See full article at: https://www.chronicle.com/article/An-Insider-s-Take-on/242235/
An Insider’s Take on Assessment: It May Be Worse Than You Thought
By Erik Gilbert January 12, 2018
Katherine Streeter for The Chronicle
No doubt many of you will spend part of the month of January looking over assessment material from the fall semester. Equipped with some pre- and post-tests, a couple of artifacts, a rubric, a curriculum map, and, perhaps, a little bourbon, you will study your data carefully, make a few quick inferences and then identify a minor problem that you can address by making equally minor changes to your course or program.
However, you may find that upon close examination the data don’t seem to be saying anything at all to you. You may even be tempted to just make something up. If you do go that route, it’s probably because you have concluded that assessment data do not tell you anything useful about your program, so there is no harm in fudging your analysis of the data.
If that was you, don’t worry. It turns out that the assessment program your college imposed on you was probably never going to improve anything. A new article by an assessment insider explains why this is so and suggests that assessors have known for sometime now that assessment does not work.
The article, in Intersection, the journal of the Association for the Assessment of Learning in Higher Education is by David Eubanks, assistant vice president for assessment and institutional effectiveness at Furman University and a board member of the association. In it Eubanks details the methodological flaws that are inherent to assessment and argues that because of the broad scale on which assessment is done, few of the methods employed by social-science research are used.
Read the rest of the article at: https://www.chronicle.com/article/An-Insider-s-Take-on/242235/
(Menippus is dialogueing with his friend Philonides. Philonides is asking Menippus to describe his trip to Hades, the place of the dead.)
Me. I can refuse you nothing, you see; what is one to do, when a friend insists? Well, I will show you first the state of mind which put me on the venture. When I was a boy, and listened to Homer’s and Hesiod’s tales of war and civil strife–
and they do not confine themselves to the Heroes, but include the Gods in their descriptions, adulterous Gods, rapacious Gods, violent, litigious, usurping, incestuous Gods–, well, I found it all quite proper, and indeed was intensely interested in it. But as I came to man’s estate, I observed that the laws flatly contradicted the poets, forbidding adultery, sedition, and rapacity. So I was in a very hazy state of mind, and could not tell what to make of it. The Gods would surely never have been guilty of such behaviour if they had not considered it good; and yet law-givers would never have recommended avoiding it, if avoidance had not seemed desirable.
In this perplexity, I determined to go to the people they4 call philosophers, put myself in their hands, and ask them to make what they would of me and give me a plain reliable map of life. This was my idea in going to them; but the effort only shifted me from the frying-pan into the fire; it was just among these that my inquiry brought the greatest ignorance and bewilderment to light; they very soon convinced me that the real golden life is that of the man in the street. One of them would have me do nothing but seek pleasure and ensue it; according to him, Happiness was pleasure. Another recommended the exact contrary–toil and moil, bring the body under, be filthy and squalid, disgusting and abusive–concluding always with the tags from Hesiod about Virtue, or something about indefatigable pursuit of the ideal. Another bade me despise money, and reckon the acquisition of it as a thing indifferent; he too had his contrary, who declared wealth a good in itself. I will spare you their metaphysics; I was sickened with daily doses of Ideas, Incorporeal Things, Atoms, Vacua, and a multitude more. The extraordinary thing was that people maintaining the most opposite views would each of them produce convincing plausible arguments; when the same thing was called hot and cold by different persons, there was no
refuting one more than the other, however well one knew that it could not be hot and cold at once. I was just like a man dropping off to sleep, with his head first nodding forward, and then jerking back.
5Yet that absurdity is surpassed by another. I found by observation that the practice of these same people was diametrically opposed to their precepts. Those who preached contempt of wealth would hold on to it like grim death, dispute about interest, teach for pay, and sacrifice everything to the main chance, while the depreciators of fame directed all their words and deeds to nothing else but fame; pleasure, which had all their private devotions, they were almost unanimous in condemning.
