2007

Tuesday, December 4, 2007

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T10-CONSTRUCTION OF A UNIT OF LEARNING WITH QQ ..

STORIES PART CONSTRUCTION

Our Learning Units is intended for children fifth grade, his goal is to highlight the geometric shapes.
Starting from the reading of the story "Little Spot bored" to Children are introduced geometric shapes (rectangle, triangle, square ...), then the child by the performance of simple geometric problems with the computer (the program QQ.storie) comes to the construction of the game of tangram through which can create new shapes using the his imagination and then find the measurements of the same figures he created. In this way, the child connects the knowledge learned from lectures on geometric figures to know how to make traditional means of interactive exercises with the computer and the tangram.

SCHEMA LEARNING UNIT:

Title: "Playing with geometric shapes"
Recipients: a class of fifth grade

Analysis of the situation
through history the teacher introduces the geometric figures and their characteristics

Objectives:
or explore models of geometric figures; build the main draw geometric figures explored
Ø Analysis of the significant elements (sides, angles , ...) of the main plane geometrical figures
Ø Identify symmetries in objects or figures given, highlighting the features.
or recognize shapes rotation or translation of figures assigned.
or operate concretely with figures performing transformations assigned.
or measure lengths.
in simple cases or determine perimeter, area and volume geometric figures known

Educational Activities planned
- Task 1: Description

Reading the story "Little Spot bored"
Introduction of geometric shapes (rectangle, triangle, square ...)

activity 2: Exercises
QQ.storie
processed through the program offers interactive exercises of QQ.Storie

Activity-3: Description

Tangram offers practical exercises through the construction of Tangram Tangram
Playing with the process of geometric problems

Tools:
teaching materials
program QQ.Storie
tangram

Method:
lessons lectures, and interactive through the use of specific instruments such as the tangram and tools (QQ.storie).

assessment method and assessment:
- ongoing: every lesson the children are asked to summarize what has been done once before. The teacher carefully observes children and tries to speak in the debate even the most timid, in order to verify the knowledge of each child.

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Tangram
By Fracesco Carion, CONTI TATIANA, ILARIA NOBLE, Gorra GIULIA

Tangram is a Chinese puzzle. Its name means "The seven stones of wisdom." E 'found a very old game. The legend says that a monaco gave his disciple a square of porcelain and a brush, telling traveling and painting on porcelain beauty that he met on his journey. The disciple, excited, dropped the square, breaking it into seven pieces. In an attempt to repair it, formed interesting shapes. He realized then that he did not need to travel, because it could represent the beauty of the world with the seven tangram pieces.
In 'Ancient China, the infinite was represented by a square with no sides. And the square was born the most famous puzzle of the story: Tangram, known as the "Square of the seven tricks" or "The square of wisdom" because it was said that command of this game was the key to wisdom and talent.
This game is very simple to construct: simply divide a square into seven parts: two small triangles, 1 medium, 2 large, a parallelogram and a square. With the seven pieces thus obtained can build thousands of different figures.
changing the position of the pieces of the game you can get an infinite number of shapes, some geometric, reminiscent of other everyday objects ... so you can build different figures, always following the rules:

All parts must be used ;

not allowed to overlap the pieces.

The quality and interest of Tangram derived from the variety of forms, both geometric and figurative, that you can get with the seven pieces that comprise it, pieces which have geometric shapes. Among the measures of these pieces are no precise relationship which, if not met, can not deliver the objectives required. Tangram is possible to get through two games.
In the first way you need to find the arrangement of parts that make up a given geometric figure which is only known from the boundary. With this activity requires geometric intuition and calculation skills.
In the second task is trying to make shapes of objects, people, animals, trying to achieve maximum expressiveness and the best detail of the details. This game is played imagination and capacity for synthesis.
In stores you can find the game Tangram made of wood, ivory or plastic.

Tangram and mathematics

Here are the next twelve convex polygons that can be composed with the seven pieces of the game. It 's a game that promotes concentration and is a great mathematical exercise, to understand the figures and space.

variants TangramQuelle following are four versions of the Tangram. The first is a different breakdown of the square, the second is a breakdown of the circle, the third in a egg-shaped figure and the fourth, breaking a heart obtained from a square to which you add two semicircles and then performs the decomposition indicated in the figure.

sitography
Software to create a billion configurations:

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PROBLEM OF LEARNING IN THE CLASSROOM TEACHING MATERIALS AND STRUCTURED

THE PROBLEM OF DRIED

We have two containers A and B of 9 and 4 liters each.

