Participation, Assessment and moderation in my life. (initial reflection, to effect a radical change ... "I must be the change you want to see in the world" Gandhi).
I. Moderate. Group is different from the Group.
"He who teaches learns twice" is the motto of the Galois group, which is planted mathematics and, moreover, citizens exercise the powers of coexistence and peace, participation and democratic accountability, plurality, identity and assessing differences. In this project the starting point is the solidarity and the concept of Group is articulator base.
In Galois mathematics is associated with the development of mental functions and operations, public education, the teacher's mathematical knowledge Guillermo León and teaching of mathematics as a key area in the primary and secondary education. Those attending the Group easier access to higher education, improve their performance in mathematical thinking and begin to project into the society in a way that probably did not even suspect.
This group uses a methodology Transmissions-developmental-social, what mix?), Characterized the pleasure to meet, share knowledge and create in children the desire to succeed, work and dream. At the same time, the Group is free Math Clinic to the community not only school but all the districts close to the community 5. Here it undermines the concept of mathematics as a unique knowledge and oriented bright minds as a place for knowledge and the social.
students started arriving at half past six o'clock. It was Monday. On the left side of the board I am now writing: Solving a simple equation in one variable. Ratios Fundamental Theorem. Properties. Comment on Theory of groups. Exercise solution proposed. We were in Tuscany Ignatian Centenary College (now Jose Antonio Bernal Hector Abad in the district), where the Galois group was 3 years old.
Sebastian Ballesteros, son of Professor Madeleine who also goes to Group Galois-reached himself. "Where's Mom?" I asked. "Bring it, you lose the base." Immediately the child was for her. The Centenary was located at that time, behind the recycling company Codesarrollo, between the Snake Creek and a dark and scary alley that connects with the neighborhood Beaches. The school really is in a dreadful opening night, which is not visible from the highway. Sebastian passes the stream to go for the mom who is finishing the school day in Tuscany. Today
arrived five new members. I asked to sit apart and started. I started with the Fundamental Theorem of proportions as if they were all at the same level. I do not really concerned about the presence of new ones. I commented on a powerful mathematical trick going to multiply or divide a term as a movement that can be done and that the fund is derived from the Theory of Groups . On this occasion we were not going to delve into the concept of Group , just use what is commonly known as transposition of Terms.
I reviewed, which is to solve an equation from the theory of groups and started solving a very simple exercise: m + 8 = 15. Compare also clear a variable with a clear a flower bush.
Every Monday go to Group 8 th grade children. They have been around 6 hours of school work and usually leave at 9:30 pm. I encourage mathematicians saying that they are born and why they are there. I say: "We are taking the saborcito him to mathematics and are tasting. " Conducted several years to raise the level of complexity. As the years go by, I'm asking: "What's next, how am I doing here with this?," Multiply this thing about this other thing? ". I do exercises in various ways.
Today I did an exercise in three ways for them to see that there are several ways that the way forward is not unique. (I stress the words sometimes repeating them. "Paso is to divide and divide," I say for example when they understood the parallel between the theory of Group and transposition of terms. The most involved are the students more time lead in Group. Listening to them, I have a feeling of calm and confidence. It is a joy to see so many mathematicians together (Daniel, Katherine, Carmenza, Paola, Emilio, Stephanie, Natalie, Louise, Cristian Berrio, Guapacha, Wander, Camilo Viana, Jorge Andres, Diana Samboni, Jennifer Agudelo, Oscar Daniel, Diana mercedes, Wendy Sergio Duque Sergio Arenas, Mario, Tejada, Juan David, Eliecer, Sebastian, Carmen, Kevin, Karen ...). I want to say that Katherine should go up at 9:30 pm when we finished, the last subway station (Santo Domingo), often on foot. I showed today
also: how are you equations found in other areas. Einstein wrote the equation (the equivalence of mass and energy) and the law of gravitation Newton. Tell them they're the same little letters, what happens is that they charged a physical context. I showed how easy it is clear the Cavendish constant and the mass of the Einstein equation. I was a little fast in this work because we were reviewing, and what he observed was that the student how to solve the equations and the relationship (comparative) group theory (abstract algebra View John B. Fraleigh).
