Is math really difficult?
You know, when I was a middle school student, our math teachers at Iran were mostly like horror movie characters: they were bad-tempered; they gave us hard problems. They were very sensitive about the homework, the cleanness of the book, and the absolute silence all during the class. Whenever we addressed to go to the board, we were supposed to know the answer of any given problem. If any other cases, unless the standards of the class, happened the punishment was very dreadful. So much stress and physical punishments. However, generally teachers were also very talented and smart, motivated and knowledgeable. The common thing that students tried to do was being silent and organized to try stay far from the punishment time. In addition, there were few math geniuses at class. The teacher, up to the end of the 2nd session, discovered them. In addition, from the third session, it was like this: everybody was silent writing what was being written on the board by teacher or those 3 – 4 geniuses. Two separated part in the class, the genius and teacher part and the stupid part (as teachers call those students). So, yes! I was in the light part of the class. I was so much better than anybody else in the math class was. Nevertheless, it is not the complete story. I started math major at high school and I was lucky enough to face with some inspiring teachers whom were kind and very patients with students. Then I changed very fast. I have had this experience in my all teaches from the first time of teaching so far: the problem is not to be dumb! The problem is not to be successful in making communication with mathematics! Math is not a bunch of pure contents, but also it is a language, it is a way of thinking and it is like three-dimensional glass in a world that people can see only two-dimensional. Anyway, I have always tried to inspire my students and to teach them the logic of the math. This is the solution. In continue, you are about to read a post from beetleypete blog which is an honest confess. We teach same book at the same rate by using same words and to different students. Different people have got different educational backgrounds, different emotional experience about math and they have different rates in learning. So all together I am coming to this conclusion that it is our duty as math teachers to teach students how to learn math, how to understand the language and the logic of the math. I think you may feel familiar with this memory:
I have recently posted about the study of both History and Geography, so though I would continue that theme with something I was not at all good at, Maths. Short for Mathematics, and simply called ‘Math’ in the USA, most of us in Britain know this school subject as ‘Maths’.
When I started school at the age of five, I was taught simple counting. Using blocks, toys, or any other accessory, I soon learned how to count up to ten and more, along with my classmates. Then easy addition, nothing too complex for my developing mind. By the time I went to Junior School, aged seven, rote learning was still popular, and we were soon getting to grips with our ‘times tables’, to form the foundations of simple multiplication. This was 1959 of course, so no calculators, and not a thought of the computers to come. Just a teacher writing numbers on a board, and conducting our recital like a band leader.
“Once five is five.
Two fives are ten.
Three fives are fifteen,
Four fives are twenty”.
And so on.
We went as far as the number thirteen, stopping there for reasons best known to the teacher. Division was also introduced, often helped along by the use of counters or visual aids, as I learned that four into twenty makes five. Then around the age of nine, that ‘Eureka’ moment, when I suddenly got the connection between multiplication and division. We also tackled currency, as at that time we still used pounds, shillings and pence, with twelve pence to a shilling, and twenty shillings in a pound. Not that I ever had much cash, but it was good to know what change to expect when I bought something. We were also using rulers, and learning how to measure short distances.
When I was eleven, it was time to go to secondary school, and begin the exam syllabus. I had a list of things I would need just for Maths lessons; this included a set of compasses, a protractor, a triangle and a ‘proper’ ruler, with measurements down to 1/16th of an inch. The first real lesson was a double period, (why was Maths always a double?) and it hit me like a whirlwind. Algebra? Geometry? Even something called Trigonometry. I thought the teacher must be talking a foreign language, but she assured us that was all to come. Meanwhile, we were hit with some serious long division. That alone was enough to make my brain ache, and I watched my ‘working out’ get further and further down the page as I struggled with something like 295 divided by 16. By the time the first month of the new school was over, I had decided that I really didn’t like Maths, and was sure I would never be good at it.
And I was right.
Then came ‘Problems’. Things like, “If a two hundred gallon water tank has a leak of a quarter of a pint a day for ten days, then half a pint a day for twelve days, how much water will be left after twenty-two days?” I didn’t even know where to start, and my hand was soon up, informing the teacher that I didn’t have a clue. Even when she showed me how to work out the solution, I still got the answer wrong. It all got worse once we started with Algebra. “If X = ? and Y = ?, what is XY squared? ” I just laughed. There was no chance I got any of that at all. The teacher later explained that X and Y had a value and it could be anything I wanted on that occasion. X could be 2 and Y 6, for example. My reply was not well-received. “Please Miss, then why don’t you just write a 2 and 6?” I was told in no uncertain terms that I was being deliberately ‘stupid’.
But I wasn’t.
Later, we were given a complex book of numbers, called ‘Logarithms’. This baffling table introduced us to decimal points and such, but might just as well have been Sanskrit, for all my brain could take it in. I wasn’t getting any better, and had to face the next year, when it was all going to get harder. Double Maths changed to a Monday morning when I was twelve, and I began to dread the walk to school,, shuffling with the reluctance of a condemned man about to be hanged. I still had the same teacher, the formidable Mrs Widdowson, who could freeze me with one of her signature glares, and had given me a terrible entry on my end of term report the previous year. Inside, I considered I was doing alright. All the other subjects were going great. I was in the top set for English, Geography, French, History, and even Religious Education, something I had little interest in. So what if I didn’t really ‘get’ Maths? It wasn’t the end of the world, as far as I was concerned.
So, I muddled along. Bad reports, bottom section of the class, and never truly understanding anything new. I did well at everything except Maths, and that was enough for me. When it came to the final exams, I just scraped though the Maths one with a Grade Four, a ‘just passed’ result. But it wasn’t all bad. That early learning left me able to recall the times table instantly, work out money without hesitation, and even able to calculate foreign currency exchanges, on my trips abroad. These days, i see young peope reach for a mobile phone, when faced with the most basic sum to work out.
Maybe we need to go back to chanting the times tables, and using a ruler?