These containers are graduated and are opaque.

We also have an unlimited capacity to tap and a well where you can drain the water.

Objective: Collect 6 gallons of water.

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AS IS LEARNED AND TAUGHT U.S. THE GEOMETRY

REVIEW of the book "Mathematics with colored blocks"
Author: Barbara Bando Irvin Publisher: Erickson

The text offers two series of operations sheets: the first deals with the study of plane geometrical figures through the use of symmetries, transformations, constructions, against the perimeters and areas, in the second part gives an insight into the concept of village and how to work with them. These are abstract concepts proposed in a concrete and operational through the methodology of problem-solving.
Attached are given a set of colored blocks that are readily reproducible and immediately used for concrete activities to be carried out before tackling the job on cards.
cards invite children to work hand in a practical and engaging, working individually, both in pairs and are used to compare the solution strategies and results.
Deliveries of the various exercises are clear and understandable, as expressed in simple but precise language, initiating the acquisition and use of correct terminology.
The drawings are large, well spaced on the sheet and accompanied by clear examples.
The book is accompanied by a short introduction provides a theoretical guide for using the teacher, explaining such concepts are addressed, the necessary preparatory activities and tasks of the proposed exercises.
It proposes the adoption of this text for the fourth grade because its clarity can be a useful tool for teachers to deepen the study of geometry and fractions, also starting from manipulative activities and graphics can stimulate interest in children for arguments so far from their everyday experience.

REVIEW OF TEXT "In the world of mathematics" Volume I
problem situations for children from 6 to 8 years.
Authors: Colombo C. Lumpkin, A. Costa, C. Alberti Editor: Erickson

Link:
http://www.erickson.it/erickson/product.do?categoryId=28&id=461

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inhabitants of our planet and Geometry

skills geometric very important to live in the world today, particularly in the environment in which I live.
Taking a page of a newspaper I showed all the occurrences of geometric symbols.
page shows a room in which we analyze the elements which compose it and you get to thinking that everything around us responds to geometric figures from:
the carpet in the shape of circles,
assume the size of the bed a parallelogram
the handles of the cabinets have
cylindrical enclosure has a parallelogram shape

The geometry is also present in the field of design, here are some examples:
links of interest: http://www.architetturaedesign.it/index.php/2007/07/20/papton-chair-seduta-sostenibile.htm

It's called Papton Chair, the chair made entirely of cardboard,
consists of a single sheet of recycled paper, suitably shaped and folded, it appears, with stiffeners in shape, extremely strong and lightweight. No glue joints or different, a true example of eco-design for a chair that weighs only 2 kg. A product
attentive to environmental issues, 100% recyclable. But effective geometric design that follows the principles of origami

The new classroom for South Africa. A product that is versatile and well designed for schools of Mdantsane (South Africa), a village with over 7000 students and just 3 schools.
The fundamental problem is therefore on the area and the number of chairs and desks needed.
This product has been realized a two-in-one, with a strong social and ecological contribution. The benches-chairs are all produced using recycled plastic with a pair plywood.

Topsy Turvy Lamp. The particular form given to the lamp makes it suitable to be laid on various surfaces in the strangest positions (upright, upside down, sideways ...).

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THE GENIUS NEXT DOOR

Interview with Tommy, my friend, the architect

What is the architecture for you?
Architecture? .. wide as an argument in the broad sense ... I mean the architecture as the world around us .. Architecture is a house, a tree-lined avenue is architecture, architecture is a lake, a fork, a portfolio, a city ..

What do you think has affected more in your choice of the faculty of architecture?
Making art school .. first I wanted to do brera .. but in the three years of art school in particular, I have directed more towards the architecture

How have affected the your teachers, friends and family as you grow your passion for architecture?

Some teachers, then some friends at university have had to grow my passion ...

Which is why, in your opinion, so did the architecture?
It 'came in response to a quota requirement of living even if at first you do not know maybe it was to do architecture, but it did ..

architecture today what is it?

The purpose of architecture for me is to create a place to live in harmony.

The architecture is a cross-discipline?

obviously .. I think it's also one of the cross-cutting disciplines .. in that it deals with places and objects of life ...

