Home » Discussion Forums » Blog Post Discussion » Extreme Brain Death
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| Re: Extreme Brain Death [message #46615 is a reply to message #46614 ] |
Mon, 28 November 2011 22:33   |
 Aaron
Messages: 319
Registered: June 2009
Location: California |
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Oh! Now I was always in the liberal-arts college track in school, so Experience May Vary, but what I had was the algebra-geometry-algebra II-DUCKING THE ISSUE BY TAKING EARTH SCIENCES† sequence. I was told that liberal-arts wusses like me always liked geometry best because . . . unh . . . it was the most describable in English, that is in language type language rather than maths type language.
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I have, as usual, failed be to be clear. The chronological sequence with geometry tucked in the middle of algebra is, I think, quite usual. I meant that there is a conceptual sequence of increasingly sophisticated arithmetic (can you tell this this is not my favourite part of the field?*) and that geometry is the only course in the chronological sequence that doesn't fit into the conceptual sequence. I don't know that this has to lead to a more theoretical, proof driven, approach but the enduring influence of Euclid does seem to be more felt here than in the rest of the curriculum.
The critical point for me is that talking about mathematical ideas is what mathematicians do, calculating things is was accountants and engineers do. I think that a number of students that might have made good mathematicians end up avoiding the field because they don't want to be accountants.
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I was in that class not because they had twigged that I was really dumb, but because of a scheduling conflict caused by being new to that school system. But I was happy with the dumb kids.
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I am interested to hear that this worked out. I got off sequence by skipping the second half of Algebra II and taking Trigonometry in the spring semester in a class consisting largely of seniors that had failed it the first time. For me at least, this was a mistake. While quietly playing blindfold chess in the back of the room with another student in the same situation was entertaining it has left my trigonometry at a "re-derive it each time you need it" level of proficiency. Conceptually complete, but too slow for real use. I took the failure to be a consequence of the different viewpoint of the other students (combined with my, admitted, lack of application). Your experience suggests that the instructor's contribution may have been what colluded with my failings to produce an unsatisfactory result.
*Does being rude about calculus fail the Pollyanna requirement?
[Updated on: Mon, 28 November 2011 22:39]
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| Re: Extreme Brain Death [message #46618 is a reply to message #46614 ] |
Mon, 28 November 2011 23:26 |
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L.R.K.
Messages: 1080
Registered: October 2008
Location: Sweden |
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LRK
Is it wrong that I now want to read “Attack of the Zorgs”? It sounds quite… exciting…
Well, let me see. Zorgs have rather long, elliptical bodies, with one large eye on a stalk, and three limbs variously used for handling and locomotion, each limb ending with a kind of hand with three grasping talons, and they are very fearsome warriors. . . .
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Thank you!  I was right - it is exciting - maybe too much so for me, as I'm now fighting an urge to hide under the bed...
On another topic - I spent my school years thinking I was extremely stupid - until 8th class, when we finally started to get grades, and I was quite... pleasantly surprised. (This is really a can of worms, so to stop myself from going babbling into regions unknown - one thing leading to another, I won't say anything more than that.)
Why, I feel all thin, sort of stretched, if you know what I mean, like butter that has been scraped over too much bread.
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| Re: Extreme Brain Death [message #46619 is a reply to message #46614 ] |
Tue, 29 November 2011 01:02 |
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danceswithpahis
Messages: 380
Registered: October 2008 |
Senior Member |
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I was fortunate with math to have gotten a good start in it before I knew what I was doing. My parents loved math (my dad worked with taxes and my mom was studying to be an accountant when she died [having left nursing because it was driving her crazy]), and my dad and I would do things like having contests to see who could figure out mental arithmetic problems first (we still do this). To me this seemed perfectly normal, and so I had a certain natural vaccination against the idea that I would be bad in math.
I was also fortunate in that my all-time favorite teacher was a math teacher who taught me for a couple of years (I had one semester when they switched me to another teacher because of scheduling issues, and I feel so sorry for that poor [perfectly adequate] teacher who had to listen to a WHOLE SEMESTER of me saying all the TIME, "Mr. Brown didn't do it like that!..."). He recently died from cancer, and his funeral was PACKED with former students sharing how much they had learned from him and how he had refused to give up on having them get the ideas as long as they were willing to try. I still have several of my homework assignments and tests that had lengthy epistles scrawled on them about my answers (especially if I'd make up snarky responses to story problems or something [I would show that I could do the math right, but I couldn't always resist making something else up along with that]), the state of the universe in general, or whatever else came up. I wish I could give everyone the chance to have a math teacher like Mr. Brown, preferably early on in their math careers so they can see that they can get math and enjoy it.
