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Improving Your SAT Score
-- what are the limits and where to stop

Slightly Skeptical view on SAT testing for non-native speakers

News Recommended Books Recommended Links Test-Taking Strategies Multiple Choice Questions Exam Strategies Mental Overload Cheating
SAT exam anxiety Math Review Vocabulary Building Essay Tips Humor Etc

The SAT Reasoning Test is the USA's oldest, most widely used -- and misused -- college entrance exam. The original intent of the SAT was to measure the innate academic ability of potential college students. It was based on naive belief that the SAT is uncoachable, that such mental tests are similar to taking a blood sample. SAT scores today correlate closely with the family income of the test takers, according to the ETS' own data. One major reason is the widespread use of expensive test preparation services, such as Kaplan and The Princeton Review.

SAT does not test intelligence. It does not determine which schools are better. The main determinant of those scores is the socio-economic level of the students: better-off students can affort more specialised tutors. Aptitude tests such as the SAT are tied to the old concept of innate mental abilities and somewhat naive belief that such abilities can be defined and meaningfully measured. Neither notion has been supported by modern research. Cultural and sociao-economic influences are probably as prominent as native abilities factors in SAT. No scientist who have considered these matters seriously would argue that aptitude tests such as the SAT provide a true measure of intellectual abilities.

SAT used to stand for Scholastic Aptitude Test, but now everyone agreed that SAT would stand for Stressed and Anxious Teenagers. And there are many better ways to spend a beautiful Saturday morning than answering questions for the SAT...

Still those wasted Saturdays can make a difference. SAT results are within certain limits coachable.. Widespread use of test preparation services such as Kaplan and The Princeton Review is indirect affirmation of the efficiency of intense, goal-directed, "take no prisoners" preparation to SAT as a specific type of intellectual sport. And that give middle class kids who can afford those courses a boost. No amount of tutoring can change the score radically, but they can definitely improve it within certain limits.

It has even greater flaws as an indicator of future college success, and it does not necessary reflect high school grades. SAT requires slightly different skill set and mindset than those required to do well in your regular classroom activities. The kind of intelligence SAT test is not some kind of mysterious, inborn ability. Simplifying we can state that what SAT measures is "your skills in taking SAT test" ;-).

Simplifying we can state that what SAT measures is your skills in taking SAT test ;-).

Academic abilities certainly play an important part in the success, but beyond certain level they are neither necessary nor sufficient. Non-native speakers face additional challenges. Think about SAT as a obscure sport not practiced in your country you need to master, then to play a couple of important for your future game and then forget about it. Like in sport making mistakes and occasionally failing the test is a price you pay for learning and improving.

If we view SAT as a special type of game, it would be honest to state that this is a pretty important game and you need to learn to play this game. In other words SAT does not directly measures now how clever you are, but it directly measures how well you are trained for taking the test. There is correlation with the abilities but training in this intellectual sport is also important and can improve your results. That means that preparation can pay off and definitely will boost your score... There are limits in improvement and like in everything, and it is true that at some point additional effort produce only marginal improvement. But at the beginning improvements for small investment of your time and effort can be dramatic dramatic. Long multi-year training does bring superior results: SAT instructors usually can pass the test with pretty high score, and not all of them are spectacularly clever; otherwise they probably would be able to find somewhat better occupation :-). .

The SAT is offered seven times a year in the United States and six times at international sites. Unfortunately the test which was bad enough is the past was recently revamped. According to College Board the newer test:

It requires specific to SAT skills in three areas:

SAT includes three kinds of questions:

First two are machine-scored.

SAT Scoring is a two-step process. At first stage raw score is determined:

On the second stage it is normalized to reflect slight variations in in difficulty between test editions.

Deficiency of the test make it a very questionable tool to predict student's success in college, estimate their value to society, and possibly be tattooed on their foreheads for access or denial to public libraries ;-). This is just an obscure sport that you are forced to play... And you better play it well and utilize those grey zones that you can use tools to your favor.

The SAT is composed of three sections, "Critical Reading," "Mathematics," and "Writing," each scored on a 200-800 point scale. The max score is 2400. For the class of 2008, average scores are:

That makes total 1511 out of 2400 or 62%. non-native speakers generally are challenged more in critical reading and writing. They also might have vocabulary problems. But the test is mostly multiple choice and on math part you definitely can do better then that with the help of prep books and TI-89 calculator. You can probably get 100 points more on math part even being a pretty average student in school math classes. The key to have good books and take many practice test: practice makes perfect....

Again I would like to stress that nearly all of 171 questions are multiple-choice. The exam now includes one brief essay. Only ten math questions require students to "grid in" the answer. By design, the test is "speeded" which means that many test takers who in principle can get right answers do it too slowly and unable to finish all the questions. This is one are where training can help.

Max score on SAT is 3*800=2400. Very few people get it. As we noted before the average is approx 1500 or 62.5% of max.

In the current over-competitive environment and due to the fact that it serves as university entrance exam few people are satisfied with their SAT score. Most try to improve it. And that desire feeds multimillion industry of private tutors, tutoring companies and publishing of huge amount SAT help books.

But the question arises: Given limitations of one's abilities what are your reasonable estimate of improvement of your initial SAT score. While exceptions are possible, I would suggest that a reasonable estimate is 100-300 points with the median around 200. There is also a variable related to the test: some tests are more difficult to you then others (for other people it might be vise versa). That means that if you take a single test you can score a lot less that is your "natural" average. That's why it is important to take several SAT tests.

Few people can improve the initial score by more then 300 point and in case of 450 points or more bureaucrats in College Board suspects cheating.

Now let's think what can be the sources of this improvement. As The Princeton Review authors noted that to improve your baseline score, you'll need to determine your problem areas. They outlined three generic problem areas:

  1. You're careless. Did you miss questions because you didn't read carefully? If so, you might benefit from practice and drill.
  2. You're crunched. Did you miss questions because you ran out of time? If so, you might benefit from the work on pacing.
  3. You're clueless. Did you miss questions because you had no idea how to answer? If so, you need to focus study of the subject. That's the most difficult and the most typical situation, especially in math sections.

