Ask the Narrator: SAT

Q: Does the college SAT accurately measure one’s intelligence level, or is it simply a comparative tool?

Narrator:

The SAT is not about intelligence. It is testing English grammar, writing, and reading skills; and algebraic interpretation and computation, along with some statistics and a bit of geometry and trig. It does not go a very good job of predicting success; high school transcripts are better, and correlate with college success fairly well.

What the SAT does do well is help the college admissions staff. Is this A average as good as that one? Does this student’s straight A transcript represent good grades in hard math courses or are the courses mislabeled? Are the teachers over- or under- grading?

If you got As in math through “precalculus” but score a 450 in math, that’s telling. If there’s nothing else in the application that explains this discrepancy, like documented test anxiety, then the school’s math department is doing a lot of “social promotion”. The SAT is a pretty good “comparative tool”, but perhaps not in the way you intended.

So why is your transcript a better predictor of college success?

Because the transcript (HS grades, really) correlates with hard work, willingness to learn and accept extra help, self-motivation, willingness to do assignments and homework as well as possible. Innate ability is a factor, but can easily be derailed by a lack of the other characteristics.

Perhaps not too surprising, those are the same characteristics that make a great college student. Innate intelligence is great in college but as a newly-minted adult with all of the responsibility and none of the external “controlling factors”, college students are far too often sabotaged by their own lack of control.

Also, Narrator:

With this attitude so widespread, is it any wonder that college kids can't get their heads straight?

Ask the Narrator: SAT prep tactics

Ask the Narrator

Q: How do I prepare for the math SAT?

A: Hard work. There is no "Royal Road to Success."

Learn math every day.

Practice math every day.

Take your courses seriously every day.

See math problems as a challenge you can beat, not a chore you have to suffer through.

It takes deliberate practice, like the stuff you do to improve at soccer or chess, instead of half-assing your way through something just to finish it; that's the only way to succeed at anything, especially math.

Improve your arithmetic skills: mental math (for quick estimation), fractions, percents. Not having to worry about these will free your mind for more complicated parts of the questions.

Practice reading word problems and converting to algebra - there are plenty of questions like this on the SAT. You can find 8 sample tests on the collegeboard website - download them and take them.

Find out if anyone in your school has taken the SAT and requested (and paid for) the wrong answer report. If you can afford it, request it yourself when you take the test. Reviewing these questions helps a lot.

Finally, understand that the SAT is made up of the stuff you learned in:

• Pre-Algebra (the statistics questions are at this level), 
• Algebra 1 (especially word problems in systems of linear equations), 
• Geometry, and a smidgeon of trig (mostly the right-triangle trig from ch8 in Geometry),
• Algebra 2 (the raw, pure algebra of weird-looking expressions that factor nicely, etc.).

SAT Prep Course, part C Resources

Resources are in the Dropbox Folder:

I've sorted through and organized a bit.  Everything is in PDF form. Some are from a test prep company that shall remain nameless; I tore apart the book and scanned it. Some are from another test prep book from 25 years ago, long out-of-print, also scanned. Other material has been cribbed from my math tests from various classes and mixed with problems from whatever source I ran across. Your value may vary. The practice tests are from ETS.

Arithmetic

• Because you may need to go back this far. I know that many mistakes are made here -- any students who scored below 500 should renew their acquaintance with this material. This is fractions, and percents, and ratios, and which is bigger. 

Algebra

• A collection of questions based on the newest category (The Heart of Algebra), as well as Algebra I papers, practice sheets and other questions.  I was surprised at the number of questions in the Practice tests that directly required writing equations to find a scenario, or writing systems of equations and solving them.

Geometry

• The amount of Geometry in the test has decreased significantly from the 2014-style tests to the 2016-style tests. There still some, so we need to review it, but the focus has shifted to Algebra.

Practice Tests from the ETS.

• Placed here for convenience. You could have downloaded them yourself, but Dropbox allows you to get a whole folder. So there's that.

Further notes, cautionary lectures and other miscellaneous materials will be placed in the main folder after July 4th.

SAT Prep Course B, Topics

I spent some time looking over the sample test and "sorting" by topic (or Proficiency, if you will). This list will morph a bit as ETS reacts to to results of the first few administrations, but it feels very much like it always has, with some updates.

My philosophy is to move from the obvious and the simple to the complex and multi-stage in each topic. Level one questions through level 4: "Easy", "Medium", "Hard", "Ignore Unless".

If the students are answering easily, jump to later questions. If they screw up, add in more scaffolding. Everything I do in SATPrep has already been "taught" - I provide the review and some test-taking strategies that are specific to the SAT. I also believe in using the old ETS question-type of Quantitative Comparisons as they provide a great opportunity to have good Number Theory discussions.