Then I realized, purposely bad to see how they were transposed of attentive students. It shows again the participation of the oldest. The surprise was great when it was an exercise in subtraction of integers as follows:-2p - p.
- What gives this - I asked him directly to Juan Pablo.
-2s - he responds.
-2p - Johnny also said, then asked Mario.
-3p - says Mario. Is the correct answer. Les
confirmed the result: Da-3p. I was stunned. I felt that with the new ones have lost all this work and time. Then immediately change strategy, I returned and I do, on the right side of the board, explain sum of integers. I'm not upset and I do it in a didactic way. In fact the new members of the group are to be received otherwise.
explained again what are like terms, I began a process of changing the variables immediate generalization of geometric figures to the point where I think I was clear. Then divided into subgroups to implement our motto: he who teaches learns 2 times. And this is where you share knowledge and is planted in children solidarity, peace and tranquility that is won when is if longing for. I confirm my brain to take several years to reach me as dictated by God, and asking other Once all the new members. Finished the year a little easier to answer P = 32 / 3.
As the previous year was a task last week, I asked how much he gave Sebastian. He tells me that 32 / 9. "Where did you get that 9?". He says he did otherwise. "Who else did?" I ask everyone. And I respond Carmenza: "It gave me the same thing to you, teacher, but I did otherwise." Catherine and Daniel, outstanding math, answers the same. I told them perfect. I ask Sebastian to review the exercise immediately with them and continued with another more complex exercise. I insisted that he has a thousand ways to get and went into a dialogue with them asking them to help me solve it. I showed them new tricks and told them "the'm doing exercises like sit on the road. Observed some students who meet with others, such as trying to adelantárseme in the exercise that follows.
"You will evolve and are putting in other ways, I told everyone tried to explain the purpose of the day. Then I went to one of the new students, Roldán, which is not my relatives. Emanuel: "If you have any questions, quiet, do it here, because in the house who is going to help unless you have a mathematical the closet, out, and ask relevant questions. The questions have to be done here where we work.
continued with another year and asked the students if they could erase. I waited until they had finished writing, then removed it and started writing another year. I ask "Why I Write", "what next", "help me", "what I put here," a permanent dialogue with students and increasingly will go up in level of complexity to the exercises.
finished for today. I got a job and signed the attendance. The boys say goodbye to me. I shake hands with a reverence almost priesthood. The respect we feel, gives me joy and strength to not miss a night. The children are happy, show joy. That fills me and makes me want to go ahead with this project. At the door is some mothers, and impatient, as some days like today left at 10:00 pm.
Today Galois group to attend children from third grade to eleventh grade boys, parents, students and teachers of the institution Priest José Antonio Bernal. The group has caused such an impression on the minds of young people who do not mind the schedule, or fatigue and the weariness of a day of schoolwork. All Group members have seen Galois mathematics courses has improved its officers. We have also earned five scholarships for undergraduate studies in Eafit. The first was Sebastián Castrillón Mojica (2007), then Felipe Grajales, Yeison Medina, John Wilmar Perez and last (2010) Emilio Sebastian Henao Bedoya. These kids are geniuses who are not guilty of being born in a vulnerable population, matched by social conflict, poverty, common crime, organized crime, gangs, drugs and neglect of the government. They are geniuses not only of mathematics. What are any science or art, as long as a human being can get to them, not with pity, themselves with the belief that they are capable. And they have shown. Just shake hands. Just to convey confidence. With the assurance of one who knows where it goes. I thank God and my parents because I have led to these narrow streets, these basements where these little people as living in a cave where the sleeping is on the floor and no furniture in the room. The spirits of these children are as hard as diamond and as strong as steel. Are legitimate descendants of Evaristo Galois.
The Galois Group operates four days a week from 6:30 to 9:30 pm. On Monday we algebra, Tuesday and Thursday Logic calculation. Thursday students attending the University EAFIT, tenth and eleventh grade of school, students from other universities like U of A, U Nal and interested adults. We work with the calculation of Stewart, experimental mathematics and Julio Uribe Calad Eafit program.
Tuesday are all interested in the logic and work the book Introduction to Symbolic Logic Dr. Hugo Guarín, on Monday are children in grades 8 and 9, we worked with the books of Julio Uribe Calad, Algebra Baldor and Algebra Fraleigh. On Wednesdays are dedicated to the care of children who are enrolled in grades 3, 4, 5 and 6. It's amazing third grade children by adding whole.