"Oh good! My dog found the chainsaw!"
-- Lilo ("Lilo and Stitch")
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| Re: Extreme Brain Death [message #46623 is a reply to message #46614 ] |
Tue, 29 November 2011 02:27 |
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Diane in MN
Messages: 2730
Registered: October 2008
Location: Twin Cities, MN, USA |
Senior Member |
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Only this time I’m not going to let them take it away.
I think this is a very good idea. When I get a new laptop, I plan to keep my current one around even if I only use it for those of my applications that exist, apparently, only in the XP world because their sources have dropped off the planet. And this might let me get away with not having to buy Windows 7 Pro in order to get a virtual XP environment. There are some charities that will take old computers and recycle them to new users, over here at least, but if I were going to go that route I'd take out my hard drive and smash it before the computer left the house.
what I had was the algebra-geometry-algebra II-DUCKING THE ISSUE BY TAKING EARTH SCIENCES† sequence.
Ah, useful earth sciences! I used geology to satisfy my physical science requirement as an undergraduate. I regret this now (not that I took geology, which I find very interesting, but that I dodged physics), but at that time it seemed reasonable.
"The point of books is to have way too many but to always feel you never have enough . . . " Louise Erdrich
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| Re: Extreme Brain Death [message #46624 is a reply to message #46615 ] |
Tue, 29 November 2011 03:34 |
CathyR
Messages: 575
Registered: July 2009
Location: NW England |
Senior Member |
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| Aaron wrote on Tue, 29 November 2011 03:33 |
The critical point for me is that talking about mathematical ideas is what mathematicians do, calculating things is was accountants and engineers do. I think that a number of students that might have made good mathematicians end up avoiding the field because they don't want to be accountants.
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A friend of mine has just completed a post-grad qualification as a maths teacher, and teaches in a secondary school. One of the classes she has to teach - A level Accounting! (A Levels are your final two years at school). I did think it seemed rather odd.
Just when the caterpillar thought the world was over, it became a butterfly.
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| Re: Extreme Brain Death [message #46628 is a reply to message #46614 ] |
Tue, 29 November 2011 08:56 |
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AJLR
Messages: 2566
Registered: September 2008
Location: England, UK |
Senior Member
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Part of what is so frustrating in hindsight is that even though I’ve known for years that a lot of my dislike of various subjects was in part due to bad teaching I have felt very little urge to find out how much because the belief that I am stupid lingered, like Greasy Build Up in your kitchen drains.
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Yes, that sort of effect can last decades, can't it. A while ago, when I was interviewing applicants to our (university) Access course, a pair of friends in their forties came along on one day. One of them said to me, during the interview, that she wasn't sure she would even be allowed on the campus - such was the effect that repeatedly being told she was dumb, at school, had had on her. I thought they were both immensely brave for being willing to try again, and I was very pleased to see that a few years later they both got good degrees. The damage done to some children/people by telling them they're stupid, just because a teacher can't be bothered to find a more engaging and accessible way of teaching a subject, is really criminal.
"Never let a computer know you're in a hurry."
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| Re: Extreme Brain Death [message #46644 is a reply to message #46631 ] |
Tue, 29 November 2011 21:53 |
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Black Bear
Messages: 3216
Registered: September 2008
Location: Indianapolis, IN USA |
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Lord, I hated timed tests. I'm also in the not-fast-at-arithmatic crowd (it still takes me ages to calculate a tip or divide up a dinner check in my head) and second grade was kind of a nightmare of unfinished homework and quizzes. Fortunately my 2nd grade teacher, Miss Cutler, was a real sweetheart and kept saying not to worry, just keep working at it and I'd catch up on basic math skills as I went along. My parents were a little worried--for some reason, I also couldn't tell time until well after most other kids in my class had mastered analog clock faces, and that had my parents wondering what the heck was going on. But Miss Cutler was right, and while I never got FAST at math, I more or less caught up with everyone else over the course of the next couple years... I hate to think how badly it all might have gone if she had been the sort to call a kid stupid. 
"The time is always right to do what's right."--MLK Jr.
