Maths curious by fdjerue7eeu


									Maths curious

 curious about mathematics education in the world

  1, curiosity is a valuable asset of mathematics education
, An important assessment of
  International Assessment of Educational Progress, according to the Organization 21
countries of the world survey of Chinese children's computing power is the world's
strongest. The survey also showed that China's middle school students in the school
time to do the math a week, 307 minutes, while other countries only children learn
mathematics of the time 217 minutes. Sadly, the Chinese students for the curious - the
wealth of the Mathematics Education "computing world" to pay not only time but also
at the expense of children's creativity. Their creativity in all the countries participating
in the survey ranked fifth from the bottom. Primary and secondary students in that
they have curiosity and imagination, only 4.7%, develop their imagination and
creativity and hope, only 14.9%.
, An important case
  In recent years, the world of mathematics there is a great achievement that the
British Wiles proved the French mathematician Fei Mati out more than 360 years that
no one can prove the "Fermat Theorem. " What is "Fermat's last theorem" mean? We
all know that commercial high-theorem, right triangle is equal on both sides of the
square and the square of the hypotenuse. 360 years ago, the French mathematician
Fermat, had raised such a doubt, the square set up, then set up not to set up 3 power, 4
power establishment is not set up ... ... He believes that, in n is a natural number
greater than 2 when no positive integer solution. This provoked a lot of people to
prove. 360 years, thousands of Fermat's problem "proof", but none holds water. This
is a mathematical problem. To 1953, the United Kingdom Wiles born,. In his 10 years
of age, the teacher taught him when the business of high theorem, telling him there is
a "Fermat's last theorem", that this is a world math problems. Under the influence of
the teacher, the 10-year-old child on the interest generated on this issue, from very
fond of mathematics, study mathematics, eventually became a mathematician. In 1985,
he made a professor at Princeton University. Over the next seven, eight years, he has
not published an article, what the meeting could not see him, everyone says that as a
young man ran out of his head, he disappeared. But after some years he finally solved
the "Fermat's last theorem."
, An important conclusion - curiosity is a valuable asset of Mathematics Education
  great story to inspire us, makes us feel that students who, without all-rounder, all
talented. The minds of students is not a container of knowledge, but wisdom fire.
Each student's fire is not the same, teachers, parents, students obliged to bring the fire
ignited. Wiles of the fire was lit teacher. Therefore, we feel that this will arouse the
curiosity of students to teachers is very important.
  former President of Fudan University, Shanghai, Professor Yang Fujia 600 teachers
have to make a report. He asked, did not know the business here have high Theorem?
We all raised their hands. He asked, who knows, "Fermat's last theorem", 11 people
raised their hands. He asked, speaking operators who told the students high Theorem
"Fermat's last theorem," and this theorem has not yet solved, is the world's problems,
only a single hand. Generated curiosity in young students, interest in his life are useful.
We go to see those inventions, they were young have a story. And in our current
examination system, making some of our young people, all in the passive learning,
through training to do title. This situation must change. We should allow students to
live a happy young man, has a strong interest in, full of curiosity.
  at the same time, students interested in doing a lot of problems and can not be simply
denied. For example, in high school, a student is very interested in a summer 1000 to
do a math problem, although not to play, but very helpful to this student. Since then,
the students are not afraid of math, and while the students also received training in
logical thinking, obviously, this is a lifetime. The question now is, by the impact
college entrance examination system, students learn to become passive, not interested
in the problem solving training, which denied the younger generation's curiosity and
  Professor Yang Fujia believe that our education, lack of curiosity lead and guidance,
while Western countries are much better than us in this regard. Eton College in the
UK is a teacher to a student. Oxford, Cambridge in the last century on the
implementation of the tutorial system. Professor Yang Fujia appreciate their words:
teacher smoking (Professor Yang Fujia is not in favor of teacher smoking), continue to
inhale the spray to the student who has been sprayed on the fire ignited their hearts.
