An Absence of History

I recently began a book called An Imaginary Tale - The Story of √−1 by Paul J. Nahin. The book traces how mathematicians regarded negative numbers and their square roots over the past ~2000 years, the birth of complex numbers, the development of complex number theories and their applications in diverse fields. My reading of the first few chapters which paints a fascinating history of the origin of complex numbers planted the seed in my mind from which this post germinates...

When we learned English (or any language) in school, the context in which the story, play or poem was written was essential to understanding its elements - setting, characters, culture, symbolism, humour and irony, objects and props, dress, societal norms etc. For instance, reading Julius Caesar required some understanding of first century BC Roman politics. To appreciate any of the romantic poets (think Wordsworth, Blake and Shelley et al.) required knowledge of the Renaissance and Enlightenment movements that preceded it. In a sense, the history of the text shaped how the text was read.

The Death of Caesar (by Vincenzo Camuccini)

When we learned geography in school, we covered topics such as rock formation, continents, flora and fauna, layers of the earth and tectonic plates, the environment etc. Geography was one of my favourite subjects - I had an excellent teacher and enjoyed studying how our planet had evolved over many millennia. The presence of species based on available resources and how the toughest ones adapted to survive in harsh climates captivated my interest. Similar to English, the history of the earth and solar system formed a backdrop to understanding geographical facts and phenomena. This history added an ancient charm to the subject that made it richer in my eyes.

Continental drift

When we learned the physical sciences (physics, chemistry and biology) in school, topics began with stories about the scientists who played a pivotal role in our understanding of the concept. I can still picture my chemistry textbook taking me from Dobereiner's Law of Triads to Newlands' Law of Octaves to Mendeleev's early version of the periodic table to the modern version built by Moseley et al. How each version aimed to modify and build on the previous one by incorporating new discoveries on the nature of matter greatly appealed to me!

In physics, the tale (whether fiction or fact!) of Archimedes shouting "Eureka" on realising that the volume of water displaced when he got into his bathtub must be equal to the volume of his body that he had immersed was a comical one used to introduce how to find the volume of irregularly shaped objects. In fact, the story goes that Archimedes was so keen to share his discovery that he jumped out of his bathtub and ran naked through the streets of Syracuse! Similar interesting tales involving Newton (gravity and forces) and Galvani (notion of animal electricity that lead to the discovery of current electricity) served as hooks to these concepts.

In biology (another one of my favourite subjects), examples such as Hooke's observation of cells in cork and Fleming's accidental discovery of bacteria not growing around a mould in his sample of Staphylococcus bacteria (leading to the discovery of penicillin that ushered in antibiotics) were a part of information boxes scattered through my textbook. Theories on evolution and studying how animals and plants adapted over time to their environment was integral to understanding how living things came to attain their current form.

Robert Hooke's microscope and slide of cork cells

Drawing attention to the fact that theories and discoveries didn't magically appear out of nowhere but were the work of scientists lent a depth to these physical sciences. This added to their relevance (in my mind, as a child) as bodies of knowledge accumulated and understood by humans over centuries.

Nahin's colourful picture of how roots of negative numbers flummoxed many a mathematician until a few geniuses hit upon a solution made me look at complex numbers in an entirely new light. It made me think about how history played some role in all my school subjects barring mathematics. This brings me to my wondering... why don't math textbooks and curricula present and connect how a topic/branch of math was born with the main concepts being learned in the topic?  Why does school math basically come down to children recalling formulae and performing numerical calculations under the time crunch of a test?

It is not that educators are unaware of this issue. The National Council of Educational Research and Training (NCERT) in India publishes textbooks for the Central Board of Secondary Education (CBSE) - one of the popular education boards in the country. The NCERT blueprints are adopted by many state government education boards while drafting their own textbooks. A few chapters in math in the NCERT books do have information about mathematicians and history (see the examples below) but these tend to be glossed over as mere footnotes, are definitely not part of any assessment and are no longer referred to once it is time to solve the exercise problems at the back of the book.

So, here is my hypothesis:

IF we (educators) can show children, in an engaging manner, the value of a math topic and how it was born out of a need to solve a hitherto problem or puzzle and use that as both a hook to start the topic and as a reference during the process of learning the topic, THEN children will begin to appreciate the wider scope of math and stop viewing it purely in terms of formulae and calculations.

Of course, such an idea will fall flat if tried either halfheartedly or in isolation. Changes in textbook design, classroom teaching and assessments would have to take place in parallel to give this idea a fair chance...

What do you, the reader, think? Do you see any merit to this hypothesis? Is this an avenue worth testing out?

~ o ~ x ~ o ~

(A concluding note: The ideas expressed in this post are largely based on my experiences as a student and teacher in urban schools in India. Furthermore, it is grounded in my opinions and vision for how mathematics education can be improved. There is no one silver bullet that can enhance math education and it will require a multi-pronged approach; what I am proposing here is a suggestion for one of the prongs.)