Can the Top-Scoring State Beat International Scores?

How does the math covered in the highest-ranking American state stack up against that of a top-scoring international performer?

International comparison studies typically focus on the comparing the scores achieved by same-age students in different countries. Also typically, students from Asian countries tend to outperform US students over and over again. Each time a report like that comes out, just as predictably there will be an out-pouring of the same old tired excuses. Their students are different from our students. Their culture is homogeneous whereas ours is diverse. Their schools are allowed to teach whereas our schools must meet social, medical and nutritional needs. Their parents value education whereas our parents, not so much. On and on. The excuses act as a sedative to put society back to sleep. Okay, society says, there are understandable reasons for the differences in performance. The results are not really comparable. Apples to oranges. What a relief. So we stop thinking about it.

Could there be something more?

Sean Cavanaugh of Edweekreports:

A host of recent studies have examined how U.S. students’ mathematics skills compare against those of their foreign peers. Now, a new analysis probes a more precise question: How does the math covered in the highest-ranking American state stack up against that of a top-scoring international performer?

Let's repeat the question: How does the math covered in the highest-ranking American state stack up against that of a top-scoring international performer? It does not matter whether the results are comparable or not. No matter the reason our kids come out second rate, other kids are beating our kids in the worldwide competition. Remember, President Obama said that if we want our kids to out-compete the world, we must out-educate them.

So how does the math covered stack up?

A study released last week finds that elementary students in Hong Kong are exposed to more difficult and complex math than pupils in Massachusetts, an elite scorer on national and international exams. The analysis, published by the American Institutes for Research, in Washington, examines the math content of Hong Kong and Massachusetts by comparing the two jurisdictions’ standardized tests in 3rd grade math.

We're talking about third grade, part of the foundation of the rest of a child's academic career. The study did not look at scores on a specially designed test for international comparison purposes. The study did not look at the content of such a specially designed test. The study examined the respective jurisdiction's in-house test, the standardized test for Massachusetts and Hong Kong. Even more interesting, the study had no interest in the children's scores on these tests. The study studied the test content itself. And why Massachusetts?

Massachusetts is also a consistent elite-scorer on the primary U.S. domestic test, the National Assessment of Educational Progress.

What the study found is that the Hong Kong test emphasizes number and measurement concepts. The test also contains a larger percentage of constructed responses rather than chosen responses. The Hong Kong test questions were more complex, requiring the application of knowledge and non-routine, multi-step solutions over simple recall. From the foundations, children in Hong Kong are tested on higher-order thinking skills than American children, even “elite” American children.

Do Chinese teachers teach to the test?

(Steven Leinwand, one of the study's authors), said the authors chose to examine test content in Hong Kong and Massachusetts because the two jurisdictions' early-grades math curricula were relatively similar—and because state tests in the United States tend to guide math instruction.

American educators “pay attention to the tests,” he observed. “If you change the state tests, it’s a powerful lever for what goes on in the classroom.”

In the US, the favorite quick and dirty way to reform education is to redesign the tests. That's what Arizona did in the 1990's with their AIMS test. Arizona created high-stakes tests for fifth, eighth and eleventh grade, as if new tests automatically change educational philosophy and encourage innovation. Even honor students flunked these tests. The overwhelming response to high-stakes tests is to teach to the test, a response well-documented by No Child Left Behind. When a test reflects existing educational philosophy, there is no need for sample tests or practice materials.


Liping Ma has documented the emphasis Chinese teachers place on concept development over computational procedures. James Stigler reiterated many of the same points. Chinese math education, exemplified by Hong Kong, already valued conceptual understanding and the test reflects that value. The US, regardless of all the pretty talk in the media, values computational procedures and the Massachusetts test reflects that value.

How did Mr. Leinwand put it? “... state tests in the United States tend to guide math instruction.” That is the large part of the problem. We are suppose to test what we teach, not teach what we test. The US mistakenly thinks testing drives instruction.

The Uncomfortable Conclusion

Laying solid foundations in the early years matters.

Hong Kong’s use of more difficult and complex test items could be connected to a higher proportion of its test-takers, 40 percent, scoring at the “advanced” TIMSS level, than Massachusetts, at 22 percent. Just 10 percent of American students, on the whole, reached that level, the authors argue. In addition, research shows a “strong correlation” between nations’ math performance in early and later grades, they say.

