I have read some of the curriculum standards adopted in various states over the last decade and have examined the item content of some of the No Child Left Behind Act state tests implemented during the same period. The curricula were often quite lousy, and the tests rather poorly constructed. But neither so constrained teachers that we can conclude that they made things WORSE for teachers than before the Act and the associated tests. Teachers are in the classroom to help pupils and students learn something. Defining part of what that something is by no means prevents teachers from teaching more. A teacher who self-educates about good quality research on human learning
and about effective teaching
can help learners learn better even if the surrounding pattern of school regulation is less than ideal.
I am a teacher of prealgebra-level mathematics in private practice. (In earlier years I was a classroom teacher of English as a second language or of Chinese as a second language.) My elementary-age pupils come to me for lessons after attending their regular school lessons each week. All my clients have to pay me (my nonprofit program also offers financial aid, up to a full fee waiver, for families with financial need) after already paying their taxes for my state's friendly public schools, and some of my clients come to my program after paying out of pocket for a privately operated classroom school or as a supplement to family homeschooling. I don't give my pupils letter grades, and tests I offer to the pupils are from national voluntary participation mathematics contests, which they take (or not) as one of several reality checks on how they are learning the course material. Parents from a wide variety of school districts have told me that their children do much better on various kinds of school tests after taking my course, even though my course is explicitly NOT test-prep, and even though I don't align my curriculum to the curriculum presupposed by any testing program.
Children who learn how to use their brains to think
can handle novel problems and are not afraid of tests. Children who are overprotected in school from learning challenges outside the standard curriculum often get scared and shut down when tested, even when tested on the curriculum content they have studied over and over. I'm all about helping young learners be unafraid to take on challenges. If a teacher is not doing that, what is the teacher doing?
It's probably worth noting for other HN participants that the blog from which this guest post was submitted has had guest posts before that many Hacker News readers caught omitting many of the key facts of the described situation,
until that hiding the ball was outed by more thorough bloggers who checked the facts.
AFTER EDIT: btilly kindly asks, in the first reply to this comment, what class size I teach. The class size I teach is lower than the typical class size at the schools of regular enrollment of the pupils I teach, and more to btilly's point, my total enrollment of students at a given time is less than the typical student load of a full-time teacher in the local public schools. That's a fair contrast between my situation and theirs. On the other hand, for the first several years of my program I was writing the whole curriculum from the ground up (as no suitable textbooks were avaiable from United States publishers) and sometimes gathering materials from three different countries just to put a lesson plan together.
More to the point of teaching large classes, it has been done and done well in many parts of the world. When my wife was growing up in Taiwan, the typical elementary school class size was sixty (60) pupils. An unusually small class would have only fifty (50) pupils enrolled. The differences in school staffing practices and teacher training to make that possible are described in book-length works
but boil down to letting classes be extra large, so that teachers can be scheduled to have joint prep time together each day in which new teachers learn from master teachers and plan lessons together. My teaching would be better if my program were big enough that I had a colleague to confer with each week, or especially each day.
as several commenters here on HN have mentioned to other persons who have shared the link, and anyway doesn't address the nub of my statement, which is that the United States, by OBSERVATION OF ACTUAL PRACTICE, is underperforming in providing lessons to young people in school,
especially from the point of view of how much the United States spends on schools.
The last time I saw a comment of this nature in a thread on the subject of mathematics education in the United States and east Asia (both places I have lived), someone advised me not to feed the troll. But that was a different troll, and taking your comment, even where you incorrectly say "highly misleading" about my comment, as an attempt to advance the discussion, I'll invite onlookers to look at the evidence.
I backed up my statement with a link
and anyone who takes a look at Exhibit 1.1 of that link (on pages 34 and 35 of the .PDF document), which is a good example of a comparative data distribution display, can see how the national median level of performance in the United States compares to the bottom quartile level for Singapore, and on the other hand where the top quartile line for the United States appears compared to the median line for Singapore. Q.E.D.
Unfortunately, once upon a time a blogger ignorant of the large body of research on textbook content and classroom practice in different countries for elementary mathematics in different countries of the world
took the lazy way out and said that if "race" is taken into account, then the United States is second to none in provision of public education, which is simply a lie. That meme has spread through some politically tendentious blog networks, but every serious professional researcher on comparative education policy can, and does, point to more meaningful differences between the United States and other countries. It would have helped that blogger also to be more familiar with the huge literature on "race" issues in countries all over the world,
but let me just disagree with the suggestion in your comment by pointing that nobody who makes the suggestion made by the blogger has actually gathered the data to show all the steps to prove that "race" as such makes any difference at all in educational attainment. Meanwhile I have taken care, in links already shown in my first comment above to document both the known inferiority of provision of primary education to some "race"-defined groups in the United States
and the degree to which other countries outperform the United States in providing primary education to the most disadvantaged groups in each of those countries.
Moreover, and this link is new to this thread, but not newly posted to Hacker News,
the United States is conspicuous in how little it meets the educational needs of its strongest students in mathematics.
in the big picture it's hard to conclude that our education is failing
There is certainly room for semantic disagreement about how bad performance has to be before it is regarded as "failing" performance, but I note for the record that the United States has abundant resources devoted to K-12 schooling
but underperforms compared to what other countries do with less abundant resources. I didn't use the word "fail" or "failing" or "failure" in my comment, but I did suggest, and I think I suggested this with warrant, that United States schools could do a better job of teaching fraction arithmetic to the young people in their care.
