Mathematics Exam Quotes

By the time the average person finishes college, he or she will have taken over 2,600 tests, quizzes, and exams. The right answer approach becomes deeply ingrained in our thinking. This may be fine for some mathematical problems where there is in fact only one right answer. The difficulty is that most of life isn’t this way. Life is ambiguous; there are many right answers- all depending on what you’re looking for. But if you think there is only one right answer, then you’ll stop looking as soon as you find one.

What did we know? This was early days. We had no idea what was out there. How dangerous it might be. It was just a school maths problem. They never asked that in the exams, did they? Like, “If John walks at three miles an hour from London to Brighton, and he's attacked by rabid grown-ups four times, and they bite his right leg off, how long will it take him to bleed to death?

All through our education we are being taught a kind of reverse mindfulness. A kind of Future Studies where- via the guise of mathematics, or literature, or history, or computer programming, or French- we are being taught to think of a time different to the time we are in. Exam time. Job time. When-we-are-grown-up time. To see the act of learning as something not for its own sake but because of what it will get you reduces the wonder of humanity. We are thinking, feeling, art-making, knowledge-hungry, marvelous animals, who understand ourselves and our world through the act of learning. It is an end in itself. It has far more to offer than the things it lets us write on application forms. It is a way to love living right now.

The task Gordan gave her was a truly daunting one: to develop the complete invariant theory for ternary forms of degree four. Whether Gordan had ever attempted this is hard to say, but one can safely say that Emmy Noether's work was the last word with regard to this problem. She was able to construct 331 associated covariants. After finishing this ambitious work and publishing it in Crelle, she passed her oral exam "summa cum laude", but later dismissed her dissertation as a piece of juvenalia (she once called it "dung").

The fact that no one made demands on her knowledge in her special field was lucky for Simochka. Not only she but many of her girlfriends had graduated from the institute without any such knowledge. There were many reasons for this. The young girls had come from high schools with very little grounding in mathematics and physics. They had learned in the upper grades that at faculty council meetings the school director had scolded the teachers for giving out failing marks, and that even if a pupil didn't study at all he received a diploma. In the institute, when they found time to sit down to study, they made their way through the mathematics and radio-technology as through a dense pine forest. But more often there was no time at all. Every fall for a month or more the students were taken to collective farms to harvest potatoes. For this reason, they had to attend lectures for eight and ten hours a day all the rest of the year, leaving no time to study their course work. On Monday evenings there was political indoctrination. Once a week a meeting of some kind was obligatory. Then one had to do socially useful work, too: issue bulletins, organize concerts, and it was also necessary to help at home, to shop, to wash, to dress. And what about the movies? And the theater? And the club? If a girl didn't have some fun and dance a bit during her student years, when would she do so afterward? For their examinations Simochka and her girlfriends wrote many cribs, which they hid in those sections of female clothing denied to males, and at the exams they pulled out the one the needed, smoothed it out, and turned it in as a work sheet. The examiners, of course, could have easily discovered the women students' ignorance, but they themselves were overburdened with committee meetings, assemblies, a variety of plans and reports to the dean's office and to the rector. It was hard on them to have to give an examination a second time. Besides, when their students failed, the examiners were reprimanded as if the failures were spoiled goods in a production process—according to the well-known theory that there are no bad pupils, only bad teachers. Therefore the examiners did not try to trip the students up but, in fact, attempted to get them through the examination with as good results as possible.

The modern educational system provides numerous other examples of reality bowing down to written records. When measuring the width of my desk, the yardstick I am using matters little. My desk remains the same width regardless of whether I say it is 200 centimetres or 78.74 inches. However, when bureaucracies measure people, the yardsticks they choose make all the difference. When schools began assessing people according to precise marks, the lives of millions of students and teachers changed dramatically. Marks are a relatively new invention. Hunter-gatherers were never marked for their achievements, and even thousands of years after the Agricultural Revolution, few educational establishments used precise marks. A medieval apprentice cobbler did not receive at the end of the year a piece of paper saying he has got an A on shoelaces but a C minus on buckles. An undergraduate in Shakespeare’s day left Oxford with one of only two possible results – with a degree, or without one. Nobody thought of giving one student a final mark of 74 and another student 88.6 Credit 1.24 24. A European map of Africa from the mid-nineteenth century. The Europeans knew very little about the African interior, which did not prevent them from dividing the continent and drawing its borders. Only the mass educational systems of the industrial age began using precise marks on a regular basis. Since both factories and government ministries became accustomed to thinking in the language of numbers, schools followed suit. They started to gauge the worth of each student according to his or her average mark, whereas the worth of each teacher and principal was judged according to the school’s overall average. Once bureaucrats adopted this yardstick, reality was transformed. Originally, schools were supposed to focus on enlightening and educating students, and marks were merely a means of measuring success. But naturally enough, schools soon began focusing on getting high marks. As every child, teacher and inspector knows, the skills required to get high marks in an exam are not the same as a true understanding of literature, biology or mathematics. Every child, teacher and inspector also knows that when forced to choose between the two, most schools will go for the marks.

