I taught shortly this morning. Took the primary kids to one corner and gave them lessons in Maths, as extension of their school work. They know skip counting many numbers and confidently complete the task. They also know concept of multiplication as they work on the Multiplication Board. So this morning was a simple exercise to test and reinforce the concept for multiplication.
Do you know that 5x3 and 3x5 are NOT THE SAME? They both yield 15 as answer but as their basic forms, they are not the same things. This was the subject of controversy just some months ago when a professor showed a test paper on the very same subject. The questions were clearing testing the multiplication concepts but even many adults had trouble understanding the concept. Amongst others, they believed that 5x3 and 3x5 are the same, since the answer to both is 15. They failed to understand or appreciate the fact that these questions were about concepts, and not the actual answer. There is no mark given for correct answer, if the equation is wrongly formed. There is no half mark either, because…. the objective of the questions was to test the multiplication concept.
What this means is… if you were one of those children who memorised one thousand times one million equals whatever but you do not know what the equation means, you are not awarded a mark. And in future, knowing and memorising all these answers is FUTILE. You will never beat the speed of a computer. You will however, need to understand and know how to form number sentences… or equations, as we know it to be. The world is full of mathematical challenges and problems and none of them come in sentences. You and your child will need to know how to analyse the data and make meaningful and mathematically sound equations.
But back to this morning…. So the kids went on a frenzy of drawing the equations. They had 10 equations to solve in pictorial form. They were screaming the answers but I wanted answers in pictures. They got cracking away drawing the bags of multiple objects. For very obvious reasons, they will not complete the equations at the same time. When you have more than 1 learner, some are bound to complete faster than the rest. Some will need more time to digest the required skill.
For those who are quick to answer and demonstrated the concept, I gave them a work extension. This is to expand their understanding of the same work (and yes, to buy time so the others can catch up and complete the basic 10 questions). On this particular morning, I asked those who completed ahead of everyone else - mainly because they were a year older - to rewrite the equation in the vertical form, paying special attention the placement values and making sure that they wrote the equation and answered in the correct columns. Therefore for these kids, they received the same multiplication exercise with an extension in placement value.
When they have completed the 10 basic multiplication questions (because honestly we don’t need 10,000 questions per day but acceptable daily repeats times a longer period of days) I asked them to take out their set of mathematical instruments and take a good look at it. Yup, after multiplication, they dived into geometry. I asked them which instrument they wished to learn today and they settled on the protractor. I taught them to draw a horizontal line, then expand it to 90°…. and 45… made them repeat on their own once, guiding them as they drew. By doing so, I reinforced basic drawing 0, 45 and 90°.
Then it was expansion activity again. By this time, the other learners completed their multiplication questions and observed this group of kids drawing and working with the right angled ruler etc. After finding the basic 0, 180, 45 and 90°, I asked them to search and draw angles that I determined… in all their glorious forms. They managed to learn basic ideas such as 360° within a circle, 180° for half a circle and search/draw the correct angle within a horizontal 0° line.
And it was not even ONE HOUR of work yet… between those minutes of work, it was relaxed, with occasional chatter and everyone had the opportunity to observe each other working through their respective questions, in TWO different mathematical skills. There were informal questions to test their skip counting 5s and 10s. And I left them with 10 more multiplication questions (5 equations and 5 pictorial forms, which again is a sneaky check on the depth of their understanding) and a BONUS of 10 drawings with the protractor.
I have a sneaky guess that they will be busy for the next hour. No teacher intervention is necessary. This part of the learning cycle is all about practising and discovering the right and wrong in their approaches to the questions. The children are left to work out the questions on their own and in collaboration with each other. They may ask the teachers for guide but essentially these questions were created to reinforce and test their skills.
And to quote the Terminator, “I will be back” tomorrow to catch their work and see how far they have gone in their lesson.
What this all means is... Education has changed. It was morphed into something borderless, timeless and infinite. Specific subjects are dropped in favour of multi disciplined learning. Learning has become learner centric, where learners decide what they wish to pursue. And teachers support their learners to pursue answers to their personal questions and interests.
What this all means is... Education has changed. It was morphed into something borderless, timeless and infinite. Specific subjects are dropped in favour of multi disciplined learning. Learning has become learner centric, where learners decide what they wish to pursue. And teachers support their learners to pursue answers to their personal questions and interests.