6Thus again disappointed of my hope, I was in yet worse case than before; it was slight consolation to reflect that I was in numerous and wise and eminently sensible company, if I was a fool still, all astray in my quest of Truth. One night, while these thoughts kept me sleepless, I resolved to go to Babylon and ask help from one of the Magi, Zoroaster’s disciples and successors; I had been told that by incantations and other rites they could open the gates of Hades, take down any one they chose in safety, and bring him up again. I thought the best thing would be to secure the services of one of these, visit Tiresias the Boeotian, and learn from that wise seer what is the best life and the right choice for a man of sense. I got up with all speed and started straight for Babylon. When I arrived, I found a wise and wonderful Chaldean; he was white-haired, with a long imposing beard, and called Mithrobarzanes. My prayers and supplications at last induced him to name a price for conducting me down.
7Taking me under his charge, he commenced with a new moon, and brought me down for twenty-nine successive mornings to the Euphrates, where he bathed me, apostrophizing the rising
sun in a long formula, of which I never caught much; he gabbled indistinctly, like bad heralds at the Games; but he appeared to be invoking spirits. This charm completed, he spat thrice upon my face, and I went home, not letting my eyes meet those of any one we passed. Our food was nuts and acorns, our drink milk and hydromel and water from the Choaspes, and we slept out of doors on the grass. When he thought me sufficiently prepared, he took me at midnight to the Tigris, purified and rubbed me over, sanctified me with torches and squills and other things, muttering the charm aforesaid, then made a magic circle round me to protect me from ghosts, and finally led me home backwards just as I was; it was now time to arrange our voyage.
He himself put on a magic robe, Median in character, and8 fetched and gave me the cap, lion’s skin, and lyre which you see, telling me if I were asked my name not to say Menippus, but Heracles, Odysseus, or Orpheus.
Phi. What was that for? I see no reason either for the get-up or for the choice of names.
Me. Oh, obvious enough; there is no mystery in that. He thought that as these three had gone down alive to Hades before us, I might easily elude Aeacus’s guard by borrowing their appearance, and be passed as an habitué; there is good warrant in the theatre for the efficiency of disguise.
Dawn was approaching when we went down to the river to9 embark; he had provided a boat, victims, hydromel, and all necessaries for our mystic enterprise. We put all aboard, and then,
continues] For some distance we floated down stream, until we entered the marshy lake in which the Euphrates disappears. Beyond this we came to a desolate, wooded, sunless spot; there we landed, Mithrobarzanes leading the way, and proceeded to dig a pit,
slay our sheep, and sprinkle their blood round the edge. Meanwhile the Mage, with a lighted torch in his hand, abandoning his customary whisper, shouted at the top of his voice an invocation to all spirits, particularly the Poenae and Erinyes,
with a string of other names, outlandish, unintelligible, and polysyllabic.
10As he ended, there was a great commotion, earth was burst open by the incantation, the barking of Cerberus was heard far off, and all was overcast and lowering;
for almost all was now unveiled to us, the lake, and Phlegethon, and the abode of Pluto. Undeterred, we made our way down the chasm, and came upon Rhadamanthus half dead with fear. Cerberus barked and looked like getting up; but I quickly touched my lyre, and the first note sufficed to lull him. Reaching the lake, we nearly missed our passage for that time, the ferry-boat being already full; there was incessant lamentation, and all the passengers had wounds upon them; mangled legs, mangled heads, mangled everything; no doubt there was a war going on. Nevertheless, when good Charon saw the lion’s skin, taking me for Heracles, he made room, was delighted to give me a passage, and showed us our direction when we got off.
11We were now in darkness; so Mithrobarzanes led the way, and I followed holding on to him, until we reached a great meadow of asphodel, where the shades of the dead, with their thin voices, came flitting round us. Working gradually on, we reached the court of Minos; he was sitting on a high throne, with the Poenae, Avengers, and Erinyes standing at the sides. From another direction was being brought a long row of persons chained together; I heard that they were adulterers, procurers, publicans, sycophants, informers, and all the filth
that pollutes the stream of life. Separate from them came the rich and usurers, pale, pot-bellied, and gouty, each with a hundredweight of spiked collar upon him. There we stood looking at the proceedings and listening to the pleas they put in; their accusers were orators of a strange and novel species.
Phi. Who, in God’s name? shrink not; let me know all.
Me. It has not escaped your observation that the sun projects certain shadows of our bodies on the ground.