Now it is clear that the major part of the increase should come from better knowledge of the test areas (math is especially fruitful field for the improvement for most students outside private schools). But two other smaller but important parts should comes from better knowledge of the environment and usage of special test-taking tactics: those skills actually are directly proportional to number of trial exams taken and increases with each actual exam try. Yet another, not mentioned above part can come from better usage of available tools (and first of all TI-89 calculator which in programming terms is actually a pretty powerful computer without a full size keyboard).

To increase your score by 200 points (8%), you need to answer about 15 more questions correctly; the exact number depends on the exact structure of the test, your previous score and some other factors such as the guessing penalty.

The SAT has always favored students who can afford coaching over those who cannot, students from wealthy suburban schools over those from poor urban school systems, and native speakers over non-native and bilingual speakers. There are four areas in which you increase your SAT score by 200 points:

  1. Math skills which help you answer approximately 5-7 more questions correctly. Additional preparation for this section of SAT produces the most noticeable boost to the final score. This part does not discriminate between native speakers and non-native and bilingual speakers. The mathematics section of the SAT contains two types of questions:

    You ability of answer both types of question reflects not only (and not so much) mathematical abilities as familiarity with the concepts used and the amount of practice in solving similar problems.

    As a programmer I see a lot of possibilities of using TI-89 on math section and shrewd usage of TI-89 can definitely improve your score.

  2. Vocabulary building which can help to answer approximately 3-5 questions correctly. This is a dangerous area even for native speakers to say nothing about non-native speakers as SAT creators have a very perverse notion about the composition of the vocabulary for a notmal teenager. You can (and probably should) work on enlarging your vocabulary before exam and that can help to get higher score but that is a difficult task as a teenager vocabulary is more then anything else reflects your social environment.

    As a programmer I see great opportunity of improving your score for this section using a computer training program instead of textbook which is extremely boring. When you find an unfamiliar words, write it down and make a flashcard. Still using SAT "official" textbook here is very important too: you can see in what areas College board uses obscure words, words that probably no normal US person knows or should know ;-). As a PhD holder I am sometimes surprised at the vocabulary requirements that are reflected in particular questions: they are difficult even for a mature adult who spend most of his life learning. Actually preparation books here can be worse than the actual test and be particular cruel and obscure which harms more then help. So please use official SAT textbook for this part and take test question in Kaplan and other source with a grain of salt: they often overdo the requirements. It goes without saying that this part strongly discriminated against non-native and bilingual students. But the proper compensation might lie in area of mathematical questions as "point of no return on investment in enhancing your vocabulary is lower then in enhancing your mathematical knowledge.

  3. Improving your critical reading skills can help you answer approximately 3-5 more questions. Using computer teaching assistant might be very beneficial for this section. Improve your vocabulary: used a computer dictionary. Read newspapers, your favorite magazines and books.

  4. Test-taking strategies (can help you to plan time better and "guess" some answers) might help you to answer another 3-5 questions correctly. This topic includes "cheating skills" and first of all the ability maximize the usage of your TI-89 calculator for solving math questions. But the key in improving your test taking strategy is the number of times you took the test. After the third time you usually understand environment pretty well and your level of anxiety is much lower, which helps to maximize your score...

The pressure is high but you need to understand that with proper books and a graphic calculator in each subsequent test try (after the first) the odds stacked against College Board (they are happy with that, basking in huge amount of money you pay for all those books, courses and tests). So there is no real reason to fret: practice makes perfect, you just need to make several tries and should not consider the first try anything but a pretty raw lower estimate of your final score, the stating point upon which to improve. And for those who are reluctant to take the test several times I would like to remind you that this is only a start in a long series of annoying and somewhat stupid tests you need to take to graduate from the college.

Relax, it is just an obscure test

But along with a reasonable desire for improvement it is important to avoid making SAT test the centerpiece of your existence. Like Talleyrand used to advice the novice diplomats: first and foremost not too much zeal. This is applicable to both kids and parents but especially important for parents. Social pressure of kids who took SAT is considerable and I think for parents it is better to avoid pushing kids too hard. After all getting into a different college that you strived is not the end of the life, but often is a pretty good life choice: it is letter to be first in the village, then the last in town. Do not overreact to the social pressure of doing good in the test. First of all you have several chances. And second this is less important then you think now. Often getting to a slightly lower level college is a blessing in disguise. See Cheating as a reaction to college application stress for more details.

You should think about SAT as a complex but manageable sport. And exam is just a game. Like in any respectable sort most good players practice a lot. And like in any sport you improve with each game...

Then on a given game the referee blows a whistle and fun starts. All players are earning some points but you will notice that some are working hard and some became discouraged. You will also notice that some players use tricks to increase the score... Like in any game players who know the environment best and who already played on the same field have an advantage. Like in sport some brad principle are applicable to SAT exam preparation:

Good luck !

Dr. Nikolai Bezroukov


Old News ;-)

[Jun 14, 2012] Retail Sales decline 0.2% in May


Whiskey wrote:

SAT scores as a metric, but given its high correlation with wealth, it appears that their conclusion is suspect.

This is largely anecdotal, but... I had to take the SAT (in Sout' Dakotah) and can tell you it is already a self-selected sample there, inasmuch as the ACT is the test that most take... unless you're applying to the Ivies, East or West coast you have almost no reason to take it in addition to the ACT, unless it's for academic scholarship purposes, which again means an even more self-selected group. I am guessing it is the same for much of the Midwest.


Smart is the new dumb.

Research Shows That the Smarter People Are, the More Susceptible They Are to Cognitive Bias

Here's a simple arithmetic question: A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?

