Thank you for your research on the stuff I
left to contextualize the videos sent to this list.
The people on the ethnomathematics list I
sent also said that the video is not good to convey my thoughts… However, since
I have some feedback from you from the list, I fell that I need to write a more
detailed article to explain my ideas.
I really liked your approach to mathematical resolution from a point of view of recursion. If I got your point right, to know the syntax of the mental space is to mediate the problems with structural features that are “intuitively” perceived bus humans.
As an anthropologist studying mathematics
as cultural production, to think beyond the illusion of literal meaning is very
difficult to have interlocutors. For mathematicians, the sensation that five is
always five does not contradicts the fact that we can go for five from four, or
got it back from six. There is no fixed point to where we can say numbers are
Such comprehension of the mobility of the mind to make a pathway to the solution is my main interest.
Even if Linguistics is the science of meaningful speech production, it is not totally a “meaning related” discipline. Structure, or more specifically, syntax, plays a main role on establishing the bases for a comprehension of the language faculty. Sure Chomsky has great insights to the question of recursion and the similarities between language and numbers.
Although mathematics is beyond language, it cannot exist without it. It also needs some semiotic medium to materially storing the mental procedures it creates. Since mathematics is then a kind of graphical system, the symbols it takes to execute it are culturally embedded.
My interest in mathematics is the discursive,
or the “how to solve it” aspect you mentioned in your text citing Polya.
My research has been conducting an analysis of mathematical word problems from the Brazilian Public Schools Mathematics Olympiad. By looking on the discursive aspect of the different strategies for the same question, I could identify patterns in the way people at the situation dealt with the resolution.
Anyway, thank you again for your interest.
To understand the number line as something that we can go through in many ways, that is, by knowing different forms of description we have access to the key to learn mathematics. The challenge is to memorize the map...the mental space we move our quantities go get the result in the end of course.
The majority of people who are reading this, as well the majority of non reading both don´t know, and don´t have positive feelings with mathematics; they recognize it, appraise it but do not want to stay with it within their bodies, in their minds...
As a researcher, among other things, I have the challenge to produce digital content for different supports, some interactive, other not. Mathematics is thought within a medium, a paper, a computer, and the stream of consciousness that make the operations possible although in our heads, needs a physical support to embed the content being manipulated.
I discovered some time ago looking for the role of language in mathematical education that in order to understand math, it was neither necessary to discover it hidden somewhere in the statement, nor it was necessary to attach meaning to it. It is the case that in order to do it, we need to just to be able describe it in many forms as possible, as the information is already there and can be seen in many ways. To narrate something is to account the whole of participant, actions, processes and events of the problem in different possibilities.
My hypothesis was to see mathematics as a cultural practice in other societies it was also possible to learn about it narratives, the specific ways each society have to achieve some general principle. How societies pass technological knowledge through the generations. It was clear that the problem was not to attach a fixed meaning but how to construct any meaning by the same fixed support. It was a language discursive problem.
Researching about a subject is the capacity of narrative about something, to describe in a stylistic form any object and still preserve it characteristics. The numerical narrative is possible, and it characteristics are described by many cultures. In the process of searching for mathematical examples I found the ethnomathematics research field. This approach to mathematics is based on the ethnographic fact that operations are made with different procedures, symbols and tools.
By 2009, at the same time I also found the data visualization field. The blog from Manuel Lima changed my mind about how deluded with anthropology I was. The possibility to think mathematics as something ethnomathematics had been appointed to other societies, the tools itself are embedded, with no meaning to be attached. It was a reading procedure instead of applying some though into it.
This blog has been used somehow to describe this story. Since then, I had contact with so many other things, like the incredible professional community of EPIC, witch had me put in contact with design research techniques that will improve my goal seeking intentions with education, culture and mathematics.
This is a story about myself. A story about how I came to this blog and how I pretend to use it forward. I am starting this effort to construct a place, a object where it is possible to come with words and get numbers, and vice versa. I can see is necessary a lot of experimentation, and I am starting it.