Monday, December 04, 2006
A month later!!!
After reviewing Chapter 3 I was left in a strange zone, I wanted to work more but did not find the energy to do so. Still, I kept reading, a little at first, and more as time went on. Then, going to the library to check on a dissertation gave me the necessity to write some more and to look at what I had read from a more global perspective. Without knowing I had worked going from a very general view of mathematics to a very specific one.
The last few weeks, I’ve been reading about math. I went from history, to mathematics as a civil right, to mathematics as a social construction, and finally to a specific case of mathematics research. Comments follow.
First, I finished reading A History of π (Pi) (Beckmann, 1971). In it mathematics was treaded as a discipline developed through time, where individual accomplishments linked together a world of knowledge. Still the focus was on the people, even though the definition of Pi was used to tie it all together.
Many times I did not agree with the way Beckman presented the mathematics world. For example, how he introduced Pascal seemed to me disrespectful. He stated,
He was talking about Blaise Pascal, a French mathematician and philosopher, who is remembered for the Pensées – and the demonstrations of God’s existence – as well as for his work in conic sections, probabilities, and the triangle of Pascal.
Secondly, I finished reading Radical Equations: Civil Rights from Mississippi to the Algebra Project (Moses & Cobb, 2001). This book can be cited as an example of how Paulo Freire’s Pedagogía del Oprimido [Pedagogy of the Oppressed] (1970) can be put in action. Moses and Cobb start by reviewing the civil rights movement, the right to vote, to read, and to do/learn mathematics. This, is the voice of one who is empowered and who has committed his life to help others see how they can also go beyond their independent means, even though there is a lot of prejudice around minority people, even though they might have to work twice as hard as others.
Then I read the second part of Sal Restivo’s The Social Relations of Physics, Mysticism, and Mathematics (1983) book. This book looks at mathematics from a social constructionist view. It fits right into the way I have conceived my dissertation project, the way I looked at mathematics. Through out his presentation he summarized the work of many mathematicians and their contributions to mathematical ideas from a social perspective. The art of questioning (Wittgentein, 1967), mathematics as fallible (Hersh, 1978), the importance of social factors in the development of mathematics (Fang & Takayama, 1975), the misconceptions about mathematics – being secretive or contemplative – (Bukharin, 1925), are only a few of those ideas that Restivo presented to evidence how mathematics is embedded in social contexts.
Restivo, based on Needham (1972), sustained,
Later, he wrote, “All knowledge is constituted of mental-and-physical activities, culture, and history. There is no a priori reason to exempt mathematics from this premise” (p. 239). He also stated, “Mathematics … grows out of practical activity and corresponds to the prevailing mode(s) of production, distribution, and consumption. … It is a product of interactions among various activities and products within a social formation” (p. 246).
These readings will help me go back to Chapter 2 and polish its flow into Chapter 3. They will help me tie in the theoretical perspective chosen for the research project, something I still had to do and was worried about.
The final stop will be to read more about writing in mathematics. For this, I have already gone over a Gómez-Jiménez’ (2005) dissertation. Hers is about cognition and writing in mathematics from an individual standpoint. Its review of literature gave me a good start. In this study, students wrote what they were thinking when trying to solve a math problem, and the teacher replied to them individually. She concluded, “transactional written communication not only helped students improve problem solving in mathematics, but also helped them better organize their thoughts when trying to solve a problem” (p. 110). Gómez-Jiménez recommended the study of transactional written communication within groups of students, precisely what I am studying in the discussion forum.
_______________
References:
Beckman, Petr. (1971). A History of ∏ ( Pi). NY: Barnes & Noble Books.
Freire, P. (1970). Pedagogía del Oprimido [Pedagogy of the Oppressed]. Argentina: Siglo XXI.
Gómez-Jiménez, I. M. (2005). El Efecto de la Comunicación Escrita Transaccional en la Solución de Problemas Verbales Geométricos Rutinarios de Estudiantes Universitarios con Diferentes Niveles de Destrezas de Lectura. Río Piedras, Puerto Rico: Facultad de Educación, Universidad de Puerto Rico.
Moses, R. P. & Cobb, C. E. (2001). Radical Equations: Civil rights from Mississippi to the Algebra Project. Boston, MA: Beacon Press.
Restivo, S. (1983). The Social Relations of Physics, Mysticism, and Mathematics. Boston, MA: D. Reidel Publishing Company.
