Tuesday, December 18, 2007

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Book review of Next Door: SUBSIDIARY "WHY '?" The

'WHY'? " is a subsidiary aimed at children in third grade.
definitely worth consult this book because, in my opinion, is a good textbook for the following reasons :
1. is fun and engaging, as it makes extensive use of drawings, pictures and colorful and original comics.
2. provides the child with many opportunities to get involved and play in person several years, inspired by the facts to come to the understanding of abstract concepts.
3. The methodology this book raises the child's motivation to get closer to mathematics, as it provides concrete examples that they understand the importance of numbers in our everyday life.



To read the report I conducted a more thorough and precise on the subsidiary above, click on the title of the book e. .. good read!

Monday, December 17, 2007

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RULES

I RULES are one of the many types of structured learning materials that can be used to teach mathematics so original and fun.
Unfortunately not all teachers use them in their lessons and this is a real shame, because they are very useful for teaching children math concepts are not easy to understand, as it is mainly mental.
The value of the rule, in fact, is that they offer a concrete representation of abstract concepts and, consequently, complex for children who are beginners with math.
With this tool you can make fun games and at the same time building that stimulate children's interest and keep alive their attention!

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JOHN NASH - The genius of The genius of the numbers

John Forbes Nash Jr. ( Bluefield, June 13, 1928) is an American mathematician. Among the most brilliant mathematicians of the original 900, Nash has revolutionized the economy with his studies in applied mathematics at " Game Theory " , winning the Nobel Prize for the economy in 1994 .
But Nash is also a brilliant mathematician pure and refined. He always had a skill in dealing with uncommon problems from a fresh and unthinkable to others, and incredibly elegant solutions to complex problems, such as those related to immersion of algebraic varieties or
parabolic differential equations.

John Nash has lived for about thirty years between the scientific and academic success and mental illness. During the brilliant scientific work in prestigious universities (such as Princeton ) or companies such as RAND Corporation, where he and logical, mathematical, physical and engineering experts game theory, worked for the government to political and military strategies of the Cold War.
had to live with schizophrenia
often and for long periods over three decades obscures the extravagance and creativity emotional isolation from the outside world.
After periods of crisis, often subsequent admissions to psychiatric hospitals, Nash returned to make
mathematical ca .
But a few months after the disease relapses. Electroshock therapy as
, straitjackets chemical injections of insulin have marked in the physical, but now that Nash is a seventy still attending the Institute to Princeton, he studied mathematics and still seems cured of the disease.

arrogant and conceited, eccentric and quarrelsome, incapable of normal social relations, John Nash had a strange way to behave. Do not follow regular course, he considered trivial, and consulted a few books on mathematics. Often whole whistling Bach pieces regardless of the discomfort to others.

Melvin Hausner remembers
"He was always immersed in thought. He sat alone in the common room. Easily happen that you pass by without seeing you. Always muttering to himself. Always whistling. Nash was always thinking. If he was lying on a table, it was because he was thinking. Just thinking. You could see he was thinking. "

A Beautiful Mind

The acclaimed film A Beautiful Mind
( 2001) of U.S. director Ron Howard , winner of four Golden Globe and many Oscar ("best film "," Best Director "," Best Adapted Screenplay and Best Supporting Actress "on Jennifer Connelly for the role of Alicia Nash) narrates, novel and omitted some parts, the amazing life of genius John Nash , played by Russell Crowe.

The facts narrated by the film are taken from the homonymous
Sylvia Nasar's biography , which tells the story of Nash topped with a myriad of details collected by mathematicians who knew him and by the same Nash (the book was published in Italy under the title " The genius of the numbers - The Story of John Forbes Nash Jr., a mathematician and crazy ).

