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    • Mini-Syllabus: Introduction to Introductory Philosophy

      Posted at 12:00 pm by Michelle Joelle, on May 11, 2016

      Every so often I put together what I call a “mini-syllabus”; roughly, I pull together several books that speak to a common theme that I think would be either fun or instructive to read together. Sometimes the lists are highly academic and focused, and sometimes the starting text is more of a springboard for further exploration, but they’re never as broad and diverse as traditional syllabi. Today, I’m going to break that trend with a miniature syllabus on my favorite topic: philosophy.

      However, this won’t be a full introduction to the subject, but rather an introduction to some of my favorite introductory texts, meaning that this list won’t get into the nitty-gritty details of epistemological, political, metaphysical, aesthetic, ethical, or critical questions that make up the discipline, but instead will acquaint you with a variety of welcoming overtures to the field. Rather than diving into bell hooks’ incredible work on race and gender, or Russell’s clarifying take on the philosophy of language, you will instead get to see how they approach approaching the work they do, and how they invite others to join in the conversation.

      My reason for building this list is because, in a lot of ways, this really is the heart of philosophy. The work that philosophers do – answering questions, analyzing possibilities, critiquing assumptions, and more – comes from a core desire that transcends the specifics of any given sub-field. There is, in all specializations of philosophy, a deep and abiding commitment to continue seeking truth and digging for new problems to solve, even when the topic seems to be settled. I’ve written my own exhortations to philosophical inquiry here, here, and here.

      —–

      Without further ado, I give you my list of favorite invitations to philosophy:

      1. bell hooks’ essay on “Critical Thinking“, from the third book in her series on teaching, Teaching Critical Thinking: Practical Wisdom: This is chapter one of hooks’ third book on the topic, and in it she uncovers the main goal – and primary challenge – of every educator I’ve ever met: guiding students to be self-motivated, critical learners and generators of knowledge. While her focus in this essay is on the classroom, the same lessons can be applied to the independent scholar encountering philosophical arguments on their own time. Rather than simply reading to be instructed, everyone can read critically, and everyone can treat that reading experience as a conversation.

      2. Richard Feynman’s commencement speech at CalTech in 1974, “Cargo Cult Science“: This speech takes the same theme as bell hooks’ essay, but looks outside the classroom to see where so many of our barriers to critical thinking come from. While his main focus is eliminating barriers to honest and authentic science, his advice is applicable to any form of intellectual inquiry; it is just as easy to be duped by prose rationalization as it is the manipulation of scientific studies. Just because an argument sounds reasonable does not mean that it is.

      3. Plato’s “Allegory of the Cave” from The Republic: While the entire text is rich and wonderful, the famous allegory is famous for a reason – it frames philosophy as a process guided by an elusive truth, along a difficult path that will force you question everything you hold certain, after which you may never view the world the same way again. The allegory functions very differently in context of the whole work, but as a stand alone piece, it’s still very effective.

      4. Thomas Aquinas’ Quaestiones Disputatae de Veritate Book 11: The Teacher, especially Article I: Can a man or only God teach and be called teacher?: In this text, Aquinas speaks of both self-guided and traditionally instructed learning as an activity of discovery, rather than as the passive reception of knowledge. In essence, we can acquire knowledge by means of discovery (guided by our own natural reason), or by means of following the discoveries of another. This means that a good teacher will not simply tell you what you need to know, but guide you by demonstrating how they discovered it (which is often much speedier, allowing our community knowledge base to grow and benefit from new discoveries). This is very dry reading (sorry Thomas), but the ideas are exciting. If you are not religious, many of the ideas presented here can be applied to an understanding of truth as natural, rather than super natural (though perhaps not the article about angels).

      5. Jorge Luis Borges’ short story “The Circular Ruins” from the collection Labrynths: A play on the theories of idealism and surrealism, this story begins to complicate the task of philosophy, identity, and teaching in a way that is also entertaining and engaging. It will make you want to explore idealism, existentialism, and more.

