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Thursday 21 January 2021

Learning What We Learn, Teaching What We Teach

"What is ml?" Unsure. Litre? "How many millilitres is equal to 1 litre?" Unsure again. So I taught the student the conversion from litres to millilitres and the reverse. Some students will be able to master the formula and “prove” to us that they understand, but do they? As teachers, tutors and adults, will you deceive yourselves and move on to the next skill, telling yourself that the student understands the concept? You should test him for his true understanding.

“Look at this packet drink? How much liquid is in it?” Silence. “Guess. Come on.” Silence again. “Come on, just guess.” What sort of Math teacher is this man?" the kid was probably wondering. “I don’t how,” the student finally replied. “I know you don’t know, but just guess.” The kid guessed a number, which was wrong, and then I said, “Look at the packet drink and see how much liquid there is in it.” The child picked up the packet drink and turned it this way and that, searching for a number.  “100!” he said. “Nope, that’s the number of calories per serving.” Finally, I pointed out "250 ml" to him, making sure he saw the number 250 and the “ml” unit. The beginning of real understanding about litres and millilitres had just begun. But I will not deceive myself into thinking that I have done a good job. Real understanding and Math mastery are still a distance away.

“Now, 4 packets drinks, each 250 ml, makes 1000 ml, which is equal to 1 litre of liquid.” Confusion. “Go to your fridge. Take out the milk.” He walked up to the fridge and removed the requested item and lay it down on the table in front of us. “You see this – “1 litre” – you know what it means?” He looked at me without revealing whether he knew it or not. I took the 250 ml packet drink and explained that the liquid from 4 packet drinks could fit into the 1-litre milk carton. From his eyes, I saw that understanding was being built. The child needed more activities to help him make the connections between Math concepts and the real world. This is the process of injecting meaning into a child's learning. 

I scanned the kitchen, looking for an appropriate measuring container to reinforce the concept. Ha! A blender with millilitre markings! “Bring that blender over here,” I requested. Obediently, the child carried the heavy glass blender over. And I spent some time getting the student to pour water from a bottle into the blender and so on. Why? Because the question in his textbook stated that someone poured x amount of juice from one container into another. I was simulating the process so that the child could imagine what the question was about. Children must see meaning in the sums they are doing. This is crucial. But do we have time for this? Some may say - Since the PSLE is just less than 9 months away, isn't spending such precious time doing activities when the child has so, so much content to master an unwise move? They emphasise that is especially true when there is so little time left before the big exam. Yes, many adults panic in year 6 of the primary school study.

Think how foolish it is to continue teaching and moving to the next skill for a child who does not understand the earlier levels. The child does not understand the basic concepts and the teacher would like to teach him to master the concepts at a higher level? Can true mastery of any concept even be attained without real understanding? Shouldn't we realise that it is because the child did not truly comprehend the concepts at earlier levels of study that he is in dire straits now at Primary 6? The logical solution is to help him master the concept in its meaning first. Only then there is hope that he can master the concept at higher levels.  

We have to teach for meaning. Why is Mathematics in our school curricula if it is not meaningful? How can we then teach a meaningful subject in a meaningless way? Strange. Stranger still when this is happening in a first world country where the public education budget is relatively high. But I am not surprised. Why? When I was a student, I asked my teachers for the purpose and meaning of the subjects they taught. A common answer they could give me was this – “focus on the tests and exams first and we will discuss this after the exams”. What an answer! Perhaps the teachers did not know how the subjects they taught were meaningful. Perhaps. 

As a teacher, I cannot teach without the meaning. Mathematics must be meaningful.