In this article, I explain how we actually conquer the math SAT practice problems...
In the other SAT related article of this issue, I mentioned that we go slow, spending a lot of time with the problem in a no pressure environment. That approach only goes so far toward productive work, especially with a 10 year old.
It is possible to work productively toward a solution despite having a tool box that is missing most of the tools. The majority of the questions on the SAT math test are basic algebra and geometry, so we'll start there.
When we first open the book, I ask my child to do any 3 problems that he thinks he can solve. Finding these is worth 2 problems (making 5). I don't care which 3 problems are chosen. The hard ones aren't going anywhere and can be solved later.
For the next few months, we'll skip hard problems, skip from test to test, and generally just skip around. Eventually, we'll move to the next level which is 'the next 5 problems on whichever test you're on', unless these are hard, in which case we'll do the first 5 problems on the next test, which are generally easier.
The first step in tackling an algebra problem is not understanding the problem. The first step is to write down the problem and simplify it with pre-algebra. We've found that the "minus minus", as in y = 25x - (5x - b) has been put there by the SAT authors to make a wrong answer more likely. Thus we decided to eliminate the headaches upfront.
In the coming months, the 'simplify' step will involve the range of pre-algebra basics. Certainly, parenthesis have to go.
There are a class of SAT problems wherein if you leave the parenthesis there, the problem solves itself. For example, (x - b)(x - 3) = 0 has a solution of x = 3 if you keep the parenthesis. The child will figure this out for himself. Instead, we'll spend a bit of time working quadratic expressions between the long form and the solution form.
Once the problem is simplified, it's back to the work of understanding the question. At this point, I've got a kid working the SAT. Much more gratifying than letting him struggle and be baffled. Next week, I won't bother to mention that the first step is simplification, he'll forget, an incorrect answer is likely, and we'll do it over.
With all things algebra, I usually recognize the form of the problem and remember a solution method. This is not true of a newby, not even if he sees the same form 3 problems in a row. A little pre-algebra goes a long way toward getting him in the game.
Algebra word problems would be solved very quickly by crafting the equation. Since we skipped pre-algebra, my children have devised algorithms to solve word problems mentally. If they get the wrong answer, we go back and produce the equation to be solved. If you short cut the step that pre-middle school and early middle-school children take trying mental gymnastics, and skip straight to formula's and the mechanics of algebra, they do not invent these algorithms and their cognitive skills are lacking for the rest of their lives. Kids with out the algorithms reach their max potential early and quit math early.
Unlike algebra, where the child will slowly become adept at pre-canned solution methods to problems from a pre-canned class of problems, when when we see a geometry diagram, the first step of solving the problem before reading the question is mandatory and will not change. Any time we see a diagram, we always solve it first and read the question later.
There are a limited number of geometry identities required: a line has 180o, a triangles angles add up to 180o, a right angle is 90o, opposite angles at an intersection are the same, etc. When presented with a diagram, the first order of business is to solve everything that can be solved. With any luck, one of the missing elements is the answer. At some point we'll take a bread to prove each one of these in order.
The diagram solving step prevents the paralyzing confusion that results from reading the question. Sometimes the diagram is full of variables and the values are in the question, so we'll pull these out and go back to solving.
This approach is on average quicker than reading the question first even for older kids. It is unlikely my children would waste time on a test doing this step first, even though I've carefully trained them to follow this approach. On a test this becomes the fallback plan. Having a fallback plan is much better than having anxiety.
No comments:
Post a Comment