The vast majority of people respond quickly and confidently, insisting the ball costs ten cents. This answer is both obvious and wrong. (The correct answer is five cents for the ball and a dollar and five cents for the bat.)

I call it the Krugman Effect!


Arthur_dent wrote:

"ac wrote: I call it the Krugman Effect!" 1+2x, I almost never agree with Krugman but I'm sure he would have got it right.

From the article:

more than fifty per cent of students at Harvard, Princeton, and M.I.T. gave the incorrect answer to the bat-and-ball question.

[Nov 24, 2011] National Testing Push Yielded Few Learning Advances Report (VIDEO)

NEW YORK -- Education policies pushing more tests haven't necessarily led to more learning, according to a new National Research Council report.

"We went ahead, implementing this incredibly expensive and elaborate strategy for changing the education system without creating enough ways to test whether what we are doing is useful or not," said Dan Ariely, a professor of behavioral economics at the Massachusetts Institute of Technology and member of the committee that produced the report.

Heavily testing students and relying on their scores in order to hold schools -- and in some cases teachers -- accountable has become the norm in education policy. The No Child Left Behind Act, the largest piece of education legislation on the federal level, for example, uses performance on math and reading exams to gauge whether schools are failing or succeeding -- and which schools are closed or phased out.

"Incentives are powerful, which means they don't always do what they want them to do," said Kevin Lang, a committee member who also chairs Boston University's economics department. "As applied so far, they have not registered the type of improvements that everyone has hoped for despite the fact that it's been a major thrust of education reform for the last 40 years."

The tests educators rely on are often too narrow to measure student progress, according to the study. The testing system also failed to adequately safeguard itself, the study added, providing ways for teachers and students to produce results that seemed to reflect performance without actually teaching much.

"We're relying on some primitive intuition about how to structure the education system without thinking deeply about it," Ariely said.

Increasing test scores do not always correlate to more learning or achievement, the study authors said. For example, Lang mentioned that high school exit test scores have been found to rise while high school graduation rates stagnate.

"None of the studies that we looked at found large effects on learning, anything approaching the rhetoric of being at the top of the international scale," Lang said. He added that the most successful effects the report calculated showed that NCLB programs moved student performance by eight hundredths of the standard deviation, or from the 50th to the 53rd percentile.

The report, released Thursday and sponsored by the Carnegie Corporation of New York and the William and Flora Hewlett Foundation, recommends more rigorous testing of reforms before their implementation. "Before we did welfare reform, we did a lot of experiments at the state level," Lang said.

"We tried different ways of doing it and we learned a lot, instead of deciding that on the basis of rather casual theorizing that one set of reforms was obviously the way to go," Lang added. "There has not at this point been as much experimentation at the state level in education."

The 17-member committee responsible for the study, according to Education Week, is a "veritable who's who of national experts in education law, economics and sciences." The National Academies -- a group of four institutions chartered by Congress to consult on various issues -- launched the committee in 2002, and since then, it has tracked the effects of 15 programs that use tests as teaching incentives.

The report comes as congress works to reauthorize and overhaul No Child Left Behind, and as states countrywide pass laws that link the hiring and firing of teachers to their students' performance on standardized tests.

"It raises a red flag for education," Ariely said. "These policies are treating humans like rats in a maze. We keep thinking about how to reorganize the cheese to get the rats to do what we want. People do so much more than that."

This reductive thinking, Ariely said, is also responsible for spreading the notion that teachers are in the profession for the money. "That's one of the worst ideas out there," he said. "In the process of creating No Child Left Behind, as people thought about these strategies and rewards, they actually undermined teachers' motivations. They got teachers to care less, rather than more," he added, because "they took away a sense of personal achievement and autonomy."

The report's findings have implications for developing teacher evaluations, said Henry Braun, a committee member who teaches education and public policy at Boston College. When "we're thinking about using test-based accountability for teachers, the particular tests we're using are important," he said. "But just as important is the way it's embedded into the broader framework. The system as a whole, as it plays out, determines whether we end up with better teachers."

WATCH: Daniel Koretz, a professor at Harvard's school of education who sat on the committee that produced the report, discusses skills needed in the 21st century.

[Nov 24, 2011] Stanford Economist Rebuts Much-Cited Report That Debunks Test-Based Education

The 112-page-long NRC study came at a critical point during the NCLB discussion -- and it read as a manifesto against the use of testing as a tool to promote learning, Hanushek claims. The report found NCLB to be the most effective test-based policy, but even then, it found that the law's programs moved student performance by eight hundredths of the standard deviation, or from the 50th to the 53rd percentile. Other more low-stakes tests were found to show "effectively zero" effects on achievement. According to the NRC report:

Test-based incentive programs, as designed and implemented in the programs that have been carefully studied, have not increased student achievement enough to bring the United States close to the levels of the highest achieving countries.

"This is an extraordinarily serious and contentious policy issue," Hanushek told The Huffington Post Monday. "I am quite taken aback by people who read the report and said that testing policies don't produce learning. The evidence that they provide indicates that accountability has provided significant positive impacts."

In response to the report, Hanushek titled his article, "Grinding the Antitesting Ax: More bias than evidence behind the NRC panel's conclusions," and jazzed up its first page with a man in overalls, well, grinding an ax. Hanushek concludes:

The NRC has an unmistakable opinion: its report concludes that current test-based incentive programs that hold schools and students accountable should be abandoned. The report committee then offers three recommendations: more research, more research, and more research. But if one looks at the evidence and science behind the NRC conclusions, it becomes clear that the nation would be ill advised to give credence to the implications for either NCLB or high-school exit exams that are highlighted in the press release issued along with this report.

The committee that produced the NRC report formed about a decade ago, in the wake of the implementation of NCLB, the strongest federal test-based accountability law ever passed. The National Academies -- a group of four institutions chartered by Congress to consult on various issues -- launched the committee in 2002, and since then, it tracked the effects of 15 programs that use tests as teaching incentives. According to the report, its members were chosen to represent a balanced mix of view points due, in part, to the "tension between the economics and educational measurement literatures about the potential of test-based accountability to improve student achievement."

