In school, I was not that great in math and did not enjoy it one single bit.
I just had to sit for class coz I need to pass and did not have any interest in taking anything more than the required class.
In secondary school whenever I did complicated operations I had to write out every single step or else I would get confused and forget. There were many things I really didn’t understand about math – I just memorized the steps that is taught to go through to solve the problem. I would often have a terrible time to get myself to understand and telling my brains about what I was supposed to do or why this or that happened because I didn’t fully understand the WHY behind it.
Let me explain what I mean - For example the simple act of “borrowing” in subtraction and the simple act of 'carrying forward' in addition.
Why do we need to borrow and why do we 'carry' another number up to the next....
Sometimes I wonder whether I am the only one who was really confused by borrowing or carrrying forward...?
I finally just memorized and followed the rhythm of doing it and it was by mere drilling and practicing using lots of practice books... ! I made my kids do the same way with lots of assessment books and just because I did not like Math , they did not like it too as I was potraying my 'likes' and 'dislikes' to them unknowing and unconsciously.
Of course no mother in the world would want that for their kids but there was no control as it was done unknowingly.
I explained to them the way I knew it and was taught in school. " You just slash through this number and write this little small number above it, then continue with the problem – but I didn’t know what it meant. Never did a teacher try to explain it to me either.
For addition if you had any number that was 2 digit - you have to put one number above the next number and continue adding...
I was shown how to do it and then told to practice. Because I didn’t really understand what I was doing, I disliked any problem that involved borrowing or adding bigger numbers.
Out of the blue one day .. I decided to enrol myself for Montessori training.
The trainer discussed the Golden Bead material which is used in Montessori classrooms to introduce children to math operations (addition, subtraction, multiplication, division).
According to MAria Montessori's philosophy of always starting with the concrete, rather than the abstract, the Golden Bead material is a concrete representation of numbers.
There are single beads, representing units or ones (1). Ten of these beads strung together in a straight line by a wire, which is called a ten-bar and represents - tens (10) . Take ten of these ten-bars and string them together to form a square and you have a hundred-square . Ten of these hundred-squares combined together make up a thousand-cube.
Now we have the concrete materials for units, tens , hundreds and thousands.
Once the trainer started introducing the materials and started going through the 4 operations, I stared opened eyed.. She used the materials to work through the problem – I quickly wanted to take a pen and write out the whole process just as I remembered I used to do but I realized that I really did not need to even write a single word at all.
It was fascinating and easy to understand for me. When she got to the borrowing part, she demonstrated and, more importantly, explained the process. It was like a sudden beam of light that triggered down and shone in my mind!
(Just like the cartoon characters that showed alight bulb blinking above their head!) It was literally just like that.
I got it. It finally made sense.
It was an 'AHA! ' moment and somehow I felt that all the other would be teachers and parents in the room all felt the same way. Actually seeing the problem worked out with physical quantities made it much, much easier to understand.
For the additing bit it was also the same as the trainer explained the simple reason for carrying the number up!
That discovery was followed by many others as I worked with the Montessori math materials. It still amazes me how much I didn’t understand about mathematics.
Most students, start doing math on paper with a pencil; while the Montessori Method uses the abstract process of math is the final step of a long series of exercises. To me, and most traditional school students, numbers on the page are just that – symbols we are taught how to manipulate.
To Montessori students, those symbols represent very concrete ideas that they have physically manipulated; they fully understand what they mean, how they work, and why we use them.
It is as though the 'How' and 'Why" questions have been anwered!
Most of the students I know come to primary school and later to sceondary without enjoying math.
Math is probably the most despised school subject… and it is no wonder.
If only all children were to learn math using the Montessori materials, almost every one of them would at least understand, if not actually enjoy, it.