<p>I have looked at both and find the SAT reading questions much more abstract.
I don’t understand the talk about ACT being more about what is learned in high school. I just went through a few of the science sections and thought they were simple, not knowing anything about the the actual “science” being questioned. It was simply looking at the chats and graphs for the answers.</p>
<p>Math seems straight forward as well…maybe that is what is meant by what is learned in school…the math section?</p>
<p>I’m on the east coast, but will probably push my D toward the ACT as she did not fair well on the reading on PSAT, but is a straight A student.</p>
<p>Geeps, a lot of this more straightforward and objective non-sense comes from the perception that the test require more “high school” reflexes, and the math is also more similar to typical high school questions. Many view questions that require logic and analysis as screwy and tricky. </p>
<p>All those views are, however, subjective as the students react differently to the same test. Some view the SAT as simple as it comes; others as pure torture. I do not consider the ACT to be easier or more difficult than the SAT, but I never found the format attractive, or superior in any way. This might show my bias about the tests that have come from Iowa! </p>
<p>It’s always possible that I saw your earlier posts, Xiggi, and internalized the concept without remembering the source. I would like to hear more about your strategies used to create virtuous cycles.</p>
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<p>The most frequent place I see this is with ACT/SAT grammar questions. Most native speakers have a good sense of what “sounds wrong.” The test makers delight in creating questions which sound right in conversational English, yet don’t follow the rules of formal written English. Here, especially, it helps to know what the formal rule is, rather than just rely on what sounds right.</p>
<p>It doesn’t help that most K-8 English teachers don’t actually teach the correct rules. For example, it’s often stated that a pronoun substitutes for a noun; it does not – it substitutes for the entire noun phrase, including the article and any adjectives. Otherwise, you would say “The young he chased the ball” for “The young boy chased the ball.” No native speaker would make this mistake, but an ESL teacher would need to define the rule more precisely. Hence, ESL learners often understand English grammar better than native speakers.</p>
<p>No, it’s probably a case of great minds thinking alike. /smile </p>
<p>Or, on a more serious and humbling note, the result of reaching for a conclusion based on common sense. I am pretty sure that many before me realized that it makes sense to check the correct answers as well as the incorrect ones. That is why after trying to condense my thoughts on the issue in that epic thread, I reached out to professional tutors to share their own views. </p>
<p>As far as the virtuous circle, the idea is to build small blocks of knowledge and use them to become blocks of confidence. A student who recognizes a question and immediately knows how to approach it will gain confidence in his or her abilities. On the other hand, a successful guess does not create the same effect. The cycles improve with each repetition and the “deja vu” effect brings additional confidence and, with it, a better grasp of the time management.</p>
<p>There is much wisdom in that old tread that you linked to in #80, Xiggi! I especially like the comment above, because it takes the fear out of test-taking: it’s just a gosh-darn game and, with repeated practice, it can be beaten. Like with pinball or StarCraft, not everyone will get the world-class high scores, of course. But get close enough and work on the rest of your “portfolio” and even the elite schools are within reach.</p>
<p>Okay, I hate to bump this thread, really I do. But I saw the QOTD and this just sprang to mind.</p>
<p>Anyway, the gist of it is that a company’s profits are based on an equation 2000<em>P-10</em>P^2, where P is the Product sold. It asks at what level of sales would profit be a maximum and gives a list of five possible answers.</p>
<p>Now, in my mind, there are three possible ways I see to do this, although there may be more. I differentiated and set it equal to zero. But some kids won’t have had even this simple differential, or be able to solve the resultant equaltiy (sad but true). Other kids may be so smart to just envision the answer based on characteristics of the equation. I don’t trust myself to be that smart, but I’m sure there are many kids on here who are.</p>
<p>But for many kids who really struggle in math, I still contend the best method is to simply plug the answer choices into the equation using your calculator. If you are fast, you can do it two or three time to check. Again, that is my experience.</p>
<p>ACT is based on school curriculum, what has been taught in high school. There are many books to prepare SAT. How about ACT? What are some of the famous books to prepare from?</p>
<p>Method 1 is not applicable to most students. Knowledge of calculus is not required for SAT. If a student must use calculus on this type of problems, then there is a flaw in his/her elementary math. Method 3 is definitely a viable approach, especially when one is running low on time; however, this approach avoids true understanding and misses a chance to build a virtuous learning cycle mentioned upthread. </p>
<p>I’ll expand on the mysterious “envision the answer based on characteristics of the equation” method. I’m also not smart enough to have the answer just pop up in my head. So how do we approach this problem? (I’m thinking in my mind how I would I teach the approach to a student.) </p>