      6. Bertrand Russell’s The Problems of Philosophy, especially chapter I “Appearance and Reality” and chapter XV “The Value of Philosophy”: This is Russell’s introductory text, written for brand new students of philosophy. In it, he writes about the difficulties of giving simple answers to what seem like simple questions, and also situates the role of philosophy among other disciplines. For more of my thoughts on these two chapters, see my Philosopher Fridays entry on Russell.

      7. Maria Lugones’ “Playfulness, ‘World’-Travelling, and Loving Perception“, published in 1987 (published online in 2009) in Hypatia: A Journal of Feminist Philosophy: This essay reads to me as a simultaneous extension of and challenge to Russell’s call to “enlargen ourselves” so that we can see things objectively. Lugones explores what makes that so difficult, and describes an alternative that allows us the philosophical benefits Russell seeks while also honoring the reality of life in the complicated context of identity. Her approach includes personal narrative, and then builds through the essay into a view of philosophy as an act of imaginative play that speaks much more practically to the way we can apply the critical thinking skills encouraged in the readings above in our daily experience.

      8. Nils Ch. Rauhut’s Ultimate Questions: Thinking about Philosophy: In philosophy, it is often difficult to find an introductory textbook that works for anyone but the scholar who wrote it (there are so many ways to approach the topic), but this one is excellent. While it does at times oversimplify complex topics, it does so in a way that invites the kinds of conversations hooks and Feynman in particular encourage above. I have a couple of minor quibbles with the presentation of some ideas (for example, including Descartes in the section on skepticism based on Meditation 1 is understandable, but perhaps a bit misleading for those who do not continue to read his resolution in Meditations 2-6 into rationalism), but overall it’s a textbook I highly recommend for anyone interested in learning the vocabulary and range of philosophical inquiry.

      9. Hannah Arendt’s The Human Condition, especially Chapter 1: No work more comprehensively lays out the history of philosophical development with such instructive generality; instead of looking in a detailed way at different philosophers, or different philosophical fields, Arendt captures the conversations between competing ideologies, and the effect of that conversation on philosophy, religion, science, literature, economics, and politics in a way that is both descriptive and itself philosophical. Her aim in this text is to shift the conversation of philosophy away from a focus on the quiet eternity of contemplative death to the noisy, complicated, needy, mortal world of the living.

      —–

      I was going for an even ten items, but I think that should be quite enough to get anyone started – actually, any one of them could easily send a reader off on a path of intellectual discovery. If you do read something here and would like recommendations of where to go next, or have suggestions for other great introductory texts, please don’t hesitate to comment.

      5/12 Correction: Lugones’ article was printed in Hypatia in 1987, and was then published online in 2009. 

      Posted in Series | 6 Comments | Tagged academia, aquinas, arendt, bell hooks, borges, feynman, learning, lugones, mini-syllabus, philosophy, Plato, reading, russell, teaching
    • The Philosopher’s Lexicon: De Dicto/De re Distinction

      Posted at 1:00 pm by Michelle Joelle, on April 17, 2015

      Welcome back to The Philosopher’s Lexicon. My primary goal in this series is to explore common philosophical vocabulary, hopefully transforming these words from useless jargon into meaningful terms. My secondary goal is to highlight how contentious some of these terms can be – especially those which seem obvious. These definitions will not be comprehensive by any means, so please feel free to add your own understanding of each term as we go. 

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      This week’s entry into the lexicon is the distinction between claims that are made de dicto and claims that are made de re. Literally, a “de dicto” proposition carries its meaning in the words that are said, while a “de re” proposition carries its meaning in the thing that exists behind the words. This is most easily understood in an example. For this, most explanations turn to Quine. The Stanford Encyclopedia of Philosophy renders his example thus:

      (1) Ralph believes that someone is a spy.

      This could mean either of the following.

      (2) Ralph believes that there are spies

      or

      (3) Someone is such that Ralph believes that he is a spy.

      The first meaning (2) is what results when the initial statement (1) is taken de dicto. The meaning of the proposition is found literally within the words given, in a self-contained way. The second rendering (3) is referring to some thing out in the world that is being represented by the words in the statement, meaning that what we are looking for is not just the meaning of the words de dicto, but the meaning behind the words, de re. 