Here, then, is what I see:
(Please add anything in comments)

Arithmetic

1. compound fractions, mental math.
2. rate, ratio, proportions 
3. percents and decimals
4. Pythagorean Theorem
5. Pure Radicals ( √300 = 10√3)
6. Stats: five-number summary, central tendency & number theory.

Algebra

1. linear functions
2. scatterplots w/ writing equations
3. inequalities
4. linear systems - all three methods
5. bar graphs, line graphs, odd choices for independent/dependent, other graphical interpretation. These are now included in the reading section.
6. stats (mostly central tendency) and probability
7. functions and function notation
8. quadratics and complex numbers
9. late algebra 2: rational, radical, polynomial functions

Geometry

1. Lines and angles
2. Similarity (proportions, part-part or part-whole) and Congruence
3. Right triangle trig
4. Circles
5. 3d shapes
6. Pythagorean Theorem, radicals ( √300 = 10√3) as used in geometric questions

English

1. Grammar - common grammatical errors. These are fun.
2. Graphical Interpretation for the math that has been mixed in with the Reading
3. Vocabulary - Latin and Greek, looking for patterns.
4. Essays types - more about rejecting English class writing in favor of brutally efficient five-paragraph format.
5. Reading non-fiction for content and vocab rather than talking skills

There is no teaching of reading skills at this level, only exposure to more reading. I assign essays, research, and articles written by college professors, scientists and other intelligent writers. "The Median Isn't the Message" by Steven Jay Gould, for example. In choosing, I look for complex sentence structure, dense thoughts, broad vocabulary and a willingness to assume the reader has a brain.

Next: some of the worksheets and problem sets.
This may take a few days because I want to wrangle things and rename files.

SAT Prep Course A, the Set-up

So, you've been allowed to create an SAT Prep Course (or assigned one). What now? Pat yourself on the back and be ready for a wild ride.

The first thing in your planning is to eliminate the idea that this will be a math class, taught like any other math class, made up of students who resemble a typical math class.

If your assignment is anything like mine have been over the years, you will have an incredible mash of abilities and a mandate to "Do something".  In no other mathematics scenario will you get a math class with honors pre-calculus students and informal geometry students at the same time. In one sense, this is a recipe for disaster. It can be managed, however.

To start with, your students will all suck at math. (No, really!) Even the best ones have forgotten the most basic ideas. √300 = 10√3 - what magic is this? Proportions and fractions - who knew?

Your goal is to teach everything from pre-algebra to pre-calculus in one-half a credit ... partly by "quick reminders" and 10 question quizzes, and mostly by a thorough cleaning-out of all the topics the test won't cover ... and they don't cover a lot.

Of necessity, the tests are very predictable in their choices of topic and question. They are predictable in their style. This is what makes them good comparisons from year-to-year.

It is at this point that many people pooh-pooh standardized tests and decry the amount of time spent preparing for them and wringing hands over the lack of engagement ... fuck that.  You need to be on-board with testing, just this once.

You need to be encouraging and instill a sense of us vs them, us vs the test-makers.  This is a competition between your students and some question makers ... and your students can win this thing.

Yes, the test is biased against black, Latinos, poor people -- so what? They still need to win this game. Yes, testing is bad, but rebelling against the system is stupid because it doesn't make you better at testing, or at taking the SAT.  "If you aren't taking the SAT, why are you here?"

Yes, this is taking time, which is why your school isn't asking the actual core courses to include this stuff.

I can tell you which questions are easy or difficult, and why, without seeing the test. By the end of your first week, so will your students.

Finally, this is not a math test, nor is it an English test. It can be manipulated and out-thought.  The essay isn't meant to be graded by your kindly, old Dr. Phillpots, chairman of the SHS English department, and 35-year veteran teacher. It will be read by (maybe) college graduate, or high school graduate, earning $10 per hour, given 45 seconds for each one. All of the math test will be scored by a machine.

Fortify yourself. Your new Prep course will run against everything you think of as a typical HS math or English course. Repeat the mantras,

• "Us vs Them". 
• "It's not a math class, it's a prep class." 
• "We won't cover everything. We are reviewing (and maybe filling in a few holes). You've already taken Geometry."
• It's scored on a curve."
• "We're always looking for improvement."
• "The course is pass-fail. The test is a number in search of an improvement."

So let's get going. Action Step One:

Get the four sample tests and scoring guides and answer sheets from collegeboard.org (make an account, if you have to) on the practice test page. Take the first test and read through each section carefully; familiarize yourself with the general type of question, seeming difficulty, topic. This will help you understand what I'm talking about when we discuss things further.

 You should start with reading the sample test through from start to finish. This is NOT the test you took when you took an SAT before applying to college. The format is different, the pacing is different, the topics are slightly different and more advanced, and the resources that your students will have access to are immensely different.

