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By Xiggi (Xiggi) on Thursday, August 12, 2004 - 12:58 pm: Edit |

In the process of finalizing my notes for my younger sister's school, I spent some time reading the latest offerings that are available in bookstores.

I started with the juggernaut: Princeton Review. In the past, I have liked their SAT books sufficiently to recommend buying them. I do, however, recommend to buy as many books as you can afford, check them out, and use the strategies that works for your individual situation.

Having read the 2005 version for the PSAT/NMSQT, my verdict is that the acronym should stand for Never Mind the Sub-par Quality of our Textbook! Seeing such books being published helps me understand why so many students do NOT do well on the PSAT. In many circles, the PSAT is viewed solely as a test run for the SAT, schools do not encourage the students to prepare for it -unless the student tries to score the the NM level. In a typical scenario, the vast majority of juniors will take the test after GLANCING at the flyers distributed at school. A great number of students will also face a parental gift: a book like the PR in question that was picked up at the local bookstore by the concerned parents. After all, doesn't the cover spell out "EVERYTHING YOU NEED FOR THE NEW PSAT"?

So, what does the typical junior do? He (or she) will roll his eyes, take the book to his room, read the first 10-15 pages, glance at the strategies, and jump to the practice tests to see what he knows.

What will he learn? He'll read that the PSAT is NOT that important and that strategies do work very well. He'll be introduced to the famous Process of Elimination (POE) but also told to guess AGGRESSIVELY. While this advice is not bad, it could have ... devastating repercussions. The student is really told that he does NOT need to know the answers and that guessing on all questions is beneficial, as long as he can eliminate one of the 5 choices. Armed with this knowledge, the common student takes a practice test and burns down in flames. What was missing in the advice? The fact that most students have the necessary education and are able to answer ALL the questions correcty. Yet, the theory is that tricks and strategies will yield a higher score. What is also missing? The fact that it takes a LOT of work to excel at the test.

Well, enough blah-blah! Let's check a few examples.

Question: If n is an integer larger or equal to 1 but smaller or equal to 20, what is the sum of the unit digits of all possible values of b when b = 2^{n}. (*Note: This could be expressed as b=2^n*)

A. 40

B. 60

C. 64

D. 80

E. 100

Here is the answer from PR: This question wants us to work with the exponential vaues of 21 through 220. So work these out and keep your eye on the unit digit 2, 4, 8, 16, 32, 64, 128, 256 ... There is a repeating pattern of 2, 4, 8, 6. Their sum is 20, and this pattern will repeat five times between 20 and 220. So that's 50 x 20 = 100.

Isn't that great? Except for a small detail: where in the world does 21 or 220 come from? Will an unsuspecting student looking to LEARN from the answer see that they MEANT to write 2^1 and 2^20?

This case is sufficient to throw any student in a tailspin of self-doubt. In addition, I have no idea why PR believes that such a question COULD show up on a SAT. I'll spare you the details but ETS will never expect a student to write out 2 to the 20th power. Even if the pattern could be verified after a handful of calculations, this is a BAD question that shows why companies like PR are NOT able to produce decent emulations of the real tests. Not only do they fail to develop the question properly, but they also display a total lack of care in verifying the proposed answers. The first part is understandable, the second part represents a cynical lack of concern for their customers.

The book published by PR has not been edited very well and has been put together with little care or attention. They recycled old material, deleted the analogies and QC, and finally added the new questions in their two tests without doing much effort to provide an adequate guidance for the new material. The wannabe tests produced by PR and others have always been dubious, this new version is simply abysmal. I am dumbfounded to see a company with vast resources producing such poorly written and researched material.

This post is getting too long. I will leave additional comments on some items that they did not update!

By Xiggi (Xiggi) on Thursday, August 12, 2004 - 01:41 pm: Edit |

Now, let's look at what has not been updated from the 2003 version.

In the very beginning of the book, we get this strategy:

To follow the example, you need to visualize a square ABCD, and inscribed inside the square a half circle CFD. The half circle diameter is also CD. In this case, the side is 8. This is a very common SAT problem and PR asks the student to identify the area represented by the square MINUS the half circle.

The 5 proposed answers are:

A. 16 - 8 Pi (Pi for p}

B. 16 - 16 Pi

C. 64 - 8 Pi

D. 64 - 16 Pi

E. 64

This is what PR proposes: We know that the value of PI is a little more than 3. Let's replace Pi with 3 in the proposed answers. Choice A and B are negative numbers. From here, you could guess C, D, or E and it is a guess we SHOULD take. However, we can also eliminate E because 8*8 is 64 and represents the whole square. What do we end up with? A one-in-two shot of getting this problem right. **Neat, huh!**

Well, not quite!

