Imagine that it’s a rainy day and that you are sitting at leisure sipping a hot cup of tea pondering over the fresh fragrance of earth that the rain is evoking. You take the time to notice the vapour from your cup and to smell the aroma of your tea. Wouldn’t your tea taste lovely?
Now imagine a slightly different scenario. You are trying to learn music and you were asked to listen to 10 songs in 15 minutes and answer 5 questions about them in an exam that follows. How would you feel about music? Would you count it as a good recipe to learn music? Could you get someone to be interested in music this way?
Whether it’s enjoying your tea, a favourite song, a heart-melting poem or for that matter savour the essence of math, the human experience always is at its best when you slow down and take the time to notice the nuances and revel in the subtleties. It is in that rumination of the frills and folds of a subject that true learning lies.
Why then, do we reduce math learning in our classrooms into a race against time in applying formulas and getting the right answers?
Mathematics is very much like the sense of sound and sight that humans have. It is the sense that humans are gifted with that helps us perceive the realities of the creation which would otherwise remain intangible to us. It’s a sense that helps us see patterns, relationships and logical connections and utilize them to envision and create new realities that didn’t exist before. This Mathematical sense is so inherent in our species that even children who never stepped into a school yet will tell you that they prefer a packet of 10 chocolates to a one that has 5.
The purpose of teaching math in schools is to help develop and fine tune this mathematical sense further. The National Curriculum Framework 2005 refers to this as the skill of Mathematization. This skill helps the students to view the world through the lens of math and understand it better. The purpose of math according to NCF, is not just to understand and utilize already established mathematical facts. It is also to help students develop the ability to think abstractly, propose coherent assumptions to solve real world problems and pursue those assumptions to logical conclusions. This requires that math be taught in classrooms as a subject that provides space for students to discuss, debate and solve problems through collective thinking. It should focus on
It is not a stretch to state that most of us grew up learning math as a set of rules that need to be memorized and applied as prescribed in the textbooks. I remember my classrooms never had the space to question the formula, wonder why the formula works or why I had to learn it in the first place. I am sure most of your math classrooms were no different. Rote memorization of disjointed mathematical facts and formulae had always been so pervasive in the way math is taught and learnt that sometimes it may be hard for us, the educators, to see how math can be taught as a thing of beauty that evokes wonder and excitement in students.
But this is where the new National Education Policy 2020 is challenging us to rise above our own dull and dry experience of learning math and make our classrooms experiential. Here are a few interesting thought experiments that are worth trying in our math classrooms:
- Propose Math as a sequence of real-world problems to be solved: Think of how each lesson in Math can be posed as a real-world problem for students. Ask the students to think of ways in which the problem can be solved. Give them time to wonder and analyse what the problem means and how it can be solved. Ask students to critique the pros and cons of the ideas proposed by others. Provide students with the freedom to explore any non-mathematical dimensions of the discussions that may come up. This method may seem time consuming and goes against the “Traditional Method” of teaching math where the teacher usually starts with an answer (the formula that needs to be applied). The traditional method leaves no room to doubt the formula, question the relevance of it or think of any alternatives. That’s why it fails so badly in inspiring students to fall in love with the subject.
- Don’t Rush to give an answer when students don’t know how to solve: Instill a sense in students that, situations where they don’t know what to do, is an opportunity to learn. Again, let them take their time. It’s important to let the students marinate the problem in their minds to figure out the answers. This builds the most essential of the skills that the students will require to do anything meaningful in their careers – the skill of Perseverance. Let them know that not knowing an answer or getting an incorrect answer is not failure. But giving up is.
- It’s ok for a teacher not to know an answer to a Student’s Question: In a free-flowing math class that explores math as a thinking skill, students might likely end up asking questions for which we as educators may not know the answer. This might feel like a real threat to the authority we carry in the classroom. But we need to understand that it is perfectly OK not to know the answer to every question that students may have. A teacher is not an answer key. If we remember that the purpose of the math classroom is to come up with genuine mathematical thoughts (i.e., the skill of mathematization), then it won’t be hard to see how we cannot expect ourselves to know an answer to every genuine mathematical thought/question proposed by students. The right response in those situations can be: “I don’t know but let’s find out”. Take the time to explore the journey together with your students to find an answer.
you might be wondering by now as to how such a teaching method can be adopted when there is “yearly syllabus to complete”. The reality is that a slow and exploratory way of teaching math is the only way in which the skill of mathematization can be developed in students. As that skill slowly blossoms in students, most of the content we teach them can be self-learnt with a bit of facilitation in classrooms. If we focus on skill, the content acquisition will happen automatically.
Here’s a humble call to all the Math educators … Switch to teaching math as an exploration and not memorization. Turn your classrooms into spaces where students can wonder, ask questions, discuss, and enjoy the beauty of mathematical thought. Let them question why everything they learn is of relevance to them in their life. And you can be sure they will find the beauty and fragrance of math.
