.  When a company feels it is cheaper to do the wrong thing and pay a low damage award if they are found at fault in a civil suit, and juries find out that was the calculation made for their business decisions, then juries tend to point out emphatically that was a callous and wrong judgment for which the company will be economically punished much more severely than they expected.

And this is part of the case I believe Washington probably had in mind in his Farewell Address, except that he seemed to have thought moral (and religious) people would not do what is wrong just because it is not illegal, because their behavior would be guided by a higher principle than mere compliance with the letter of the law.  That meant that laws with strong teeth (i.e., serious punishments for breaking them), and morality based on religious punishment, were only necessary in order to try to make scoundrels at least have to think twice before willingly harming others or the public fabric.  For those without conscience, justified fear of punishment and justified fear of severe social sanctions would have to serve as a deterrent as much as possible.

But for the rest of us, that is normally not necessary.  Conscience and awareness of right and wrong serve better than threat of punishment as a deterrent. Very few of us refrain from burglary or murder simply because it is against the law or because we would be punished if caught and convicted, or because we might be consigned to hell.  We refrain because we know it is wrong, not because we think we cannot get away with it.  Many acts are not illegal, and yet we refrain from them simply because we know they would be wrong – whether keeping found money whose owner we can identify or keeping excess change given to us in error or cheating on our golf score. 

We do things for others without reward and often without recognition, merely because it is right, not because it is required by law.  A friend of mine was buying a lot of clothes on sale in a major upscale department store, and was completing the purchase as the store was already closed.  When she exited, they had to unlock the door by hand to let her out.  After she was well out of the store, it occurred to her something seemed wrong with the total amount of the purchase.  She checked her sales receipt, and noticed that the girl who had waited on her and who had been talking the whole time, had missed some $300 worth of merchandise.  She was already out of the store. The store was closed.  The mall was closing. It was not the city in which she lived, and she was due to fly home early the next morning. She could have simply left and had a real bargain.  But instead she went back to correct the error, and had to demand to be let back into the store by a staff who did not want to open the door to her.  It would have been easier to have walked away, but she didn’t.  And there are millions of people like her; the people Washington had in mind.  She had not shoplifted; the salesperson had removed all the store alarm devices, and had bagged the merchandise for her. She had broken no laws, but she knew the right thing to do was to pay the proper amount.  She did not want to have the mistake in her favor any more than she would have wanted the store to have made the same error in their favor and charged her too much.  She did not want to be the beneficiary of someone else’s error any more than she wanted to be the victim of one.[5]

But she was of a generation, like most generations until today, who were taught not just to follow rules (though they were supposed to follow rules – at least morally good rules), but were taught to “do the right thing” which involves more than just following rules, and which sometimes requires disobeying immoral rules (as the Nuremburg trials pointed out for those who seemed to think doing what is directed, or required by law, absolves them from moral culpability when they do wrong).  “Doing the right thing” is an open-ended dictum that requires insight, effort, experience, reason, thought, sensitivity, and hard work.  It is much more difficult to understand and to heed than is simply following rules.  Many of us learned to distinguish right from wrong behavior by trial and error -- receiving admonishment at best or punishment at worst, usually without trial, when we erred.

Of course, the serious problem of punishment without specific laws is that anyone can then be brought up on charges for acts that there was no reason to believe were wrong, and that may not even be wrong.  While laws are not foolproof methods of preventing punishment for morally innocent acts (or even some morally right acts such as the intentional breaking of immoral laws),  they at least give some warning about what a community will not tolerate whether it is actually intrinsically morally wrong or not. To avoid the spectacle of criminal charges brought randomly by personal whim, the United States became a formal system of laws, rather than a system based on morality or moral (or natural) law, mainly, I believe, under the influence, urging, and even perhaps dictates, of Chief Justice John Marshall.  But before that happened there was considerable debate about its reasonableness.  Today we take it for granted, and yet we lament that in a formal legal system there are often obvious miscarriages of moral justice, as when the clearly guilty go free because of loopholes, technicalities, or behaviors that were never thought needed prohibiting.  This happens particularly when technology or overly creative financial “inventions” make possible bad acts previously not even thought about by legislators or the public. But we are equally outraged and justifiably so when a miscarriage of justice imprisons someone who is actually innocent and there is clear evidence of that which is not allowed in court.