Therefore, we say that curiosity is a valuable asset of mathematics education.
  second important task of mathematics education - stimulate children's curiosity
, Tends to infinite curiosity is a treasure
  curious child's nature may be. When the three-year-old child, when, if the parents
took him to the outskirts of every day to let him in touch with nature to observe the
ever-changing nature. Sometimes, parents Abstract flower to flower cut open and
explained, and sometimes catch insects, and taught him knowledge of insects, of
course, parents should be very easy to understand explanation, in case he did not
understand the question, Parents will be honestly told his son: I do not understand this
question, let us find the answer right.
  In general, occur when a child's curiosity after all sorts of questions will be raised,
although many parents would not refuse, but often is casually perfunctory, not to be a
teacher like his father did , with their children do not understand the problem and find
the answer, they did not know that these half-hearted, actually kill the child's thinking
ability, but not until after school, they found that their children not doing well, began
to worry. But how can they afford their own memories of what the first move?
  for our children we should have very good patience and responsibility. When I took
to the streets, do not bother and put their children at home, we can use the shopping
streets of the opportunity to work with street children, their children will pay attention
to observe the magic of things.
  as the bus, we can automatically switch their attention to the door, and then
explained to him; If you live in an apartment building, you can plant flowers in the
balcony, give a child a flower pot, so that his own basin sowing the seeds for him to
find seeds, leaves, flowering mystery.
, perhaps, students are curious about the problems encountered can not all understand,
even when parents introduce him to some knowledge, he could not remember.
However, he at least paid attention to some phenomena, perhaps, he may from the
other things associated with the phenomenon of the answer.
  Mathematics is the most mysterious world, the face of mathematics in the world, we
can not imagine a child with curiosity. Subjects in primary and secondary schools,
mathematics is the most charming, almost to its original appeal to be added to. In
particular, the great mathematics problem-solving capabilities, so that the students felt
so true: Mathematics is the most magical world. Unfortunately, our primary and
secondary mathematics education is not a good value of this valuable asset, since the
day when children learn mathematics, the mathematical calculation becomes boring,
practice, the most magical mathematical world into a child suffering simple
duplication. Knowledge of psychology tells us that repetition is the most fatigue,
simple duplication of the most curious child to be injured in the growth of nature.
  man is a child of nature, tends to infinite curiosity is a treasure, curiosity is a
precious asset of humanity. Human understanding of nature requires curiosity,
appreciation of the natural needs of human curiosity, human needs and nature of
, An important task of mathematics education - stimulate children's curiosity
  I in 1990, "Mathematics," No. 6 "Mathematics Education in the implementation of
the Mastery Learning Strategies on the" one article pointed out: Mathematics
Education There are three levels of the pursuit. . This is the first level: to acquire
knowledge; second level: the development of capacity; the third level: the formation
of good character qualities. And stimulate the curiosity of students formed on the
responsive nature of the quality of students has a very good personality an important
role. Therefore, the important task of mathematics education is to stimulate the
curiosity of students. This new curriculum standards are the same.
, Curiosity training
  curiosity is aroused by the stimulation of a new orientation, attention, close, explore
the psychology and motivations. It is the motivation of human behavior one of the
strongest. The strength and the external stimulus novelty and complexity is closely
related to the more complex the more novel stimuli, the individual's curiosity will be
  curiosity of the generation and culture and is closely related to environmental
stimulation. Rich environment is to stimulate and foster the necessary conditions of
curiosity, but monotonous, dry environment will suppress and stifle the curiosity of
students, so the creation of suitable environment (including the natural environment,
the problem situation, emotional climate) on the curiosity of students heart is
extremely important. The correct guidance and training should note the following:
  (1) Select the appropriate environment to stimulate the
  stimulated human peripheral environment is rich and colorful. When the world show
different styles of things, specifically when in front of students, let them personally to
see, hear, smell, taste, and even touching, breaking, demolition and other tinkering
with something. This is in fact the child to explore the mysteries of their lives in the
process. For young children, allowing them to see the colorful activities, or can, be
able to voice their toys, such as a variety of dolls, driving force of the cars, aircraft
and small bell crotch, toys, musical instruments, etc., from the beginning to enrich
their understanding of the world vision. For the students, allowing them to play puzzle,
ride a small bike, swing outdoor swing, seesaw ride and see all kinds of comic.