Interestingly enough, creative geniuses seem to think a lot more like horses do. These people also spend a rather large amount of time engaging in that favorite equine pastime: doing nothing. In his book Fire in the Crucible: The Alchemy of Creative Genius, John Briggs gathers numerous studies illustrating how artists and inventors keep their thoughts pulsating in a field of nuance associated with the limbic system. In order to accomplish this feat against the influence of cultural conditioning, they tend to be outsiders who have trouble fitting into polite society. Many creative geniuses don’t do well in school and don’t speak until they’re older, thus increasing their awareness of nonverbal feelings, sensations, and body language cues. Einstein is a classic example. Like Kathleen Barry Ingram, he also failed his college entrance exams. As expected, these sensitive, often highly empathic people feel extremely uncomfortable around incongruent members of their own species, and tend to distance themselves from the cultural mainstream. Through their refusal to fit into a system focusing on outside authority, suppressed emotion, and secondhand thought, creative geniuses retain and enhance their ability to activate the entire brain. Information flows freely, strengthening pathways between the various brain functions. The tendency to separate thought from emotion, memory, and sensation is lessened. This gives birth to a powerful nonlinear process, a flood of sensations and images interacting with high-level thought functions and aspects of memory too complex and multifaceted to distill into words. These elements continue to influence and build on each other with increasing ferocity. Researchers emphasize that the entire process is so rapid the conscious mind barely registers that it is happening, let alone what is happening. Now a person — or a horse for that matter — can theoretically operate at this level his entire life and never receive recognition for the rich and innovative insights resulting from this process. Those called creative geniuses continuously struggle with the task of communicating their revelations to the world through the most amenable form of expression — music, visual art, poetry, mathematics. Their talent for innovation, however, stems from an ability to continually engage and process a complex, interconnected, nonlinear series of insights. Briggs also found that creative geniuses spend a large of amount of time “doing nothing,” alternating episodes of intense concentration on a project with periods of what he calls “creative indolence.” Albert Einstein once remarked that some of his greatest ideas came to him so suddenly while shaving that he was prone to cut himself with surprise.

More where do you see yourself in a few years’ time? More what career path would you like to pursue? More think very carefully about your future. More it will all pay off in the long run. All through our education we are being taught a kind of reverse mindfulness. A kind of Future Studies where—via the guise of mathematics, or literature, or history, or computer programming, or French—we are being taught to think of a time different to the time we are in. Exam time. Job time. When-we-are-grown-up time. To see the act of learning as something not for its own sake but because of what it will get you reduces the wonder of humanity. We are thinking, feeling, art-making, knowledge-hungry, marvelous animals, who understand ourselves and our world through the act of learning. It is an end in itself. It has far more to offer than the things it lets us write on application forms. It is a way to love living right now. I am coming to realize how wrong many of my aspirations have been. How locked out of the present I have found myself. How I have always wanted more of whatever was in front of me. I need to find a way to stay still, in the present, and, as my nan used to say, be happy with what you have.

I agree with John Holt that the true test of intelligence is not what you know or can regurgitate from memory on an exam. It’s not what you know how to do, but “what you do when you don’t know what to do.” Harold Gardner has convincingly shown that we have eight or nine different kinds of intelligence. Unfortunately we only measure literacy and mathematical intelligence for our IQ.

On the SAT exam, boys who took the test during 1988–89 at Permian had a combined average score of 915 (433 verbal, 482 mathematical), 19 points below the national average for boys. Girls had a combined score of 840 (404 verbal, 436 mathematical), 75 points below their male counterparts at Permian and 35 points below the national average for girls. Of the 132 girls who took the test during the 1988–89 school year, there wasn’t one who got above a 650 in either the math or verbal portions of the exam.

Mathematically: moment = weight 180 lb × arm 85 in. = 15,300 lb-in, or 153 mom/100. Nontabulated Weights For nontabulated weights, it will be necessary to interpolate when using the tabular data. For example, find the mom/100 for a passenger weighing 177 pounds in the rear seat. There are several ways of interpolating, as follows: for a difference of 10 pounds between 170 pounds and 180 pounds, there is a mom/100 difference of 12. A moment/100 difference of 12 for 10 pounds = 1.2 per pound—therefore, for 7 pounds = 7 × 1.2 = 8.4 mom/100, plus the 206 gives 214 mom/100; or for a difference of 7 pounds between 170 pounds and 177 pounds, there will be a mom/100 difference of 7/10 of 12 = 8.4 (say 8), and for a weight of 177 pounds, the mom/100 = 206 + 8 = 214. Note. For nontabulated weights, or for weights outside the table, it is easier to use the mathematical method to find the moment index. Weight-Shift Calculations If, after calculating the weight and balance, you find that the CG is outside the limits of the CG range, it will be necessary to shift some weight to bring the CG position back within limits. Note. The tabulated method shown here does not require the use of a formula. Some instructors prefer to use a formula for weight-shift and weight-change problems. We discuss the formula method at the end of this chapter in the section for commercial pilots. Example 11-5 You have calculated the total weight to be 4,000 pounds with the CG located at 100 inches aft of datum. What is the new CG position if you shift 50 pounds of baggage from the rear baggage area at station 200 to the forward baggage area at station 50?

A classroom library containing both fiction and non-fiction books should be located centrally, and include newspapers, magazines, telephone books, restaurant menus, etc. Teachers should also integrate literacy across the curriculum by reading and assigning texts that support their learning units in subjects such as mathematics, sciences, and social studies.

What was the importance of this exam? It enabled a young man or woman to study at a university, to go into a profession. My inclination was toward medicine but there was no faculty in town and there were no chances to be admitted in Bucharest. The faculties of medicine and engineering were practically closed to Jewish students. A strict "numerus clausus" assigned a tiny percentage to Jewish applicants, perhaps two or three percent of an incoming class. That left law and teaching as the only choices. The chances became remote that one could even teach at a state school, thus one chose to study languages, mathematics or law. In case of emigration, languages and math were useful skills. School became the outside world that hardened you for the years to come. I registered as a student of foreign languages: French, German and I started to study English.

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