If you want to take it yourself as a refresher, feel free. Download, print, and go. Follow the directions and stick to the posted times.

I'll check back in again in a couple of days.

Leveling the Playing Field for the SAT.

I got the email the other day:

Exciting news: Khan Academy is partnering with the College Board so that all students who want to go to college can prepare for the SAT at their own pace, at no cost. The College Board just announced that they’re redesigning the SAT for 2016, and we’re partnering with them to make free, world-class prep materials. 

I'm underwhelmed. There are thousands of SAT practice sites around the Internet, some good and some not-so-good. There are thousands of SAT practice videos on YouTube, you just have to look. In my mind, the one thing that Khan is providing is a moderately well-organized list of boring-ass videos.

By spring 2015, you’ll have access to state-of-the-art, interactive learning tools that give you deep practice and help you diagnose your gaps. All of this will be created through a close collaboration with the College Board specifically for the redesigned SAT. 

So they will need at least 12 months to put this together. Seems like a lot of time spent on a test, but maybe it will be worth it. Screw you if you need anything before our planned roll-out date, of course, but Khan Academy isn't about the student.

Our goal is nothing short of leveling the playing field for every student taking the SAT, so please help us reach as many people as possible.

There's the rub. You can't level the playing field with a test-prep course. If test-prep could do that (and it doesn't), it would indicate that a few hours of knowledge-blitz is enough and would validate all those thousands of dollars spent on Kaplan and Princeton Review and everyone else in this test-prep sucker's game.

But test-prep helps, right? No, not really.  What 10 weeks of 4 hours a week test-prep will do is ease student tensions, help them focus, warn them of some of the obvious pitfalls, advise the students of "tricks" the test makers tend to play. This amounts to about 50 points "improvement" over untrained students ... which sounds like a lot, but it's well within one standard deviation, and about what happens when the student takes the test A SECOND TIME. That's right, test-prep eliminates some basic errors in test-taking, not in subject ability and knowledge.

"But the guarantee?" Yep, they have a guarantee. "Do 100 points better or we'll let you retake the course for free."  First off, 100 points better than what score if you haven't taken it? Second, if you don't improve by that amount, what kid is going to sit through another 10 weeks of this course, even if it is free?

I've convinced my school to allow me to offer SAT prep as an elective. Am I being hypocritical? Nope. What I do daily is work on math or English. I do the test-prep, too, but mostly I focus on filling all those little gaps in their knowledge and then we have time to practice them. It's a tutorial.

I'm looking to improve the math knowledge and understanding, not just talk about tricks. Sure, I'll focus on only certain parts of Algebra I, but they've already taken algebra I ... I'm filling many of the gaps. Not all, but it's an improvement.

I'm looking to improve vocabulary and grammar and I have the time to do it. It's often surprising to me how much students can appreciate grammar ... about five years after they've learned it. (Or after they've taken a language.)

I'm looking to have them write the stilted and boring essays that get scored well, while telling them all of the ways they can deviate from the stilted and boring pattern if they want to, for the English teacher or for their own personal writing.

Perfect Practice is not poison. Perfect Practice is not drill and kill. Perfect Practice leads to Automaticity, which allows the student time to think and gives her a knowledge base to work with.

Fallon is right, but I'll talk about why, next time.

Teacher Magnet School is Bad

h/t to Darren,

Students at the Teacher Training Magnet School don't understand math, or English for that matter?

Crenshaw Senior High 5010 11th Ave., Los Angeles, 90043
» Schoolwide Performance California Standards Test (STAR)
Students scoring proficient or above: English 18.9% Math 2.3%
# Students in advanced math: 15%

No Child Left Behind (AYP)
Fail: Missed 16 of 23 federal targets for 2009
Fail: Missed 25 of 25 federal targets for 2008
Fail: Missed 16 of 22 federal targets for 2007

SAT Reasoning Test Composite Average 1098
Math: 363 Verbal: 367 Writing: 368
Source: state data reported for 238 participants

How is this possible? An average of 363 means that some were higher and some were lower. The standard deviation for the SAT is about 100 points. Think about that. Then consider that these folks are in the teacher training program.

This is Crenshaw Teacher Training Magnet School.

---

LA's 141 Magnet Schools, Ranked in Ascending Order.
(percentages are percent proficient in Math, English

Dorsey Police Academy Magnet 0.0% 16.3%
Washington Communication Arts Magnet 0.0% 29.8%
Crenshaw Teacher Training Magnet 1.1% 28.6%
Washington Music Academy Magnet 1.2% 45.5%
Washington Math/Science/Technology Magnet 2.1% 36.5%
Fremont Math/Science/Technology Magnet 3.7% 39.8%
Dorsey Math/Science/Technology Magnet 4.4% 38.3%
Jordan Math/Science/Technology Magnet 4.9% 45.1%
Wilson Police Academy Magnet 5.0% 25.0%
Dorsey Law/Public Service Magnet 5.6% 36.6%
Manual Arts College Prep Magnet 7.0% 30.9%
Wilson Administrative Law Magnet 7.5% 44.9%
...