During the holidays can take them to see movies, plays, visits students activity center.
Zoos, museums. To increase their knowledge; recognized around the world Hiroyuki
large. Teachers and parents should guide students to observe, to think, to explore, to
stimulate his curiosity and thirst for knowledge, gradually develop interest in learning.
In particular the nature of the flowers and trees, birds insects and fish, beautiful
scenery and so full of secret knowledge, endless appeal to students, can use the
opportunity to guide children about nature walk.
  in mathematics education to choose the appropriate environment to stimulate the
main problem is the educational concept. Because the main carrier of mathematics
education is a problem - real problem and the mathematical problem has been treated.
The problem is the heart of curiosity, as long as mathematics educators to stimulate
children's curiosity as the pursuit of mathematics education, to choose the appropriate
environment to stimulate the space is huge. For example, angles of a triangle and the
theorem, as long as some of fewer teachers and students can stimulate curiosity, their
idea of diversity far beyond our imagination.
  (2) full use of the charm of the story
  story is colloquial language of art to express, and it has content, a plot, vivid, the
children generally love to listen. Story not only enrich the knowledge of students,
expanding children's horizons, but also play an enhanced attention and imagination, to
arouse curiosity in the role. If a father to the contents of books compiled stories to tell
children to listen to. And then told him: "If you understand the word, then it can be
their own stories of." In order to stimulate their reading and desire. One educator
recommendations; when the child who just turned 6 months, you can sit on adults lap
time, it should be read to him or under comic books, art storytelling to him, that caress
and warm the atmosphere can cultivate children's books feelings.
  primary and secondary school mathematics in the story are many, but more of a
classic stories of the students is great, if the math teachers seize the opportunity to talk
about these stories, often receive unexpected effect.
  (3) let the children find the answers
  students are new things and phenomena around, what would like to know, adults
must consciously inspire them to actively think about, looking for answers. Encourage
curiosity aroused from a variety of exploration activities. Students should always pay
attention to the problems raised by the unusual and valuable ideas, seize the
opportunity to inspire induction, which in daily life has not only educated the children
cultivate their curiosity and thirst for knowledge. For example, a child playing hoops
games, suddenly found: "straight forward than suggested;` roll morning till end of
rolling, "and then asked:" Why? "At this point, the teacher took the child with a ruler
and measured the straight line the length of the curve of the length of the re-enable the
child to understand: between two points, the shortest straight line distance! Some
children will immediately enlightenment: "Teacher, I went to school should go
straight piece, and should not go near the rotary draw bending piece Road, because
piece is not a straight line, to detour the natural." Teachers should be timely praise,
encourage children's positive thinking. In children want to know not very clear, would
like to say is not clear, we should in time, patience, and enthusiasm inspire children to
answer children's questions, so that not only meet, strengthen and encourage the
child's curiosity, but also make them learning activities in their knowledge, increase
competence. Any bored, and repudiation of the attitude of prevarication will stifle
intellectual curiosity and creativity of students, teachers and parents must recognize
that students understand the characteristics of the world process and the "bright spot",
good at capturing the opportunity, use of time, the children's awareness of facilities
the correct and scientific guidance.
  Unfortunately, the reality of mathematics education in primary and secondary
schools, by telling students the answer has become commonplace, let the children
search for answers not always be conscious of Mathematics Teachers. If our students
are not fully in the development of primary and secondary schools, mathematics
teachers, we should bear a great responsibility.
  (4) provide students with mental and physical, hands-on opportunity
  child imitation under strong dynamic characteristics of love, allowing them to take
full advantage of the tools at hand. Full use of all senses, their own observations,
it-yourself operation, let the children experience a sense of accomplishment and
self-pleasure. If, through the daily observation of small experiments and activities let
students to acquire knowledge; also allow students to freely make simple toys, their
design a game. They have their own brains to figure out what to do yourself out of
something, there is a preference and special interests, and thus help inspire similar
activities in their thirst for knowledge, to gradually develop from the interest in
  had an experienced teacher, she was talking about before pi. Students often let
yourself go to volume size of the diameter and circumference of a circle, and then
divided by the diameter and circumference were used, so let the students themselves
found that all the ratio of circumference and diameter is 3.1416, so the student's
interest arises spontaneously , in the hopes of the atmosphere not only learn the
knowledge, but also cultivate a capacity.
