READ, dangit!

There exist SAT and ACT tutors who fill out a form after the test outlining for parents why the student didn't get the score they wanted.  I think it's a CYA thing, and I can see the motivation, but it seems a bit mean.  However, if I DID fill out such a form, "Doesn't read enough" would be one of the check-boxes.  "Didn't do what I told him to" would be another, and for many students this would amount to the same thing.

Students (and their parents) are told the importance of reading over and over again.  We all know we should be reading, but many people -- teenagers in particular -- don't.  Even if a student is a big reader, sometimes they don't read a wide enough variety of texts.  How many times have you heard, "They can read ANYTHING! It doesn't matter!  Find something they enjoy!"  This is only true up to a point.  When it comes to college readiness, the ability to read non-fiction at a college level is crucial.  However, you can't count on colleges to teach the student how to do this.  They expect their students to arrive already reading at a college level.  In fact, college entrance exams are specifically intended to measure the ability to do this.  High schools haven't traditionally done such a great job either.  They tend to focus on the types of fictional reading the practice of which will come in handy if you major in English Lit.  The Common Core Standards are supposed to address this issue.  We'll see.

When I get a student who needs work in the reading section, I usually assign reading homework.  I send home articles that were written "for grownups."  The students get to choose what to take home, although I encourage them to choose articles on topics they know little about rather than articles they think they would enjoy.  This is the homework that is least likely to get done.  I'm not sure why.  Is it because they can't bring themselves to read "boring" stuff?  Is it because they don't see the immediate connection between the assignment and improving their test scores?  Is it because the improvement is not as immediate or obvious?

An aside--  If you are reading this, and you are one of my current students:  I can tell when you didn't really read the article.  I may have chosen not to embarrass you, but I know.

Usually when a child's reading score is low, it's because he really doesn't read all that well.  You can't fix that without reading.  So, READ, dangit!

Check back tomorrow for some specific reading suggestions.

Study materials review: Up Your Score ACT

Up Your Score for the SAT was originally introduced in the 1980's.  It is periodically updated by a fresh crop of perfect scorers.  (You can read my review of that book here.) This is the first ACT version.  It was put together by a test prep tutor (Chris Arp) and 3 perfect-scoring students who are now in college.  Like the SAT version, the book is cute and clever.  Also like the SAT version you have to wade through an awful lot of cute and clever to get to the actual meat of the advice.  As you may have gleaned from my previous reviews, I like the books that offer targeted practice.  This one does not.  It was not written as a stand-alone resource; you'd have to buy a guide with actual practice tests as well.  As of this writing (June 2014) the price isn't bad - about $14.  Still, there's no reason not to just check a copy out of the library.

There is some fairly interesting study advice that will apply to subjects other than the ACT, and, as I mentioned in a previous post, the section on punctuation is particularly useful.  If you really need to own your own copy, there is a link below.

It's hard to solve the triangle if you don't know what a "guy wire" is.

Happily all of my students currently studying trigonometry know that one would find a shadow on the ground, and all of them know how a kite works!  However, I did have to tell three students in a row what a "guy wire" is.

I'm not sure how we should be trying to address this problem.  On the one hand, we don't want a student who knows how to solve a triangle to miss the question because he doesn't know a non-math vocabulary word.  (And what about the ESL kids?) One solution might be to provide a labeled diagram with each question.  However, many would argue that being able to model the problem involves the student drawing his own diagram. Is there even a description of a guy wire that doesn't essentially tell the student how to draw the diagram?  And if we restrict ourselves to vocabulary that was used for examples in class, then how do we ever present a student with a novel problem?

The fact is that a word problem has to be about something.  And if the student has no experience with that "something" then it's a lot harder to work the problem.

(For more context, see this earlier post.)

Another great punctuation review for the ACT!

