On Culture, Geometrical Thinking And Mathematics Education
By Paulus Gerdes
In this article, Paulus Gerdes, investigates the mathematics education in the Third World Countries. He discovers, in these countries, learning new mathematics (come from developed countries) has been difficult for students because they could not make a connection between its content and their real life. Gerdes comes up with the idea of making a curriculum based on student’s culture and tradition. However, he knows making curriculum based on a culture that has been crushed (from whatever reason) is difficult and sensitive. So, he faces with this question how we can retrieve the traditions “when probably many of them have been - as a consequence of slavery, of colonialism... - wiped out.” He proposes to look to the geometrical forms and patterns of traditional objects like baskets, mats, pots, houses, fish traps, etc. He believes this exploration reveals the mathematical knowledge that has been used in creating these objects.
Gerdes’ exploration shows many examples of using mathematics in the real life. The first discovery was using the characteristics of the rectangle in making rectangular based house. Then, Gerdes finds out how artisans in the north of Mozambique make a funnel. He shows this method can be employed to create an equilateral triangle, regular pyramid or even regular octagon. Afterward, he investigates the southern parts of Mozambique and notes that people fasten the top of a basket by pulling a little lassoo around a square-woven button. Gerdes carefully considers these patterns and realizes this is a right triangle surrounded by 3 squares which it represents the Pythagorean Theorem. Then he discovers the formula of the internal angel of a polygon or sum of the first n odd numbers from the pattern in regular hexagonal holes that has been used in making the “Litenga” and “Lema”.
Gerdes’s study is very interesting for me, as I never though connecting culture to mathematics education can be important. I always though wiping out a culture has the influence on people behavior, social study, history or even geometry but not mathematics! It made me think of my own culture and tradition and its hidden mathematical knowledge that I never noticed. I remember visiting Persepolis, an ancient city in Iran from 2500 years ago (Figure 1), the architecture of buildings and the shapes of statues exhibits the geometrical knowledge of my ancestors. I always knew these structures are unique but never thought of its hidden mathematical knowledge. Moreover, the design and patterns of ancient Iranian carpet (Figure 2) also suggest to what extent my ancestors have employed their mathematical knowledge in their real life. However, in my country, teachers barely refer to our traditional mathematics to teach us new mathematics. Now, I understand it was easier to learn not only mathematics but also other science if we were referred to our ancestor’s work and knowledge as most of us have samples in our home.
Figure 1: A view of Persepolis
Figure 2: Iranian Rug (carpet)
The important question is how we can connect to our traditional mathematics? How we can understand to what extent we have improved our ancestor’s knowledge or simply forget them and borrow new mathematics from other colonies or countries?
I think that your question is interesting and important. And, I really like your connections to your own ancestors’ work. My ancestors are mainly northern European. I am not sure what their traditional mathematics were, but I would like to find out. I am not sure how we can measure improvement, maybe through application?
ReplyDeleteAs mentioned in the article, Western academic mathematics can be elitist. To understand mathematical thinking and practice by our ancestors or cultures other than our own, it seems necessary to be open to pragmatic and cultural constructions and events as such. I am curious about the connections of other than traditional Western mathematics to mathematical thinking, such as narratives, embodiment, and spirituality.
Connecting mathematics to history and culture will definite boost students' appreciation of learning and therefore attenuate some unhelpful beliefs about mathematics such as "math is all about getting marks". Also, in a culture-rich context, students are offered opportunities to connect their lives with "real people" and "real moments" so that they are more likely to value the processes of formation and abstraction of important mathematical concepts. The challenge for teachers is to consistently seek cultural links, especially from the perspective and cultural background from the teacher him/herself, to exemplify the richness of mathematics.
ReplyDeleteI agree that it is an interesting challenge to connect mathematics to culture. I, like Amanda, come from a northern European culture that I had not considered as having history to draw from. This makes me think that historically significant locations, such as Stonehenge, could be an interesting starting point in researching this topic. What mathematical skills would the culture that built that have had?
ReplyDeleteUntil only recently, I was not aware how recent the development of mathematics symbols and numerals was. Once Arabic numerals were published by a Persian, al-Khawarizmi, based on his study of Hindu numerals, about 1200 years ago, it took my ancestors, Europeans, until about the 16th century to adopt them! Learning about the history of “new mathematics” is in itself a study of numerous cultures.
Connecting culture to mathematics, and indeed all subjects, is another tool to improve students’ depth of understanding in all school subjects. Although mathematics may be a more challenging subject than others, it does not mean it is less valuable.