      There is, of course, a lot of complexity in working out this sort of ambiguity in our language with logical notation and categorical distinctions, but what is more interesting to me is how this ambiguity plays out not just in our syntax, but in our affirmation of truths, our understanding of the world, and in our beliefs.

      This distinction between de dicto and de re beliefs has been on my mind recently because of a short comment made at a theological ethics talk I attended a few weeks ago. The topic of conversation (very loosely rendered) was whether (and of course, how) the morality of an act depended upon a person’s express belief in its morality de dicto, or upon the alignment of the particular act with an objective moral standard de re.

      This is, of course, a fairly easy dilemma to solve if we’re operating under expressly Abrahamic assumptions. If there is an objective standard of goodness against which all acts must be measured, then clearly that standard will supersede our own human understanding and linguistic representation of it. Moving into an expressly Christian framework, if a person professes to believe in the word of Christ de dicto, but acts in a way that is contrary to all Christian teachings, the acts themselves are still immoral.

      It gets a little more contentious if we shift the model around, however: if a person uses the language wrong and perhaps misunderstands the laws in their express rendering, but follows the spirit – de re – of Christ’s teachings, then she is, for many Christians, still behaving in a moral way. Of course, for many other Christians, both an express belief de dicto and a spiritual enactment of Christ’s teachings de re are important, but it’s generally clear that while de dicto belief is debatable, de re belief is not. Romans 2 gets a little tricky with the language, but drives generally at this point:

      For it is not those who hear the law who are righteous in God’s sight, but it is those who obey the law who will be declared righteous. (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.) (Romans 2:12-15, NIV).

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      A great exemplar of the de re form of Christianity that the ethicist who inspired this lexicon entry brought up in the informal discussion that followed her talk can be found in C.S. Lewis’s Narnia tale The Last Battle (spoiler alert, FYI). There is a scene where a man finds himself face to face with Aslan in the afterlife after having spent this life piously praising and praying to another God (Tash). In re, Tash is a cruel and oppressive deity, while Aslan is a good and forgiving figure, but in dicto, the man took his God Tash to be good, loving, and protective. In describing his exchange with Aslan, he says this:

      Then I fell at his feet and thought, Surely this is the hour of death, for the Lion (who is worthy of all honor) will know that I have served Tash all my days and not him… But the Glorious One bent down his golden head and touched my forehead with his tongue and said, Son, thou art welcome. But I said, Alas, Lord, I am no son of thine but a servant of Tash. He answered, Child, all the service thou has done to Tash, I account as service done to me… if any man swear by Tash and keep his oath for the oath’s sake, it is by me that he has truly sworn, though he know it not, and it is I who reward him. And if any man do a cruelty in my name, then, though he says the name Aslan, it is Tash whom he serves and by Tash his deed is accepted (Lewis 204,205).

      This same model remains useful if we remove it from a theological context but still maintain an objective standard de re. When it comes to mathematics, a de dicto approach would focus on notation, equations, and formulas, while a strictly de re approach would relegate mathematical language to the role of tool which merely helps us find answers. This probably seems extremely obvious, but in practice we often focus far more on the way mathematics is expressed than on the rational truths being expressed, when in truth, we really need a balance of both. In previous posts on education I’ve called this a “vocabulary-based” approach, but the de dicto/de re distinction is perhaps more precise.

      A great exemplar of this distinction can be found in an anecdote from the essay “He Fixes Radios by Thinking!” from Surely You’re Joking, Mr. Feynman!:

      While I was doing all this trigonometry, I didn’t like the symbols for sine, cosine, tangent, and so on. To me, “sin f” looked like s times i times n times f! So I invented another symbol, like a square root sign, that was a sigma with a long arm sticking out of it, and I put the f underneath. For the tangent it was a tau with the top of the tau extended, and for the cosine I made a kind of gamma, but it looked a little bit like the square root sign… I thought my symbols were just as good, if not better, than the regular symbols – it doesn’t make any difference what symbols you use – but I discovered later that it does make a difference. Once when I was explaining something to another kid in high school, without thinking I started to make these symbols, and he said, “What the hell are those?” I realized then that if I’m going to talk to anybody else, I’ll have to use the standard symbols, so I eventually gave up my own symbols (Feynman 24).