Teacher Training Magnet is one of the worst. Couldn't see that coming.

Learn Vocabulary in Bite-sized pieces.

I'm usually talking about math here, but I've found a website that cracks me up, is free, and helps with vocabulary in a clever way.

Give it a try.

Scores vs Income

From Schools Matter

The new Census Bureau report on income is out, and the New York Times has some interesting analyses. Here are a few of them summarized:

For the first time since the Census has been keeping records, median income is less than it was ten years ago. And even though the top quintile of workers' incomes increased, the decrease in the other four quintiles was significant enough to make the median income in 2008 less than it was in 1998. In short, the rich have gotten richer, and everyone else, poorer.
In terms of the relation between family income and SAT test scores, the Times analyis shows the statistical relation a monstrous direct correlation (.95). This same correlation, by the way, can be found in any set of state test scores for elementary school children, too. Poor kids do worse on high-stakes standardized tests, so let's keep them poor and contained by using these tests to determine who gets a chance for the best teaching, the best colleges, and the best jobs. Simple. The rest will get the corporate welfare apartheid charter schools with minimally-qualified missionaries from Teach for America, along with no libraries, no art, music, athletics, or even cafeterias. And thus, The New Eugenics in Action.
As family income and wealth goes, so go the test scores, so let's blame, once again, the schools and the teachers for the flat or diminishing test scores, rather than the corporate exporters of jobs over the past decade or the greed of CEOs or the enemies of workers' rights or the anti-educational curriculums of the testocrats.

Read the rest of it.

Find the Area of a Triangle

In discussing the following problem over on Math Notations, there's been an interesting mix of methodology.

In the coordinate plane, what is the area of ΔPQR given the coordinates P(4.5,4.5), Q(8.5,8.5), and R(6,0)?

The first level of difficulty lies, of course, in getting the image correct. Leaving this up to the kids makes for a tougher problem. Here's the diagram.

So the question fairly begs for a solution and it was interesting to me how many different ideas came up. Before you scroll down and see what the others did, try this problem yourself.

Dee-dee-dee-dee, dee-dee-dee, dee-dee-dee-dee-DUM-da-dee-dee
(Badly transcribed Jeopardy theme tune)

Here we go!

All of them are valid but operate under different frames of reference - your starting point, I think, depends a lot on what you're working on in math or the most recent similar problem you've solved.

Here's probably the simplest version. Big triangle minus the yellow one:

(1/2)(6)(8.5) - (1/2)(6)(4.5) = 12

I did the problem mentally and didn't twig on the two triangles. Instead I found a base and an altitude. 1/2* 4(root2) * 3(root2) like so:

The most interesting one was done by a student:
Translate the points P and Q down the line y=x. The orange and red triangles are still equal areas because they have the same height and equal bases.

Now find the area of the orange triange with a height of 4 and a base of 6.

Ain't that cool?

To repeat my comment on MathNotations:
We all approach problems differently depending on what frame of mind we're in at the time.

A basic math student would probably use the 2triangles method. An algebra student who just got through pythagorean theorem, distance formula and simplifying radicals might gravitate to the other. The algebra student who's been translating stuff might think of that - though the idea that sliding the two points down y=x doesn't change the area is NOT something that many students can do in their heads! Someone else might go to the trouble of flipping out Heron's formula or 1/2ab*sinC if the points were set up differently. Still others use Pick's formula since they can see the points in the diagram.

If your student weren't able to immediately follow your using PQ as a base and finding the altitude to it using perpendicular slopes (the problem, it seemed to me, was set up to push the solver in that direction) then he isn't really comfortable with algebra.

Don't knock your initial instincts until they get in the way of solutions. Students do like to see patterns that flow through many courses and like to see that old ideas are springboards to new solutions. We tell them all the time to "use critical thinking" and "Choose the best method," so we should show them different methods when the opportunity arises.

Hindsight is 20-20 in mathematics, too. For the record, my first instinct was 1/2 PQ * altitude. Had P and Q not been on y=x, I might have changed course but the solution was easy enough.

Here's some variations on this theme which may push the solver in different directions depending on what he's just been working on:

P(4.5,4.5), Q(8.5,8.5), R(5,1)
or
P(4.5,5.5), Q(8.5,9.5), R(6,1)
or
P(1.5,6), Q(4.5,4.5), R(6.5,8.5)

Just a few thoughts on a Saturday morning early Sunday afternoon.