The architecture responds to social needs?
course (I also do some examples: when designing a garden, a city, a hospital, a district in subsidized housing ...)

What aspect of architecture appeals to you most?
Its complexity and facet

Which architect follow as a model of aspiration? Why?
There are a number unknown .. but I would say that I follow current minimal and modern .. the simple things are always the best

What work fascinates you?
do not know .. perhaps because I tend to look very professional bias ... all .. I look and I think .. and I might be intrigued by a tap as a cornice as a historic building ... everything fascinates me ...

When you see an architectural What attracts you most?
Attraction perhaps too .. but I would say that as I said .. I tend to observe a critical eye on everything around me .. thinking about how and why it did so .. as I would have done ... or how it might be better to do .. I feel that a certain thing ... so I'm a huge range of feelings that I get every day ... and who in some way I can say I attracted .. as my eye focuses of them .. (Trees, roads, panoramas, landscapes, buildings, cars, motorcycles, shopping, clothes, furniture ...).

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"The genius of the numbers story of John Nash, the mathematician and mad," Sylvia Nasar

Life of Sylvia Nasar

Sylvia Nasar was born in Germany and grew up in New York. He studied literature at Antioch College and a master's degree in economics at New York University. He then attended the School of Journalism Columbia University.
business journalist who has served on the editorial staff of Fortune and U.S. News & World Report, in 1993, while he was writing an article for The New York Times economy has encountered in the story of mathematician John Nash and the brilliant scientist was fascinated , ill with schizophrenia. We begin to investigate the life of John Nash, discoverer of the theorem of equilibrium, which is considered a major contribution to game theory. In this way The genius of numbers, a book half way between the biography and the novel, which won in 1998, when he left, the prestigious National Book Critics' Circle Award and was shortlisted for the Booker Prize the same year. Now famous throughout the world for the film version A Beautiful Mind, winner of several Academy Awards, The genius of the numbers is an international bestseller that has consecrated Sylvia Nasar among the most famous journalists of the United States.

Life of John Nash

John Forbes Nash was born in Bluefield, June 13, 1928 is an American mathematician. The father, who was called by the same name, was a native of Texas and had an unhappy childhood, redeemed only by studies in engineering. The mother was Margaret Virginia Martin, before she married and started a career as a teacher. John Forbes Nash jr. already reveals a little lonely and bizarre character. Even his attendance
school has many problems. Some examples of those who knew him describe him as a little boy and singular, solitary and introverted. Also seemed to have more interest in books rather than the sharing of hours of play with other children.
The family atmosphere, however, was largely peaceful, with parents who showed him their affection. After a few years also will be born a girl, Martha. Thanks to her sister that John manages to integrate a bit 'more with their peers, even managing to get involved in the usual games of childhood. However, while the others tend to play together more often than John prefers to remain on his behalf. His father, then treat it as a adult, continuously providing books on science and intellectual stimulation of all kinds.
The school situation is not rosy at first. The teachers are not aware at all of his genius and his extraordinary talents. His lack of "social skills" puts him in a bad light in respect of colleagues and faculty. Nash was probably bored with school.

In high school, however, his intellectual superiority over the fellow serves primarily to obtain consideration and respect. Also received a prestigious scholarship thanks to a work on chemistry in which there was but also his father's help. He went then to Pittsburgh, to study its chemistry. Over time, However, his interest in mathematics is increasing more and more. This field displays of exceptional skill, especially in solving complex problems. Among friends, however, behaves more and more eccentric, and so are unable to establish friendly relations. Join the
Putnam Mathematical Competition, a coveted prize, but did not win: this will be a bitter disappointment, which I'll even after several years. In any case, it immediately shows a mathematician of the first order, so as to obtain offers from Harvard and Princeton to do a PhD in mathematics. Chooses Princeton.

Nash had great hopes from the start in maths. During his years of teaching at Princeton, Nash showed a wide range of interests in pure mathematics: topology, algebraic geometry, from game theory to logic. He wanted to solve a problem with his strength and his conceptual tools, searching for the original as possible approach to this issue.
In 1949, while studying for his doctorate, he developed the considerations that 45 years later made him win the Nobel Prize. During that period Nash established the mathematical principles of game theory game theory .

Nash has revolutionized the economy with his studies in applied mathematics, 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.