It has the college experience of the teacher (professor at the School of Engineering, UPB), morale and the willingness to make this work. It also has the interest and the physical and mental strength of the students to bend or return journeys in the afternoon studying in the morning. We do not like give them a snack to children who are bent on the journey, but despite this, young people and children enjoy the experience of Galois GROUP and every evening we see how the classroom is filled with them.
didactics used the Galois group is a mixture of Traditional and Development (the developer's proposed Teaching in 1934 to support Vygotsky's position that education leads towed and development, and that does not matter, that the child is mature from the point Piaget's view). I try to work in the Zone of Proximal Development. The contributions of the students are very important issues and questions are held until the student is satisfied. I try to make learning meaningful in the sense of Ausubel and the young is independent.
II. Participate. Evaristo Galois in an enchanted forest. Evaristo
Galois lived only 20 years. He was born on October 25, 1811 in Bourg La Reine, Paris. He died on May 31, 1832 in Paris. "(...) Looking for conditions on the GROUP implicating the solubility of the polynomial equation by radicals ...." Finally showed that a fifth degree equation in general can not be solved by radicals, ie, there for a fifth degree equation as a formula for the second degree.
Polytechnic School, the most prestigious French university to study mathematics, twice rejected the person who solved the following problem: When polynomial equation is solvable by radicals? Problem that exhausted the minds of most brilliant mathematicians to Gauss.
Polytechnic School Galois underwent oral examinations twice that Galois did not approve, thus being demonstrated once again that the mathematical spirit is stronger than educational institutions.
Galois died aged 20 years, enough time to develop and build the main ideas of the theory now known as abstract algebra, where one learns more time One night the concepts of Group Permutation Group, Group ratio, ring, prime ideal, Theorem of Galois and why the quintic can not be solved by radicals.
Galois says "You will please ask the Jacobi or Gauss publicly to state their opinion, not about truth but about the importance of these theorems ..."
discovered in an enchanted forest creatures as removed stories, peasants, giant butterflies perched on my hand and a large bird with feathers of blue and green (Burrowing), some of which preserve.
remember I interned for two years in the forest of Piedras Blancas in Copacabana, with the book of Fraleigh (Abstract Algebra) and accompanied by Alighieri (my dog) to study theory of groups, rings, fields and Galois theory.
What a wonderful time. No one knew who enjoyed most of the sun and water in the gorge of Piedras Blancas it was crystal clear if or I Alighieri. There
understand some of the structure of polynomials. I understood why the associative properties, modulated and inverted (we all show them as fallen from heaven) have a coherent explanation and a birth in the Group. I wrote a proposal for the teaching of polynomials and understand the three Greek problems (duplication of the cube, squaring the circle, the trisection of an angle).
Beside the stream read eight times the Chosen of the Gods (the life of Evaristo Galois) and four, the Divine Comedy by Dante Alighieri (and had read before). He was 27. But my first lessons were in childhood.
The September 8, 1541 celebrated the first Mass in Copacabana by Father Facundo Martín de la Parra in San Juan de la Tasajera. This data was embedded in my brain for life. At the age of seven years, I learned this my first lesson in social, with a very particular approach: my mother made me read the page and a half (I first wrote Martha Lucia, Professor) throughout the afternoon and at night I do not know why because I wanted the memory said. Well, I could not. The stripping was such that even the memory. In return I got up at four o'clock with the news that I said. Since that day, I never said that study. I became an excellent student (thanks mom).
While in ninth grade, the teacher Olga, the Pascual Bravo gave me an exercise in factoring that marked my way to the algebra. I fought and fought to factor this year until the blade was black both clear and broke. In the end, the only thing I wrote on the sheet was: Can not factored. That day did not betray my brain and it worked. The technical answer was: can not be factored into real ones, but anyway I put 10 now 5, is excellent.
teacher I have known worse than my professor of mathematics at grade 10 No. Pascual. I thank God that I do not remember the name. He was unable to perform a factorization for a problem of analytic geometry. So I left the room and I did. That forced me to become self-taught.
But the great lesson, gave me life when I taught to serve. Yes, I learned to serve. I know, which is why, to which one comes to the earth but some learn it later. The life I became a teacher of mathematics.