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| Re: Extreme Brain Death [message #46646 is a reply to message #46644 ] |
Tue, 29 November 2011 22:42 |
Jacky
Messages: 34
Registered: October 2011 |
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Sigh. I was good at math and learned fast at just about everthing but fluff. Oh, and getting where I was going. I was real good at getting lost. Everyone told me I was brilliant, and because of this, I was better than others. I always had my doubts about this. My next younger sister had a hard time learning to read. these days she would be diagnosed with a learning disability. Instead she was told she wasn't too bright, but that was OK, because she was pretty. Niether of us were very impressed with either message. I knew my sister was just as smart as I was, but just learned different. But instead of looking at ways to help her learn, she was told not to bother because she was pretty. Luckily, she was both smart and stubborn. She kept trying, and working hard, and eventually graduated high school with average grades through an amazing amount of hard work. about 5 years out of school she went to be trained as a mortgage loan officer. She looked around her at the other students, and found, that not only wasn't she at the bottom of the class, she was helping her fellow students learn. And she felt smart for the first time of her life. And then not only were we proud of her, so was she. 
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| Re: Extreme Brain Death [message #46659 is a reply to message #46614 ] |
Wed, 30 November 2011 10:59 |
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Mrs Redboots
Messages: 943
Registered: October 2008
Location: London, UK |
Senior Member |
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I was fundamentally innumerate (due to poor teaching in the first few years); for me, the fact that 16 and 4 makes 20 was just something I was told and had to remember, like Henry VIII having 6 wives or Battle of Hastings 1066.
Even now, when I am knitting squares with patterns on them and have to follow instructions like K2, p20, k8, it always amazes me that every single time the stitches in each row add up to 30, no matter how you divide them up. It still seems some arcane branch of magic!
Having said that, I did get quite a good Maths O level (the exam that preceded GCSEs way back in history), but it was mainly because I'm good at learning rather than that I understood how it worked. I still don't understand logarithms, only nobody does them any more now that we have calculators, so I don't suppose anybody can explain them.
Mrs Redboots
I love my computer because my friends live in it!
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| Re: Extreme Brain Death [message #46663 is a reply to message #46614 ] |
Wed, 30 November 2011 17:24 |
judith
Messages: 246
Registered: October 2008
Location: United States |
Senior Member |
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It may be worth noting that in one sense Geometry is the most Mathematical course that most students take in the field. The arithmetic-algebra-trigonometry-calculus sequence is very useful but it is usually taught in a relatively applied way. Geometry is frequently taught from a more theoretical point of view emphasizing why things are true rather than what you can do with them.
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I've been behind in keeping up with this line of discussion, so forgive me if this question has already been answered somewhere, and please refer me to that answer.
I adored geometry in high school. I would, quite literally, spend my free time in the library doing geometrical proofs for fun. As for the rest of math -- it was taught pretty much as, do this and get that result. With geometry, it was intuitive to me what was happening and why, because it seemed to have ties to the concrete world, whereas I never quite grasped any connection between the concrete world and the rest of math, despite being given word problems; it was just, do this when you get that kind of problem. Such an approach made it so that I could never quite decide when to use what equation, etc. to solve a problem.
I have an advanced degree in the physical sciences, and at the graduate level the courses were absolutely fascinating -- delving into the fundamental nature of reality. But I would always come up short against my barely functional math skills, and thus felt that I never quite grasped things as fully as I wanted to. Courses like Newtonian Mechanics in physics are fairly easy because you can understand and visualize things like pulleys and inclined planes and friction, but when it comes to things like electricity and magnetism, I was pretty much asea because there wasn't much to visualize; it was just, use this equation and get that result. And if I couldn't figure out the correct equation to use, it wouldn't make intuitive sense to someone who understood the subject matter, but I never quite reached that level of understanding...
So -- I'm wondering if there are any books out there that explain advanced algebra, trigonometry, calculus, differential equations, matrix algebra, etc. in a way that explains WHY they work, similarly to the way that one understands geometry -- perhaps an intuitive approach as opposed to an approach that simply teaches one how to do the equations in a vacuum without any integrated knowledge of the subject. I'd love to read them and perhaps get the full benefit of my prior education (and maybe even understand the Schrodinger equation on a gut level!). I have the "For Dummies" books but haven't yet picked them up.
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| Re: Extreme Brain Death [message #46693 is a reply to message #46659 ] |
Fri, 02 December 2011 01:52 |
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danceswithpahis
Messages: 380
Registered: October 2008 |
Senior Member |
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| Mrs Redboots wrote on Wed, 30 November 2011 10:59 |
Having said that, I did get quite a good Maths O level (the exam that preceded GCSEs way back in history), but it was mainly because I'm good at learning rather than that I understood how it worked. I still don't understand logarithms, only nobody does them any more now that we have calculators, so I don't suppose anybody can explain them.