• Plot
In
1949, the twenty-one and talented mathematician John Nash joined the prestigious Princeton University with a scholarship for doctoral . Refractory to establish social relations, Nash has only two friends, Charles, his roommate, and mathematical formulas.
Obsessed with the thought of finding an original idea to apply its formulas, John succeeds in his goal: a doctorate in only 27 pages of exhibits fundamental intuitions development of the "Game Theory
", thus becoming outdated economic theories of Adam Smith .
His ideas earned him fame and an important place as a researcher at MIT
of Boston, where he confirmed his understanding mathematics.
In full "
Cold War " is contacted by the army for its incredible ability to decoder. Log in touch with the 'eminence grise "William Parcher, dark character that the government hires a top secret mission . At the same time John is also the love of Alicia, a young physics student, who became his wife.
Nash's life at this point is shaken by a terrible discovery. Charles, her granddaughter and the same Parcher are really just projections of the troubled mind of Nash, who suffers from a severe form of schizophrenia .
Wandering like a ghost between clinics and asylums are subjected to numerous sessions
insulin shock and a massive dose of drugs.
With affection and closeness of family,
Alicia in particular, and his mental strength to be able to ignore his hallucinations, overcoming incredible disease and returning to a normal life.
Reborn,
Nash becomes professor at Princeton , and 1994 he was awarded the Nobel Prize 's economy.

• Curiosity
Since the beginning of the film are obvious, albeit cleverly disguised, the signs of the madness of the protagonist:
- Charles does not appear as a friend or the girl to John, although the latter continues to tell others about it as if it existed, what emerges from the dialogue between Alice and Dr. Rosen.
- Parcher When John goes for the first time in the "secret base", the mathematician says, "I had said that these warehouses were abandoned."
- The granddaughter of Charles runs among the pigeons, but they do not fly up or moving. A sign that the child exists only in the mind of John.
- When Nash Parcher blocks to his office door and enters with him, you can see the puzzled look of the guard at the entrance of the building. Just a few scenes later, the colleague of Nash when he calls Parcher for the corridor.


For more insights on John Nash , read the brief research I conducted on this mathematical genius!

Wednesday, December 12, 2007

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NEXT DOOR

One of the course "Elementary Mathematics from a higher point of view," he asked to do, was to interview a genius next door (obviously a mathematical genius!).
Initially I did not know where to turn, but eventually I had an epiphany and I immediately thought of interviewing one of my high school teacher, who still teaches physics and mathematics in High School and a Language High School.
Before coming to high school, however, has taught in several schools in the province of Pavia: initially worked in middle school, then went to secondary school, teaching both in technical professional, both in high schools.
identified the teacher to be applied to the interview, I can not just have to think about what to ask for a fairly complete picture, but his experience with mathematics, both at school and in everyday life.


Here are the questions that I raised and its respective Responses:

1. "As has been prudent to have a passion for math?"
Even as a child I was always attracted by the numbers, geometric forms and phenomena related to physics. Attraction was obviously unconscious, but over time I started to become increasingly aware.
My father told me that back when I attended primary school, when I came home from school and told him everything I had done during the hours of mathematics and for hours I did not know (and did not want to) talk about something else. Then my father submitted those classic "problemini" for an adult are logical, but who are able to puzzled children (for example the question "weighs more a pound of iron or a pound of feathers?"). Unfortunately I do not remember all of my childhood, but I remember that I had so much fun to solve all those problems and headaches.
Not to mention when I accompanied my mother to buy bread! The always wondered, in fact, to count me the money to pay the bill and any remainder to be received. My mother, at times, especially when in a hurry, it was a bit 'annoyed by my "vice" because I was good at counting, but I was still fast in it, so I missed the time ... Fortunately, however, realizing the my little passion, has always left me to do and helped me with the passage of time, to keep alive my passion.
I think it's these little things that I started, slowly, to realize that I loved math and all that was connected to it. And now, here I am teaching for many years!

2. "That passion is innate, or it was built over time?"
Certainly, as I mentioned before, is partly innate, but like every talent and every passion, must be cultivated and enhanced over time, because if you do you risk losing it, or better yet, forget about it, and this would be a shame. Unfortunately it often happens that many talents are lost only because they are ignored, or worse yet, not identified and valued.
I, fortunately, I had two parents can understand my passion is for this reason that they were also willing to make many sacrifices to allow me to cultivate it and take it forward.

3. "What was the path (both studies, both of life) that brought her to teach?"
My attraction to math, found both in elementary and in junior high, led me to attend the High School , after which I enrolled in the Faculty of Mathematics and, after so hard and so hard, I graduated.
I embarked on the difficult path of teaching because I realized, while studying in high school and university, to be particularly inclined to explain to others what I learned, to do so, moreover, has always given me great satisfaction and satisfaction. Upon graduation I decided to pursue a career school, hoping to make people love a bit 'more math to those who do not have the same passion.