Phi. How should it have?
Me. These, when we die, are the prosecutors and witnesses who bring home to us our conduct on earth; their constant attendance and absolute attachment to our persons secures them high credit in the witness-box.
Well, Minos carefully examined each prisoner, and sent him12 off to the place of the wicked to receive punishment proportionate to his transgressions. He was especially severe upon those who, puffed up with wealth and authority, were expecting an almost reverential treatment; he could not away with their ephemeral presumption and superciliousness, their failure to realize the mortality of themselves and their fortunes. Stripped of all that made them glorious, of wealth and birth and power, there they stood naked and downcast, reconstructing their worldly blessedness in their minds like a dream that is gone; the spectacle was meat and drink to me; any that I knew by sight I would come quietly up to, and remind him of his state up here; what a spirit had his been, when morning crowds lined his hall, expectant of his coming, being jostled or thrust out by lacqueys! at last my lord Sun would dawn upon them, in purple or gold or rainbow hues, not unconscious of the bliss he shed upon those who approached, if he let them kiss his breast or his hand. These reminders seemed to annoy them.
Minos, however, did allow his decision to be influenced in one13
case. Dionysius of Syracuse was accused by Dion of many unholy deeds, and damning evidence was produced by his shadow; he was on the point of being chained to the Chimera, when Aristippus of Cyrene, whose name and influence are great below, got him off on the ground of his constant generosity as a patron of literature.
14We left the court at last, and came to the place of punishment. Many a piteous sight and sound was there–cracking of whips, shrieks of the burning, rack and gibbet and wheel; Chimera tearing, Cerberus devouring; all tortured together, kings and slaves, governors and paupers, rich and beggars, and all repenting their sins. A few of them, the lately dead, we recognized. These would turn away and shrink from observation; or if they met our eyes, it would be with a slavish cringing glance–how different from the arrogance and contempt that had marked them in life! The poor were allowed half-time in their tortures, respite and punishment alternating. Those with whom legend is so busy I saw with my eyes–Ixion, Sisyphus, the Phrygian Tantalus in all his misery, and the giant Tityus–how vast, his bulk covering a whole field!
15Leaving these, we entered the Acherusian plain, and there found the demi-gods, men and women both, and the common dead, dwelling in their nations and tribes, some of them ancient and mouldering, ‘strengthless heads,’ as Homer has it, others fresh, with substance yet in them, Egyptians chiefly, these–so long last their embalming drugs. But to know one from another was no easy task; all are so like when the bones are bared; yet with pains and long scrutiny we could make them out. They lay pell-mell in undistinguished heaps, with none of their earthly beauties left. With all those anatomies piled together as like as could be, eyes glaring ghastly and vacant, teeth gleaming bare, I knew not how to tell Thersites from Nireus the beauty, beggar Irus from the Phaeacian king, or cook
continues] Pyrrhias from Agamemnon’s self. Their ancient marks were gone, and their bones alike–uncertain, unlabelled, indistinguishable.
When I saw all this, the life of man came before me under16 the likeness of a great pageant, arranged and marshalled by Chance, who distributed infinitely varied costumes to the performers. She would take one and array him like a king, with tiara, bodyguard, and crown complete; another she dressed like a slave; one was adorned with beauty, another got up as a ridiculous hunchback; there must be all kinds in the show. Often before the procession was over she made individuals exchange characters; they could not be allowed to keep the same to the end; Croesus must double parts and appear as slave and captive; Maeandrius, starting as slave, would take over Polycrates’s despotism, and be allowed to keep his new clothes for a little while. And when the procession is done, every one disrobes, gives up his character with his body, and appears, as he originally was, just like his neighbour. Some, when Chance comes round collecting the properties, are silly enough to sulk and protest, as though they were being robbed of their own instead of only returning loans. You know the kind of thing on the stage–tragic actors shifting as the play requires from Creon to Priam, from Priam to Agamemnon; the same man, very likely, whom you saw just now in all the majesty of Cecrops or Erechtheus, treads the boards next as a slave, because the author tells him to. The play over, each of them throws off his gold-spangled robe and his mask, descends from the buskin’s height, and moves a mean ordinary creature; his name is not now Agamemnon son of Atreus or Creon son of Menoeceus, but Polus son of Charicles of Sunium or Satyrus son of Theogiton of Marathon. Such is the condition of mankind, or so that sight presented it to me.
