I have believed for a number of years that, the traditional approach to teaching has been incorrect. It was based on the need for “Tally Clerks” during the Industrial Revolution and it has hardly changed since.
Think about the way maths was taught to you, now how about your parents? and your grandparents?
My grandparents and father never flew on an aeroplane, none of them had a cellphone, tablet or a computer, how the world has changed in one short generation, because now my grandchildren have tablets, interactive TV etc
We are told that we have a “Child-Centred” Education system (Be damned we have not) We are told we are educating for the future (Be damned we are not)
Where is the creativity in Maths Teaching? The Thinking? The Cooperation? The open-ended questions? the child-centred investigations?
When was the last time you brought a flower, some fruit, into the classroom and asked the question “where is the maths? or, What can you see in the object?
When was the last time you asked the class, what do you want to know about: fractions, or, measurement, or, geometry, or, art and maths?
Len Cooper, retired maths adviser/consultant and teacher:
https://mathslen.blogspot.com/
Charlotte Wilkinson, “The Wilkie Way” (NZ) in her last newsletter asks similar questions so I share her thoughts and questions.
Maths and The Arts
Traditional school maths with endless practicing of calculating. The standard written algorithms are procedures that have been taught for endless years since the introduction of the base ten algorithmic number system (About 2000 years).In making maths modern - mental strategies were the new way of solving - these quickly became more procedures for students to memorise (or not).
Why does school maths have such an unhealthy fixation with procedural knowledge?
The era of human computers has passed, so many of the arbitary skills promoted by school maths are also archaic - long multipication and long division, adding and subtracting fractions to name just a few.
We are presented with acronyms STEM and now STEAM which implies Maths is separate to Science, Technology and Engineering and now Art too.
While it is relatively easy to dismiss the stupidity of thinking mathematics is unrelated to science, technology and engineering let us now consider Mathematics and the Arts.
Bertrand Russell (Nobel Laureate, Philosopher, Mathematician) once said: “Mathematics, rightly viewed, possess not only truth, but supreme beauty - a beauty cold and austere...sublimely pure, and capable of stern perfection such as only the greatest art can show.”
GH Hardy Another famous mathematian in the earlier part of the 20th century known for being a harden purist advocating for rigour and abstraction, ultimately declared that: “I am interested in mathematics only as a creative art.”
If mathematics is an art form, what are mathematicians. Hardy called them “makers of patterns”. The late Maryam Mirzakhani, the only female recipient of the Fields Medal (the highest accolade in mathematics) was often mistaken by her daughter for an artist.
To mathematicians, school maths is something of a desecration of their subject. There is no doubt the rise of numeracy has crowded out more conventional arts subjects but it has also concealed the true nature of mathematics.
Paul Lockhart (American school maths teacher and research mathematician) wrote in his book A Mathematicians Lament - “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial.”
Even where calculation has its place, the mathematican seeks rich representations that illuminate the procedures they call upon.
Do you see times tables as just a matter of memorising number facts (learn them by rote) or do you spend time exploring the myriad of patterns within a multiplication table and between the multiplication tables.
We spend alot of time talking about 21st century education - I see modern learning environments, I see school maths curriculums as completing workbooks. I see students working on laptops and maths apps but the mathematics I see them doing is still archaic, procedural and not the kind of mathematics our students need.
The kind of mathematics that our students need, that our world is increasingly dependent on, is much more aligned to its artistic tenent. I think this is why STEM has become STEAM. Skills like curiosity, persistence and resilience are not divorced from mathematics, they are the very traits that mathematicians through the ages have brought to their problems.
As with any art, there is a subjective element to deciding what should go into a mathematics curriculum, or how to assess these broader skills. However that is no excuse for persisting with an outdated brand of the subject that brings joy to so few and value to fewer still.
The history of mathematics is entwined with the history of technology. Humans have precedent for updating their ways of doing mathematics based on the tools available to them. (OK the complete change from using Roman numerals to the base 10 system took about 200 years). With the technologies now available at our fingertips, we can put calculation in its rightful place as the footnote to mathematical thinking power.
Calculation is simply the price we once paid to do mathematics.
When maths anxiety is a real issue for many people, and so many others show an indifference to a subject that promises such immense power and beauty, the price to continue with a fixation on procedural calculation as the backbone to school mathematics is too high.
Samantha, a year 5 student once said to me: “ I love doing sums (calculations) because you don’t have to think.”
How true - once a procedure is memorised no thinking is required.
While the content is the curriculum, how you choose to teach it to your students is dependent on your own creative flair and knowledge of the subject matter.
My own daughter’s advice to Primary school teachers given 5 years ago was
“Calculate less, estimate more”
Mathematics will never be replaced by the Arts.
Mathematics is an art, and it is time we embraced it as one.
©Copyright N C Wilkinsons Ltd 2019
i couldn't agree more!!!
ReplyDelete