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Everything posted by mathwonk

  1. I'm so happy you found some help for this. The only thing I know is to repeat some positive affirmation when a trigger strikes. But in reghard to this thread, in my opinion there is no work of art so important that it should be attended to if it is a negative trigger.
  2. This thread has me wondering why and which things disturb me. I thought it was visualness that is so powerful but realized last night that some tv shows I encounter a lot offer the same disturbing images I recall from 60 years ago, but now they don't stay with me. So maybe it has to do with the age we encounter them, as you all probably know well. Maybe I have learned now to "look away" both mentally and physically so as not to store up these images, whereas as a young child I was very focused on taking in the content in a naive wondering and fascinated way. As a child I also read some content over and over. I say these things in hopes of suggesting to people how to help children avoid embedding these disturbing images in their brains.
  3. This thread has me recalling my childhood acquaintance with that book in some detail. I saw the black and white movie, and read the illustrated comic book, and eventually read the novel itself, the first and last perhaps as an adult. Interestingly, I do not recall any lines from the novel and only one scene from the movie, but can recall rather faithfully the illustrations from the comic book, even the colors of the characters' clothing, their facial expressions, and the gory details of the bad stuff. This is over 60 years later. The good news is they don't scare me any more. But young memories are really strongly impacted by these things, in my case especially visual memory. So judicial editing may be prudent.
  4. I liked Pickwick papers, Our mutual friend, Great Expectations, David Copperfield (and the WC Fields movie version), you know, come to think of it, in spite of the pleasure i derive from the brilliant descriptions of people's behavior and manners in Dickens, he does depict a lot of sadness. one can skip it with my blessings. Or read him selectively. I always suggest to those who find Moby Dick intolerable, just read the first delightful chapter and quit there. "And I never slept better in my life."
  5. My thoughts: Nothing that causes trauma is essential reading. Its just a book. Even without childhood associations some events from that novel gave me bad childhood dreams, that I can still summon up. If your daughter reads it just tell her you don't care to discuss that one because it is too unpleasant. Someone else can handle that task.
  6. I agree with putting everything on there. I had a colleague who did this and I ridiculed it until I noticed he eventually won every kind of reward we could give. Think of all the actors you have heard described as an academy award nominee. This does also remind me of our favorite recommendation letter for my brilliant mother in law as a nursing student, that ended up "and she is always just as neat as a pin!" The webpage management has changed here but in the old days I think I had a picture on my profile of a second place high school geometry contest certificate. Of course it was sort of a joke, but that doean't mean I wasn't proud of it.
  7. We all have topics we prefer not to dwell on in our reading or conversation. In my childhood home in Tennessee I learned early on about the mass infanticide that motivated the flight from Egypt and the earlier one that is commemorated in the feast of the passover, but was shielded from awareness of 19th century scientific ideas like the theory of evolution. It is also unavoidable that in present day America depictions and discussions of violence and pathological sexual behavior seem almost ubiquitous and even accepted, at least in the media. It is extremely challenging to some of us at least to find a watchable tv show at night. Moreover it seems we have no chance of keeping our children from exposure to ideas and stories we and they may find disturbing, whether they meet them in school or from friends or on tv, movies, books or online. Still I think we can provide an example in our own homes and our conversation of avoidance of unpleasant and disturbing topics, and focus on stimulating and positive ones, so that when they come away from those other influences, they will know they have a choice to create and maintain a cleaner and more enjoyable environment in their own lives than the one imposed from outside. So I am suggesting we not worry too much about what they are asked to read, but how they see us live. Just a thought on this somewhat difficult topic.