Phi. Now, if a man occupies a costly towering sepulchre, or17
leaves monuments, statues, inscriptions behind him on earth, does not this place him in a class above the common dead?
Me. Nonsense, my good man; if you had looked on Mausolus himself–the Carian so famous for his tomb–, I assure you, you would never have stopped laughing; he was a miserable unconsidered unit among the general mass of the dead, flung aside in a dusty hole, with no profit of his sepulchre but its extra weight upon him. No, friend, when Aeacus gives a man his allowance of space–and it never exceeds a foot’s breadth–, he must be content to pack himself into its limits. You might have laughed still more if you had beheld the kings and governors of earth begging in Hades, selling salt fish for a living, it might be, or giving elementary lessons, insulted by any one who met them, and cuffed like the most worthless of slaves. When I saw Philip of Macedon, I could not contain myself; some one showed him to me cobbling old shoes for money in a corner. Many others were to be seen begging–people like Xerxes, Darius, or Polycrates.
18Phi. These royal downfalls are extraordinary almost incredible. But what of Socrates, Diogenes, and such wise men?
Me. Socrates still goes about proving everybody wrong, the same as ever; Palamedes, Odysseus, Nestor, and a few other conversational shades, keep him company. His legs, by the way, were still puffy and swollen from the poison. Good Diogenes pitches close to Sardanapalus, Midas, and other specimens of magnificence. The sound of their lamentations and better-day memories keeps him in laughter and spirits; he is generally stretched on his back roaring out a noisy song which drowns lamentation; it annoys them, and they are looking out for a new pitch where he may not molest them.
19Phi. I am satisfied. And now for that decree which you told me had been passed against the rich.
Me. Well remembered; that was what I meant to tell you about, but I have somehow got far astray. Well, during my stay the presiding officers gave notice of an assembly on matters of general interest. So, when I saw every one flocking to it, I mingled with the shades and constituted myself a member. Various measures were decided upon, and last came this question of the rich. Many grave accusations were preferred against them, including violence, ostentation, pride, injustice; and at last a popular speaker rose and moved this decree.
‘Whereas the rich are guilty of many illegalities on earth, 20 harrying and oppressing the poor and trampling upon all their rights, it is the pleasure of the Senate and People that after death they shall be punished in their bodies like other malefactors, but their souls shall be sent on earth to inhabit asses, until they have passed in that shape a quarter-million of years, generation after generation, bearing burdens under the tender mercies of the poor; after which they shall be permitted to die. Mover of this decree–Cranion son of Skeletion of the deme Necysia in the Alibantid 1 tribe.’ The decree read, a formal vote was taken, in which the people accepted it. A snort from Brimo and a bark from Cerberus completed the proceedings according to the regular form.
So went the assembly. And now, in pursuance of my original21 design, I went to Tiresias, explained my case fully, and implored him to give me his views upon the best life. He is a blind little old man, pale and weak-voiced. He smiled and said:–‘My son, the cause of your perplexity, I know, is the fact that doctors differ; but I may not enlighten you; Rhadamanthus forbids.’ ‘Ah, say not so, father,’ I exclaimed; ‘speak out, and
leave me not to wander through life in a blindness worse than yours.’ So he drew me apart to a considerable distance, and whispered in my ear:–‘The life of the ordinary man is the best and most prudent choice; cease from the folly of metaphysical speculation and inquiry into origins and ends, utterly reject their clever logic, count all these things idle talk, and pursue one end alone–how you may do what your hand finds to do, and go your way with ever a smile and never a passion.’
22It was now late, and I told Mithrobarzanes that our work was done, and we might reascend. ‘Very well, Menippus,’ said he, ‘I will show you an easy short cut.’ And taking me to a place where the darkness was especially thick, he pointed to a dim and distant ray of light–a mere pencil admitted through a chink. ‘There,’ he said, ‘is the shrine of Trophonius, from which the Boeotian inquirers start; go up that way, and you will be on Grecian soil without more ado.’ I was delighted, took my leave of the Mage, crawled with considerable difficulty through the aperture, and found myself, sure enough, at Lebadea.