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When I was taking math classes from my aforementioned math teacher, I asked him one day about what a logarithm was. It was between classes, and he didn't really feel like explaining something he would be going into in depth in another trimester or so. Instead he drew me two pictures. One had a straight, plain log-shaped object. The other had a curvy, bending log with motion lines next to it. He explained to me with utmost solemnity, "This here's a log... and this is a log with RHYTHM!"
"Oh good! My dog found the chainsaw!"
-- Lilo ("Lilo and Stitch")
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| Re: Extreme Brain Death [message #46694 is a reply to message #46667 ] |
Fri, 02 December 2011 01:57 |
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danceswithpahis
Messages: 380
Registered: October 2008 |
Senior Member |
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| katinseattle wrote on Wed, 30 November 2011 22:36 |
| Julia wrote on Wed, 30 November 2011 05:23 |
Also, all this talk of learning and intelligence and different ways of knowing makes me think of this.
“Everybody is a genius. But if you judge a fish on its ability to climb a tree, it will spend the rest of its life thinking it’s an idiot.” -Albert Einstein.
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I've read that Einstein wasn't considered very bright in school either.
I've come to believe that everybody is good at something. The difficulty is discovering what that is. How would someone who's a brilliant jet plane pilot have done in caveman times? Some people seem to have a natural affinity for and understanding of animals. What if they'd been brought up in a city, with no pets? Et cetera.
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I've wondered about your question, but my guess is that people will generally find ways to use their gifts in the culture and society they find themselves in, unless so totally oppressed and cut off from whatever they need that they're not able to develop them. A brilliant jet pilot would find other responsibilities using quickness of mind, the ability to make snap judgments, fine motor skills that can be honed to an amazing degree, etc. Someone with a gift for animals might volunteer at a shelter, or at the zoo, or (as I did for awhile) make friends with pets. Or perhaps their gift is to be patient and kind and willing to wait rather than rush around, so they are brilliant with small children, or giving physical therapy to those who have to progress one infintesimally small and frustrating step at a time. Just my thought.
"Oh good! My dog found the chainsaw!"
-- Lilo ("Lilo and Stitch")
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| Re: Extreme Brain Death [message #46698 is a reply to message #46663 ] |
Fri, 02 December 2011 04:52 |
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3rdragon
Messages: 34
Registered: October 2010
Location: USA |
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now I am asking the students to draw pictures of what the math means and WHY they drew the picture the way they drew it. The ones that used to do well, take much longer to find the answer and those that struggled are flying past the 'more advanced math students'.
With this chat of 'earth science routes' and the different 'subjects' of math, I wonder if it's a question of HOW math is taught in the younger years.
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I adored geometry in high school. I would, quite literally, spend my free time in the library doing geometrical proofs for fun. As for the rest of math -- it was taught pretty much as, do this and get that result. With geometry, it was intuitive to me what was happening and why, because it seemed to have ties to the concrete world, whereas I never quite grasped any connection between the concrete world and the rest of math, despite being given word problems; it was just, do this when you get that kind of problem. Such an approach made it so that I could never quite decide when to use what equation, etc. to solve a problem.
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I think that what we're talking about here are different ways of thinking about math. To my mind, it's not so much a matter of how it's taught (although that is very important, and it's true that high school geometry is often taught in a manner more like college math courses, with proofs and the like), but how the student learns. Some people are conceptual numbers people, and can mold and manipulate numbers in their heads, and just know that x plus y is equal to z, without the intermediate steps of calculation, at least for small and relatively simply xs and ys. Some people need to see it in pictures, or it doesn't make sense. Some people know that it's true, but can't explain it.
I remember that when I was in sixth grade, we were using a book that wanted you to show your work and explain your answer, and I just couldn't do it. I would look at 2x=6 and know that x was 3, and at that point I didn't have the flexibility to slow down and explain the calculation; I was very straightforward, and they wanted me to show my work, and I didn't have any, I just looked at it! It wasn't that I couldn't solve equations the conventional way, but that at that point in my mathematical arc, I needed a more complicated problem to be able to explain how I solved it, because if I needed to do work, I could explain it. It took several years before I acquired the mathematical sophistication to be able to break down my intuitive processes and explain them to other people.
I remember seeing the different mathematical styles very strikingly when I was taking a Modern Algebra course my senior year of college. One of my fellow students was trying to explain to a fellow student (using a perfectly valid method) that look, if you just listed all the possibilities, you could see that this was the way it was, and that was why everything worked out -- but that wasn't the way the other girl needed it explained. She could
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