Moreover, the line between prosecuting people for breaking those and only those laws which are explicitly stated, and prosecuting people for behaviors that are not expressly forbidden is not as clear a line as might be thought.  As I have written in the essay “Law and Order and Morality” (http://www.garlikov.com/philosophy/LOM.html) the television series Law and Order portrays a prosecutorial philosophy that tries to prevent “loophole” miscarriages of justice by arguing that an obviously immoral act can, in many cases, be interpreted as illegal under a law that was enacted for a totally different purpose.  The idea is that if someone who has done something obviously wrong cannot be convicted under a law most directly related to his/her action, their action can be interpreted to fall under another law that they will have broken if the interpretation holds up in court.  What this does, given the plethora of laws enacted, is to make the criminal justice system somewhat closer in practice to a system of moral or natural law, though with more constraints.  Still, there will be a tension between prosecutorial whim and necessary flexibility.  But the point is that the issue of institutional or legal governance by means of specific rules/laws versus a more philosophical and moral principles approach is a serious issue that has serious consequences.  And I believe we are seeing some of those consequences now play out badly in institutional settings, particularly educational systems or schools, where it is mistakenly believed that conduct needs to be specified in advance in order to be fairly expected and in order to be punished fairly in its breach. 

There are two things I want to add to what I have said already in regard to law: (1) although some laws and contracts require specifically stated obligations, law does not generally require acts of kindness or benevolence, or even all acts of responsible behavior, that morality does.  The law does not normally require one to benefit others even if it would be easy for you to do so.  And even though law recognizes negligence, the threshold is normally very different from what would morally be considered negligence. The law allows people to get away with behaviors that their parents or society would typically hold to be unacceptably irresponsible.  For example, parental legal obligations do not require one to spend quality time with one’s children as long as one is not neglecting their physical needs.  The law does not require you to read to your children or to take them to the zoo or to otherwise enrich their experiences, enhance their education, or to help and inspire them to lead productive lives. The law does not require sales clerks to be helpful or pleasant or in many cases even to wait on you in a store.

(2) Without a sense of right and wrong there would be no incentive to amend or rescind bad laws or to resist immoral ones that ought not to be followed.  The trials at Nuremburg made clear that immoral orders are not to be obeyed.  By extension, the same would be true of following rules or laws that are immoral.  But if following the law was the only requirement, then there would be no reason or incentive for changing the law or saying it is wrong and needs to be disobeyed even whenever it is clearly immoral, particularly when it seems to serve the majority and harms mostly the minority or otherwise powerless.  There has to be a moral basis for certain laws or there would be no reason or motivation to create them.

Again then, Washington’s view (as I interpret it) is, I think, correct, that law alone without [religious or secular] morality and a sense of obligation to others, would be inadequate to enhance or even protect the social fabric.  Without morality, without personal moral conscientiousness, people would be less likely to obey laws they thought they could get away with breaking, and they would not be obligated to go beyond the minimal duties prescribed by law, which are relatively few when compared with what is actually morally obligatory.

Relevance to Education

There are a number of ways in which Claim 2 and its corollary adversely affect education, but the basic point is that it promotes students becoming passive readers and listeners -- passive recipients of information-- and that is not the same thing as learning. A passive reader is only a small step above a lazy or careless reader.  Claim 2 and its corollary also delay or hinder student maturity and the kind of conscientiousness for going beyond what one is simply told to do.

Moreover, telling students only those things they need to know for a test[6] is not teaching, except in those cases where what needs to be learned is complete and self-contained, as in learning a particular procedure such as assembling an engine, performing a specific surgical technique, or cooking a particular recipe.  But even in cooking, merely following recipes is not necessarily being a good cook.  In cooking and in performing surgery one needs to know more than just a particular algorithm if one is going to achieve optimal results, especially when some variation may be necessary under unexpected circumstances.  In those cases, a deeper underlying understanding is usually important.  Knowing the procedure perfectly is necessary but not always sufficient.  And one cannot likely improve upon an engine design if all one knows is how to follow a procedure for assembling that engine; one must usually have some idea of the principles involved in its working. Achieving only minimal understanding should not normally be the goal of learning or teaching. Students need to strive for more than that, and they need to be held to a higher standard and told up front that they will be held to a higher standard that itself will not be explicitly spelled out, but the implication of which they should nevertheless readily understand.

Students often want to know “what they have to study” for a test, or what they have to do to get a higher grade, and by that they mean they want very specific directions, tantamount to being told the answers or told what to say or what to do in order to receive extra credit.  If you give them questions they can answer using the material they have been assigned (e.g., an “open book test”) they will say they cannot find the answers in that material if it requires them to make deductions from (i.e., “think about”) what has been presented in the material. Even worse, if you do not tell them specifically which part of which assignment an issue is addressed, they frequently say they have not been able to find the answer.  If you tell them the answer is not to be found, but to be deduced from what they are to read, they do not understand what you mean and think that is not fair.  They want to be told what they are supposed to know, meaning what they are supposed to say, and they will memorize it and say it back, either by directly copying it or by stating what they think it says, whether they understand it correctly or not.