The last few weeks, I’ve been reading about math. I went from history, to mathematics as a civil right, to mathematics as a social construction, and finally to a specific case of mathematics research. Comments follow.
First, I finished reading A History of π (Pi) (Beckmann, 1971). In it mathematics was treaded as a discipline developed through time, where individual accomplishments linked together a world of knowledge. Still the focus was on the people, even though the definition of Pi was used to tie it all together.
Many times I did not agree with the way Beckman presented the mathematics world. For example, how he introduced Pascal seemed to me disrespectful. He stated,
- “one of the most brilliant mathematics and physicists of the 17th century, or at least, he could have been, had he not flown from flower to flower like a butterfly, finally forsaking the world of mathematics for the world of mysticism”
He was talking about Blaise Pascal, a French mathematician and philosopher, who is remembered for the Pensées – and the demonstrations of God’s existence – as well as for his work in conic sections, probabilities, and the triangle of Pascal.
Secondly, I finished reading Radical Equations: Civil Rights from Mississippi to the Algebra Project (Moses & Cobb, 2001). This book can be cited as an example of how Paulo Freire’s Pedagogía del Oprimido [Pedagogy of the Oppressed] (1970) can be put in action. Moses and Cobb start by reviewing the civil rights movement, the right to vote, to read, and to do/learn mathematics. This, is the voice of one who is empowered and who has committed his life to help others see how they can also go beyond their independent means, even though there is a lot of prejudice around minority people, even though they might have to work twice as hard as others.
Then I read the second part of Sal Restivo’s The Social Relations of Physics, Mysticism, and Mathematics (1983) book. This book looks at mathematics from a social constructionist view. It fits right into the way I have conceived my dissertation project, the way I looked at mathematics. Through out his presentation he summarized the work of many mathematicians and their contributions to mathematical ideas from a social perspective. The art of questioning (Wittgentein, 1967), mathematics as fallible (Hersh, 1978), the importance of social factors in the development of mathematics (Fang & Takayama, 1975), the misconceptions about mathematics – being secretive or contemplative – (Bukharin, 1925), are only a few of those ideas that Restivo presented to evidence how mathematics is embedded in social contexts.
Restivo, based on Needham (1972), sustained,
- “The general program for the sociology of mathematics is the study of how forms of social organization influence the origins and growth of mathematical knowledge, and the role of mathematics in the social formation of a given time and place” (p. 192).
Later, he wrote, “All knowledge is constituted of mental-and-physical activities, culture, and history. There is no a priori reason to exempt mathematics from this premise” (p. 239). He also stated, “Mathematics … grows out of practical activity and corresponds to the prevailing mode(s) of production, distribution, and consumption. … It is a product of interactions among various activities and products within a social formation” (p. 246).
These readings will help me go back to Chapter 2 and polish its flow into Chapter 3. They will help me tie in the theoretical perspective chosen for the research project, something I still had to do and was worried about.
The final stop will be to read more about writing in mathematics. For this, I have already gone over a Gómez-Jiménez’ (2005) dissertation. Hers is about cognition and writing in mathematics from an individual standpoint. Its review of literature gave me a good start. In this study, students wrote what they were thinking when trying to solve a math problem, and the teacher replied to them individually. She concluded, “transactional written communication not only helped students improve problem solving in mathematics, but also helped them better organize their thoughts when trying to solve a problem” (p. 110). Gómez-Jiménez recommended the study of transactional written communication within groups of students, precisely what I am studying in the discussion forum.
_______________
References:
Beckman, Petr. (1971). A History of ∏ ( Pi). NY: Barnes & Noble Books.
Freire, P. (1970). Pedagogía del Oprimido [Pedagogy of the Oppressed]. Argentina: Siglo XXI.
Gómez-Jiménez, I. M. (2005). El Efecto de la Comunicación Escrita Transaccional en la Solución de Problemas Verbales Geométricos Rutinarios de Estudiantes Universitarios con Diferentes Niveles de Destrezas de Lectura. Río Piedras, Puerto Rico: Facultad de Educación, Universidad de Puerto Rico.
Moses, R. P. & Cobb, C. E. (2001). Radical Equations: Civil rights from Mississippi to the Algebra Project. Boston, MA: Beacon Press.
Restivo, S. (1983). The Social Relations of Physics, Mysticism, and Mathematics. Boston, MA: D. Reidel Publishing Company.