Up until now my favorite ACT punctuation review was Barron's ACT 36.  However, I have another favorite!  I am in the process of reviewing Up Your Score ACT: The Underground Guide.  I haven't finished it, yet, so stay tuned for the full review. However, I have reached the punctuation review in chapter 4, and it's pretty good.  The ACT 36 review is more thorough, but the Up Your Score ACT review is funnier and easier to remember.

If you really struggle with punctuation questions, choose the Up Your Score review.  If you are trying to get those last few questions for a perfect English score, go with the ACT 36 review.

A while back I wrote a full review of Barron's ACT 36 which you can read here.  I recommended that you borrow a copy for the punctuation review rather than buy the whole thing.  

Cheating on the college entrance exams

My kid went off to a prestigious college. He came home for Christmas break convinced that he was one of the few people on the planet who didn’t cheat on his college entrance exams. Apparently, everyone there had a story about his cousin’s boyfriend’s sister who cheated on the exam by doing fill-in-the-cheating-method-here. Some of the stories sounded rather unlikely to me, but the news at the time was all about that kid in ….New York was it? …who made a gazillion dollars impersonating other students and taking their exams for them.

In May of 2013 I took the SAT II Math Level 2 exam and I assure you, none of the cheating techniques would have worked. That’s not to say they never work, but the cheating techniques I hear about all depend upon having a dishonest or incompetent proctor. How prevalent is that? I don’t know. I do know that if your testing strategy depends entirely on having a bad proctor, you are likely to run into trouble.

I was recently asked to review a book entitled SAT SNEAK ATTACK: How Computer Geniuses Hack, Beat and Cheat America's Most Feared Exam by Peter Wayner. At 33 pages, it would make a better magazine or newspaper article than it does a book. The gist of it is this: 1. Poor pay causes the proctors to do a bad job. (There are no statistics on the percent of proctors doing a bad job, but since they are all paid poorly I suppose we are supposed to assume that they all are therefore doing a bad job.) 2. Because the proctors are not paying attention you can hide helpful information in your calculator, such as a dictionary. (Having your calculator out at all during the verbal sections is forbidden, so this requires a very inattentive proctor.) 3. You can also hide a program that helps solve math problems, although, based on the description, it sounded to me like this particular help would only be useful for students who would otherwise score very low in the math section. 4. Large numbers of students are cheating using this method. (Again, no actual statistics. This is based on anecdotes from college students.) 5. The author personally alerted the ETS to this egregious problem and they metaphorically rolled their eyes. 6. This means that the math help program is apparently “legal” and any test-taker would be stupid not to avail himself of this advantage.

The SAT was designed in such a way that you do not need a calculator AT ALL. You are allowed to use a calculator because too many high school students think they can’t do math without one, and because they aren’t really testing you on arithmetic anyway. The top test-takers know that using your calculator as little as possible will actually help you go faster in the math section. Spending time and money downloading some program that will solve triangles for you is pretty silly. The triangles on the SAT can nearly always be solved in your head. In the time it would take to practice using the program, you could just practice the math in the first place. But I guess then you wouldn’t have a fun anecdote about how you cheated the SAT.

You want the 700, but you don't have number sense: try this!

This post is a follow up to yesterday's post which describes the difference between a student who scores in the 700's on the math section of the SAT and a student who scores in the 500's.

So I've told my 500's student that getting a 700 on the SAT will be "a lot of work."  But what should that work consist of?  I have some activities we could do and some problems we could work, but we need to do the activities and work the problems over a long period of time so that she can actually internalize the lessons.  Unfortunately, working one-on-one with me for that period of time would be prohibitively expensive for a lot of people.  Is there a cheaper alternative?  Can someone do it on her own?

I have been using materials from Art of Problem Solving with a handful of elementary school students, and I am struck with the fact that they place more emphasis on the number sense than they do the algorithms.  They walk students through steps toward comprehension that focus on the meaning and assume that the algorithm will come on its own.  That process works best for the advanced kids, but that is their target market.  Still, I thought they might have something useful for the high school student who has learned the algorithms, but would like to retro-actively work on the number sense.

