A 21st Century Economic, Educational and Ethical Mathematics Curriculum Policy

By Aikenhead, Glen S. | The Mathematics Enthusiast, January 2017 | Go to article overview

A 21st Century Economic, Educational and Ethical Mathematics Curriculum Policy


Aikenhead, Glen S., The Mathematics Enthusiast


A. Issue:

High school mathematics directly influences Saskatchewan's economic sustainability.

B. Preamble:

Saskatchewan's economic sustainability depends in part on having a government reliant on employed Indigenous taxpayers compared to an Indigenous population reliant on social welfare. Graduation from high school is therefore critical. A major hurdle for many Indigenous students is mathematics (e.g., linear and quadratic functions, radicals, and geometric sequences), which often depresses Indigenous students' graduation rates more than other high school subjects do.

C. What Do We Need to Know about Mathematics?

1. Mathematics is a human invention that has developed from its origins in ancient civilizations. Every major culture has developed its own mathematics system in tandem with their everyday cultural activities, such as: counting, locating, measuring, designing, playing, and explaining. For instance, the mathematical process of designing is found in Indigenous embroidering and in Western (Euro-American) civilization's mathematics modelling, which forecasts the weather, for example. Mathematics' symbolism is a very powerful human tool.

2. Mathematics in any culture can be thought of as a symbolic technology for building a relationship between humans and their social, economic and physical environments.

3. What we teach as school mathematics today is one of many mathematics systems currently existing worldwide.

4. If we don't know the history of our own Euro-American mathematics, how can we move forward in a rational transformative2 way?

D. What Do We Need to Know about the History of School Mathematics?

1. After the Dark Ages ended, ancient mathematical ideas found their way into Europe. Academic thinkers appropriated these ideas in a way that made sense to them. This was before universities existed.

2. When these early mathematicians appropriated an ancient mathematics idea, they ignored the culture-rich connotations associated with ancient numbers, symbols, and shapes. In their place, European mathematicians unconsciously attached their own culture's connotative meanings. European mathematics went on to invent other clever mathematical ideas, for example, geometry systems different from Euclidean geometry.

3. The Renaissance period of history brought about universities. The Renaissance version of mathematics slowly found a home in elite British universities, such as Cambridge and Oxford during 17th -18th century England3. Mathematics had to compete with the classics, history, ancient languages, etc. that were purposefully made very difficult. To be accepted and survive in these elite universities, mathematicians taught their most abstract ideas without any context to help students think about mathematics' everyday use. They followed Plato's way of thinking: The world is made up of only two things: either ideas in our head or everyday concrete things and phenomena. These Platonist4 mathematicians promoted Plato's "World of Ideas" and ignored anything that gave mathematics a human dimension or an everyday context.

4. The elite British Grammar Schools at the time prepared the aristocracy for elite universities. So their mathematics curriculum was the elite Platonist version of mathematics.

5. The Industrial Revolution ( 18th- 19th centuries) brought about the British public education system in the mid-19th century, quickly adopted in Canada and the U.S.A. Mathematics became a core subject. At the time, however, educators debated over which version of mathematics should be taught: academic elite that had no context? or practical relevance that would connect students with their real world around them?

6. The Platonist educators won the battle over their utilitarian colleagues by using a rhetorical trick. They invented a dichotomy that divided mathematics education into: formal and informal5. Formal mathematics was defined in a way that conformed to Plato's philosophy that the universe is made up of mathematical abstract concepts. …

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