4. "What is your relationship with your students?"
Speaking of the relationship with my students, I can say with joy that has always been very open and positive. Of course, not all I see a good eye (after all it is almost impossible when you consider the high number of students I met during my school career), but overall I can say I "love and in agreement "with a good percentage of students.
The only thing for which I sometimes feel criticism is that at certain points of the program go a bit 'too fast, but unfortunately (not always to my will), I have a schedule and deadlines to meet, and this sometimes leads to having to necessarily speed up a little 'time to keep up with everything. On the other hand, however, from 5 or 6 years now (and you you know, since you were one of my students) I have given my full availability to anyone who needed further clarification, because I managed to obtain permission from the Dean to stay at school a couple of afternoons a week, after the lessons, to make a sort of "repeat" to my students most in need (everything, of course, free!).
This additional opportunities that I could give my students has made my relationship with them even more serene and constructive.


5. "His method of teaching has changed over time or is it still the same? "
Early in my career I found myself a bit 'crowded out. The first few times I taught tended to be very cold and stiff. My classes were purely theoretical and, therefore, very boring. But these are errors that are often novice teachers.
Fortunately, with time, I have softened and started to constantly change my approach and my method of teaching, learning to understand the interests and the real capacity of my students to leave and to plan for this basarmi my lessons.
Usually, when I explain the concepts quite difficult, I tend to do a lot of practical examples (of course where you can) and a number of years, so that all my students, or at least most, understand and be able to follow without too much difficulty the next part of the program.
What I want to understand is that it is very important for a teacher to review and reflect on their methods, because sometimes the poor performance of students does not depend on their commitment or just a little study, but dall'inappropriato teaching method used by the teacher .
recognize, sometimes, you were wrong approach, it is a humiliation for the teacher, but it is a sign of great humility and maturity. It 's a constant to get involved.

6. "What tools are used to teach mathematics to children?"
Generally, as a base, use textbooks and manuals, but just to give children a reference point from which to draw.
In class, in fact, tend to perform many exercises at the blackboard, trying to ask all my students every time, in order to create a climate of cooperation (for example, if the guy who is performing the exercise on the chalkboard or wrong is in trouble, I ask his companions to help him solve the problem and explain where he was wrong).
In recent years I also began to give lessons using the computer, the use of this tool has proved very useful for two reasons: first, because it allowed to perform tasks manually that would be very difficult and much longer to run, and secondly, because it has motivated a lot of my students, making them closer to the field and stimulate their interest.
Also, since I introduced in my method of teaching this new technological tool, I found significant improvements in the performance of many of my students.

7. "What were the most frequent problems encountered in teaching this subject?"
The problems I have encountered in recent years of teaching are not so different from those I met early in my career.
Many students have trouble with math because they are not stupid, but simply because they do not apply and do not exercise, probably due to the lack of desire. Others, however, undertake a lot, but still put all struggle to understand. For others, however, it is simply attention problems, that do not understand what I explain to the simple fact that while I think these guys to another class or chatting with her boyfriend.
Well, except for students with serious learning deficits, for other students who encounter problems with my area are multiple and result from a multitude of factors different.
What can I do it groped to involve as much as possible students who show less interest and try to help students who really have difficulty understanding, despite their efforts.

8. "I think the resentment of many young people in mathematics is due to inappropriate teaching methods, or other factors take over?"
As I previously mentioned, often the method used by the teacher is a key factor for success and involvement of their pupils. Obviously, the method is effective with some students might not be for others. The biggest difficulty for
a teacher is precisely in this ambivalence. Unfortunately nowadays the number of students per class is very high, so it is almost impossible to use a method that works for everyone.
What you can do, if it is not possible to individualize the work is to offer support and assistance to all students who need them.
I do not think, however, that the method of teaching is the only factor that impacts the interest in mathematics. On it, in fact, may also impact the family, personal passions, motivation, the utility that each of us attaches to this matter, sympathy / antipathy for the professor.
short, there may be several reasons why a person does not like math, but I remain of the view that one of the most influential factors is the methodology used by the teacher.

