I feel that my knowledge cannot be easily transferred. I was self-motivated after certain age. Students that come to me without prior motivation have a hard time getting something out of my work. My colleagues seem to have more of a clue how to get everybody working on the subject matter. When my students are mature, there is less of a problem, but the younger they are, the more of a challenge it is for me to get them interested in abstract work.
I have to find a place where my knowledge and attitudes are useful, I am not in a good place right now. The students and I did not synchronize well.
Wednesday, February 28, 2007
Tuesday, February 27, 2007
¿Qué Se de Matemáticas?
Las matemáticas las he estudiado al menos desde el primer año de primaria. En este ensayo escribo sobre mis conocimientos de matemáticas. Estudié matemáticas en la escuela durante diecisiete años. Además por mi cuenta he estudiado matemáticas durante los nueve años en que trabajé en mi tesis doctoral, y los veintiséis años desde entonces.
Introducción
En la escuela primaria estudié principalmente aritmética, y un poco de geometría. En la secundaria estudié álgebra, geometría más avanzada, y trigonometría; la principal diferencia es que hice demostraciones. En la vocacional, además de estudiar más álgebra y geometría analítica, estudié cálculo diferencial e integral, y álgebra vectorial, a diferencia de la secundaria ahora aceptamos soluciones complejas además de reales. En la escuela de ingeniería proseguí con cálculo, pero ahora con demostraciones, llegando hasta análisis matemático con variables complejas. Estudié teoría de conjuntos. La geometría la aprendí ahora con vectores y álgebra lineal. Llevé cursos de ecuaciones diferenciales, probabilidad y estadística, análisis funcional, y programación de computadoras. En la maestría además de estudiar más profundamente lo anterior, estudié teoría de grupos y geometría diferencial.
Desarrollo
En la primaria las tablas de multiplicar ocuparon gran parte del trabajo del segundo año. Hice multiplicaciones y divisiones con más de dos cifras significativas. En el tercer año aprendí a sacar la raíz cuadrado de un número arbitrario. Los quebrados también ocuparon mi tiempo en la primaria. Aprendí a calcular áreas, perímetros y volúmenes.
Estudié los conceptos de punto, línea, y superficie. En la secundaria demostré teoremas sobre los ángulos formados por un par de líneas paralelas y una diagonal a éllas. Empecé el estudio del álgebra elemental, hasta llegar a la ecuación de segundo grado, y sistemas de ecuaciones lineales. Aprendí las fórmulas para el cálculo de áreas y volúmenes.
En la vocacional repasé inicialmente las matemáticas de secundaria, e hice muchos más ejercicios hasta dominar el álgebra, y las identidades trigonométricas. Con esta base aprendí a calcular derivadas e integrales, usando varias técnicas algebraicas como la integración por partes. En geometría llevé un curso de geometría proyectiva en la clase de dibujo. Hice una serie de diagramas técnicos que todavía están en la casa de mi mamá en México. Las demostraciones geométricas ya fueron más completas que en la secundaria. En este nivel de estudios también aprendí el concepto de función exponencial y su inversa, el logaritmo. Con las tablas de logaritmos y de funciones trigonométricas aprendí a calcular más eficientemente problemas de ingeniería y ciencia.
En la carrera de ingeniería tuve gran dificultad con el primer curso de cálculo, éste tuvo un nivel de rigor matemático al cuál yo no estaba acostumbrado. En la vocacional aprendí técnicas para obtener derivadas e integrales con ayuda de transformaciones algebraicas, pero no era capaz de demostrar que esas fórmulas eran correctas. Además para el análisis numérico necesario para programar computadoras no era muy hábil en obtener el error en el cálculo. La teoría combinatoria necesaria para el curso de probabilidad y estadística también me causó dificultades.
En la maestría además de estudiar con más detalle los temas anteriores aprendí que las funciones se pueden considerar como vectores en espacios de infinitas dimensiones y cómo aproximar una función cualquiera con un número infinito de funciones como en la serie de Fourier y de Laplace. Estas técnicas son útiles para resolver ecuaciones diferenciales parciales. Los cursos que no había tomado antes fueron de teoría de grupos y geometría diferencial. Aprendí el concepto de tensor y de curvatura intrínseca inventado por Gauss.