Let's look at the problem. How fast can we solve it?

1. Area of square? 8*8 = 64 .... 5 seconds

2. Area of half circle? Any student sitting for the PSAT or SAT should be able to play with the areas of circles, squares, and triangles. In this case, the 1/2 circle has a diameter of 8, hence the area of the 1/2 circle should be radius^2 * Pi * 1/2. The answer is 16 Pi/2 or 8 Pi. Time to compute this ... 15 seconds

3. Guess what? The answer to the question is 64 - 8 Pi. Check answer C after about 25 seconds?

What is bad about the PR method? First, if forces the student to write down FIVE calculations. Despite being trivial, it introduces potential errors. Most students make careless mistakes and calculating 16 times 3 easily falls in that category. Assuming the student does not make any error and gets it done rather quickly ... now, he still has TWO choices or a 50/50 chance. It could mean a plus 1 or a ...MINUS 0.25 in his tally, a swing of 1.25!

Why is the particular message wrong? It tells the student to forego attempting to solve a problem that most 7th graders can solve FAST and CORRECTLY. It also reinforces the idea that the test is all about gimmicks and tricks.

While the POE taught by PR is a GOOD technique, I do not quite understand why they selected this problem to illustrate their method.

By Xiggi (Xiggi) on Thursday, August 12, 2004 - 02:10 pm: Edit |

The next one involves a perennial favorite problem on the SAT: the average rate of speed

A girl rides her bicycle to school at an average speed of 8 mph. She returns to her house using the same route at an average speed of 12 mph. If the round trip took 1 hour, how many miles is the round trip.

A. 8

B. 9 3/5

C. 10

D. 11 1/5

E. 12

PR proceeds with this solution: First the problem is a hard problem (level 5). TCB assumes that the common student will not attempt to solve the problem and pick the trick answer of 10 since it represents the average of 8 and 12. The common student second choice will be to pick a value that is stated in the problem: 8 or 12. PR provides the strategy to eliminate those Joe Blogg answers. Again, the conclusion of PR is to end up with two choices and pick between B and D. In their words, the student will be in great shape!

What's my beef with this? In my eyes, a 50-50 chance is really not good enough. When you consider how this problem can be solved, the recommendation to guess becomes highly dubious.

What could a student have done. Know the formulas for related rates -an opportunity that PR strangely forgets to mention. Is this formula really complicated? Here it is:

[2*Speed1*Speed2] / [speed1 + Speed2] or in this case:

2* 8 * 12 / 8 + 12.

Most everyone will notice that the answer is 2*96/20 or simply 96/10. This yields 9.6 or 9 3/5. The total time to do this, probably 20-45 seconds. Not a bad method to know!

It could even get better. How would I solve it?

1. Check the problem to make sure we have a ONE hour unit. Most often, TCB will use a one hour limit and not a different number of hours.

2. As soon as I verify that the unit is 1 hour, I will check B because I know that the answer is ALWAYS a number slighly BELOW the straight average. It takes only a few problems OF THAT TYPE to realize that it ALWAYS works.

3. My total time including reading the problem: about 10 seconds!

Here you have it: two methods that are faster and are bound to yield the correct answer and a healthy dosis of self-confidence!

By Northstarmom (Northstarmom) on Thursday, August 12, 2004 - 02:37 pm: Edit |

Xiggi,

Your review is helpful and comprehensive. I think you should find a place that will pay you to publish it.

By Achat (Achat) on Saturday, August 14, 2004 - 09:21 pm: Edit |

I agree. You should get paid for this!!

By Vadad (Vadad) on Sunday, August 15, 2004 - 12:31 am: Edit |

Xiggi:

Great work, as always. Hope you can find an entrepreneurial outlet for all this work, though I imagine you might have already.

Are you still recommending that prep for the "new PSAT" basically follow your recommendations for prep for the old one? Should our kids be practicing the old "genuine SAT's" minus the analogies? Thanks.

By Backhandgrip (Backhandgrip) on Sunday, August 15, 2004 - 09:04 am: Edit |

Wow.

Mini, where are you?

By Carolyn (Carolyn) on Sunday, August 15, 2004 - 02:16 pm: Edit |

Xiggi - Thank you so much - I have been looking at various books for the PSAT and new SAT and haven't found any really good ones yet. The PR book won't be on my list now. Thanks to your advice, I'm on the wait list at Amazon for the "new" Real SATs. It won't be out until October, though, too late to help with the PSATs.

Would you say there is any value in just buying the old 10 REAL SATs and using that as a prep book for the October PSAT math section?

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