      While we can use any symbols or language we want to explain and understand principles de re, we need a common de dicto understanding for communication. Where we often run into problems, mathematically, is that we tend to treat the way that mathematics is expressed as the truth of thing – we spend our time learning nothing but mathematics de dicto and find ourselves with little to no understanding of mathematics de re. I’m sure that the same thing could be said for nearly any subject or course of study. Feynman found this to be the case even in his classes at MIT:

      I often likes to play tricks on people when I was at MIT. One time, in mechanical drawing class, some joker picked up a French curve (a piece of plastic for drawing smooth curves – a curly, funny-looking thing) and said “I wonder if the curves on this thing have some special formula?”

      I thought for a moment and said, “Sure they do. The curves are very special curves. Lemme show ya,” and I picked up my French curve and began to turn it slowly. “The French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal.”

      All the guys in the class were holding their French curve up at different angles, holding their pencil up to it at the lowest point and laying it along, and discovering that, sure enough, the tangent is horizontal. They were all excited by this “discovery” – even though they had already gone through a certain amount of calculus and had already “learned” that the derivative (tangent) of the minimum (lowest point) of any curve is zero (horizontal).  They didn’t put two and two together. They didn’t even know what they “knew”

      I don’t know what’s the matter with people: they don’t learn by understanding; they learn by some other way – by rote, or something. Their knowledge is so fragile! (Feynman 36,37).

      What is clear to me in both the theological and the mathematical examples is that while the re is different, so long as we believe there is some objective external standard of truth to be found, this distinction is absolutely necessary, as collapsing the distinction tends to lead to an erosion of understanding. In religious frameworks we end up focusing on trivial contradictions and minute, seemingly arbitrary details at the expense of the general spirit or message a particular religion is attempting to prioritize. In mathematics, we focus so much on the process that we miss out on the end result. In taking the de dicto meaning of a proposition for the de re, we shift our focus from finding truth to merely affirming agreement.

      Of course, if there is no re that exists outside of our representation in language and symbols, then this distinction naturally falls apart. But while I’m unwilling to stake a claim on the exact nature of what is objectively true de re, I’m committed enough to its existence to find this distinction – and this particular piece of jargon – invaluable.

      Posted in Series | 16 Comments | Tagged academia, C.S. Lewis, de dicto/de re distinction, definitions, dictionary, feynman, lady philosophy, lexicon, logic, mathematics, philosophy, Romans, symbols, syntax, theology
    • On Teaching and Learning

      Posted at 12:00 pm by Michelle Joelle, on March 11, 2015

      Over the past few weeks I’ve been collecting articles, posts, and quotes on the nature of teaching and learning with the idea that I would compile them into a longer essay. But as my list grew and my thoughts crystallized, I decided instead to keep my comments brief and let these vignettes take center stage. To put it succinctly, what all of these examples suggest is that teaching is not preaching, no matter what the subject, and that learning is far more than simply receiving knowledge – no matter how brilliant the source.

      First, from Richard Feynman on his time teaching teaching physics in Brazil:

      After a lot of investigation, I finally figured out that the students had memorized everything, but they didn’t know what anything meant. When they heard “light that is reflected from a medium with an index,” they didn’t know that it meant a material such as water. They didn’t know that the “direction of the light” is the direction in which you see something when you’re looking at it, and so on. Everything was entirely memorized, yet nothing had been translated into meaningful words. So if I asked, “What is Brewster’s Angle?” I’m going into the computer with the right keywords. But if I say, “Look at the water,” nothing happens – they don’t have anything under “Look at the water”!

      Later on:

      I taught a course at the engineering school on mathematical methods in physics, in which I tried to show how to solve problems by trial and error. It’s something that people don’t usually learn, so I began with some simple examples of arithmetic to illustrate the method. I was surprised that only about eight out of the eighty or so students turned in the first assignment. So I gave a strong lecture about having to actually try it, not just sit back and watch me do it.