No llevé un curso completo de geometría no-euclideana pero sí aprendí lo suficiente para entender la gran contribución de Einstein en su Teoría General de la Relatividad.
También fué durante mis estudios de maestría que entendí la gran importancia de las matrices para realizar rotaciones en espacios vectoriales.
Conclusión
He estudiado matemáticas por muchos años. Ahora puedo aplicar este conocimiento a diveros aspectos de la realidad que se pueden estudiar así: como son la Química, la Física y la Ingeniería Eléctrica. Además de la programación de computadoras y el análisis numérico. Mi manera de pensar es más organizada ahora que he estudiado matemáticas, que cuando no sabía matemáticas. Con la aritmética, el álgebra, la
geometría, la trigonometría, el cálculo, y las ecuaciones diferenciales; ahora puedo entender las contribuciones de grandes matemáticos como: Eudoxio, Arquímedes, Gauss, Descartes, Newton, Liebniz, y Riemann, por mencionar solo unos cuantos.
Mi aspiración es algún día poder contribuir a este río de conocimientos, que nos sirven para resolver los problemas que se presentan cada vez con mayor frecuencia en el mundo moderno e industrializado en que vivimos.
Introducción
En la escuela primaria estudié principalmente aritmética, y un poco de geometría. En la secundaria estudié álgebra, geometría más avanzada, y trigonometría; la principal diferencia es que hice demostraciones. En la vocacional, además de estudiar más álgebra y geometría analítica, estudié cálculo diferencial e integral, y álgebra vectorial, a diferencia de la secundaria ahora aceptamos soluciones complejas además de reales. En la escuela de ingeniería proseguí con cálculo, pero ahora con demostraciones, llegando hasta análisis matemático con variables complejas. Estudié teoría de conjuntos. La geometría la aprendí ahora con vectores y álgebra lineal. Llevé cursos de ecuaciones diferenciales, probabilidad y estadística, análisis funcional, y programación de computadoras. En la maestría además de estudiar más profundamente lo anterior, estudié teoría de grupos y geometría diferencial.
Desarrollo
En la primaria las tablas de multiplicar ocuparon gran parte del trabajo del segundo año. Hice multiplicaciones y divisiones con más de dos cifras significativas. En el tercer año aprendí a sacar la raíz cuadrado de un número arbitrario. Los quebrados también ocuparon mi tiempo en la primaria. Aprendí a calcular áreas, perímetros y volúmenes.
Estudié los conceptos de punto, línea, y superficie. En la secundaria demostré teoremas sobre los ángulos formados por un par de líneas paralelas y una diagonal a éllas. Empecé el estudio del álgebra elemental, hasta llegar a la ecuación de segundo grado, y sistemas de ecuaciones lineales. Aprendí las fórmulas para el cálculo de áreas y volúmenes.
En la vocacional repasé inicialmente las matemáticas de secundaria, e hice muchos más ejercicios hasta dominar el álgebra, y las identidades trigonométricas. Con esta base aprendí a calcular derivadas e integrales, usando varias técnicas algebraicas como la integración por partes. En geometría llevé un curso de geometría proyectiva en la clase de dibujo. Hice una serie de diagramas técnicos que todavía están en la casa de mi mamá en México. Las demostraciones geométricas ya fueron más completas que en la secundaria. En este nivel de estudios también aprendí el concepto de función exponencial y su inversa, el logaritmo. Con las tablas de logaritmos y de funciones trigonométricas aprendí a calcular más eficientemente problemas de ingeniería y ciencia.
En la carrera de ingeniería tuve gran dificultad con el primer curso de cálculo, éste tuvo un nivel de rigor matemático al cuál yo no estaba acostumbrado. En la vocacional aprendí técnicas para obtener derivadas e integrales con ayuda de transformaciones algebraicas, pero no era capaz de demostrar que esas fórmulas eran correctas. Además para el análisis numérico necesario para programar computadoras no era muy hábil en obtener el error en el cálculo. La teoría combinatoria necesaria para el curso de probabilidad y estadística también me causó dificultades.
En la maestría además de estudiar con más detalle los temas anteriores aprendí que las funciones se pueden considerar como vectores en espacios de infinitas dimensiones y cómo aproximar una función cualquiera con un número infinito de funciones como en la serie de Fourier y de Laplace. Estas técnicas son útiles para resolver ecuaciones diferenciales parciales. Los cursos que no había tomado antes fueron de teoría de grupos y geometría diferencial. Aprendí el concepto de tensor y de curvatura intrínseca inventado por Gauss.