  8. i like the interplay between algebra and geometry. euclid (especially in Book 2) uses geometry to make algebra visual. e.g. the algebraic process of squaring is called that literally because you take the length you want to square and you make a square out it, by using the same length for the height as for the width of the square. And then the algebra formula for (A+B)^2 becomes an expression for a square made out of a length equal to A+B. In the geometric picture you can see how there are two smaller squares inside the (A+B) square, namely an A square and a B square, and most beautifully of all you can see the two AxB rectangles along the sides that are needed to fill up the (A+B) square. Without this picture lots of kids are doomed to wondering whether (A+B)^2 equals A^2 + AB + B^2, or A^2 + 2AB + B^2. As regentrude suggested a "cylinder" is actually a general construction, composed of vertical lines erected on a given base. If the base is a circle it is a (usual) circular cylinder, but the same volume principle applies to all cylinders (sometimes called prisms) - namely the volume is just the area of the base, whatever it is, times the height. A book about a country kentucky teacher I liked, called The thread that runs so true, by Jesse Stuart, tells of a country man not wanting his boy to attend school but to stay home and work, and driving his wagonload of coal to the school to say so. The teacher takes time to ask the man if he knows how much coal is on his wagon, and he doesn't but he knows how much he is usually paid for the load. The teacher does the math for him, the volume of the wagon times the price of coal, and he learns he has been cheated every time he sold his coal. Of course he leaves the child at the school. There are infinite ways algebra and geometry enhance each other, and that geometry is useful in everyday life, designing a house, estimating how much of something to buy for any given job.... I liked regentrudes examples very much. A more subtle volume formula is for a cone, whose volume equals 1/3 of the area of the base times the height, but this formula too holds no matter what shape the base has, as long as the solid is made by joining all point of the base to the same vertex by straight line segments. If you can visulaize what Archimedes meant when he said a ball is merely a cone whose base is its surface and whose vertex is its center, you can see why the volume of a spherical ball equals 1/3 of the product of the radius and the surface area. (Well a ball is formed by joining every point of the surface to the center, by a radius.) More basic, is understanding why area formulas are expressed in terms of the square of the length involved and volume formulas are expressed in terms of the cube. Without this simple insight many college students do not know whether the volume of a ball of radius R is a multiple of R^2 or of R^3. Euclid knew this much, but I believe it fell to the great Archimedes to actually supply the constant multipliers. Unfortunately geometry is often taught simply as memorizing instead of understanding geometric ideas. Jacobson is a good source as is the book for elementary school teachers by Sybilla Beckmann. Of course, as in all cases, we don't use in life anything we don't understand, but we do find ways to use things we do. When my young son took a math contest after studying algebra with me at home I asked if the test required algebra, and he said "you don't need algebra for this test, but if you know algebra you can see ways to use it." Oddly, considering the reputation of gemetry for proofs among laypersons, many mathematicians regard geometry as the source of intuition compared to algebra as the realm of precise logical argument. There has a been a powerful movement in the mid 20th century to render geometry more rigorous by translating it entirely into algebra. I love the famous reaction to this by the great mathematician Herman Weyl (I remind that topology is the most fundamental form of geometry): "In these days, the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics." You may know I am a professional algebraic geometer, and if I knew more literature and philosophy, I could probably make a more compelling argument.
  9. I raised my kids to be pacifist, in particular I did not let my son take karate when he wanted to. Some years later. I changed my mind, I should have put him right in that karate class. Fortunately he learned on his own to take care of himself. But if I had let him learn self defense while young, as well as the proper use of that ability, I do not believe he would have become a bully, he would have just been able to stop this kind of nonsense sooner. One childrens' book on this topic I enjoyed as a parent, was titled I believe "A bundle of sticks": http://www.amazon.com/Bundle-Sticks-Pat-Mauser-McCord/dp/1880336863/ref=sr_1_1?s=books&ie=UTF8&qid=1444348491&sr=1-1&keywords=a+bundle+of+sticks There is a very instructive scene in that book where the youngster goes to a drive - in with his karate instructor and witnesses that trained fighter avoid confilct with some bullies rather than beat them up unnecessarily. But who knows the answer to all problems that arise? I agree with your decision to take the child out of that school. Something is wrong there. There seems absolutely no reason to remain in a pathological environment. They may even deserve to be investigated. I have read more of the story and I sympathize, but in my opinion, no matter how needy that bully is, he doesn't benefit from taking it out by hitting another kid. Just my opinion. [edited] And I have learned something here. I used to always say I hated bullies, but now I will say only I hate bullying, for you have taught me even bullies may be pitied.
  10. reminds me of the student (whom i have told of before) in my college "honors" calculus class who, when she got a 94 on the first test of the quarter, said "i don't like the way this is going", and dropped out. In particular I want to argue against the idea that teaching people more, while giving them lower grades is "hurting" them. I realize there are other situations, such as honors based on grades, but e.g. when a professor assesses a student for admission to an advanced class, he/she usually just interviews the student to see what they know, rather than mindlessly looking at their gpa. and it is for precisely the reason we are discussing here that the gpa does not carry useful information. sorry, getting down now from stump.
  11. To me if children are interested early there is no problem in letting them go as far and fast as they want. I myself, and my older child, just learned on our own from looking at the words while being read to. The only problem arises when, like one of our others, they don't want to read for a long time after you think they should have started, like years and years, and their skills are behind. I began to try teaching early from the materials i had inherited from my kindergarten teacher parent, but he hated it and it went nowhere, so i gave up for years. (The child may have thought that if he learned, we would stop reading to him.) Still I agree the only way they will really read is if they are interested, so eventually, much later than any of your kids described here, I tried to find reading material that was interesting for that child, and in this case I got him a subscription to sports illustrated, the only topic of interest at that time. now years later that child reads infinitely more than i do, maybe more than the other early reader, and even gives me stuff to read that i never get through (like social anthropology). he also writes unusually well and creatively, moreso than the rest of us.