      After the lecture some students came up to me in a little delegation, and told me that I didn’t understand the backgrounds that they have, that they can study without doing the problems, that they have already learned arithmetic, and that this stuff was beneath them.

      So I kept going with the class, and no matter how complicated or obviously advanced the work was becoming, they were never handing a damn thing in. Of course I realized what it was: They couldn’t do it!”

      He draws an analogy between the way these students are being taught science and the act of learning a language merely by its sounds and rules:

      Then I gave the analogy of a Greek scholar who loves the Greek language, who knows that in his own country there aren’t many children studying Greek. But he comes to another country, where he is delighted to find everybody studying Greek – even the smaller kids in the elementary schools. He goes to the examination of a student who is coming to get his degree in Greek, and asks him, “What were Socrates’ ideas on the relationship between Truth and Beauty?” – and the student can’t answer. Then he asks the student, What did Socrates say to Plato in the Third Symposium?” the student lights up and goes, “Brrrrrrrrr-up” – he tells you everything, word for word, that Socrates said, in beautiful Greek.

      But what Socrates was talking about in the Third Symposium was the relationship between Truth and Beauty!

      What this Greek scholar discovers is, the students in another country learn Greek by first learning to pronounce the letters, then the words, and then sentences and paragraphs. They can recite, word for word, what Socrates said, without realizing that those Greek words actually mean something. To the student they are all artificial sounds. Nobody has ever translated them into words the students can understand.

      The entire essay is worth reading – actually, all of his essays in Surely You’re Joking, Mr. Feynman are – but these excerpts illustrate an attitude still present in a lot of educational environments.

      Second, an essay from Mere Inkling on C.S. Lewis and the transfer of knowledge:

      When I attended the University of Washington, we had to learn the old-fashioned way—by studying. Now they are anticipating downloading information directly into students’ brains.

      Literal brain dumps are actually still in the future . . . but researchers have documented the first indisputable brain-to-brain interface between humans!

      My first paragraph is not an exaggeration of what researchers think may one day happen.

      The project could also eventually lead to “brain tutoring,” in which knowledge is transferred directly from the brain of a teacher to a student.

      The student would view this shortcut as advantageous. (It could also save a great deal in tuition expenses, if each course only took, say, an hour or two of brain interfacing.)

      The university sees another advantage—circumventing limited teaching skills.

      “Imagine someone who’s a brilliant scientist but not a brilliant teacher. Complex knowledge is hard to explain – we’re limited by language,” said co-author Chantel Prat, a faculty member at the Institute for Learning & Brain Sciences and a UW assistant professor of psychology.

      The editor of Mere Inkling, Robert Stroud, goes on to counter this idea with some questions and quotes form C. S. Lewis on education which are highly worth reading also, but my thoughts turn to the above-quoted Chantel Prat.

      Even if we were able to transfer knowledge in this way, we would fail to truly teach or learn by that method. As shown in Feynman’s experience, learning is not just about the collection of information, but rather training ourselves to figure it out. Teachers, when they’re good, guide their students through that discovery, and geniuses who come up with new and better ways to do things enable us to discover more things more quickly, but invariably, we still have to struggle through the process ourselves. Memorizing “2+2=4″ gives you no knowledge unless you can walk through the process yourself and then reapply it to other equations.

      Simply transferring the knowledge from the brain of the scientist to the brain of the student wouldn’t give you any better handle on the material than if the scientist said that same information out loud – it would still need to be unpacked and rebuilt by the student, helped by a teacher who can walk them through the process.

