Wow, you get slight gains in tests when you start forcing teachers to "teach to the test".
It's like managing programmers by rewarding high LOC / day. There's pros and cons to this approach. The pro is you control the system, and don't just let brain-dead practices remain. For example, you sack the programmers who don't actually program, or encourage the teachers who don't actually teach to lift their game. Welcome back to the 1920s.
The con is that people start gaming the system.
It's like putting a patient in an iron lung. It keeps them above a certain minimum level, but it's also a sign that things were well and truly screwed before hand.
One thing most people never get with this topic is the enormous variation between groups, whether regional, socio-economic, ethno-cultural, etc. Fareed Zakaria has said something to the effect that America could be cleanly split into two nations, where the children of one perform at or better than the level of European and even some East Asian nations, whereas the children of the other perform abysmally, on par with the poorest of the developing world. In America, aggregate measurements are meaningless.
I think Eric Hanushek and Paul Peterson do a better job of showing their work any time they write than Fareed Zakaria, and they point out that the top students in the United States are laggards by international standards, because they are underchallenged by the meager United States curriculum.
I can verify that statement because I have seen mathematics curriculum materials from other countries. (I read Chinese, and own dozens of Chinese-language mathematics textbooks from China and Taiwan, and I have found English translations of textbooks from several other countries in academic libraries in my town.) Doing thorough research on this subject, not the kind of research that a weekly magazine columnist or blogger does, but THOROUGH research, puts the lie to the idea that it is mainly demographic characteristics of the United States population that put the United States so far behind the top-performing countries. Review just how stark the differences in performance levels are,
and then check the work of researchers who are analyzing where the problem really is in the United States.
There is a problem of a bottom-performing group in the United States, but it is a problem of a bottom-performing group of teachers who are unable to teach primary school subjects. Encouraging the bottom 5 percent of teachers in the United States year on year to find new occupations would help enormously,
but meanwhile some people are showing the courage and research orientation to identify ways to help the learners in the United States who need the most help to learn more mathematics and other subjects.
I was trying to test the same hypothesis too and the fact that there was only 1% increase in students with math proficiency told me that perhaps the gap between the two groups is not closing. Otherwise, you would see a much higher number of students with math proficiency today compared to a decade ago.
Professor Hung-hsi Wu of the University of California Berkeley writes many interesting articles about mathematics education reform in the United States.
he points out a problem of fraction addition from the federal National Assessment of Educational Progress (NAEP) survey project (the same "Nation's Report Card" mentioned in the article submitted here). On page 39 of his presentation handout (numbered in the .PDF of his lecture notes as page 38), he shows the fraction addition problem
12/13 + 7/8
for which eighth grade students were not even required to give a numerically exact answer, but only an estimate of the correct answer to the nearest natural number from five answer choices, which were
(a) 1
(b) 19
(c) 21
(d) I don't know
(e) 2
The statistics from the federal test revealed that for their best estimate of the sum of 12/13 + 7/8,
7 percent of eighth-graders chose answer choice a, that is 1;
28 percent of eighth-graders chose answer choice b, that is 19;
27 percent of eighth-graders chose answer choice c, that is 21;
14 percent of eighth-graders chose answer choice d, that is "I don't know";
while
24 percent of eighth-graders chose answer choice e, that is 2 (the best estimate of the sum).
I wrote an email to Richard Rusczyk about Professor Wu's document, and he later commented to me that if only 24 percent of eighth graders in the United States can find the best answer for that question from that list of choices, that's suggestive that 76 percent of American young people have no hope of having any career that demands mathematical competency.
Some countries set much higher standards of mathematics competency for young learners. My wife is from one, Taiwan, and I know various first-generation immigrants to the United States from other countries where primary mathematics instruction is much better than in the United States. Chapter 1: "International Student Achievement in Mathematics" from the TIMSS 2007 study of mathematics achievement in many different countries includes, in Exhibit 1.1 (pages 34 and 35)
a chart of mathematics achievement levels in various countries. Although the United States is above the international average score among the countries surveyed, as we would expect from the level of economic development in the United States, the United States is well below the top country listed, which is Singapore. An average United States student is at the bottom quartile level for Singapore, or from another point of view, a top quartile student in the United States is only at the level of an average student in Singapore. That is despite the fact that most students in Singapore in my generation attended school in a foreign language (English, which was not a language they spoke at home) so that there is no more than one generation in Singapore that can even be relied on to carry on a conversation at home in the sole language of school instruction there.
The United States is making some painfully slow gains, as the article reports, but it has a long way to go to provide "world-class" education to all pupils, even though my local school district is one of many that claims to be providing "world class" education.
It's like managing programmers by rewarding high LOC / day. There's pros and cons to this approach. The pro is you control the system, and don't just let brain-dead practices remain. For example, you sack the programmers who don't actually program, or encourage the teachers who don't actually teach to lift their game. Welcome back to the 1920s.
The con is that people start gaming the system.
It's like putting a patient in an iron lung. It keeps them above a certain minimum level, but it's also a sign that things were well and truly screwed before hand.