...my students being 14-15 don't know if 1/3 is bigger or smaller than 1/7? Or when they say that 3.4749 has a higher value than 54.1 just because the first number has a higher number of digits involved? Or when they grab a calculator and really need it in order to determine that 5x20=100?
These were some of the things I asked myself back some years ago when I faced this problem for the first time - while I tried to teach. Now, some years later I can still ask myself the same questions. The individuals have changed but the situation is still pretty much the same. Something really is wrong, even if some people try to get away from realising this. As long as they decide to close their eyes for this then the situation will stay the same.
I am usually trying to do something about this. Each time I teach I try to get away from ending up in the situation of "ok, open the books and start doing the exercises there without really understanding why you do it".
I am also not happy with my students using calculators during the time they do their exercises unless the exercises require the use of them.
The calculator is a really nice tool if you use it in an appropriate way. If you use it the wrong way you more or less end up in the situation above, when people can not say that 5x20=100...and I can tell you that a lot of the young people in the world has already reached this state in which they can no longer use their own brain to figure things out.
So why did I start thinking about this again? It is simple - I ran into two 14 year old girls the other day (I had these two in a geometry class some weeks ago...). Now they were really trying to figure out what they would have to pay if they bought this bag they were looking, currently having a 10% discount. So imagine the two of them standing there with a cell phone each, trying to solve this "if I take away 10% of the original price, how much do I still have to pay?" by simply using the calculator that comes with the phone!
These were some of the things I asked myself back some years ago when I faced this problem for the first time - while I tried to teach. Now, some years later I can still ask myself the same questions. The individuals have changed but the situation is still pretty much the same. Something really is wrong, even if some people try to get away from realising this. As long as they decide to close their eyes for this then the situation will stay the same.
I am usually trying to do something about this. Each time I teach I try to get away from ending up in the situation of "ok, open the books and start doing the exercises there without really understanding why you do it".
I am also not happy with my students using calculators during the time they do their exercises unless the exercises require the use of them.
The calculator is a really nice tool if you use it in an appropriate way. If you use it the wrong way you more or less end up in the situation above, when people can not say that 5x20=100...and I can tell you that a lot of the young people in the world has already reached this state in which they can no longer use their own brain to figure things out.
So why did I start thinking about this again? It is simple - I ran into two 14 year old girls the other day (I had these two in a geometry class some weeks ago...). Now they were really trying to figure out what they would have to pay if they bought this bag they were looking, currently having a 10% discount. So imagine the two of them standing there with a cell phone each, trying to solve this "if I take away 10% of the original price, how much do I still have to pay?" by simply using the calculator that comes with the phone!
It really made me think again and ask myself
"what is wrong with this world if this has to happen?"
"what is wrong with this world if this has to happen?"
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