No llevé un curso completo de geometría no-euclideana pero sí aprendí lo suficiente para entender la gran contribución de Einstein en su Teoría General de la Relatividad.
También fué durante mis estudios de maestría que entendí la gran importancia de las matrices para realizar rotaciones en espacios vectoriales.
Conclusión
He estudiado matemáticas por muchos años. Ahora puedo aplicar este conocimiento a diveros aspectos de la realidad que se pueden estudiar así: como son la Química, la Física y la Ingeniería Eléctrica. Además de la programación de computadoras y el análisis numérico. Mi manera de pensar es más organizada ahora que he estudiado matemáticas, que cuando no sabía matemáticas. Con la aritmética, el álgebra, la
geometría, la trigonometría, el cálculo, y las ecuaciones diferenciales; ahora puedo entender las contribuciones de grandes matemáticos como: Eudoxio, Arquímedes, Gauss, Descartes, Newton, Liebniz, y Riemann, por mencionar solo unos cuantos.
Mi aspiración es algún día poder contribuir a este río de conocimientos, que nos sirven para resolver los problemas que se presentan cada vez con mayor frecuencia en el mundo moderno e industrializado en que vivimos.
Tuesday, February 20, 2007
Academic Language in a Classroom
According to Vygotsky and Halliday, if students are not exposed to academic language in the classroom, it is unlikely that they will get it in the street. A minimum goal for a classroom is to get the students talking academic.
Monday, February 19, 2007
Michael Halliday
Michael Halliday has studied linguistics in English, Chinese, and Japanese, among other languages. One of his discoveries is that it is in the social interaction that humans produce semiotic artifacts, e.g. language, to satisfy survival needs.
Gordon Wells from the University of California at Santa Cruz, has found close connections between Halliday's and Vygostky's ideas.
Halliday and Vygotsky make the following assumptions:
1. In order to understand any form of human behavior, it is necessary to adopt a genetic approach.
2. Both phylogenetically and ontogenetically, development is dependent on the availability of tools; for intellectual development, semiotic tools are of particular importance.
3. Language is a particularly powerful semiotic tool because its semantic structure:
encodes the culture's theory of experience , including the knowledge associated with the use of all other tools;
enables its users to interact with each other in order to coordinate their activity and simultaneously to reflect on and share their interpretations of experience.
4. In ontogenesis, development is raised to new levels by the appropriation of the tools created by previous generations. In particular, in learning their mother tongue through situationally based conversation, children also appropriate the knowledge and practices of their culture.
In less technical words, Vygotsky and Halliday believe that language is at the basis of knowledge and is learned in the house, the street and the school. Now one can add that children also learn meaning online.
Gordon Wells from the University of California at Santa Cruz, has found close connections between Halliday's and Vygostky's ideas.
Halliday and Vygotsky make the following assumptions:
1. In order to understand any form of human behavior, it is necessary to adopt a genetic approach.
2. Both phylogenetically and ontogenetically, development is dependent on the availability of tools; for intellectual development, semiotic tools are of particular importance.
3. Language is a particularly powerful semiotic tool because its semantic structure:
4. In ontogenesis, development is raised to new levels by the appropriation of the tools created by previous generations. In particular, in learning their mother tongue through situationally based conversation, children also appropriate the knowledge and practices of their culture.
In less technical words, Vygotsky and Halliday believe that language is at the basis of knowledge and is learned in the house, the street and the school. Now one can add that children also learn meaning online.
Children of Men
Alfonso Cuarón's dystopia presents a world where the birth of a child is a moment of hope. Every born child brings us hope for a better future, but in this movie this miracle is more important because the most recent birth took place more than twenty years before. Humans find themselves at the verge of extinction due to worldwide infertility.
I do not believe that a species could go away that way. But then again, the future is unknowable.
What I like about this movie is the sense of urgency that we must have to face the real threats upon us right now. Inuit people are abandoning their way of life because the Arctic is warmer than in any time of recorded history. Europe is having heat episodes killing thousands of people, and the desert is encroaching Darfur, where millions of people are dying. This is apocalyptic.