Introducing Alcumus.  Alcumus is a free online problem bank.  Once you register, it will give you a math problem.  Get that right, and you will get a more difficult problem. Complete enough problems in a row, and you will move on to the next topic. It is somewhat similar to the practice modules on Khan academy with a couple of notable differences:  First, you will be given an explained solution even if your answer was correct!  In fact, to get anything out of this exercise, you need to carefully read every explanation to see if there was a different, more intuitive (as opposed to algorithmic) method of solving the problem.  There are a few videos to watch for more instruction, but Art of Problem Solving believes in a problem-first approach.  There are also references to chapters in Art of Problem Solving math text books. (The books can be a bit pricey.  If you have the means, buy a couple of copies and donate one to your school library.)

Try to see if these methods lead to being able to solve complicated-looking problems in your head.  (It goes without saying that you should NOT be using a calculator.)  You will be led through addition, subtraction, the distributive property - simple stuff, but there are lessons here for how to think about these problems differently.  How to use your head instead of that hand-held machine you have been using as a crutch.

Try it!  I'd love to hear how it works out!

What does a 700 student look like?

Yesterday, a student who last scored in the 500's on the math section of the SAT asked me what it would take to score above 700 by fall.  She asked me during a class change at school, so there wasn't much time to say more than, "a lot of work." However, once she had gone on to class, I asked myself:

What is the difference between this young lady, and that hypothetical person who scores above 700?

Both students have taken all of the math courses listed as prerequisites and then some.  (This is true of all of my tutorees.)  Both have good grades in math (A's and B's.)  What is true of that 700 kid that isn't true of everyone else?

The short answer:  all of the kids can tell me that a certain math fact is true, but the 700 kid behaves as if the math fact is true.  For example, all of the kids can give me a definition of an even number.  They can all recognize one when they see it (if it is written as a number and not an expression.)  The 700 kid can glance at a problem, see that 2 will have to be a factor of the answer, and eliminate the answer choices that are not even.

A 700 student can promptly tell me that 1÷ (1/16) is 16.  A 500 student will either labor through the algorithm for dividing by a fraction or, more often, sit stymied because s/he doesn't recognize that the dividing-by-a-fraction algorithm is relevant. (Note:  this most often happens when the above exercise is expressed as a compound fraction in the first place.)

A 700 student understands additive inverses and therefore doesn't sit gaping in horror if I ask him or her to add all of the integers from -25 to 26 inclusive without a calculator.

A 700 student can tell me that the square of the square root of 2 is 2 without laboring through the algorithm for multiplying square roots.  (She or he also remembers from one day to the next what fractional and negative exponents represent.)

A 500 student may or may not be able to recite the commutative properties of addition and multiplication, although he or she will confirm that numbers can be added or multiplied in any order.  A 700 student may or may not be able to recite the commutative properties of addition and multiplication  depending on whether or not she or he remembers which property goes by the name "commutative."  However, she or he will not hesitate to rearrange addends or factors to find the most efficient way to compute the answer.

A 700 student recognizes that every integer has a unique prime factorization and understands that any factor of that integer must be the product of some combination of those prime factors. If asked, the 500 student can find the prime factorization of a positive integer, but he or she will not recognize those occasions when finding the prime factorization of an integer would be useful.  If the student has found the prime factorization of an integer (with or without prompting) to be 11 x 17, and if you ask the student if the original integer is divisible by 6, the 700 student will say, "no."  The 500 student will whip out a calculator and do the computation.

In short, the 700 student has a characteristic called "number sense".  The 500 student does not.  These two students might be in the same math class, at the same school, earning the same grade, but the 700 student is only working half as hard.  Furthermore, this will have been true for years.  I am currently working with two elementary school students - brothers.  One has number sense, the other doesn't.  I can already predict what their first SAT scores will be (or perhaps would have been if the test weren't changing.)

So now you're a junior and you don't have number sense, but you want that 700.  AND you're willing to do the work.  What should you do?  Check in tomorrow for instructions.