This is a question I often ask parents and other teachers. Fractions are taught as a chapter in Grade 5. At the end of the year students are given tests on fractions. And they pass with good or bad marks. But this has nothing whatsoever to do with understanding of fractions.
We really can't say when we understood fractions. Somewhere from age 9 onwards the sense of a "fraction" gradually builds. Some interesting twists in fractions may occur to us many years later. For example, its not easy to realize that 1/5 of something can be greater than 1/3 of something else. Then we see how fractions are also related to percentages and to decimals. This is how any true knowledge is built - gradually and through different experiences. Over time, different aspects of the concept are polished. We make mental and graphic links with related concepts and a deeper understanding is built.
If this is how we learn and learn well, then why are our Tests not designed for this. While learning is a continuous and interactive process, testing is not.The Exams expect that everyone in the class must learn fractions in Grade 5 to the given competence level and prove it by getting passing marks. Our exams say, you better know this here and now, else you have failed.
This create two bad trends. Firstly, students just learn to operate numbers by given rules and get the correct answers. Getting marks makes them think that they now know fractions. But there is no real understanding happening. Secondly, students who can't grasp the rules fail, nearly fail or barely pass. They have no second chance. In Grade 6 we move onto other Math things, too bad for you.
Our Exams are designed to disrupt the learning process, to encourage learning rules and to disqualify those who can't do it here and now.
We really can't say when we understood fractions. Somewhere from age 9 onwards the sense of a "fraction" gradually builds. Some interesting twists in fractions may occur to us many years later. For example, its not easy to realize that 1/5 of something can be greater than 1/3 of something else. Then we see how fractions are also related to percentages and to decimals. This is how any true knowledge is built - gradually and through different experiences. Over time, different aspects of the concept are polished. We make mental and graphic links with related concepts and a deeper understanding is built.
If this is how we learn and learn well, then why are our Tests not designed for this. While learning is a continuous and interactive process, testing is not.The Exams expect that everyone in the class must learn fractions in Grade 5 to the given competence level and prove it by getting passing marks. Our exams say, you better know this here and now, else you have failed.
This create two bad trends. Firstly, students just learn to operate numbers by given rules and get the correct answers. Getting marks makes them think that they now know fractions. But there is no real understanding happening. Secondly, students who can't grasp the rules fail, nearly fail or barely pass. They have no second chance. In Grade 6 we move onto other Math things, too bad for you.
Our Exams are designed to disrupt the learning process, to encourage learning rules and to disqualify those who can't do it here and now.
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