I do not believe that a species could go away that way. But then again, the future is unknowable.
What I like about this movie is the sense of urgency that we must have to face the real threats upon us right now. Inuit people are abandoning their way of life because the Arctic is warmer than in any time of recorded history. Europe is having heat episodes killing thousands of people, and the desert is encroaching Darfur, where millions of people are dying. This is apocalyptic.
Saturday, February 17, 2007
Lev Vygotsky and Sheltered Instruction
The Russian thinker Lev Vygotsky made a model of how we learn. The brain has a schedule ,but we cannot just wait until everything happens as if watching a rose grow. Vygotsky intervened in that process. The Zone of Proximal Development (ZPD) exists in all of us. We are not omniscient.
From Wikipedia we can get, "Omniscience is the capacity to know everything infinitely, or at least everything that can be known about a character's including thoughts, feelings, life and the universe, etc. In monotheism, this ability is typically attributed to God. This concept is included in the Qur'an, where God is called "Al-'aleem" on multiple occasions. This is the infinite form of the verb "alama" which means to learn."
The teacher has to know the ZPD of the student, and work from there on. This is the Goldilocks principle, not too cold, not too hot, just right. Children can be moody, if one looses their attention they go away.
English learners need sheltering as much as the students that Vygostsky worked with. One has to provide "scaffolding", so they can build their own egos from that basis. Defectology is the study and practice of handicapped students learning. In some non-pejorative sense one can say that an English learner student needs special attention.
English learner students are special.
There is a group of teachers involved in the development and application of the ways to address the needs of these special students.
One can read from their Website:
The Sheltered Instruction Observation Protocol (SIOP) Model (Echevarria, Vogt & Short, 2004) was developed to provide teachers with a well articulated, practical model of sheltered instruction. The SIOP Model is currently used in most of the 50 states and in hundreds of schools across the U.S. as well as in several other countries. The intent of the model is to facilitate high quality instruction for ELLs in content area teaching.
From Wikipedia we can get, "Omniscience is the capacity to know everything infinitely, or at least everything that can be known about a character's including thoughts, feelings, life and the universe, etc. In monotheism, this ability is typically attributed to God. This concept is included in the Qur'an, where God is called "Al-'aleem" on multiple occasions. This is the infinite form of the verb "alama" which means to learn."
The teacher has to know the ZPD of the student, and work from there on. This is the Goldilocks principle, not too cold, not too hot, just right. Children can be moody, if one looses their attention they go away.
English learners need sheltering as much as the students that Vygostsky worked with. One has to provide "scaffolding", so they can build their own egos from that basis. Defectology is the study and practice of handicapped students learning. In some non-pejorative sense one can say that an English learner student needs special attention.
English learner students are special.
There is a group of teachers involved in the development and application of the ways to address the needs of these special students.
One can read from their Website:
The Sheltered Instruction Observation Protocol (SIOP) Model (Echevarria, Vogt & Short, 2004) was developed to provide teachers with a well articulated, practical model of sheltered instruction. The SIOP Model is currently used in most of the 50 states and in hundreds of schools across the U.S. as well as in several other countries. The intent of the model is to facilitate high quality instruction for ELLs in content area teaching.
Thursday, February 15, 2007
When Somebody Quits
There is a difference between being asked to leave and quitting. Recently two people I know decided to leave a difficult situation. I asked one of them to reconsider the move and see what can be done. I asked the other if there was a consideration of the most likely outcome of that decision.
I hope both people find a better position for themselves. But why did they leave?
I guess I am asking myself if I rather stay where I am or should move on. I was surprised in the past when I decided to leave a position and the boss did not try to retain me. I had made my mind, but still it felt strange that the person in charge did not ask me to stay.
No one is indispensable, there is always somebody else that takes the space we leave. That in a sense is good, but it leaves in me a strange feeling that we do not matter.
I prefer to think of this choice as the ultimate expression of free will. I will do what I think is best under any circumstance. That is the purpose of life. We only live once.
I hope both people find a better position for themselves. But why did they leave?
I guess I am asking myself if I rather stay where I am or should move on. I was surprised in the past when I decided to leave a position and the boss did not try to retain me. I had made my mind, but still it felt strange that the person in charge did not ask me to stay.