In the West and in the East, there has always been wisdom contrary to the conventional wisdom that small class sizes are always better. Indeed, the Roman author Quintilian, writing about rhetoric, derided teachers who insisted on small class sizes. In Quintilian's view, the true test of a teacher was being able to engage and enlighten a large class. Quintilian described teachers who could only handle small class sizes as no better than baby-sitting slaves. He wrote, "all good teachers like a large class and think they deserve a bigger stage" while it is the "weaker teachers, conscious of their own defects, who cling to individual pupils and seem content" (Book I of his Institutio Oratoria).
East Asian schools, which are still plainly superior to those of the United States in the view of informed observers,
have characteristically large class sizes, the better to ensure that teachers are more stringently selected and that they have work hours during the school day to confer with master teachers of their subject. More details of how schools are organized in some of the conspicuously successful countries can be found in
(By the way, the scatter of data points around the regression line in their plot suggests that the model is subject to large degrees of error in prediction.) It would take an experimental design (randomly assigning one group of teachers in the same country to receive pay raises while another group does not, with before-and-after comparisons of pupil performance) to show that paying teachers more results in higher pupil performance.
There have been hundreds of studies of educational interventions over the years,
and many thoughtful international comparisons of teaching practice,
but none of those conclude that simply raising teacher pay, without changing teaching practices and perhaps also the composition of the teaching workforce, will have much to do with raising pupil performance in any place. Raising teacher pay systematically has been tried in the United States (notably in the state of Connecticut) and has not been shown to markedly raise pupil performance.
An economist who closely studies education policy has suggested that pay and other incentives be used to encourage the least effective teachers to seek other occupations while rewarding the most effective teachers with increased compensation and more professional support.
Such a policy, he estimates (showing his work in his article) would raise United States educational achievement to the level of the highest-performing countries. This is something worth verifying by experiment, although that will be politically difficult in any state of the United States
and perhaps in Britain as well.
P.S. I'm curious about why the United States underperforms so much compared to salaries paid to teachers in the chart shown in the submitted blog post.
was able to verify what I had read in other official sources on international testing programs, namely that United States students underperform (because their schools underperform) on an ethnicity-matched basis. One detailed report on the issue that I think you will find to be interesting reading is the Education Next report on mathematics learning opportunities for top mathematics students in the United States,
which shows that United States students miss opportunities in school to develop their abilities to the fullest. A look at the content of mathematics textbooks in different countries, and specialized studies on differences in teaching practices
in different countries have helped me understand the differences I frequently observe between people of the same ethnicity who received their primary and secondary education in different countries.
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. I have lived for years in one of the other countries that regularly outperforms the United States in those studies, Taiwan, and will also comment on the Taiwan educational experience as a reality check on the comments on Finland in this thread.
I am amazed that persons from Singapore in my generation (born in the late 1950s) grew up in a country that was extremely poor (it's hard to remember that about Singapore, but until the 1970s Singapore was definitely part of the Third World) and were educated in a foreign language (the language of schooling in Singapore has long been English, but the home languages of most Singaporeans are south Chinese languages like my wife's native Hokkien or Austronesian languages like Malay or Indian languages like Tamil) and yet received very thorough instruction in mathematics. Singapore is very diverse linguistically--the MAJORITY of the population in my generation spoke NONE of the four official languages (Mandarin Chinese, Malay, Tamil, or English) in standard form at home, and certainly not the main language of school instruction, English, but Singapore has become part of the "outer circle" of use of English internationally and now maintains a high degree of multilingualism. I hope that all of us here in the United States can do at least that well both in language learning and in mathematics learning in the current generation.
The article "The Singaporean Mathematics Curriculum: Connections to TIMSS"
by a Singaporean author explains some of the background to the Singapore math materials and how they approach topics that are foundational for later mathematics study. The key aspect of Singapore's success is a MUCH better curriculum in primary school mathematics than is used in the United States. Homeschoolers in the United States, including quite a few parents of top-scoring students on the American Mathematics Competitions tests, have become aware of the Singapore curriculum materials,
and those are generally helpful for American families who are looking for something better than the poorly organized, often mathematically incorrect materials used in United States schools.
Professor Hung-hsi Wu of the University of California--Berkeley has written about what needs to be reformed in United States mathematics education.
Other mathematicians who have written interesting articles about mathematics education reform in the United States include Richard Askey,
Roger E. Howe,
All those mathematicians think that the United States could do much better than it does in teaching elementary mathematics in the public school system. I think so too after living in Taiwan twice in my adult life (January 1982 through February 1985, and December 1998 through July 2001). I have seen (and used) the textbooks from Singapore and from Taiwan. They are much more clear in their presentation and much more conceptually accurate than the typical United States textbooks. Moreover, elementary mathematics teachers tend to specialize in teaching mathematics while other elementary teachers teach other subjects, at much younger ages than when United States pupils typically encounter specialist teachers. The United States model of elementary education is to have teachers who are jacks of all trades and masters of none, and who do equally poorly (by reasonable international standards) in teaching reading, mathematics, science, and all other elementary subjects.
The United States could do a lot better and reach the level of Finland by staffing reforms
and by using best practices
in provision of elementary education.
This essay was the second essay (after "Why Nerds Are Unpopular) that made me aware of pg's interest in education policy.
See also the book The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom for ways that school could be done better.
Where my wife grew up, it took one teacher to teach 60 pupils. A class size of 50 was an exceptionally small class size. Several of the countries that best the United States in academic achievement
have much higher class sizes per teacher than the United States has. It is definitely possible to improve teacher productivity over the low level maintained in the United States. There are whole books on the subject.
That's a mistake of the system in the United States. In many other countries, teachers specialize by subject in the elementary grades, the better to teach their subject effectively. See Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States
for a detailed discussion of elementary math teaching, or The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom
for a broader perspective on other ways to organize schools.
Fresh book recommendations delivered straight to your inbox every Thursday.