  12. when i saw it as a kid, both the monkeys and dorothy hamilton's witch character scared me too near the end, but when she got melted i think i breathed a sigh of relief. do you guys remember when people read "grimm" fairy tales as young children? those were pretty scary too i recall. also disney's snow white, bambi, etc..., not to mention the old testament, which however i recall was reserved for much older reading.
  13. To me, area of a rectangle is exactly the same as understanding multiplication, since in at least one conceptual approach to multiplication you multiply say 3 times 4 by drawing a rectangle with 4 rows of 3 blocks in each row and show that the area is the same as the product 3x4. So this is a case where conceptualizing one process spills over and enhances and teaches another one. I.e. this is a wonderful example of the benefits of asking why. In this case one relevant "why ?" question relates to commutativity of multiplication, or why 3x4 = 4x3. In the rectangle appropach one observes that the area of the rectangle, or the total number of blocks making it up, can be counted by rows or by columns, and the result is the same. i.e. 4 rows of 3 blocks each equals 3 columns of 4 blocks each. I love this geometric stuff, it makes it so visual. By the way many of you know Euclid treated algebra this way, illustrating (a+b)^2 = a^2 + 2ab + b^2 by showing a square with sides of length a+b and how this decompoises the big square into teo smaller squares, one with side a, and one with side b, and there are 2 axb rectangles left over. I did not learn that until I was a senior in college, from a class in psychology of learning given by Jerome Bruner.
  14. I had fun teaching ideas like "regrouping" for addition, from Beckmann. I came up with other ways to illustrate it like using English money denominations to change a large number of pence into shillings and pounds and so on. Also using cartons and cases of different capacities to pack a large number of empty pop bottles. I had never learned elementary arithmetic myself sytematically as a kid and this was quite helpful to me as well. Her book has a lot of challenging problems for the child to think through, such as going to a party, shaking everyone's hand once and asking how many hand shakes that takes.
  15. I don't know Van de Walle's book but I agree with the idea to use a book for teacher training. The one I know and have used is by my colleague Sybilla Beckmann. I once read it was very highly rated by some professional organizations. Here also is a used copy at a cheap price. I know only the book, not the activities manual. This 2nd edition is only $4, while the 4th edition would cost $142. In my life long teaching experience, earlier editions are almost always actually better. The two books recommended may have slightly different perspectives, since Van de Walle had a PhD in mathematics education and Beckmann has hers in pure mathematics, specializing in arithmetic algebraic geometry. At a certain point in her career she switched from research in algebraic geometry to research in elementary education, maybe about the time her own children began to learn math. The two books may complement each other. http://www.abebooks.com/servlet/SearchResults?an=sybilla+beckmann&sts=t
  16. still kicking myself for giving away my copies of jacobs' books when i moved, but a lot of things just had to go. somewhat foolishly i kept mostly the advanced books (for my own learning), whereas now it is the elementary ones i need for teaching. moving is traumatic. I was thinking of posting something like this too: "maybe this seems nuts, and probably is nuts, but the algebra book Elements of Algebra, by the great mathematician Euler actually covers more bases than almost any book you can find and does so in a supremely masterful way. The obstacle is that he uses advanced language, i.e. "big words" like enumeration, diminution,....,as opposed to "counting, getting smaller",..., but he explains absolutely everything, from the meaning of mathematics to addition and subtraction and logarithms and fractions, etc etc...." But when I looked at it, I did find a couple small mistakes (claiming that sqrt(a).sqrt(b) = sqrt(ab), in all cases, when this fails for complex numbers, i.e. there is no getting around the fact that sqrts have two possibilities and there is no consistent way to choose just one and still make that formula true) and so I thought you would have to hand - hold a lot through this book to explain the meaning of the words. But if you want to do that, it would be a fantastic experience. He wrote it for his butler it seems, who knew no mathematics. But Jacobs needs very little supplementation and your "plate" is probably quite full as it is. And Jacobs is not so much work as fun. It is apparently proven scientifically that the "sesame street" approach, of making it all fun, actually increases learning. Although not exactly fun, Euler is at least charming, with problems about milk maids selling cheeses and so on, at least for us second generation farm children.