  (5) must not dampen the enthusiasm of the students and ask questions
  student interested in anything. Have a strong spirit of exploration. For example,
often ask, "Why do birds fly?" "How the fish stay in the water," a class of problems,
and like Tracing the source. However, some parents are often "no time and you say
that these", "In the future you will see" and perfunctory, the Cypriot duty to respond if
a child is exactly the stranglehold of the child's curiosity. Parents should be aware,
curious about the child understand the world, the starting point of social, if not
support and encouragement, will dampen their enthusiasm. In order to satisfy the
curiosity of students and proper guidance by parents and teachers should see their
own deficiencies, and effectively correct.
  third problem is the heart of curiosity, curiosity is the question the mother
  strengthening the awareness of problems, is curious about the creative talents created
one of the keys. Curiosity began "problem", curiosity led to innovation. With curiosity,
would raise new problems, or from a new angle to think about old problems, often
leading to new discoveries and breakthroughs, marking real progress of science.
  "problem" arises from "curiosity" and "challenged." "Problem" is the main message
on the outside perception and response. "Problem" will help get rid of the fixed
thinking Zhise and help activate the imagination and creativity.
  "problem" can be divided into three categories: presentation type, type, and creative
discovery. To create a truly scientific issues that require a variety of conditions and the
various efforts.
  "stop rumors wise" is a blessing, the "problem" beyond the wise man is regrettable.
To create innovative talents, updated traditional with "the construction, FAQ," for the
mission concept of teachers is imperative.
  The question now is how the new concept of education, talent, quality concept into
practice, and subsequent updates and teaching methods of teaching the concept of
change, to make education truly appreciate and nurture creative talent site. Strengthen
the awareness of problems, is creating one of the key creative talents. And how to
make the students to maintain a strong spirit of curiosity and requesting different, and
its action towards the real scientific innovation, should be the existing teaching model
change an entry point.
, Curiosity begins "problem"
  history of the development of a science is the exploration of the mystery and the
history of the answer to your question. Newton discovered gravity, under the apple
tree started his curiosity and thinking: "Why Apple fell from the tree, rather than fly to
heaven?" It is noted that the relationship between knowledge and problems, Hu 6 in
1932 open to graduates of Beijing University on the shamisen, "Defensive
prescription", the first taste is the "problem Dan." He said: "The problem is
knowledge of learning ancestors; ages of all the production and accumulation of
knowledge, because to answer questions." "Imagine Galileo and Newton have many
books? How many machines? Them, but there is a question. With the problem then
they would, Zaochu equipment to answer their questions. no problem with people, not
kept in the library books, locked in the test room, it would not be found. "and" do not
mind the date of issue, is your knowledge of life come to an end when! "
," problem "arises from" curiosity "
  strong curiosity will increase people's sensitivity to external information on the new
situation and The new changes in a timely manner to respond, identify problems, and
roots is to stimulate thinking, lead to the desire to explore, start innovation.
  lot of seemingly accidental discovery implies an inevitable fact: the discoverer must
have a strong curiosity. Lack of curiosity, is bound to slow to the outside information,
turn a blind eye to the many meaningful, and indifference to the issues of creativity
and invention is indeed useless. Einstein had a famous saying: "I do not have any
special talents, I just like the roots of the problem underground to pursue nothing
more." This passage gave away the true meaning of innovation and discovery:
curiosity, problem awareness and perseverance The quest for scientific success is a
, "Problem" of classification and the value of
  professor of psychology at the University of Chicago J · W · Gaizeersi had the
"problem" can be divided into three categories:
  First, type the question presented . They are given questions (raised by teachers or
textbooks), the answer is often readily available, the solution is ready-made ideas.
