One thing really stood out for me in these tests was the survey of how much children enjoy school. This ran alongside the tests, and the results are generally the polar opposite of the performance in the tests. Those who enjoy school the most did not do well in the tests, those who enjoy it the least did the best.
I would be very interested to see how the lower performing countries rank against the higher performing ones academically for lifelong learning. I think we now live in a culture and society that embraces lifelong learning far more than any in the past. The generation before mine many of whom are retired now are being forced to learn new skills with IT. I remember my parents saying how hard it was to learn when you are older, I really do not believe this and think it was indoctrinated in the education system they grew up in.
There is already talk of training students purely for these inter-country ranking tests, clearly thought up by people who have no real interest in education, teaching to a test is far from educating, it is merely dictating. It is forcing acceptance without personal development and only requires students to follow instructions with no thought or understanding.
Something else interesting is our Governments devolution of the education system in England. Specifically within maths, Michael Gove stated he wanted algebra to be taught to primary school children, yet the high performers in the Pisa tests do not do this (see here). They develop an understanding of how numbers are built up before bringing in unknowns. We are told we must get the 'times tables' drilled into students at an early age. This is the worst way to inspire young minds to learn what I think is the most creative universal subject. The answers to the times tables are just a tool, they are not the foundations of mathematics hence anything built upon false foundations will not last. Understanding how they are formed is the key to inspiration in the subject, and the creative ways to answer simple to complex multiplications (and division).
For example, when I ask what is 12x13 younger (start of year 7) students claim they cannot answer this mentally as they only know up to 12x12. Some will be brave and go for 10x2 and 3x2 as they are able to split the calculation apart from experience. What I try to get them to understand is how 12 is formed in the first place, it is 3 doubled twice. So I tend to Triple a number (lower numbers are quite natural to triple quickly), then Double it and Double it again. This is mathematics, this is the creativity involved and this leads to algorithmic development, times tables do not!
Try it, as a parent or teacher you will probably know your 8 times table, stop thinking that way. 8 is 2x2x2. With this method you can do 231x8 in seconds and are not stuck past 8x12. You are no longer limited to the regimental thinking forced upon you in school.
231x8 = 462x4 = 924x2 = 1848 This is the formal maths.
Mentally I just bounce, doubling doubling and doubling.
Try things like this for starter activities, or fillers for those with 100minute lessons.
Another example is the 5 times table. This I think of as the 10 times table halved (halving is a quick mental process, as is 'thirding'). Mentally the 5's are easy to remember, but what is 231x5?
Well it is easy to see 231x10 is 2310. So half of that is 1155.
The depth of learning mental multiplication this way is endless, it leads to understanding of Prime Factors, to understanding HCF and LCM, to Indices and Standard Form, ultimately leading to Calculus. What I ask the GOVErnment to do is to ban times tables teaching from the maths curriculum. Times tables do not develop thinking skills, they are repeating without understanding and are just slow and laborious to use.
I have made my opinions perhaps an exaggeration of the real truth here to spark debate. I do not know the answers to this problem, but my instinct knows I developed a much better understanding of Mathematics when I stopped thinking in times tables.
I would be very interested to see how the lower performing countries rank against the higher performing ones academically for lifelong learning. I think we now live in a culture and society that embraces lifelong learning far more than any in the past. The generation before mine many of whom are retired now are being forced to learn new skills with IT. I remember my parents saying how hard it was to learn when you are older, I really do not believe this and think it was indoctrinated in the education system they grew up in.
There is already talk of training students purely for these inter-country ranking tests, clearly thought up by people who have no real interest in education, teaching to a test is far from educating, it is merely dictating. It is forcing acceptance without personal development and only requires students to follow instructions with no thought or understanding.
Something else interesting is our Governments devolution of the education system in England. Specifically within maths, Michael Gove stated he wanted algebra to be taught to primary school children, yet the high performers in the Pisa tests do not do this (see here). They develop an understanding of how numbers are built up before bringing in unknowns. We are told we must get the 'times tables' drilled into students at an early age. This is the worst way to inspire young minds to learn what I think is the most creative universal subject. The answers to the times tables are just a tool, they are not the foundations of mathematics hence anything built upon false foundations will not last. Understanding how they are formed is the key to inspiration in the subject, and the creative ways to answer simple to complex multiplications (and division).
For example, when I ask what is 12x13 younger (start of year 7) students claim they cannot answer this mentally as they only know up to 12x12. Some will be brave and go for 10x2 and 3x2 as they are able to split the calculation apart from experience. What I try to get them to understand is how 12 is formed in the first place, it is 3 doubled twice. So I tend to Triple a number (lower numbers are quite natural to triple quickly), then Double it and Double it again. This is mathematics, this is the creativity involved and this leads to algorithmic development, times tables do not!
Try it, as a parent or teacher you will probably know your 8 times table, stop thinking that way. 8 is 2x2x2. With this method you can do 231x8 in seconds and are not stuck past 8x12. You are no longer limited to the regimental thinking forced upon you in school.
231x8 = 462x4 = 924x2 = 1848 This is the formal maths.
Mentally I just bounce, doubling doubling and doubling.
Try things like this for starter activities, or fillers for those with 100minute lessons.
Another example is the 5 times table. This I think of as the 10 times table halved (halving is a quick mental process, as is 'thirding'). Mentally the 5's are easy to remember, but what is 231x5?
Well it is easy to see 231x10 is 2310. So half of that is 1155.
The depth of learning mental multiplication this way is endless, it leads to understanding of Prime Factors, to understanding HCF and LCM, to Indices and Standard Form, ultimately leading to Calculus. What I ask the GOVErnment to do is to ban times tables teaching from the maths curriculum. Times tables do not develop thinking skills, they are repeating without understanding and are just slow and laborious to use.
I have made my opinions perhaps an exaggeration of the real truth here to spark debate. I do not know the answers to this problem, but my instinct knows I developed a much better understanding of Mathematics when I stopped thinking in times tables.
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