No one is indispensable, there is always somebody else that takes the space we leave. That in a sense is good, but it leaves in me a strange feeling that we do not matter.
I prefer to think of this choice as the ultimate expression of free will. I will do what I think is best under any circumstance. That is the purpose of life. We only live once.
Tuesday, February 13, 2007
VMware
Virtualization may be the way to go to address the challenge of eighty cores in one chip.
When I was working at Lucent Technologies my friends and I patented a way to use Virtual State Machines (VSM), to control Internet Transmission. This method was invented by my boss, Joe Lennert, to solve a practical problem at the shop at Lucent. How to automatize the transmission of big files around the world from our location? The method of VSM turned out to be very powerful, and no operator was needed to send these big files to the Netherlands. Robust Process Automation (RPA), is a method to increase the reliability of the virtual machines.
Now there is a company that independently discovered this and is having its Initial Public Offering (IPO) for EMC soon.
Check their press release:
IPO.
When I was working at Lucent Technologies my friends and I patented a way to use Virtual State Machines (VSM), to control Internet Transmission. This method was invented by my boss, Joe Lennert, to solve a practical problem at the shop at Lucent. How to automatize the transmission of big files around the world from our location? The method of VSM turned out to be very powerful, and no operator was needed to send these big files to the Netherlands. Robust Process Automation (RPA), is a method to increase the reliability of the virtual machines.
Now there is a company that independently discovered this and is having its Initial Public Offering (IPO) for EMC soon.
Check their press release:
IPO.
Snowed Out Again
This is the second time this school year when snow impedes regular activities. Again I was inside the building when they told me, no classes today. My son is happily playing with the Wii now.
I have to grade some papers, and this snow gives me a little time.
I am not satisfied with the level of mathematics skills at my school. Can I change that?
I am trying.
I have to grade some papers, and this snow gives me a little time.
I am not satisfied with the level of mathematics skills at my school. Can I change that?
I am trying.
Monday, February 12, 2007
Multiple Cores in One Ship
Intel announced recently that in five years time there will be a chip in the market with eighty cores.
We have a challenge, how to program eighty threads without getting tangled?
We have a challenge, how to program eighty threads without getting tangled?
Pan's Labyrinth
Guillermo del Toro's most recent movie moved me to tears. A little girl refuses to take an innocent life when she is asked to. She prefers to suffer herself than to be unjust. By doing so, in the fairy tale part of the movie, she is rewarded, in the real part of the movie she is killed.
At the end, all of us die, but some of us choose to die well and some bad.
At the end, all of us die, but some of us choose to die well and some bad.
Saturday, February 10, 2007
What to Do When a Promotion Is Not So Good?
Recently I received comments from two former students to the effect that they liked my class better than the ones the were "promoted" to.
Of course other promoted students seem not to complain.
I teach in Spanish in a bilingual program. Besides the obvious advantage that the students are fluent Spanish speakers, and their English is not so good. In my self serving mind I like to think that, at least for these two, I am a better math teacher than the one they got. After all I have a Ph.D. in Physics and they do not.
What can these students do? Nothing, I think. Just bear it and keep moving forward.
Of course other promoted students seem not to complain.
I teach in Spanish in a bilingual program. Besides the obvious advantage that the students are fluent Spanish speakers, and their English is not so good. In my self serving mind I like to think that, at least for these two, I am a better math teacher than the one they got. After all I have a Ph.D. in Physics and they do not.
What can these students do? Nothing, I think. Just bear it and keep moving forward.
Sunday, February 04, 2007
Apocalypse 2012
Lawrence Joseph has written Apocalypse 2012.
This consultant believes that the end is very likely to come in that year. He bases his hunch on some Mesoamerican documents that point to that date; 12/21/12.
I do not believe in predictions, even less about the future. Nevertheless there are strong signs of a deteriorating environment that make me pay attention.Ray Kurzweil predicts Utopia for 2045. Who is right?.
Many years ago Buckminster Fuller wrote a book with the same great or dire outcomes.
What can I predict?
I predict that the Earth will still be in orbit around the Sun in 2012, we may be a little warmer, and by 2045 I will be alive only if Kurzweil is right.
Who knows?
This consultant believes that the end is very likely to come in that year. He bases his hunch on some Mesoamerican documents that point to that date; 12/21/12.
