I teach the upper grades in my school, yet I continue to see kids who do not even have basic algebra skills in place. As a parent, I'm very aware of what my own children are learning in school. For the most part, I've been happy with their progress, but as they rise in grade level, I'm starting to see more emphasis on a loose understanding of the concepts and less emphasis on skills__particularly skills with arithmetic of fractions. The main problem with what I see with my students and my own children is that kids are taught "concepts" and are not taught skills__unless they're lucky enough to have a teacher who knows better. Most particularly, children are not taught mastery of arithmetic with fractions. Unfortunately, virtually all of their future math education depends on being able to do fractional arithmetic.

People have to start from the ground, then first step, second, third and so on to reach their destination floor. Exactly the same way students have to start from Kindergarten, then grade one, grade two and three and so on to reach their math destination. Also, if some of the steps are broken in the staircase, it is still hard to reach the desired floor using those steps. Same way, if you are missing some of the basic concepts from elementary grades, math for you is still hard. Now, the kindergarten, first grade and second grade are like first couple of the steps of the stairs. You can learn this level of math easily, as you can jump enough to take yourself to second or third step of the stairs easily. As it is very hard to reach sixth or seventh step of a stairs by jumping from the ground, exactly the same way to learn grade five or higher grade math is very hard (or impossible) without having the good knowledge of the kindergarten to grade three or grade four math. Now, consider one person is jumping on the ground to reach the third floor of a building. Can this person make it? Never, if he is not Spiderman. For this person, to reach the third floor by jumping is impossible or very hard and finally he gave up saying that it was very hard to reach third floor.

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