Problem solver as long as "what you want," the rules, can get the same result with the
standard answer, "do not need nor the opportunity to imagine or create."
  second, and found that type problem. They also have known some of the answers,
but the question is raised by the students themselves or their discovery, and not by
teachers or textbooks given.
  third, creative problem. These are all problems that people have never raised before.
For example, the troubled, tortured, Einstein 10 years question: "If I speed of light C
and light a campaign, I was not the observed light is still stationary in space, the
electromagnetic vibrating it?" The problem itself on the value of scientific innovation
is the classical physics of Newton has been a breakthrough.
  above three "problem" is not equivalent. Has simply to "present problems" as "false
problem", because, first, they are not the product of active participation students;
second, they tend to pursue the "only correct answer", thus always suppressed
requesting different, question the spirit of creative play prevent. "Creative problem"
because of its unique, innovative and full of scientific significance and very valuable.
What we call "enhanced awareness of the problem," is designed to allow students to
freely explore, positive thinking, daring to ask questions, reveal the problem.
Exploration of this question and have found that not every time, create, advance; a
large number of "discovery-type problems", only a few are able to produce innovative
scientific value. So some people call it "intellectual adventure." In fact, the
"intellectual adventure" is not the meaning of the major found the correct answer, but
rather to stimulate students to question, to maintain a sensitivity and curiosity of the
phenomenon through critical thinking, and form their own independent views. It is
focused on the goals and values, it was argued in the system of education should be
conscious of learning and exploration between the "search for balance" in favor of the
students "put the problem scenario, let them think of ways"; This kind of "intellectual
adventure" ", if not lead to positive results, it should be a priority and get the system
of support."
, To prevent "the problem limited to the wise"
  tradition of "missionary, Tuition, the construction, Dispelling the" concept of
teachers for the purpose, obviously difficult to adapt to high-quality creative talents of
the 21st century for the mission education. "Gossip stop wise men" is a great blessing;
and "problem (think) stop the wise" is not only unfortunate, but is related to national,
ethnic, and overall social. Unfortunately, the "problem (think) beyond the teacher" has
become the normal state schools. Demanding a clear idea of the following new -
  (1) not only to "the construction, FAQ," but also to Creative, located the suspect,
cited without hair.
  as a teacher, really difficult to answer the students, guiding them to understand and
eliminate academic life confusion encountered on the road, but not pre-empt the
replacement of the students themselves. Moreover, "the construction, FAQ" is not to
doubt all the "vanish", but to guide the students to understand the suspect on the basis
of the old thinking of new and deeper problems, and sometimes even to "set the
  (2) not to cover up his oversight on certain issues, or even ignorance.
  teacher can never be proficient in all. In particular, the arrival of the information
society of today, teachers no longer possible as the ancient and modern societies,
monopoly of knowledge and information. In front of students freely admit their own
inadequacies, and students to discuss and think, should be the relationship between
teachers and students of the 21st century intelligent choices. To equal, open and
honest manner, for enhanced self-confidence of young people, incentives for the
formation of thinking, be creative and not afraid of mistakes, and good for the
atmosphere of exposed short.
  creative talents to produce, very free and relaxed environment to explore the issue.
Encourage bold challenge to recognize that every student, even if their problems seem
ridiculous, or away from the reality, should also be expressed and discussed, to share
with others. Some people call it "thinking to remove brake." Because if the request
"problem" has a very mature ideas or to publish, share, would amount to de facto
abolition of questions, questions. Plausible answer is not to stop because of the
curiosity of students creative impulse.
  teacher because experience spans a wide and expressive, sometimes the students
answer questions, often very "round", "timely and" to resolve the concerns of students,
can not really solve the problem. Teachers, students out of the worship, in the face of
this paradoxical response is often suspended further thought and inquiry, a number of
valuable problem will be shelved. Teachers must respect and seriously consider the
students to ask questions, not to "question (thinking)" stop himself.
  we know that mathematics is the problem posed by the world, the students is in
understanding, analyzing and solving problems in the process of developing their own.
The problem is the heart of curiosity, curiosity is the question the mother. Curiosity is
an important quality of creative talents, so we say, curiosity is a valuable asset of
mathematics education. This article comes from [the website of Education] collection and sorting, for the original author. / Center>

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