Are you confused when you read the title of this article? What comes to your mind at first?
That’s the point of this article, to tickle you to think. 😊
Recalling the first time we had a lockdown situation in Jakarta, it has been about 2.5 months that I have been staying at home to do most of the work I usually did. How about you? What have you been doing during this period of time?
I have been fortunate, honestly speaking, because I could use my time to enroll in mathematics online courses (How to learn math for teachers, by Stanford online, youcubed.org and Introduction to mathematical thinking by Keith Devlin on Coursera), watch YouTube videos related to mathematics teaching and learning (mainly Eddie Woo’s channel, if you know), and ultimately reflect on my teaching practices. These are things that I could be grateful for. I would say that I enjoy my time learning at home, aside from doing my work as a teacher at school and other stuff with my family.
I feel that I have learned a lot of things. Really. Literally. Especially on the “How to learn math for teachers” course and the Eddie Woo’s YouTube channel. It is halfway done, but I have been learning a lot of things and got feedback to improve my teaching practices as a mathematics teacher. One learning that I’ve encountered on the online course, which turns out to be overlapping with one YouTube video by Eddie Woo, is about thinking deeply about simple things.
Learning mathematics is often seen as a difficult and challenging subject for many people, and people hate or at least dislike this subject because of that reason. “It’s difficult!” “I am too lazy to think!” One of the main reasons that people hate or dislike mathematics is because they could not “see” the benefit of learning mathematics. At least, they could not “see” that while they were still at school. As people grow older, they start to realize how learning mathematics has actually helped them be who they are. This might not be the case for some people, still. But, at least there is a bright side, isn’t it?
I’ve learned mainly from the online course and the YouTube videos I’ve watched that learning mathematics essentially is about learning how to think. It is not about the symbols or formulas that are important, but how we develop our thinking skills. More importantly, we learn how to think deeply about simple things.
What does it mean by “think deeply about simple things“?
Mathematics is a conceptual subject whereas the topics or discussions that we encounter while learning maths are related to one another. Thus, learning maths is not about memorizing formulas and/or following procedures to solve a problem. Instead, it is about understanding the concepts and connect the ideas for us to make sense of what they mean.
For example, fractions, one challenging topic that we “have to” learn in primary school, is actually related to ratio, proportion, scale, simple function, linear equation, vector, gradient, etc. Let us take a fraction 1/3 for instance, and here are some ideas that we could connect to the meaning of this fraction:
- Equivalent fractions and ratio: 1 out of 3 options, equivalent to 2 out of 6 options, 3 out of 9 options and so on
- Scale: could mean 1 cm on the map to 3 m on the actual
- Vectors, velocity: for every movement of 1 unit to the right, the point/object moves 3 unit upwards
- Function, linear equation, gradient: a function or equation y=3x, where the gradient of the line is 3/1=3
Another example, when we learn about addition (concept of sum), we could connect this to multiplication (the concept of product) as that’s the definition of multiplication, subtraction, number lines, place values, fractions, algebra, and so on. For instance, learning the addition of (17 + 28) could also lead us to learn about:
- Place values, commutative and associative property of addition: 17 + 28 = (10 + 7) + (20 + 8) = (10 + 20) + (7 + 8) = 30 + 15 = 45
- Subtraction, algebraic concept: 17 + 28 = 15 + 30 = 45
The essence of learning to think deeply is basically to follow our feeling of curiosity. By questioning things related to what we are learning, that could lead us to a higher level of mathematics that, based on school curriculum and syllabus, is not supposed to be learned by primary level students. For example, curiosity in learning about calculating the area of 2D regular shapes could lead us to ask questions such as:
- How do we find the area of a circle? — Circle, primary level math in Grade 5 or Grade 6.
- How do we calculate the area of shapes that are irregular, such as a lake? — Integration, something that we learn in Grade 11 or Grade 12.
- How if we combine the 2D shapes to make 3D shapes? — Surface area and volume of 3D shapes, primary and high school level maths
If we were given the time and space to ask questions while learning mathematics, wouldn’t it be so wonderful? We all could really learn how to think deeply in a natural manner, due to our curiosity. This could lead us to think so deeply because we keep questioning things so that these all make sense to us and those satisfy our crave or quest for knowledge. This is the essence of learning mathematics, and we all might love to learn mathematics!
Do you want your friends, children, or students to feel that excitement of learning mathematics? So do I. That’s the reason why I write this article and share my learning through my YouTube channel. I believe that we all could benefit from learning mathematics, and it is not a privilege, but a right. And, this is not the job of a single person or teacher. Therefore, let’s all learn more to be able to facilitate better to teach how to think deeply about simple things through mathematics.
Happy learning, happy thinking! 😊
One thought on “Deeply simple think about things”
Very good article.