      Third, St. Augustine explains in De Magistro (Garry Wills translation) why teaching is so difficult, even when we have great knowledge:

      The most, then, that can be said for the scope of words is that they afford us an occasion for examining something, but they do not demonstrate it to our understanding. -36

      And later:

      Do teachers advertise that they verbally transmit their own acts of understanding, or the truths of their discipline, for students to receive and retain? What father sense a child to school with the silly aim of finding out what the teacher’s understanding is? Rather, when all subjects, even those concerning virtue and wisdom, have been expounded by those who profess them, then students, if they are really to be called that, investigate within themselves whether what they are hearing is true, strenuously putting it to the test of their own interior truth. That is the point at which they learn. And when they read an inner conviction of truth, they praise their teachers, not realizing that, even if the teachers knew what they were saying, the praise rightly belongs tot he taught ones not the ones who taught. – 45

      Even if you don’t believe we have an interior truth (either in terms of innate reason or in the image of God), the point is that knowledge is be gained by the experimentation or problem-solving act of the student, effectively prompted by the words of the teacher, but not executed by the teacher.

      Fourth, we see a similar rendering of this idea from Thomas Aquinas in De Veritate, Question 11:

      In effects which are produced by nature and by art, art operates in the same way and through the same means as nature. For, as nature heals one who is suffering from cold by warming him, so also does the doctor. Hence, art is said to imitate nature. A similar thing takes place in acquiring knowledge. For the teacher leads the pupil to knowledge of things he does not know in the same way that one directs himself through the process of discovering something he does not know.

      Now, in discovery, the procedure of anyone who arrives at the knowledge of something unknown is to apply general self-evident principles to certain definite matters, from these to proceed to particular conclusions, and from these to others. Consequently, one person is said to teach another inasmuch as, by signs, he manifests to that other the reasoning process which he himself goes through by his own natural reason. And thus, through the instrumentality, as it were, of what is told him, the natural reason of the pupil arrives at a knowledge of the things which he did not know. Therefore, just as the doctor is said to heal a patient through the activity of nature, so a man is said to cause knowledge in another through the activity of the learner’s own natural reason, and this is teaching. So, one is said to teach another and be his teacher. This is what the Philosopher means when he says: “Demonstration is a syllogism which makes someone know.”

      The teacher is here useful, but not necessary, for the act of learning.

      Fifth, we see this idea taken even further in a blog post from Book Geeks Anonymous on the damaging effects of teaching people that they need teachers:

      In an interview with CUNY TV, Irish poet Paul Muldoon advanced his theory for why so many people, particularly students, struggle to understand and enjoy poetry. According to Muldoon, it has to do with the way that poetry is taught in schools: in high school, he says, students are given the impression that they will never be able to understand poetry without a teacher or other sort of “expert” there to tell them what they’re reading.

      Muldoon makes a good point: most schools’ ways of teaching–not just poetry, but all subjects– cause students to doubt or neglect their own abilities. Because they, from the time they were waist-high, were spoon-fed their lessons, they become convinced that they cannot accomplish anything academic without involving a teacher. I believe college professors call this “freshman syndrome.” But this, I think, is only part of the reason why students struggle with poetry.

      When we make the teacher a source of knowledge, rather than a guide through the process of learning, we set very specific, arbitrary standards – teaching students not how to interpret poetry, but how to interpret the teacher, to find the “trick”, identify the “catch” in any question of evaluation. And we don’t just do this in the humanities.

      Sixth, another Feynman essay illustrates how we start this process early on, even in our elementary science textbooks:

      For example, there was a book that started out with four pictures: first, there was a wind-up toy; then there was an automobile’ then there was a boy riding a bicycle; then there was something else. And underneath each picture it said, “What makes it go?”

      I thought, “I know what it is: they’re going to talk about mechanics, how the springs work inside the toy; about chemistry, how the engine of the automobile works; and biology, about how the muscles work.”

      It was the kind of thing my father would have talked about: “What makes it go?” Everything does because the sun is shining,” And then we would have fun discussing it:

      “No, the toy goes because the spring is wound up,” I would say.

      “How did the spring get wound up?” he would aks.

      “I wound it up.”

      “And how did you get moving?”

      “From eating.”

      “And food grows only because the sun is shining. So it’s because the sun is shining that all these things are moving.” That would get the concept across that motion is simply the transformation of the sun’s power.

      I turned the page. The answer was, for the wind-up toy, “Energy makes it go.” And for the bicycle, “Energy makes it go.” For everything, “Energy makes it go.”