Mere surface knowledge becomes particularly problematic when the material is complex, because just repeating specific things others have said does not mean one understands the material.  For a simple instance, suppose a woman tells her husband she will have to work late and will not be able to leave her office until around 7pm and won’t be home till 8.  He might perfectly well be able to repeat that and understand she will be home around 8pm and not before.  But if he does not understand the ramifications of what that means, he may not realize he has to pick the children up from school, bring them home, feed them dinner, help with their homework, let the dog out and also feed it, and perhaps have a dinner prepared for his wife when she does get home.  He might even say he didn’t know that was what she meant when she said she was working late, even though he perfectly well knows he has two young children who attend school miles away, that they do not ride the bus, that they need to get home, and that though they are fairly independent workers, they do not always understand their homework assignments and may need some monitoring in order to do it correctly.  And even though he knows the dog stays indoors during the day and needs to be let out as early in the afternoon as possible.  If he does not “think about” what his wife’s being home late signifies, it does not matter that he can repeat what she said “Yes, I heard you; you will not be home until around 8 tonight.” 

“Open-ended concepts”, those which cannot be precisely defined in words very easily or that are difficult to understand just from the words alone, are particularly difficult to teach students educated under the influence of Claim 2 and its corollary, because if you give them examples, they cannot get past them to generalize or extrapolate to other cases.  They do not actively try to find the underlying relationship that makes those examples work.  It is as though you were teaching them the color red by showing the crayon, the tomato, the fire truck, and the red delicious apple, and the best they do in “showing other examples of red things” is to point to other fire trucks, apples, or tomatoes.  They would be unable to point out a red shirt or the red stripes in the American flag because you never told them those things were also red.  Obviously this case is an exaggeration, but every teacher who tries to teach abstract concepts or relationships can point to examples that are very similar. 

For example, many students, particularly of this current college generation, have great difficulty understanding the central concept of logic –validity-- which seems to be something very new and foreign to them.  A valid line of reasoning is one in which the evidence actually logically implies the conclusion.  Validity is important because if you are given evidence that is all true, but it does not logically imply the conclusion drawn from it, then there is no good reason based only on that evidence to justify believing the conclusion.  The conclusion may be true, but you cannot know it is true from the evidence given.  You may as well have faulty or false evidence for all the good it will do you to justify believing the conclusion.  There are many ways to explain this and there are many examples one can give of obviously invalid arguments, those in which the evidence or premises do not imply the conclusion. But if students cannot look beyond the example to get the intuitive idea of the concept, and instead only try to remember the examples that are valid and the examples that are invalid, they cannot distinguish which other arguments, even in many simple cases, are valid and which are not.  And if you give them even simple principles or rules of inference for distinguishing conclusions that follow from those which do not, they cannot apply the rules or even make any sense of them.

There are many examples in math, which is part of what makes math so difficult for many people.  Students have trouble with place value, with fractions, with rate-time-distance problems, with understanding what algebra “does” or how it works in general. Probably the main reasons students have difficulties with “word problems” in math are that 1) they have not learned to see mathematical relationships, but have only learned math “facts”, 2) they have learned how to follow recipes to do calculations without understanding how those calculations might be useful or what they mean, and 3) word problems are open-ended in that they do not tell you or suggest what steps you need to follow in order to solve them.  To solve them, apart from the few that are just like the ones you have been taught to do by recipe or formula, you need to understand the math concepts and relationships involved in them.  Then you can devise which calculations will likely yield fruitful results, and be able to tell whether they have done so or not.

This is important because life is even more difficult and more complex than word problems. In life, problems do not usually come labeled as problems with a solution. Normally one might see that things are not going the way one wants, but does not see that as being the result of a specific problem that needs to be defined, addressed, and solved.  Another significant difference is that in school when you cannot do a word problem, you find out about it with a low grade, but in life you just lament things are not the way you wish they were – without realizing you might really have been able to change that if you had figured out the root cause of the problem and figured out how to solve it.

Higher Expectations

There is no good reason that students and others should not be expected to know more than what they are simply told or that they should not be expected to do more than is explicitly required.  The human mind is normally quite able to extrapolate beyond mere surface level information and it should be encouraged, and even required, to do so. While that does not mean one should be expected to know everything, it does mean that in some cases one should be able to be held accountable for far more than what has been specifically stated or required.  The case should be able to be conclusively made that in some, but not all, particular situations one ought to have learned more than one has learned or that one ought to have behaved better than one behaved.  We can, of course, always debate in a specific case whether someone’s behavior or knowledge is reasonable or not based on the information s/he had available and based on an expectation of reasonable, non-negligent conscientiousness on his/her part.  And we can sometimes disagree  whether they should have known or done better or whether they were indifferent or negligent.  But there is no reason that the courts or schools must rigidly accept or adhere to the two claims and corollaries stated at the beginning of this paper.

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