9. "His passion and his interest in mathematics has never wavered?"
Not particularly. Obviously, when you encounter obstacles, risks lose heart and to have second thoughts about the choices made or grown on the passions, but we need not fear the challenges that life presents us. If you face these challenges, once overcome and made you feel stronger than before. I have had moments of blacks, especially at the beginning University and during my first years of work, but I always tried to overcome the difficulties that stood in front me. The fact that mathematics is for me a deep and genuine passion, has helped me to overcome obstacles and move forward.

10. "Finally, may list some key terms that describe, if only in small part, what is the math for you?"
I find it very difficult to encapsulate in a few words all that for me is math, because it meant a lot in my life.
I know it's a bit 'generic, but to respond honestly to the question "What is for my math, I can think of only one answer that encompasses many others, but that is the most significant of all: For me math is my life.



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U.S. and Mathematics I and Mathematics

to notice that mathematics is constantly present in our daily lives, just look around. In the experiences and events of everyday life, in fact, we find an infinite number of numbers or mathematical concepts. Even I, for one day, I wanted to try to concentrate on that aspect of my life, ie on which and how many meetings in my day an ordinary . Unfortunately Hit the numbers I found were so many that I was unable to bring them all in writing, but they still managed to write down the most important ones:
· 5.50 : the time of first Wake
· 5.55 : the time of the second alarm
· 6.00 : the time of the third (and thankfully last) Wake
· 30 : the latter uses the microwave to thaw the sandwich, of course, forgot to pull misono out of the freezer the night before
· 3 : slices of ham in the sandwich that I put just thawed
· 10 : I put the candy in his pocket before leaving home (to fill glieventuali and frequent bouts of "desire for something sweet")
· 6.45 : time out of her house
· 10 : the minutes you use to reach the station
· 12.50 : The euro spent on the weekly subscription Train
· 7.03 : time of train to Milan
· 20 : the minutes of delay that the train usually leads
· 45 : the minutes it takes to get to Milan
· 15.5 : the pages of a book on bullying that I read on the train
· 2 tickets Stations I buy the morning
· 2: The euro spent on tickets metro
· 8.30 : start time of the lessons
· 2 : the foil, the average usage for each hour of class
· 7 : the lessons of the day
· 3506857 : the serial number of my University
· 18.00 : train timetable to return home
· 4: The friends I met on the train
· 2 : the times I had to call my mother because she forgot to take the train venirmia
· 20 : the minute that I had to wait before my mother came
· 5 : the minutes available (given the delay in arriving home) percambiarmi the bag and prepare to go to training volleyball
· 9 : the companions of this square the training
· 2 the hours of training
· 8 : volleyball exercises conducted
· 132 : the total points made during the volleyball game
· 50 : inflections of punishment that had to make the team that lost
· 25 : the euro, which I had to pay for the monthly usage of the gym
· 15 : the minutes used to make the shower · 10.00: time to return home
· 2: plates I ate pasta for dinner
· 112 : channel "Sky" on which I have tuned in after dinner
· 2: episodes of "CSI" as seen on TV
· 01.15 : time that I decided to go to sleep
These are just some of the numbers I have met during the day. I could have scored a lot of others, but to write them all I would have served three times the space.
However I can say that it was fun to find all occurrences of the day, numerical ... is something I'd never done before, but after this experience I am sure I will notice the numbers that I most often occur during the life of all day.
It 's amazing how the vast amount of numbers that we all encounter during our lives normally, the funny thing is that not even realize it, because often we tend to take for granted many things, including, of course, this one.
This little exercise, however, it is useful to realize how mathematics is an important and dominant in our lives, something that has always existed and which men will always have to do.
Therefore, to appreciate the value of this discipline, you need not be geniuses and mathematicians have an innate passion for power, because we all have to do with the numbers since our birth, I am sure that even those who hate mathematics more than anything I miss it if it was (hypothetically) to be missed!
The world is full of mathematical concepts, there is no field or industry that does not use numbers and sizes of events or to express concepts. All of us in our daily lives, we will always have something to do with mathematics and with everything that is connected to it.
E 'undeniable now, that numbers and mathematical concepts are a very important element in our lives everyday. This is demonstrated by numerical infinite occurrences encountered in a typical ordinary day, but not only! To understand what the numbers are essential in every field and area of \u200b\u200bour lives, just try to read some newspaper articles, and soon you will realize that without numbers, measures or as many things could not be said!
short, mathematics is fully a part of our existence, and to prove it I decided to look at some
newspaper articles dealing with issues and different areas, to understand how there is no area of \u200b\u200bour lives that has nothing to do with numbers!
To make more evident the presence of high numbers and mathematical concepts within articles, I pointed out all occurrences of numbers in the same proposed.