  17. I always recommend Harold Jacobs' Elementary Algebra, but it is hard to find and pricey now. Still a library may have it. https://www.rainbowresource.com/proddtl.php?id=010026&subject=Mathematics/10&category=Elementary+Algebra+%28Jacobs%29/2235
  18. I second using the computer to blow up things. I had a student with very poor eyesight in a graduate math class and I wrote notes for the class and just blew his way up. His handwriting, in his twenties, looked like a very young child's crayon writing. In his case ultimately he was unable to manage the graduate PhD course in pure math but later became a Bill Gates scholar and got one or two advanced degrees from Cambridge in England. He is a computer whiz, and his firts project was to program a speaking program on a computer to have a southern accent to make it sound more human and less robotic, since he had to listent to it all the time for his lessons. Think Steven Hawking with a more rounded and pleasing accent.
  19. I taught for 37 years and I once missed a class from just forgetting to go. (I never missed one from commuting 2 hours one way every day.) My day was so busy, and I had students and other professors coming in with questions at any time at all, and I just started talking with them and sometimes forgot about the time. Your job is just to be there all day with your door open and dealing with everything that comes in as it comes in, so it can be hectic, and at our school there were no bells to remind you of the class changes. Still it only happened once in 37 years, and it certainly was not the first day, which is kind of hard to forget about. (Of course sometimes you come in on day one and your schedule has been changed the night before and you only find out that morning.) It kind of hurt my feelings that no student came up one floor to my office to see why I hadn't come down to class, since they all knew me pretty well by then, but perhaps some were glad to get a holiday.
  20. Here is a nice story about a presumably high IQ kid, Ken Ono, who struggled to find his place and earn it. We apparently missed out on him at UGA by not offering him a tenure track job before he was famous. But since he is apparently happy now where he is, I am happy for him. He seems to be a great mentor, and has some comments on the importance of recognizing talent that may not be apparent from test scores (his own grades were not that good from lack of effort and motivation), and then nurturing it. There may be some lessons on how to motivate a bright kid who does not necessarily want to follow what seems to the parent like his obvious path. http://www.emory.edu/EMORY_MAGAZINE/issues/2015/summer/index.html
  21. I have been thinking about this more while hauling wood. It seemed to me that IQ tests I am familiar with measure usually ability to see patterns, learn word meanings, understand written passages, and in olden times make analogies, and do all of these quickly. Hence I am not sure that a high IQ helps someone empathize with others, understand whom to trust, incorporate wisdom into life choices, understand body language, appreciate art or natural beauty, realize what motivates people, summon courage, exhibit tenacity, control anger and frustration, show gentleness, have patience, or even express oneself clearly. Thus the qualities involved are somewhat technical, and maybe less important compared to what makes one successful and happy in life. I don't regard a high IQ as a handicap, it just may not necessarily take one very far in the long journey. As a trivial analogy it may be like being given more money than someone else, but not necessarily knowing how to manage it well. High IQ kids are perhaps most at an advantage in school, and life is mostly lived out of school. There are differences I think between formal intelligence, judgment, and wisdom, not to mention character, and the latter ones are perhaps more essential. I apologize if this seems silly.
  22. If IQ measures qualities that are already obvious, like visibly quick and/or early learning and large vocabulary, I don't see what difference it makes to have it verified by an IQ test, unless you are trying to document it for admission to a program. But in one case I know of, there were two siblings, one quick and verbal with a steel trap memory, and the other slow and dreamy and forgetful. One was thought to have a high IQ and the other not. When testing showed both had almost exactly the same (pretty high) IQ, the parents began to search opportunities for them both that might have been limited to the first one. Thus the test gave useful information that benefited the child and affected the way they were treated. (The two children had different types of giftedness it seems, the second one having more of the Paul Torrance "creative" giftedness, and the first more of the usual kind that teachers notice more.) After learning a child has a high iQ, one useful result is knowing it will be work for the parent to keep him/her challenged. If this is not done, they run the risk of growing up intellectually lazy, from school work being too easy. So this is important information. Some of the most brilliant students I had in college were so lazy they could not succeed, from an almost total commitment to never working hard, presumably learned early as a part of their identity as "gifted". These cases struck me as sad and a waste. This is my immediate take on the matter, from the viewpoint of a teacher and parent, but everyone's experience is unique.
