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<p>It’s not a matter of concept or method. (I’ve never even heard of Newton’s method.) Squares and square roots are very simple concepts, and I’m sure your daughter knows what they are. It’s a matter of mathematical reasoning: 95 is between 9^2=81 and 10^2=100. Therefore, the number that you would square to get 95 is between 9 and 10. Logic.</p>
<p>A lot of high school math seems like an attempt to impart this kind of logic on the students–figuring out how to manipulate equations so you can solve them–but I don’t think it works very well. Kids tend to memorize: they look for the formula, the method that will allow them to solve a specific type of problem. If they don’t remember the method or the problem is unfamiliar to them, they just give up. (Someone with good mathematical logic, on the other hand, can use what they know about the properties of the numbers and operations to find their own method of solving the problem.) To them, it doesn’t really matter–they can pass their tests just fine–but memorization is fleeting.</p>