Its 17 members included economists such as Duke's Dan Ariely and Boston University's Kevin Lang, educational experts like Harvard's Dan Koretz and Stanford's Susanna Loeb, in addition to a former superintendent, a psychologist, a sociologist and a political scientist. The committee also saw presentations from various experts, including Hanushek himself.

According to Hanushek's analysis, the panel's thorough examination of multiple studies is not evident in its conclusions.

"Instead of weighing the full evidence before it in the neutral manner expected of an NRC committee, the panel selectively uses available evidence and then twists it into bizarre, one might say biased, conclusions," Hanushek wrote.

The anti-testing bias, he says, comes from the fact that "nobody in the schools wants people looking over their shoulders."

Hanushek, an economist, claims that the .08 standard deviation increase in student learning is not as insignificant as the report makes it sound. According to his calculations, the benefits of such gains outweigh the costs: that amount of learning, he claims, translates to a value of $14 trillion. He notes that if testing is expanded at the expense of $100 per student, the rate of return on that investment is 9,189 percent. Hanushek criticized the report for not giving enough attention to the benefits NCLB provided disadvantaged students.

The report, Hanushek said, hid that evidence.

"They had that in their report, but it's buried behind a line of discussion that's led everybody who's ever read it to conclude that test-based accountability is a bad idea," he said. Hanushek reacted strongly, he said, because of the "complacency of many policymakers" who say education should be improved but that there are no effective options.

But Lang, a member of the committee who produced the report, said Hanushek's critique is misguided. "His objection is that he feels that we said stop test-based accountability," he said. "We very clearly did not say that."

Rather, Lang said, the report showed that test-based policies don't produce the effects claimed by their proponents. "What we said was test-based accountability is not having the kind of effect that the rhetoric suggests," Lang continued. "The rhetoric behind test-based accountability is the major force for education reform."

But Paul Hill, a research professor and director of the University of Washington's Center on Reinventing Public Education who also sat in the NRC committee, saw merit in Hanushek's critique. "The conclusions were more negative about the contributions of test-based accountability than his review of the evidence would suggest," Hill said. "That's well worth considering."

Hill said he was slightly concerned with the report itself, and that its tone was a product of a committee comprised of experts with mixed views on testing. "It said that test-based accountability alone won't raise achievement," he said. "I believe that. Test-based accountability, though, with reasonable supplementary policies … is a good idea."

The apparent anti-testing bias, Hill said, came from those on the committee with backgrounds in education.

"This is not a group of wackos," Hill said. "Inside the education profession, there's a lot of resentment against the use of tests."

[Nov 21, 2011] SAT Test - SAT Dates and Deadlines

January 28, 2012 SAT &
Subject Tests
December 30, 2011 January 13, 2012
March 10, 2012 SAT only February 10, 2012 February 24, 2012
May 5, 2012 SAT &
Subject Tests
April 6, 2012 April 20, 2012
June 2, 2012 SAT & Subject Tests May 8, 2012 May 22, 2012

[Nov 16, 2010] The Best and the Brightest Have Led America Off a Cliff by Chris Hedges,

December 9, 2008 | AlterNet

The elite schools, which trumpet their diversity, base this diversity on race and ethnicity, rarely on class. The admissions process, as well as the staggering tuition costs, precludes most of the poor and working class. When my son got his SAT scores back last year, we were surprised to find that his critical reading score was lower than his math score. He dislikes math. He is an avid and perceptive reader. And so we did what many educated, middle-class families do. We hired an expensive tutor from the Princeton Review, who taught him the tricks and techniques of taking standardized tests. The tutor told him things like "stop thinking about whether the passage is true. You are wasting test time thinking about the ideas. Just spit back what they tell you." His reading score went up 130 points. Was he smarter? Was he a better reader? Did he become more intelligent? Is reading and answering multiple-choice questions while someone holds a stopwatch over you even an effective measure of intelligence? What about those families that do not have a few thousand dollars to hire a tutor? What chance do they have?

These universities, because of their incessant reliance on standardized tests and the demand for perfect grades, fill their classrooms with large numbers of drones. I have taught gifted and engaged students who used these institutions to expand the life of the mind, who asked the big questions and who cherished what these schools had to offer. But they were always a marginalized and dispirited minority. The bulk of their classmates, most of whom headed off to Wall Street or corporate firms when they graduated, starting at $120,000 a year, did prodigious amounts of work and faithfully regurgitated information. They received perfect grades in both tedious, boring classes and stimulating ones, not that they could tell the difference. They may have known the plot and salient details of Joseph Conrad's Heart of Darkness, but they were unable to tell you why the story was important.

Their professors, fearful of being branded political and not wanting to upset the legions of wealthy donors and administrative overlords who rule such institutions, did not draw the obvious parallels with Iraq and American empire. They did not use Conrad's story, as it was meant to be used, to examine our own imperial darkness. And so, even in the anemic world of liberal arts, what is taught exists in a moral void.

[Nov 16, 2010] Without Geometry, Life is Pointless

Habits of Mind

This is still a work in progress (and feedback would be greatly appreciated), but I've decided to explicitly teach (and assess...more on that later) 4 "categories" of mathematics this year.

  1. Skills (I know how to...)
  2. Concepts (I understand and can explain why...)
  3. Connections (I see and can explain the relationship between...)
  4. Mathematical Habits of Mind (I can use and appreciate the process of...)
I've decided not to use the term "problem solving" because I believe this term is often misused to include be limited to solving problems and because the motivation for problem solving skills seems to be to solely help you get an answer. While I believe that they can be very helpful in finding answers, I see mathematical habits of mind as also being mathematical in and of themselves. So...while searching for patterns may help you solve a problem it is also DOING mathematics.

