Conventional schooling makes learning mathematics an entirely cerebral exercise unrelated to the real world, but it really doesn’t have to be
Maths can be learnt through day-to-day life and through play. Maths doesn’t need to be pitted against art or music, the way it is in school. In school the focus on maths pushes out time for the other subjects. It is studied in isolation, unconnected to life. But there is maths in music and in art, in biology, in cooking, in making clothes, in making furniture.
Below are some articles, thoughts and resources on how maths can be learnt through life.
Maths – turning hate to love and understanding
Tim Gowers is a British mathematician. He is a Royal Society research professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge
“So how might mathematics education be different? The way it is often taught, children are asked to take a huge leap of faith: that the symbol manipulation that seems pointless now will one day be useful to them. But this is true for only a small minority of children, who enjoy the symbol manipulation for its own sake and later find themselves drawn towards Stem subjects, where it is indeed very useful. The rest know perfectly well that they will never reach this promised land. What can be done for them?
We could also ask children open-ended questions, such as whether it is more dangerous to travel by car or by aeroplane. A question like this is not explicitly mathematical, so it is less likely to trigger the brain’s off switch. And if it doesn’t, the ensuing discussion will convey why we should care about multiplication, division, averages and probabilities, what we can say about them when we do not have exact numbers handed to us on a plate, and how to frame mathematical questions to help make decisions that are of practical interest.”
Maria Droujkova – Natural Math
Maria Droujkova has almost twenty years of experience in mathematics education research and development. She works with diverse learners and situations, such as early algebra and calculus with family groups, Math Circles, MOOCS, and courses and workshops for K-12, college students, and teachers. Dr. Droujkova is the founder of several online educational communities, including the Natural Math network and Math Future interest group. She has MS in Applied Mathematics from Tulane University and PhD in Mathematics Education from NCSU. Her studies have been supported by grants and have been published and presented nationally and internationally.
“Calculations kids are forced to do are often so developmentally inappropriate, the experience amounts to torture,” she says. They also miss the essential point—that mathematics is fundamentally about patterns and structures, rather than “little manipulations of numbers,” as she puts it. It’s akin to budding filmmakers learning first about costumes, lighting and other technical aspects, rather than about crafting meaningful stories.
This turns many children off to math from an early age. It also prevents many others from learning math as efficiently or deeply as they might otherwise. Droujkova and her colleagues have noticed that most of the adults they meet have “math grief stories,” as she describes them.
Far better, she says, to start by creating rich and social mathematical experiences that are complex (allowing them to be taken in many different directions) yet easy (making them conducive to immediate play). Activities that fall into this quadrant: building a house with LEGO blocks, doing origami or snowflake cut-outs, or using a pretend “function box” that transforms objects (and can also be used in combination with a second machine to compose functions, or backwards to invert a function, and so on).
Professor of mathematics at the University of California, Berkeley, which he joined in 1997 after being on the faculty at Harvard University. He is a member of the American Academy of Arts and Sciences, a Fellow of the American Mathematical Society, and the winner of the Hermann Weyl Prize in mathematical physics. Author, filmmaker, writer, speaker.
Love and Math – book by Edward Frenkel
“What if you had to take an art class in which you were taught only how to paint a fence, but were never shown the paintings of van Gogh or Picasso? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. Mathematics, he writes, directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars.
At its core, Love and Math is a story about accessing a new way of thinking, which empowers us to better understand the world and our place in it. It is an invitation to discover the hidden magic universe of mathematics.”
Maths professor teaches a math class using tools such as knitting, beach balls and measuring tape to get past the maths hate and get students to understand maths in the way that professional mathematicians do, as problem solving and analytical, playful.
At Cornell University, students enrolled in “The Art of Math: Mathematical Traditions of Symmetry and Harmony” use music, games, journal writing, discussion, history, and cross-cultural study to grasp mathematical abstractions. “Math is about exploration and strategy and creatively finding solutions,” explains Courtney Roby, an associate professor of classics who teaches the course with a music and medieval studies specialist. “We turn concepts into games to encourage students to think about how to prove them. The activities distill proofs into other ways of thinking.”
“It’s better to understand something than to know it. Although the concepts are related, knowing and understanding are distinct. Knowing is static and refers to discrete facts, while understanding is active. It’s the ability to analyze and place knowledge in context to form a big picture. Without knowledge, understanding is impossible. But having knowledge doesn’t necessarily lead to understanding of a greater narrative, which is the real point of learning.”
“But more of a travesty than this is the way traditional education has presented maths as a set of disconnected procedures: add these two numbers, multiply the base by the height, find x …
This bores me.
I taught maths as a high school teacher and had to teach like this. My students were bored too.
There are two big things missing: connection of ideas and connection to the real world.
To present maths in a way that isn’t horribly boring, you actually only need one of these two (but both together is great as well).
I’ve been doing something different lately in my work with Scitech as a professional learning consultant: inquiry maths. I go into classes and bring coloured geometrical shapes, rods and fraction circles, and I set focused tasks of exploration.
Students play, seek out patterns, ask their own questions, discuss and debate their ideas.
I used to ask a class of 30 students who liked maths, and two students would put their hand up.
I’ve taken this approach into more than 60 classrooms and consistently seen a whole classroom engaged and excited about mathematical ideas.
People enjoy connecting ideas.
In an example of real-world maths, I recently set a task for a couple of hundred students to figure out how much area it would take to power the whole of WA in solar power. They worked in small groups, fully self-motivated to tackle the problem for an hour.
People enjoy tackling big problems that connect to the real world.”
Vi Hart makes amazing, thought-provoking maths and music videos which explain mathematical concepts through doodles. This won her this years’ Communications Award of the Joint Policy Board for Mathematics.