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The mathematics course faced during the year has given me the opportunity to reflect more deeply on the importance of this discipline in their daily life and my relationship with it. Here, therefore, the history of my relationship with math, from childhood until now .
Even as a child, I always had a passion for science, including mathematics. Over time, the love of science, biology and chemistry has been (or even increased), while the Math has always been more weakened and eventually disappear altogether ... well, on occasion has even turned to hate! The first approach to this matter is engaging and enjoyable, even in elementary school because I was very lucky to find teachers trained and competent people who have known me appreciate even the most difficult materials temute.Ricordo and even my teacher had us always use slide rules for calculations and to make us understand the concept of unity and ten. This was for me a very funny and at the same time, definitely utile.Dopo teaching us the basics, my teacher went on to explain the various arithmetic operations, using to support not only the unforgettable subsidiary, but also practical tools (in this case made us "play" with the set). The part that I recall with less pleasure, is one in which we questioned every day on the tables for us students ... it was not fun at all this "habit", but I must admit that over time it became very costruttiva.Insomma, after all the My first experience with math was not so traumatic, indeed, I must admit I was even divertenti.Ma was all too good to be true! The first problems appeared with math in junior high, despite the ability but, Above all, the patience of my professor, who vainly tried to save me and my mates when we were sinking into oblivion ... So, when the level of knowledge and expertise in this field has risen, I was increasingly difficult to understand and memorize all the terms of this matter, so that the teacher made us stay in school one afternoon a week just to make us play the "mini-audits" (problems, equations, and various operations) on the program explained that momento.Alla up to the end, however, so much effort and commitment, the averages are always able to cavarmela.Per regarding high school, however, during the five years I have had several ups and downs, probably also due to professore.Ricordo frequent changes in first high school I had a very good and patient teacher, always willing to re-explain concepts if they had not understood. With her went very well, because he had a very effective way of working, I say effective because it could make me understand the different math concepts explained to us that (very difficult task, considering the huge gaps in my regard). But this time (note my "luck") things did not last more than lungo.In second, in fact, we changed teacher, teaching mathematics and got a very strict and demanding teacher (Hitler called it all!), but he could do his job. Also with her, in fact, I had some good results and could not understand a good deal of explaining things in class, so all in all, despite more stringent methods, I was not so bad. This, however, regarding the results. If I talk about my mood and my mood every time he came into class, then things change ... In fact, had clear and effective methods, was so severe and "bigoted", I was always anxious and agitation (which came during the height intererogazioni!). I think, therefore, that my hatred of math is born in that periodo.In upper third, to make matters worse, I changed my professor again, this time, However, the new teacher followed my class until the fifth (and thus, was also examined by the state). With her, the situation was reversed from the previous year. This teacher, in fact, was a bit 'harsh (just enough to hold off a class of wild like mine), but it was also very kind and helpful. In class could create a serene and peaceful, totally different from what is established with the previous insegnante.Purtroppo, however, is not always all that glitters is gold ... in fact, to my chagrin, after a few lessons I realized that I did not understand anything I explained! I never really understood why, but all of a sudden I became a real Somara! So, slowly I began to falter and to understand less and less, and since the mathematics program of the following years, if you had not figured things done before you could not understand new concepts, I was lucky to even further behind ... despite the many failures and the continuing disappointments, I managed to get by the stesso.Non say that the experience of the last years of school has traumatized me (it takes a lot more!), but has definitely damaged my relationship with math. It is probably for this reason that when I read that in the curriculum of the University system were examined as math, a bit ' I had a knot in my stomach, but, fortunately, the way in which it was built this course has reassured me and made me closer to this subject so difficult, but also very beautiful and fascinating.