Here's the current version of the mathematical habits of mind I think are important. I hope to explore (in varying depths) every one of these and have already shared the list with my 6th graders.

This is definitely a work in progress and some of these are based on work by Cuoco, Driscoll, Schoenfeld, and others.

Habits of mind

1. Pattern Sniff

A. On the lookout for patterns
"Ok. We've been working on this staircase problem and it seems that you can't write perfect squares powers of two as a sum of consecutive whole numbers."

B. On the lookout for shortcuts
"It would be nice if there were a faster way to do 57x34 than adding 57 to itself 34 times. Think we can find a way?"

2. Experiment, Guess and Conjecture

A. Can begin to work on a problem independently
"I'm not sure how to solve this problem, but I'm confident I can make some progress."

B. Estimates
"Without doing any calculations, I'm guessing that it will take him 30 seconds to walk up the down escalator."

C. Conjectures
"Based on my work, I think the following is true."

D. Healthy skepticism of experimental results
"Boy, it sure seems like this 4, 2, 1 thing always repeats but we don't have a proof yet."

E. Determines lower and upper bounds
"I know it will take the people at least 10 minutes to cross the bridge because the 10 minute soldier has to cross the bridge. I also found a solution that takes 19 minutes so I know the final answer is somewhere between 10 and 19 minutes."

F. Looks at small or large cases to find and test conjectures
"I made a table of the first 5 cases and I think I see a pattern. I'm going to see if this pattern holds for the 100th case."

G. Is thoughtful and purposeful about which case(s) to explore

H. Keeps all but one variable fixed

"So I'm exploring the equation y=mx+b and I'm wondering how the graph changes as m and b change. For now, I'm going to set m to 1 and just look at how the graph changes when I change b."

I. Varies parameters in regular and useful ways

(Even/odd example)

J. Works backwards (guesses at a solution and see if it makes sense)

3. Organize and Simplify

A. Records results in a useful way
"I'm going to make a table."

B. Process, solutions and answers are detailed and easy to follow

C. Looks at information about the problem or solution in different ways

D. Determine whether the problem can be broken up into simpler pieces
"I think I can solve this problem by solving these other 2 simpler problems."

E. Considers the form of data (deciding when, for example, 1+2 is more helpful than 3)

"I'm going to leave my fraction as 6/36 because the 6 represents the number of ways you can roll a 7 with 2 standard dice and the 36 represents the total number of rolls."

F. Uses parity and other methods to simplify and classify cases
"Next time we play 21 Nim I'm going to keep track of whether the running sum is a multiple of 3, one more than a multiple of 3, or 2 more than a multiple of 3."

4. Describe

A. Verbal/visual articulation of thoughts, results, conjectures, arguments, process, proofs, questions, opinions

B. Written articulation of thoughts, results, conjectures, arguments, process, proofs, questions, opinions

C. Can explain both how and why

"The algorithm for dividing fractions is simple. Now I just need to work on making sense why this works."

D. Creates precise problems

E. Invents notation and language when helpful
"For the sugar weighing problem, I don't want to have to write out every solution in words so I'm going to let the symbol 3w~3s stand for the act of putting the 3 pound weight on one side of the balance scale, measuring out 3 pounds of sugar on the other side of the scale, and then setting aside the sugar."

F. Ensures that this invented notation and language is precise
"I need to be careful that I am differentiating between sugar that I am measuring and sugar I am using as a weight."

5. Tinker and Invent
A. Creates variations

B. Looks at simpler examples when necessary (change variables to numbers, change values, reduce or increase the number of conditions, etc)

C. Looks at more complicated examples when necessary

D. Creates extensions and generalizations

E. Creates algorithms for doing things

F. Looks at statements that are generally false to see when they are true

G. Creates and alters rules of a game

H. Creates axioms for a mathematical structure

I. Invents new mathematical systems that are innovative, but not arbitrary

6. Visualize

A. Uses pictures to describe and solve problems

B. Uses manipulatives to describe and solve problems

C. Reasons about shapes

"I see how this structure is made."

D. Visualizes data

E. Looks for symmetry

F. Visualizes relationships (using tools such as Venn diagrams and graphs)

G. Vizualizes processes (using tools such as graphic organizers)

H. Visualizes changes

I. Visualizes calculations (such as doing arithmetic mentally)

7. Strategize, Reason and Prove

A. Moves from data driven conjectures to theory based conjectures

B. Tests conjectures using thoughtful cases

C. Proves conjectures using reasoning

E. Looks for mistakes or holes in proofs

F. Uses indirect reasoning or a counter-example (Park School)

E. Uses inductive proof

8. Connect

A. Articulates how different skills and concepts are related

B. Applies old skills and concepts to new material

C. Describes problems and solutions using multiple representations

D. Finds and exploits similarities between problems (invariants, isomorphisms)

9. Listen and Collaborate

A. Respectful to others when they are talking

B. Asks for clarification when necessary

C. Challenges others in a respectful way when there is disagreement

D. Participates

E. Ensures that everyone else has the chance to participate

F. Willing to ask questions when needed

G. Willing to help others when needed

H. Shares work in an equitable way

I. Gives others the opportunity to have "aha" moments

10. Contextualize, Reflect and Persevere

A. Determines givens

B. Eliminates unimportant information

C. Makes and articulates reasonable assumptions

D. Determines if answer is reasonable by looking at units, magnitudes, shape, limiting cases, etc.

E. Determines if there are additional or easier explanations

F. Continuously reflects on process

G. Works on one problem for greater and greater lengths of time

H. Spends more and more time stuck without giving up

[Nov 20, 2009]

A lot of interesting links

A term meant to convey a person's inability to make sense of the numbers that run their lives. Innumeracy was coined by cognitive scientist Douglas R Hofstadter in one of his Metamagical Thema columns for Scientific American in the early nineteen eighties. Later that decade mathematician John Allen Paulos published the book Innumeracy. In it he includes the notion of chance as well to that of numbers.

The linked articles below will help in understanding the extent of innumeracy and it's consequences.

Fear of Math and Statistics Results in "Innumeracy"
.... Ned Rozell

Not Just a Number: Critical Numeracy for Adults
…… Sandra Kerka, ERIC/ACVE

Math Illiteracy Spells Trouble
…… Valerie Strauss, Washington Post

The New Literacy
…… Lynn Arthur Steen, Extend

[Nov 15, 2008] The SAT Prep Wiki - Proprofs (Part of ProProfs/The Knowledge FREEway)

Welcome to the SAT prep wiki page , a resource for finding and sharing articles and notes on the SAT exam. On this page are some articles, tips, and tricks related to the SAT in general, the reading and writing study guides, and the reading and writing cram sheets.

ProProfs invites all users, (both educators & students) to make contributions, edits, and improvements to this Wiki to create a continually-improving, comprehensive guide to the SAT. We encourage you to do your part in helping to make this Free resource the best and most thorough SAT guide available on the web.

[Nov 15, 2008] SAT Training Course

Welcome to AfterHigh's SAT preparation course! We've put six lessons together to teach you everything from what to do the night before the test, to strategies for tackling the toughest problems.

At the end of each unit, you can test your knowledge with the unit quiz which will be dynamically graded so you you don't have to wait until the test day to see how well-prepared you.

Once you finish the course and have taken all of the quizzes, you can pick up your official AfterHigh diploma!


[Nov 14, 2008] Ace the SAT - How to Improve your SAT Scores - Blog

The SAT is designed to provide college admission officers with two things: a predictor of first-year academic achievement and a yardstick to compare students from a wide range of educational backgrounds. You are being measured on the knowledge, understanding, and skills you have acquired throughout your education. This knowledge is cumulative and not something you can cram for. Learning how to take a test can increase your test score. Below are a few pointers that may help you raise your SAT scores:

The SAT writing test lets you demonstrate your skills in planning and writing a short essay.

The SAT writing exam consists of two sections: the written essay and a multiple-choice test on proofreading and editing.

The essay portion asks you to write a persuasive essay on an assigned topic in 25 minutes. The topic will be one that does not require any specific knowledge. Your essay is not a test of your creative or informative writing, but of your persuasive writing skills. You'll be asked to take a position on an issue and to back up your position with reasons and supporting examples. There is no "right answer" on the essay. Your score will be based on what you say and how you say it – how do you justify your position and do you do it clearly, coherently, and logically? Your essay will be scored by two people independently using a scale of 1 to 6. Your score will be the total of their marks.

The multiple-choice proofreading and editing section does not test you on spelling, capitalization rules, or punctuation. You are tested on grammatical concepts such as: idiom errors, pronoun errors, singular-plural errors, comparison errors, and lack of parallel structure. This section is scored in the same manner as the other multiple-choice sections of the SAT.

Accommodations can be made for test-takers with disabilities. If you feel you may need accommodations, contact your guidance counselor. They can provide you with information about eligibility, documentation requirements, how to request accommodations, and what types of accommodations can be made. Requesting an accommodation means extra deadlines, so start the process as soon as you can.

What you know will determine how well you do on the SAT, but other things may influence your performance. The following will help you do your best:

[Nov 13, 2008] The Lowell - Creative insults improve SAT scores and life (2-06) by Michelle Lambert

Language matters: Depending on what you say you could sound like a dopamine addict or a Mr. Drain. For example: If you went to the store, you could say, "I walked to the store," or you could say, "I gleefully skipped to Albertsons, singing all the while." One sounds bland: The other sounds like you're on Prozac.

People talk all the time, echoing derogatory words without thinking about their historical background. However, oft-used curses, such as "f---ing" and "sh-t," can easily be replaced if we start looking in our dusty, five-inch-thick dictionaries for more interesting insults. If we replace these crude insults with something far more disturbing, our vocabularies (and SAT scores) will improve, we will outwit everyone within earshot and our emotions will be far more eloquently expressed.

Swear words limit us: We are forced to accuse each other of having sexual relations with someone's mother and practicing promiscuous behavior. We call each other pieces of solid excrement, refer to various parts of our anatomy, and imply that our irritating friends are not human but pregnant dogs.

One word, the n-word, shouldn't have a place in our society at all. This word proves nothing except that the user lacks any knowledge of history. It's even worse when white or Asian kids call each other the n-word. It shows that they are either blind or insensitive.

When you're pissed off at someone, it is generally at what they have done, not their physical appearance. You want to rip their head off, not prove that you can see, unless they've accused you of being blind. Even then, there are better ways to prove your observational skills. If you really feel the need to use an n-word, pick up that dusty dictionary I talked about earlier and look in the "n" section. Among the many nouns you could call someone are necrophiliac (a person who gets turned on by dead people), newt (especially nature-lovers), or narwhal (a small Arctic whale.)

Please, unless you really want to prove your stupidity, get more creative with your insults. Unearth the dusty dictionary from the depths of your pile of unused books and look something up; your SAT score will go up, and your opponent will look stupid. Stretch your mind, not just your body, you nugatory nubbin.

[Nov 12, 2008] Improving Your SAT Score - Proprofs

Many students complain that they are overwhelmed by the length and depth of the SAT, and that the material covered in the three sections is just too much to handle. We have good news for you: you don't necessarily need to handle it all!

The vast majority of colleges ask you to report your best SAT score on each section, meaning that the score you report will be the composite of your best attempts at each section. For example, let's say you took the test three times, with these results:

Although each of the total scores are roughly comparable for the three testing dates, your actual reported score will include the best of these three sections, so:

SAT Score CR 700 M 650 W 700

This is a much higher score than any of your three testing dates. So, the point is that you should focus on improving one section at a time rather than trying to improve all sections at a time if you need a major score increase.

[Nov 12, 2008] SAT Improve SAT Score with SparkNotes The Discipline of Discipline

The Discipline of Discipline

Back in the day, the SAT claimed to be impervious to studying, coaching, or preparation of any sort. Now the same people who write the test offer their own test-prep books. How times have changed.

The message is clear. You can prepare for the SAT. And the more you prepare, the more you'll boost your score. That's good news because it means your score and your future are in your own hands. But it's going to be tough to sit down and train for the SAT when you've got countless diversions tempting you at all times. And studying for the SAT isn't like studying for school: There's no teacher to scold you or give you a D. Getting yourself to do the work is up to you. But there are ways to make yourself more disciplined.

[Nov 11, 2008] [PDF] 07E02_ACT_and_SAT_Test_Scores

Contains a table with average scores for several states.

[Nov 11, 2008] Improving Your ACT or SAT Score The Princeton Review

To improve your baseline score, you'll need to determine the problem.

Finally, it's time to find the solution that works best for you. We recommend The Princeton Review's ACT and SAT test preparation resources (sure, we're a little biased). Whatever approach you choose, start planning well in advance. You'll do better if you set aside time each week to prepare rather than cramming it all in at the last minute.

[Nov 10, 2008] Important dates

[Nov 9, 2008] Improving your SAT Scores

You should take this estimates with a grain of salt...

... ... ...

2. Score at least as high on the SAT as the national average for your GPA in high school. Colleges and universities use SAT scores to compare students from different high schools across the country. They don't usually know how difficult or easy your high school is or the classes you took. So they use your SAT to compare or "validate" your GPA. Your SAT score should be roughly equivalent to your GPA (or better!).

Use the table below to help you set your SAT goals:

High School GPA Average SAT Score
2.1 800
2.4 850
2.6 900
2.7 950
2.8 990
2.9 1020
3.0 1040
3.1 1060
3.2 1090
3.3 1130
3.4 1160
3.6 1200
3.7 1240
3.8 1280
3.9 1320
4.0+ 1400

[Nov 08, 2008] Prepare for the SAT Test, or Play With Your iPod Have It Both Ways - New York Times by MARIA ASPAN

June 25, 2007 | NYT

...The three programs, in critical reading, mathematics and writing, correspond to the three graded sections of the exam. The programs cost $4.99 each and are available in the iPod games section of the iTunes store ...

"Learning styles have changed a lot since Stanley Kaplan founded Kaplan in 1938," said Kristen Campbell, the national director of SAT and ACT programs for Kaplan. "Students take their iPods with them all the time, whether they're in a car driving to baseball practice, or at home, or sitting at school waiting for their parents to come and pick them up."

The programs include about 1,000 practice questions and hints and strategy sessions on subjects like "Top 10 Test-Taking Tips" and "SAT Math Basics." They can be used only after being downloaded to an iPod, not in iTunes. The company also recently introduced a MySpace page ( and a series of vocabulary-building manga, or graphic novels.

[Nov 08, 2008] Kaplan Introduces Test Prep on iTunes Store

Now Kaplan is selling SAT test prep programs on iTunes, so you can sit in the corner with your fancy iPod-and learn some vocab, Mister!
It's not just text or audio: the $4.99 modules you download on iTunes are interactive, and focus on Critical Reading (sentence completion, reading comprehension), mathematics (algebra, geometry, arithmetic, etc.) and writing (how to improve sentences and paragraphs, sentence error identification).

June 21 2007 |

Kaplan Test Prep and Admissions today announced the availability of three interactive SAT* prep programs that students can purchase and download from iTunes® (, enabling them to practice for the college entrance exam on a fifth generation iPod®**. Among the key features of the programs: students receive detailed analyses of each completed quiz they take, as well as feedback and an option for tracking quiz score progress. The $4.99 programs focus on the exam's three graded sections: Critical Reading, Mathematics and Writing.

"Students don't go anywhere without their iPods and Kaplan has always sought to make test prep as convenient as possible for our students so it's a natural fit to offer test prep on iTunes. As students have embraced new trends over the years, from new learning and entertainment channels to new technology, we've adapted our materials in ways that are relevant to their lifestyles," said Mark Ward, president, Pre-College Programs, Kaplan Test Prep and Admissions.

Kaplan's SAT test prep being offered reflects the three graded sections of the SAT (Critical Reading, Mathematics, Writing):

Each download includes explanations on the exam structure, expert Kaplan strategies for the SAT, plus tips and information about the increasingly competitive college admissions process. Students also have the option to take the quizzes timed or untimed, with or without music, and can see their quiz score progress through graphically dynamic charts and graphs which identify their key areas of success and weakness.

The Kaplan SAT prep downloads are available on iTunes® beginning June 21.

Over 2 million students take the SAT every year; Kaplan prepares tens of thousands of students annually for the test. These latest supplemental SAT prep offerings come on the heels of Kaplan's recent debut of SAT/ACT Vocabulary-Building Manga, a series of graphic novels with hundreds of frequently tested words on the exams, as well as its launch on (

*SAT is a registered trademark of the College Entrance Examination Board, which neither sponsors nor endorses this product

**iPod® is a registered trademark of Apple, Inc. All rights reserved.

About Kaplan Test Prep and Admissions

Kaplan Test Prep and Admissions (, a division of Kaplan, Inc., is a premier provider of educational and career services for individuals, schools and businesses. Established in 1938, Kaplan is the world leader in the test prep industry. With 4,000 classroom locations worldwide, a comprehensive menu of online offerings and a complete array of books and software, Kaplan offers preparation for more than 80 standardized tests, including entrance exams for secondary school, college and graduate school, as well as English language and professional licensing exams. Kaplan also provides private tutoring and college and graduate admissions consulting services.

[Nov 07, 2008] Official SAT® Practice Test 2008-09

The practice test will help you most if you take it under conditions as close as possible to those ofthe actual test.

• Set aside 3 hours and 20 minutes of uninterrupted time

That way you can complete the entire test in one sitting. Note: The total testing time is 3 hours and 45 minutes, but you save 25 minutes because the unscored section* from this practice test was omitted.

• Sit at a desk or table cleared of any other papers or books

You won't be able to take a dictionary, books, notes, or scratch paper into the test room.

• Allow yourself the specified amount of time for each section

Pace yourself by using a watch (without an audible alarm), which is what you are allowed to use on test day.

• Have a calculator at hand when you take the math sections

This will help you determine how much to use a calculator the day of the test. Use a calculator with which you are familiar-preferably the same calculator you will use on test day.

• Read the test instructions carefully

They are reprinted from the back cover of the test book. On test day, you will be asked to read them before you begin answering questions.

• Make sure you use a No. 2 pencil

It is very important that you fill in the entire circle on the answer sheet darkly and completely. If you change your response, erase it as completely as possible. It is very important that you follow these instructions when filling out your answer sheet.

• Record your answers on paper, then score your test

Use the answer sheet when completing a practice test on paper to simulate the real testing environment. After completing the practice test, you can score the test yourself with "Scoring Your Test," or you can return to to enter your answers online and receive a score report and answer explanations.

[Nov 06, 2008] Intelligent Insights on Intelligence Theories and Tests (aka IQ's Corner) Humor break - SAT test

[Nov 05, 2008] Score Choice

Designed to reduce student stress and improve the test-day experience, the College Board has approved Score Choice, an important change to the current SAT score-reporting policy. This new policy will give students the option to choose the SAT scores by sitting (test date) and SAT Subject Test scores by individual test that they send to colleges, at no additional cost. This will allow students to put their best foot forward on test day by giving them more flexibility and control over their scores.

Score Choice is optional, and if students choose not to use it, all scores will be sent automatically.

The new score-reporting feature will launch in spring 2009, and will be first available to students in the class of 2010 participating in the March 2009 test administration.

[Nov 04, 2008] The New SAT A Better Test or Just a Marketing Ploy FairTest


The general format and content of the "new" SAT-I is largely unchanged. It is still primarily multiple-choice and administered under strictly timed conditions. The SAT-Verbal has been renamed "Critical Reading" and includes additional short Reading Comprehension passages in place of the much-criticized verbal Analogies. The math section now contains some Algebra II questions (it formerly covered only Algebra I and geometry), and the arcane Quantitative Comparison items were removed.

Responding to criticism about the SAT-I being far removed from classroom learning, the College Board added a so-called "Writing" component. The new section is modeled on the SAT II: Writing Test, previously an optional exam with such weak predictive value that it was required by fewer than 100 colleges nationally. The SAT-I "Writing" test includes 35 minutes of multiple-choice, copy editing questions with the remaining 25 minutes allotted for drafting one, short essay. Each section is still graded on a 200 to 800 point scale, so the addition of the third section bumps up a "perfect" SAT-I score to 2400. The total testing time rises from 3 hours to 3 3/4 hours. These changes were accompanied by a cost increase of $12 per test-taker, boosting the College Board's revenues by more than $30 million a year.

[Nov 03, 2008] The SAT Questions and Answers (PDF) FairTest

[Nov 2, 2008] How to Improve Your S.A.T. Score

We have amassed some simple rules that we hope will help you improve your SAT score. While these are not fool-proof, they have been helpful to numerous students in the past.

  1. Take a Practice SAT Test ...
  2. Sign up for a Review Course (optional) ...


  1. Set up a private study plan

    Now that you have your basic test score, you can set up a study plan (without the review course. If you have chosen a review course, all of the following steps will be given to you in the course of the class.) Give yourself approximately two months prior to the test to make sure you have enough time to understand the test mechanisms, can learn to unwind the testing secrets, and ultimately overcome your weaknesses.

  2. Take an untimed test

    Within these two months, you will give yourself two untimed tests, after which you will go through each question and learn the reasons you answered correctly and incorrectly. Then you will go on to the next step. Now that you have studied the books you have purchased, you will take a timed test.

  3. Take a timed test on Saturday morning a month before the test

    You have taken an untimed test and studied all answers. Now, you are ready to set up a room in the same testing situation that you will find on the actual SAT. This means, completely timed, quiet, and timely. Set up a room with the same conditions you will face when the real test comes around. Have a parent or friend time you and begin the test at 9am on Saturday morning as to train your body for the real test in a month.

  4. Take a timed test on Saturday morning three weeks before the test

    Repeat the same exercise. You should be improving your score now.

  5. Take a timed test on Saturday morning two weeks before the test

    Repeat the same exercise. You should be close to your "goal score" by now. Do not fear if you are not, there is still plenty of time to continue studying and practicing.

  6. Do nothing on the Saturday morning one week before the test

    The Saturday (and week) prior to the test will be rather stressful. Consequently, we recommend that you do nothing too strenuous regarding the SAT. Too much pressure placed on this week may cause you anxiety. It will be hard, but stay away from those study books.

  7. Prepare the night before

    Set several alarm clocks and back-up methods of waking up in due time. A few days prior to the test, it is helpful to drive to the testing site so that you know where you must go on the morning of the test. You do not want to stress or even arrive late because you are lost. Set out your clothing, bag, and several No.2 pencils.

  8. Morning Preparation

    On the morning of the test, eat a healthy large breakfast. Pack your bag one more time. Be sure to dress in layers, so that when it gets hot or cold, you can remove the appropriate amount of clothing and always find comfort. Have several No. 2 pencils sharpened and ready, and pack a snack. You do not want hunger pains in the middle of the test.

The SAT, like all sports, is a test that can be studied, attacked, and conquered. If you treat it like you would treat a football or baseball game, you will overcome its foibles. You must train your brain, like you train your body, to understand the language of the standardized test.

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