  23. Boy I'm glad I don't have to take these tests. When I clicked on a link above to peruse the practice materials, I learned I would need a calculator which I don't have, I considered some of the reading comprehension questions entirely a matter of opinion and fairly undecidable, and the math question #8. on page 16, seemed to me completely wrong. I.e. the graphs of the functions f(x) = x-3 and g(x) = (x^2-9)/(x-3) have none of those properties. Probably a typo and g(x) should have been (x^2-9)/(x+3), but I would think that would have been caught before now. Then the answer would have been (E). Of course I am often wrong myself, but I thought about this twice. Please correct me if it is my error. But maybe too much effort was spent by the booklet editor choosing photos of people smiling and running and jumping, instead of having the content checked for accuracy. Brave new world. Good luck in it. This may not be relevant, but I am trying to suggest that college professors like me have little respect for whatever these tests are measuring, and I hope they do not play a huge role in admission decisions. On the other hand maybe this is why my students in college math classes had so little clue as to how to succeed. This is kind of a catch 22 for those of you navigating these waters, if admissions is based on these things, while college success is more related to deeper understanding, such as obtained by working through AOPS courses. On the topic of quick short answer responses versus lengthy thoughtful investigations, I would suggest also that spending time in advance in lengthy thoughtful investigations increases ones speed at answering short timed questions. I.e. things you have spent a long time thinking through come back to you more quickly on a test. So I believe that deep AOPS courses are good preparation even for the sort of shallow timed questions found on an SAT test. Of course some practice at working quickly on such questions is also advised. So I recommend spending the most time in careful, thoughtful study, and then spending some time tuning up for a specific test. It has been over 50 years, but my own preparation was to take all the solid math classes available, then participate in competitive math team contests regularly. Afterwards these SAT math tests, subject as well as quantitative, were a walk in the park; (and we only took them once). Of course the fact that calculators are now recommended or required is a change, and I cannot think of any mathematical reason for this. I never allowed calculators in my college math classes. So you have to be guided by todays conditions, but I still want to tilt on the side of learning the content, augmented by practicing the format.
  24. I want to acknowledge that there are times when the vita, or resume, is the primary tool for conveying ones value to others. I remember once while young being on leave from my own university to a top level research institution where there were several world experts in my field. While there I simply spoke with these men and communicated to them what I was doing and received their personal response. If they seemed pleased with my results that was all I cared about, and I often did not even bother to write them up or publish them. They were pleased, and even seemed poised to offer me a job, but in the end I returned to my original department elsewhere with few if any senior people to talk to who understood my work. In this setting my accomplishments were evaluated by looking at my vita and counting publications, which at that point barely existed. I thought it should be sufficient that I received numerous outside invitations to speak to distinguished national and international audiences, but this did not seem to count much. Eventually a friend drew me aside and pointed out that although people there thought I was a good faculty member they had nothing to show their superiors to document my value, and that I needed to publish my work in accepted channels. I began to do this and this critical stage passed. In that environment, which is probably the normal working environment, I seemed to notice that people were recognized and rewarded based on paper documentation of works sometimes more than on what was discernible from talking to them, and I was puzzled a bit. In particular it was challenging, and occasionally impossible, to make a case for promotion of even a brilliant individual whose value could only be gleaned from conversation with him/her. Sometimes what worked in such instances was a joint project between two workers, one of whom was less reluctant to write the work up for publication. Of course this might be taken as an argument not to try to survive in an environment where your advancement depends on people who do not understand what you are doing, but sometimes you may have little choice.
  25. In cases of admissions decisions to grad school where I have not met the student, I do consider where they went to college, but i consider far more what the professors at those colleges whom I know say in their letters. Those are the people who have spoken to and taught the student. Sometimes afterwards we also interiew the student. I am saying that personal impressions by professionals are more important than paper qualifications. In cases where we do not have real impressions, we rely on paper ones. In such cases I have often been sorely disappointed. Mostly I am trying to say actual qualifications, in terms of visible talent, and demonstrated accomplishments, really do matter more than paper qualifications. I admit I am unusual, in that for example when serving on the hiring committee I attended research talks at meetings where job candidates would speak, and took notes on their abilities, so that when they applied I would know something about them beyond what was written. And there are certainly cases when the resume helps the less able student get a leg up, but this is usually only temporary, until the ability or lack of it becomes visible. I recall cases where someone from an elite school was hired and introduced to the department with great fanfare, and some people from lesser known schools were introduced with much less enthusiasm. Some time later, the capable ones from the minor name schools were still there, and the less capable ones, from the fancy schools, were gone. Of course it is right to pay attention to the resume, as students deserve written credit for what they do, but eventually talent will out. A related quote comes to mind by the great chess master Aaron Nimzovitch on the contrast between reputation and ability: roughly, and from aged memory after 45 years; "criticism can do many things, e.g. embitter the existence of young talent, but one thing is not given to it, it cannot permanently forestall the incursion of powerful new ideas." When I was a young professional, and wanted to impress people at schools I attended, I was concerned about my publications. My own advisor however told me bluntly was that what people I met would evaluate was not my publications, but me.
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