III. Evaluation. How I became a teacher.
arrive on a Friday afternoon at a building that looked more like an old train station, was the secretary of education in Medellin. There I attended Dona Hortensia. Then I found out I was in charge of purchasing equipment in the secretariat. Like all the respect Antioquia (bold), but very timidly, I gave the sheet. She looked up and said
-Umm ... Math.
"Yes, ma'am," he said. He asked me if I could give a class to her son. I prepared myself to do it, as prescient in a state of appreciation, of how good I was then Secretary. But I want you to know that one does not become a mathematician and mathematics teacher less than a day pa'otro.
remember and I am in the dining room table divisions explaining to my cousins. Was 9. Fifth grade I had studied in the preparatory Camilo Torres (remember all the lives of Amparo Cano, Amparo Amparo Lopez and Zapata) and I graduated as Bachelor of Pascual Bravo. I remember always been an excellent student.
I am the eldest of a family of four children (Clara Victoria, Juan Carlos and Angela Maria), we get a year apart and all proved to be excellent students. I was a professor of mathematics at all, but especially in her teammates and fellow students of the Pedro Justo Berrio and Normal Girls of Copacabana. I have a reputation for good mathematician since then. But, as anyone who can not manage a fortune, I became cocky, arrogant. I thought that knowledge of physics and mathematics were the only truth. Had completed mathematics at the University National begun studying pure physics at the University of Antioquia.
why I went crazy looking around the concept. My only concern was to drink from the fountain, down to the birth of the concept itself. Chased drink from the fountain as a convict seeks freedom or as a patient desires health. But I got tired of downloading and I left the university to see atomic physics, electromagnetism 2 and I do not remember what else. Many years later I understood that there is no philosopher's stone which we derive all mathematical knowledge. That was how I realized that all mathematical theory of a primitive terms, concepts and axioms, that is, objects that have no simple explanation for most of human understanding and that we must accept in order to build: The truth is the original concept for the bivalent logic. The point is the term primitive geometry. The number is the primitive concept of number theory is the term primitive set of set theory. That is, I finally understood to be from something, accept it in the heart and then uploading it to the brain. I finally understood why at the source of stream water is out, but no explanation there, because there is water.
After
all this, I officially retired a few years of college. But I continued to attend the courses of Professor Javier Escobar (Escobar of the crazy UPB) in 1990 and 1991. I would never go back to mathematics. Left to compete in science and I sold leather goods in the company of my sister Clara. In 1992 the company was born GUILLERMO ALIGHIERI ITALY, where I worked in the manufacture and marketing of a shirt created by a physicist. I did very well economically and devoted myself to the pleasures of life. The company went bankrupt. But thanks to my mother Martha Inés Sosa Zea, who has never stopped believing in me and my father William Roldan Carvajal always supported it, came to the University of Medellín, where I graduated from a degree in Mathematics.
never crossed my mind to be a college professor and less degree in math, but life took me there. I returned to the National University in 2006 and took: Number Theory with Abraham Asmar, Calculus and Jorge Mejía Jorge Cossio; Geometry and Logic Deborah Tejada Carlos Mario Parra (Elliott Mendelson's book).
SOW is my desire, through which mathematics. Serving the community they belong. I am convinced that the spirit of Galois flapping, even beyond the educational institutions seeking justice. And I'm convinced that he who teaches, to learn twice. I am a good teacher of mathematics, but I want to understand the way I teach. I feel like a person who wants to, without longing for.
I started as a professor at the municipality of Medellin in the institution Mariscal Robledo, there was the developer and operator of the project: WEEK OF CREATIVE MATH, awarded by the municipality of Medellín with 10 million pesos for the institution. In the institution José Antonio Bernal am the creator and promoter project Galois Group (Civic Medal Luis Fernando Vélez Vélez). I am currently a student of the masters: Teaching Science in the UV of Tecnológico de Monterrey (grant from the awards "the most educated Medellín) and Master of Education in learning environments mediated by ICT in the Far UPB the enchanted forest, now on the side of the river Medellin, Hector Abad district, continue sowing mathematics. Now I want to include ICT into a new adventure. I have to make changes and the first will be on my way to learn, not so much in my teaching, unless it is teacher myself.
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