      Now that doesn’t mean anything. Suppose it’s “wakalixes.” That’s the general principle: “Wakalixes makes it go.” There’s no knowledge coming in. The child doesn’t learn anything: it’s just a word!”

      Even if it were the right word (and here Feynman argues vehemently that “energy” signifies far too broad of a concept to possibly be the right word), the word itself is merely a symbol representing a concept – learning the word by itself gives you nothing, and teaches students that the answer to a scientific question isn’t about figuring out how things work and why, but is instead about learning – or guessing – the right vocabulary word.

      Seventh, in offering a new way to teach shapes, Christopher from Talking Math with Kids, makes a similar claim about how vocabulary-centric learning often denies us conceptual learning:

      Most shapes books—whether board books for babies and toddlers, or more sophisticated books for school-aged children—are full of misinformation and missed opportunities. As an example, there is nearly always one page for squares and a separate one for rectangles. There is almost never a square on the rectangles page. That’s a missed opportunity. Often, the text says that a rectangle has two short sides and two long sides. That’s misinformation. A square is a special rectangle, just as a child is a special person.

      He goes on to describe a book of shapes that allows for children to think a bit more freely, and get a lot of new information – all without the arbitrary limitation of insisting on a set answer to a particular question. Each page displays four shapes, and asks the question: “Which one doesn’t belong?” And there are a variety of possible answers:

      If you are thinking, “It depends on how you look at it,” then you’ve got the idea… There is no answer key. This is intentional–to encourage further discussion, and to encourage you to return to the book to try again.

      The book will be available in PDF form for free download until the author makes it available for sale in hard copy.

      Eighth, we can trace this same pattern to the teaching of ethics and values by looking at a recently popular opinion article by Justin P. McBrayer in the New York Times questioning “Why our children don’t think there are moral facts”:

      This is repeated ad nauseum: any claim with good, right, wrong, etc. is not a fact.

      In summary, our public schools teach students that all claims are either facts or opinions and that all value and moral claims fall into the latter camp. The punchline: there are no moral facts. And if there are no moral facts, then there are no moral truths.

      However while I think this is a great essay, McBrayer himself falls into the exact trap he is criticizing. I agree with Self Aware Patterns’ dissatisfaction with McBrayer’s assumption that there are moral facts:

      I can certainly understand the strong desire for moral precepts to be facts similar to mathematical truths or scientific conclusions. I wish they were myself. It would make ethical debates so much easier. It would merely be a matter of testing a proposition or perhaps putting together a logical proof. But moral values can only be proven in relation to other moral values. Eventually, as you dig down through the moral axioms, you unavoidably hit a wall of subjectivity.

      He later adds that:

      Moral values are more than just whimsical opinion, but they don’t rise to the level of being absolute facts.

      What comes through is that the dualistic understanding of all knowledge as either “fact” or “opinion” is damagingly inadequate. In this case, the “fact/value” distinction is important, as is the “fact/opinion” distinction, but it is just as important to explore a “value/opinion” distinction, a “fact/axiom” distinction, a “fact/theory” distinction, a “theory/hypothesis” distinction, and more. Perhaps university is the right place to introduce these sorts of complexities, but I can’t help but think that it’s disingenuous – and damaging – to teach students that ideas are either correct facts you cannot question, or else utterly dismissible opinions that you cannot treat with rigor or respect.

      Generally speaking, when we treat teaching like the mere transfer of unquestionable data, school becomes a place to leave the real world (and the real way we do things) behind, leaving us no tools with which to apply whatever we do learn in class. Of course, facts and definitions and details are absolutely necessary for both clear communication and for guiding students quickly through discoveries that others have already struggled to make, but the goal should always be to enable students to go out of the classroom and use what they learn in both expected and unexpected ways – to stand on the shoulders of giants, not cower in their shadows.

      And of course, that is far easier said than done.

      Posted in Essays | 13 Comments | Tagged academia, aquinas, Augustine, de magistro, education, ethics, feynman, learning, links, longreads, morality, philosophy, quotes, selfawarepatterns, shapes, talking math with kids, teaching
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