<p>...but they can't make you DO algebra.</p>
<p>A recent thread has got me thinking about how they test algebra on the SAT. There have definitely been questions which check whether you can read a problem and write the equation that goes with it. Look through the blue book or other CB tests and you'll see things like:</p>
<p>If x is the first of three consecutive integers, and the average of the 3 consecutive integers is 10 more than the product of the larger two, which of the following equations can be used to solve for x? [That's not BB...I just made it up to illustrate what I mean.]</p>
<p>Then, you have to pick the one that models what they said. So you have to be able to write it, but not solve it. The reason for this is that if they asked you to solve it, they would have to give you answers. At that point, the problem would be vulnerable to attack by trial and error. Even it were a grid-in, you could still use trial and error. So if they separate the algebra-writing process from the solving process. And to their credit, they USUALLY make the solution one that would be hard to find by guessing. (Sometimes, you can guess the solution through trial and error and then plug it into each equation to see which one works. But that is rarely the quicker way.)</p>
<p>So for students who have trouble solving the equations, at least be comforted that all you have to do is come up with them -- not solve them.</p>
<p>Also, if you are that student who can set up the equation but often struggles with the solution process, you may benefit from switching to a TI89 and learning to use the algebraic solver (F2, Enter...). I know that not everyone needs this, but it definitely helps some students. You have to figure out if you are one of them...</p>
<p>You bring up an interesting point. But I wouldn’t recommend using the algebraic solver for everyone, especially since A) TI89s are pricey and B) in the end it’s better to know how to do it.</p>
<p>Yeah, I don’t recommend it for everyone either. I find that weaker students get lost in the technology and stronger ones can do it faster the “right” way. But there’s definitely that group in the middle, really maybe only 10-15% of the kids I see who get a one or two question boost. And I never send a kid out to buy one just for the test.</p>
<p>I must be misunderstanding; you seem to be saying that there are no algebra problems on the SAT in which an equation needs to be solved. But every SAT I’ve seen has these, and yes, you can often solve them simply by trying the answers. E.g., 2x + 1 = 3x - 2 ; what is the value of 2x + 1 ?</p>
<p>Right. But what I mean is that it’s hard for them to write a problem that REQUIRES algebraic solutions. As you have pointed out, your example…</p>
<p>2x + 1 = 3x - 2 ; what is the value of 2x + 1 ? </p>
<p>…while easily solved by algebra, is also vulnerable to trial and error (and to a TI89).</p>
<p>In school, we teach that algebra word problems are to be solved by:</p>
<ol>
<li>assigning variables to the quantities</li>
<li>developing an equation (or system of equations) that express the relationships</li>
<li>soving the equation(s)</li>
</ol>
<p>Now try to write a multiple choice question to assess whether students can do these things…you find that it’s hard to construct an item that requires this entire process. The best you can do is assign the variable for them and then ask them to pick which of the answer choices has the correct equation. </p>
<p>So with your example, here’s what they could have done:</p>
<p>Mary’s age is one more than twice Xavier’s. And Jane’s age is two less than three times Xavier’s. If Mary and Jane are the same age, which of the following equations can be used to solve for Xavier’s age, x?</p>
<p>Your equation would be the right answer and they would dredge up the usual suspects for distractor answers. </p>
<p>But my original point was that as soon as they ask for actual numeric solutions, the problem becomes vulnerable to all of the classic SAT work-arounds. And say what you will about the work-arounds, but they do in fact work. It seems that some students and tutors feel that there is something unrighteous about enabling those students who lack algebraic fluency to still get these problems right. To them I say: go write a better test, but don’t tell the students who have to face THIS test not to do what they can to improve.</p>
<p>Ah yes that’s what I thought you meant, no argument here. And even algebra problems with algebraic answers can be foiled with strategies such as plugging in numbers.</p>
<p>I sometimes see questions that try to avoid being solvable through plugging in by asking for x + y or something.</p>