Through colonization and imperialism, the colonizers would not only exploit the resources of other countries but would also give them a weapon to spread their cultural values all over the world. Even if the domination happened a long time ago, their ideas continue to persist today. In this article, Bishop started to question us whether the ideas in mathematics are really culture-free. He used the term “Western Mathematics” to posit that the ideas from western European culture still dominates in contemporary times.
Gone were the days that imperialism only wanted to colonize indigenous countries to extract their raw materials at a cheaper price but Bishop argues that the kind of imperialism that exists today has to do with the domination of western cultural ideas and values worldwide. The term secret weapon as used by Bishop is to show that even in contemporary times people still believe that Mathematics is a culturally free body of knowledge.
The reason behind this perception is that we think that mathematical truths have universal validity.
It may seem that they [mathematical truths] are culturally neutral knowledge because they are abstract and accepted worldwide. For example, when one tries to draw a triangle, whether is it ugly or not perfectly shaped, we assume that the angles in a triangle equal to 180 degrees. We do not bother to question why the triangle is considered to have 180 degrees but we tend to accept this mathematical idea only on the basis that it is universally valid. Another example that is similar to what was mentioned in the article is that when one goes to a supermarket and buys a kilo of Bangus (Milkfish), it is equivalent to 2.
20462 pounds and this conversion is valid in every part of the world. Thus, Bishop (1990) argues that why is that kilo and pounds are used for standard measurement of mass and why is it the case that a kilo is equivalent to 2.20462 pounds?
To answer this question, he pointed out that “mathematical ideas, like any other ideas, are humanly constructed and they have a cultural history” (Bishop 1990:52). In other words, mathematical ideas are culturally and humanly produced; thus, both western and non-western mathematical ideas have a cultural history that was agreed upon by their ancestors. But, the question still remains as why western mathematical ideas dominate. I think, if we go back to our history, they were the first to navigate the world. They engaged in trading. When it comes to trading with other countries, they must have to have a standard measurement and conversion for them to have a smooth business transaction. They were also the most dominant country in the past which may be the reason why their ideas still remain today.
In this article, he also emphasized the use of ethnomathematics to find alternative mathematical systems that exist in other cultures or indigenous communities. Ethno-mathematics is defined as “a more localized and specific set of mathematical ideas which may not aim to be as general nor as systematized as ‘mainstream mathematics” (Bishop 1990:53). This means that we can find another way of discussing arithmetic, geometries and others to name a few which are not part of western mathematical ideas. He also mentioned that there are different counting systems in the world; for example, in Papua New Guniea, Lean (1991) has documented various cycles of numbers which are not all base 10. They also used their body parts to count, beads and knotted strings. They even carved on wooden tablets or rocks.
In the Philippines, we also have different ways to measure things that are not used by other cultures. Filipinos used “dangkal” which refers to the length from tip of our thumb to tip of our middle finger, “gatang” which we use to measure bigas or rice grains, “talampakan” which refers to afoot and other Filipino measurements. Similar to Papua New Guinea, we used our body parts not to count but to measure things. Moreover, in the first wave of discussion in our Math 10 class, Professor Balmaceda pointed out that there are different methods of counting in other parts of the world. For example, Babylonians used a positional numeration system where the set of numeral changes values as it changes position. On the other hand, the Incan Quipu of Peru recorded their numerical information by knotting ropes and strings. These are just some of the examples of alternative mathematical systems used by other cultures; but, sadly, some of these totally disappeared and can only be seen in historical books.
For me, this also creates a cultural hegemony where there is a dominant power/ruling class who manipulates a culturally diverse society. Furthermore, I think this article is not only limited to mathematical ideas because there are certain disciplines that also borrow from western European culture. If I were to relate it to my field, Sociology, it has a lot of similarities. We continue using the ideas of Karl Marx, Max Weber and Emile Durkheim which are all European sociologists. Just like in my field, the dominant knowledge came from the west and we just tend to apply it in the context of the Philippines. Just like the use of the English language, we often discuss things in English. I, myself, am guilty of that. We wrote almost all of our academic materials, as well as Philippine Constitution and laws, in English which most of the Filipinos could hardly understand. Mathematics also suffers from the same dilemma whose ideas are not really culturally neutral knowledge. What we can do now? I think the best thing that we can do is to continuously re-examine the historical construction of knowledge not only in Mathematics but also in other disciplines. We also need to go back to our very own culture and re-consider the indigenous ideas or what Bishop (1990) referred to as ethnomathematics in order for us to have a greater awareness of our culture.