See Full Article at Wikipedia: https://en.wikipedia.org/wiki/Topological_data_analysis
In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools.
The initial motivation is to study the shape of data. TDA has combined algebraic topology and other tools from pure mathematics to allow mathematically rigorous study of “shape”. The main tool is persistent homology, an adaptation of homology to point cloud data. Persistent homology has been applied to many types of data across many fields. Moreover, its mathematical foundation is also of theoretical importance. The unique features of TDA make it a promising bridge between topology and geometry.
See Full Article at Wikipedia: https://en.wikipedia.org/wiki/Topological_data_analysis
“His method was inefficient in the extreme, for an immense ground had to be covered to get anything at all unless blind chance intervened and, at first, I was almost a sorry witness of his doings, knowing that just a little theory and calculation would have saved him 90 percent of the labor. But he had a veritable contempt for book learning and mathematical knowledge, trusting himself entirely to his inventor’s instinct and practical American sense. ”
See the full article at https://doi.org/10.3389/fnhum.2014.00068
Original Research ARTICLE
Front. Hum. Neurosci., 13 February 2014 |
The experience of mathematical beauty and its neural correlates
- 1Wellcome Laboratory of Neurobiology, University College London, London, UK
- 2Department of Physics, Imperial College London, London, UK
- 3School of Mathematics, University of Edinburgh, Edinburgh, UK
Many have written of the experience of mathematical beauty as being comparable to that derived from the greatest art. This makes it interesting to learn whether the experience of beauty derived from such a highly intellectual and abstract source as mathematics correlates with activity in the same part of the emotional brain as that derived from more sensory, perceptually based, sources. To determine this, we used functional magnetic resonance imaging (fMRI) to image the activity in the brains of 15 mathematicians when they viewed mathematical formulae which they had individually rated as beautiful, indifferent or ugly. Results showed that the experience of mathematical beauty correlates parametrically with activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources.
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty”
The beauty of mathematical formulations lies in abstracting, in simple equations, truths that have universal validity. Many—among them the mathematicians Bertrand Russell (1919) and Hermann Weyl (Dyson, 1956; Atiyah, 2002), the physicist Paul Dirac (1939) and the art critic Clive Bell (1914)—have written of the importance of beauty in mathematical formulations and have compared the experience of mathematical beauty to that derived from the greatest art (Atiyah, 1973). Their descriptions suggest that the experience of mathematical beauty has much in common with that derived from other sources, even though mathematical beauty has a much deeper intellectual source than visual or musical beauty, which are more “sensible” and perceptually based. Past brain imaging studies exploring the neurobiology of beauty have shown that the experience of visual (Kawabata and Zeki, 2004), musical (Blood et al., 1999; Ishizu and Zeki, 2011), and moral (Tsukiura and Cabeza, 2011) beauty all correlate with activity in a specific part of the emotional brain, field A1 of the medial orbito-frontal cortex, which probably includes segments of Brodmann Areas (BA) 10, 12 and 32 (see Ishizu and Zeki, 2011 for a review). Our hypothesis in this study was that the experience of beauty derived from so abstract an intellectual source as mathematics will correlate with activity in the same part of the emotional brain as that of beauty derived from other sources.
Plato (1929) thought that “nothing without understanding would ever be more beauteous than with understanding,” making mathematical beauty, for him, the highest form of beauty. The premium thus placed on the faculty of understanding when experiencing beauty creates both a problem and an opportunity for studying the neurobiology of beauty. Unlike our previous studies of the neurobiology of musical or visual beauty, in which participating subjects were neither experts nor trained in these domains, in the present study we had, of necessity, to recruit subjects with a fairly advanced knowledge of mathematics and a comprehension of the formulae that they viewed and rated. It is relatively easy to separate out the faculty of understanding from the experience of beauty in mathematics, but much more difficult to do so for the experience of visual or musical beauty; hence a study of the neurobiology of mathematical beauty carried with it the promise of addressing a broader issue with implications for future studies of the neurobiology of beauty, namely the extent to which the experience of beauty is bound to that of “understanding.”