I do not believe in predictions, even less about the future. Nevertheless there are strong signs of a deteriorating environment that make me pay attention.Ray Kurzweil predicts Utopia for 2045. Who is right?.
Many years ago Buckminster Fuller wrote a book with the same great or dire outcomes.
What can I predict?
I predict that the Earth will still be in orbit around the Sun in 2012, we may be a little warmer, and by 2045 I will be alive only if Kurzweil is right.
Who knows?
Friday, February 02, 2007
Woman in the Zócalo Handing Out Corn
“This is the first time you’ve got a real agricultural shock to the economy,” he said. “The market economy isn’t as benevolent as a state-run economy. The market is characterized by fluctuations. You have to live with it and know how to deal with it.”
The marchers clearly directed their blame at the government. “When they get involved in something as elemental as tortillas, well that’s just irresponsible,” said Francisco Ruiz, 48, a telephone worker.
Carola Ortega, 64, a member of a peasant group, said: “We’re here because the government always takes advantage of the poor. First it was tortillas, but we’re not stupid; if tortillas go up, everything else does too.”
Thus ends a report on the New York Times By ELISABETH MALKIN on the Food Demonstration in Mexico City.
This looks like the beginning of a fundamental fight for survival by the Mexican people. Without corn Mexicans are nothing.
Thursday, February 01, 2007
Chávez and Bush
President Chávez from Venezuela has gotten into some heated confrontations with George W. Bush. At the UN he even said that President Bush is the devil, that he could smell sulfur on the podium, when he spoke there a little after Bush did. Those are not words of peace, nor diplomatic, it seems that the US and Venezuela are in one of the lowest points in their bilateral relationship.
I write here some thoughts about these two men.
Bush was elected both times with a very slight majority, it is even arguable that he stole both, or at least one of these elections. Chávez tried to seize power with a coup d'état, but failed. He comes from the military, even though he is from the working class, he decided that the military was the only way to get power in Venezuela, and he was able to go up in the Venezuelan army.
Now both men are very much in power in their respective countries and they do not have the same political agenda.
Chávez wants to change Venezuela's Constitution to remain in power for a longer time, like Fidel Castro in Cuba, or Porfirio Díaz in México.
The political agenda of Chávez is good for the working class, but the way he wants to achieve it is not democratic. Eight years is enough for any man to state his vision for his country and then he should move out so others have a chance to keep the movement going.
I write here some thoughts about these two men.
Bush was elected both times with a very slight majority, it is even arguable that he stole both, or at least one of these elections. Chávez tried to seize power with a coup d'état, but failed. He comes from the military, even though he is from the working class, he decided that the military was the only way to get power in Venezuela, and he was able to go up in the Venezuelan army.
Now both men are very much in power in their respective countries and they do not have the same political agenda.
Chávez wants to change Venezuela's Constitution to remain in power for a longer time, like Fidel Castro in Cuba, or Porfirio Díaz in México.
The political agenda of Chávez is good for the working class, but the way he wants to achieve it is not democratic. Eight years is enough for any man to state his vision for his country and then he should move out so others have a chance to keep the movement going.
The Same Person Twenty Years Apart
Yesterday I met a man trying to get his High School Diploma in an adult education class. He had his chance when he was a teenager. He let that opportunity go, but here he goes again.
He says that he needed more direction when he was younger. Now he knows more things and seems determined to get his GED diploma. For those that may be reading this and are not Americans, GED stands for General Education Development, and is an alternative for a whole course of high school classes.
How could four years be equivalent to one day of tests?
That is up to the employer to decide, after all life is complex.
I ask myself, is this man the same person that let the opportunity pass him by twenty years ago?
My answer is no. Each one of us dies and is reborn in the course of the sixty or more years that we live.
Until we die, there is always another chance.
He says that he needed more direction when he was younger. Now he knows more things and seems determined to get his GED diploma. For those that may be reading this and are not Americans, GED stands for General Education Development, and is an alternative for a whole course of high school classes.
How could four years be equivalent to one day of tests?
That is up to the employer to decide, after all life is complex.
I ask myself, is this man the same person that let the opportunity pass him by twenty years ago?
My answer is no. Each one of us dies and is reborn in the course of the sixty or more years that we live.
Until we die, there is always another chance.
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