Nash has lived for almost thirty years of scientific achievements, academic and mental illness. During the brilliant scientific work in prestigious universities such as Princeton University, or in companies such as RAND Corporation, where he and logical, mathematical, physical and experienced engineers, working for the government to Cold War political and military strategies. He had to live with schizophrenia often and for long periods during his life obscures the extravagance and creativity emotional isolation from the outside world.
After periods of crisis, often following admissions to psychiatric hospitals, Nash returned to mathematics. But a few months after the disease relapses. Therapies such as electroshock, straitjackets chemical injections of insulin have been scored in the physical, but now that Nash is a seventy still attending the Institute in Princeton, he studied mathematics and still seems cured of the disease.
In the early 90 ', the crisis seems to have no end. Nash can then return to his work with greater serenity, increasingly integrated into the system and the international academic learning to talk and exchange ideas with other colleagues. The symbol of this rebirth is marked in 1994 with the Nobel prize for economics.

The review of the film "A Beautiful Mind"

PLOT OF THE FILM:
Year 1947. Although it is not the scion of a prestigious family, the young John Forbes Nash jr. was admitted to Princeton for postgraduate specialization in mathematics. After all the social niceties have no meaning for Nash, as well as the lessons does not occur. John is haunted by one thought: to find truly original idea. For him this is the only thing that could have a value. One evening, while in a bar with some friends, watch their behavior in a beautiful This blonde. Look gestures and patterns, and suddenly emerge in the mind feels that pursuing that idea for some time. His subsequent report on game theory, the mathematical discipline that analyzes the optimal behavior of individuals, or coalitions, in situations of strategic interaction, openly contradicts the theories of Adam Smith the father of modern economics. The thought of one hundred and fifty years after Smith passed suddenly appears. Following this discovery, Nash gets a post of professor at MIT, but it gets even more satisfaction when one William Parcher, a secret agent, contacted him for a risky job, we are in a cold war, and Nash is asked to decode the codes secrets of the enemy. Meanwhile, at MIT, Alicia, a student of physics, can also open the door to the street in the heart and feelings. The two married soon, but Nash does not say anything to his wife of its work secret. Too much tension, fatigue, danger in the end have the upper hand: obsessed with paranoia, visions, nightmares, Nash is declared with schizophrenia and hospitalized in a psychiatric hospital. From that moment his life takes place between prolonged periods of hospitalization and return home. Sustained by Alicia, Nash seems to be able to cast their hallucinations. In October 1978 he was back to Princeton. In March 1994, while sitting at the table of the library where almost 50 years earlier he had admired veteran of the university, it was announced that the Academy in Stockholm awarded him the Nobel Prize for the theory of the modern economy. In December 1994, Nash takes the stage, receives the award and thanked his wife in the room. "You are all my reasons," he says, turning to her.

sitography:

http://www.math.it/libri/genionumeri.htm
http://www.zam.it/home.php?id_autore=1049
http:/ / en.wikipedia.org / wiki / A_Beautiful_Mind_ (film )
http://www.cinefile.biz/mind.htm

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the shape of things to interact with the great mathematicians

EVERY DAY WE ARE IN CONTACT WITH THE GEOMETRY Unknowingly, when we awake until the time you go to bed.

IS EVERYTHING 'AROUND GEOMETRICAL FIGURES get the idea, meeting certain scientific laws.

AND ALL THAT 'around us and' ASSOCIATION Geometric shapes ...

THE FACE OF MY ALARM E 'a circle;

THE BED has a rectangular shape ...

furniture (wardrobes, bookcases, chest of drawers) are rectangular shaped and SQUARE;

L ' BOX, TIRES, notebooks have a rectangular shape

I PASTELS are cylindrical ...

WHEN TRAVEL BY CAR GEOMETRY I need to RECOGNIZE THE FACT I HAVE TO BE ABLE TO TRAFFIC distinguish

A LINE FROM A CONTINUOUS INTERMITTENT;
I HAVE SIGNS OF DANGER TRIANGULAR FORM;
I POSTERS STATEMENT TO HAVE rectangular or square shape;
I SIGNS OF PROHIBITION have a circular shape;

CDs ARE IN THE FORM OF CIRCLE

ALSO LIKE THE GAMES TANGRAM, or the respective types LEGO GEOMETRIC

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ENVIRONMENT IN VIVO

Ossrvando the environment in which I live, I can see that I am part of a set of environments, from a wider observation indicates that: