In “To Really Learn, Quit Studying and Take Tests,” Pam Belluck of the New York Times discusses the results of a recent study which indicates that tests are not only useful to confirm how much we have learned, but are also useful in the learning process itself.  She writes:

The research, published online Thursday in the journal Science, found that students who read a passage, then took a test asking them to recall what they had read, retained about 50 percent more of the information a week later than students who used two other methods.

Participants in the study were divided into four groups, each of which used a different study method.  Those in the group that scored highest were asked to take a “retrieval practice” test, which involved studying a passage, writing a 10-minute “free-form essay” on what they recalled from the passage, rereading the passage, and taking the test again.

This study confirms two things we have always believed at Stylus.   First, it affirms the importance of “writing to learn,” the practice of short, low-stakes writing assignments to cement learning.  Second, it reinforces our recommended method of preparing for standardized tests, which involves repeated testing but, more importantly, thorough understanding of what makes an answer right or wrong.  It is not enough to merely take and score the practice section; we see much more improvement among those students who carefully review the mistakes they made, predict and confirm why the correct answer is right and their answer wrong, and then retake a similar (or even the same!) section.  This practice is particularly beneficial in studying for the SAT because College Board tends to use very similar questions from year to year–variations on a theme.

The Times article is worth reading in full to explore how it might apply to techniques of learning in general.

The New York Times has compiled a searchable collection of demographics and student performance on standardized tests over the past ten years for every school district in New York, “to help put the numbers in context.”

The results of the NAEP national reading test are in, and while fourth graders showed significant improvement on reading tests, eighth graders did not.  Despite the fourth graders gains, the scores are still strikingly low, on city-, state-, and nationwide levels.

Nationally, only 31 percent of fourth- grade public school students are at or above the “proficient” level in reading, a standard defined by the test as “competency over challenging subject matter.” Sixty-five percent are at or above the “basic” level, with partial mastery of knowledge and skills that are considered fundamental.

Among fourth graders in New York State public schools, 36 percent are at or above the proficient level in reading, and 71 percent are at or above the basic level — both better than the national results for public school students. In the city, 29 percent of fourth graders are at or above proficiency, and 62 percent are at or above the basic level — both figures that are below the national percentages, but better than those of many other urban school systems.

To read more, follow this link to the New York Times article discussing the test results.

Here’s  a question from the May 2006 SAT exam:

19. A container in the shape of a right circular cylinder has an inside base radius of 4 inches and an inside height of 9 inches.  This cylinder is completely filled with water. All of the water is then poured into a second right circular cylinder with a larger inside base radius of 9 inches. What must be the minimum inside height, in inches, of the second cylinder.

(A) 4/3

(B) 16/9

(C) 9/4

(D) 4

(E) 6

Don’t worry about the terminology — it’s not important that you know what a right circular cylinder is. It is, however, important to remember that any time you’re asked about a cylinder, you’re most likely being asked about volume. It’s not necessary to even memorize the volume formula since it’s given to you on the reference information portion of the section (right below the directions).  However, we at Stylus suggest you memorize the formulas anyway because it will save you the time of flipping back and forth.  Cylinder volume is fairly easy to memorize if you already know the formula for the area of a circle.  Think of a cylinder as being a circle with the added dimension of height.  Thus, the formula for volume of a cylinder is the same as that of a circle, but with height added: V = πr²h.

Since this question appears toward the end of the section, we can bet on needing to do at least two separate calculations.  One way the makers of the SAT love to make geometry equations more complex is by asking you to solve one equation and plug that solution into a second (or even a third) equation to solve for a different variable — to plug and plug again.  This equation is no different.  Eventually, we’ll need to solve for the height of the second cylinder, but before we can do that, we need to solve for the volume of the original cylinder.

Since the first cylinder is completely full, we only need to plug the given numbers into the formula to find the original volume of water: V = π(4)²(9) = π(16)(9).  Don’t bother solving this equation yet — doing so won’t give us the answer we’re looking for, and any time you avoid using a calculator to do messy calculations, you save yourself time.

Onto the second equation: If the water is poured into the second cylinder, it needs to have at least the volume of the original cylinder.  So we need to use the volume formula once again, this time using the volume from equation 1 and solving for the height of cylinder 2.

V = πr²h

π(16)(9) = π(9)²h

Divide both sides by 9π to get

16 = 9h (see why I told you not to bother with the calculator?) and then divide by 9 again to get

16/9 = h, choice B.

The Educational Testing Service has announced that in 2011 it will unveil a modified version of the GRE, the standardized test required to gain admission into many graduate programs.  The test will increase in length by 45 minutes, but overall the test will be friendlier to applicants, according to ETS.  Some of the other changes include:

• the option to skip questions within sections, rather than needing to answer all questions sequentially
• computer adaptive changes in difficulty occurring between sections rather than between questions
• a new scoring system of 130-180, replacing the old scale of 200-800
• the elimination of antonym and analogy questions, to be replaced by additional questions on reading comprehension
• the availability of a computerized calculator for use on the math sections

For more information on anticipated changes, see these articles from the New York Times and Inside Higher Ed.

According to a recent Wall Street Journal article, “U.S. Math  Scores Hit a Wall,” there has been little to no improvement in math scores achieved by fourth and eighth grade students, despite the educational changes imposed by the No Child Left Behind plan.

Fewer than four of 10 fourth- and eighth-graders are proficient in mathematics, according to a highly regarded federal test given in early 2009, adding to recent evidence that the U.S. drive to become more economically competitive by overhauling public education may be falling short.

The National Assessment of Educational Progress — often called the “nation’s report card” — found fourth-graders had made no learning gains since the last time the NAEP math test was given, in 2007. Previously, fourth-graders had made scoring gains on every NAEP math test given since 1990.

Significant scoring gaps between white students and their Hispanic and African-American peers also haven’t changed much in recent years, the test results showed.

The responses to the results have been mixed: some educators caution against reading too much into the scores, while others see a need for more drastic change.  The article continues here.

New York State has apparently lowered its standards for the statewide math test.

For many students, bungling more than half the questions on a test would mean an F and all that comes with it — months of remedial work, irksome teachers and, perhaps, a skimpy allowance. But on New York State’s math exam this year, seventh graders who correctly answered just 44 percent of questions were rewarded with a passing grade.

What gives?

Three years ago, the threshold for passing was 60 percent. In fact, students in every grade this year could slide by with fewer correct answers on the math test than in 2006.

The rest of the article can be found here.

An article in the New York Times looks at the recent focus on statewide standardized tests in New York City public schools, which has been a hallmark of Mayor Bloomberg’s administration.

By the numbers, the program appears to have been a success: Eighty-two percent of New York City students passed the math exam this year while 69 percent passed the English exam.  Compare these to 42 and 38 percent, respectively, in 2002.

“In its campaign to extend the mayor’s school control law, which the State Senate is expected to take up this week, the Bloomberg administration has used the rising test scores as evidence of improved teaching and learning under its direction. Still, educators continue to debate the true value of the tests and a curriculum guided by them, arguing that some of the rise in scores is attributable simply to students’ growing comfort with test-taking, and that some of the skills developed to prepare for the exams, like time-allocation techniques and multiple-choice shortcuts, are poor substitutes for true understanding of key concepts.”

Critics point to a drop in SAT scores statewide; if the ELA and math scores indicated improved education, shouldn’t all standardized scores rise equally?   Some wonder whether the test-score inflation is a result of “teaching to the test,” rather than focusing on overall instruction.  Another point of contention is the racial achievement gap: while scores of black and Hispanic students have increased, the gap between their scores and those of their higher-scoring white and Asian classmates remains.