<p>Well, P (product sold) is an integer by common sense, and the question asks for a value of P when the equation reaches a “maximum”. This means that if you increase or decrease P by one from the answer, the result would be smaller (or may be equal, but this the SAT, so we can skip this concern) than the maximum. This insight suggests two inequality equations. Usually solving one is good enough to reach the correct choice.</p>
<p>Students should be able to use basic algebra to solve these simple equations. Solving first equation shows P > 99.5 and the solving the second one shows P < 100.5. One can also tell that the correct answer must be between 0 and 200 because the original equation is zero at these two points.</p>
<p>I have to say this problem would be a “hard” math problem on the SAT.</p>
Hi PCP. That’s a very clever approach, and I agree that the problem might be classified as hard on the SAT, but I posit if it weren’t for the fact that they give you five numerical answers to pick from, it might realistically be classifeid as “Impossible” for a large subset of students. I’m talking about sub-500 math students.</p>
<p>But if you can just take each of the five given answers, and plug them back into the question equation with your calculator, it becomes doable for far more students. So it may take a little more time, but with the calculator it moves from the Impossible to the Possible column. THat’s my reason for posting this as part of this little pseudo-debate I’m having with xiggi and LI.</p>
<p>And of course, you could always plug in the given answers and work it out by hand. But that’s also far more time consuming and sibject to error.</p>
<p>And I’ll also add that learning is great, virtuous or otherwise I suppose. But some kids just want to break 500 so they can get that pitching scholarship, or make it into their state school period. When you have kids on the upper end of the Math bell curve it’s hard to envisage I suppose.</p>
<p>This problem reminds me of a visible gap in high school/middle school math curriculum. Our math teachers rarely spend time on inequalities, and even when they do, they rarely provide good and interesting problems that illustrate real-life application of this discipline. Things are rarely equal in the real world and heuristics (involving inequalities) plays a major role in solving real problems. </p>
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<p>My guess is that sub-500 SAT math students may have serious gaps in their understanding of basic algebra, which may be needed if they are to succeed in the desired college programs that require 500+ SAT math score. I agree that using plug-n-see approach on a couple problems might just be enough to lift the student over the hurdle (and I support it wholeheartedly), but it will be done at the expense of true understanding. </p>
<p>These students should be encouraged to spend serious time to review/relearn/practice basic algebra, until they have a solid grasp of the fundamentals. Btw, the plug-n-see approach would be a pure guessing approach if one of the choices is either “None of the above” or “There is no maximum”.</p>
<p>There is another approach to the SAT QOTD problem above. For those of us who still remember the Quadratic Formula, which I believe is assumed knowledge for SAT math, we can apply a form of this formula to solve this problem. </p>
<p>Because this is a quadratic equation with a negative ‘a’ (coefficient on P^2) value, we know from algebra that this is a downward-facing parabola. As such, there is exactly one point in this equation for which a ‘y’ value has a single corresponding ‘x’ value. Everywhere else, there are two ‘x’ values for each ‘y’ value. We know from quadratic formula that the only time where there is a single ‘x’ value in the solution is when the discriminant (b^2 – 4ac) is equal to zero. When this happens, what’s left of the formula is only –b/2a, which in this case is -2000/(2)(-10) = 100. </p>
<p>My son told me they were taught in algebra this method to find the vertex of a parabola.</p>
<p>I just went to College Board’s QOTD page and looked at its “official” solution, and I must say I was surprised that the official solution seems to imply getting the solution by punching in the equation to a graphing calculator and look for the maximum in the graph. This method was posted by mamabear1234 earlier.</p>
<p>High school and college math and SAT math, well rarely do the twain meet. A kid who can barely hit the median on the SAT is not likely to be pursuing a math heavy college curriculum. But they should be at least able to figure out what this question is asking and use the tools at their disposal to get a correct answer. I have degrees in both Physics and EE and I still think my first instinct on this problem would be to use the calculus and if I couldn’t do that to just try the answers. I can work brain teasers on my own time. I know it makes me come off like.a dummy but that’s okay. It wouldn’t be the first time.</p>
<p>I just asked my D who is a senior in her first calculus class, and she immediately said differentiate. I reminded her that she had not had calculus last Oct when she took the SAT, and then she said the -b/2a thing. (Then she said calculus is so easy, they should teach it earlier than senior year.)</p>
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But some kids just want to break 500 so they can get that pitching scholarship, or make it into their state school period. When you have kids on the upper end of the Math bell curve it’s hard to envisage I suppose.</p>