Why Standardized Testing Will Always Fail

The most basic characteristic of any test is validity, that is, whether the test actually tests what it purports to test. Everyone, from the “professionals” who write standardized tests, to the everyday classroom teacher putting together a five-point quiz, learns that a test that does not actually test what it claims to test is worthless. They all learned about validity in the colleges of education.

So John Pearson makes a great point when he observes that every test is a reading test.

TAKS is stressful enough to prepare for at the 3rd grade level, and our kids at least can get reading assistance on the math test! There has been a little bit of debate over exactly what that means, but at least it is specified that, on an individual basis, a student may ask to have a word or a question read aloud. This helps immensely, especially with a child who is a struggling reader and/or an English Language Learner.

However, after 3rd grade, the kids are completely on their own for every TAKS test -- excepting those kids with special modifications, of course. The vast majority of kids taking these tests every year cannot ask to have a word read, cannot ask for clarification on a question, cannot ask ANYTHING except a question about the directions, and the directions are usually "Pick the best answer."

So what it comes down to is that these kids are taking a series of reading tests. Some of them are ABOUT math or ABOUT science, but they don't strictly assess those subject areas as much as they assess whether or not the child can read the questions, some of which are highly complicated.

I knew a little boy in Japan who was completely bilingual in both Japanese and English, but who had attended only Japanese preschool and kindergarten. The first thing to understand about his situation is that the Japanese kindergarten ends near the end of March, so when he “graduated” from kindergarten, his parents decided to enroll him in an international school where instruction was conducted in English. The principal said the first grade teacher needed to access the boy's readiness.

On the appointed day in March, this boy sat down with a clearly unhappy first grade teacher. She did not want any new students entering her class so close to the end of the school year, especially one whose parents had the idea the child would go on to second grade after less than three months in first grade. The teacher asked a number of questions about fairy tales and a few addition problems and announced that the boy was “marginal.” She would allow him into her first grade class on the condition that the parents understood that in September he would very likely have to “repeat” the first grade. The parents accepted the condition.

In April, the school gave the annual Stanford 9 bubble tests. The first grade teacher made a copy of this boy's answer sheets to hand grade, because the score reports would not be available before the end of the school year. She needed ammunition for the parent-teacher conference she was sure she would need when she planned to tell the parents that yes, indeed, their son would have to repeat first grade.

To her utter astonishment, the boy had almost a perfect set of answer sheets. The score report, when it eventually arrived, placed the boy in the 99th percentile on every battery. Obviously he went to the second grade along with his class. Eventually the same boy graduated from an American university at age eighteen with a degree in chemistry.

So why did the teacher consider the boy marginal? Mostly because he did not know who Rumpleskilskin was. The boy could have told her all about Momotaro, a Japanese fairy tale character the teacher had never heard of, if only she had known to ask, except Momotaro was not included in the school's first grade curriculum anyway.

Imagine going to live in Russia for a year and taking a math class. After 3 months, you are given a math test in Russian, consisting of word problems and lengthy questions. I don't know about you, but I would fail that test miserably. Would ANYONE in their right mind think that that means I don't know math?? Or that that test accurately gauged my knowledge??

I was a teacher in that international school in Japan. I taught math and science to the middle-schoolers. Every year fully 50% of my students were non-native speakers of English. One year four of my students were non-English speakers who had transferred from the Japanese school just that year. Lucky for me I also speak Japanese. I was the only American teacher in the school who spoke Japanese. There were a few Japanese-speaking teacher's aides.

I made all kinds of accommodations to help my non-native English-speaking students. I paired each one with a native speaker for labs. I translated my instruction to Japanese on the fly on a regular basis. I adapted reading instruction techniques usually used in much lower grades to the science book as if the science book were a basal reader. I read words or whole questions from my tests for any student who asked. And for those four non-English speakers, I translated the whole test to Japanese. I did all these things because I knew what every tester should know, that is, the purpose of the tests. The purpose of my tests was to evaluate the student's mastery of my instruction with the corollary purpose of giving the students the best chance for success.

We may think the purpose of standardized is to evaluate individual student's knowledge, but in reality, the tests serve to rank students compared to the norming population, and then by extension, to rank the quality of the school relative to the norming population. The reality will always frustrate because the nature of norming means that half will be above the 50th and half will be below the 50th percentile when compared to the total population.

If some schools can attract an overabundance of topside students, obviously other schools will end up with an overabundance of bottomside students. Testing can, by design or not, perpetuate the inequality of educational opportunity and undermine any promising efforts of school reform.

So who would want to perpetuate inequality of educational opportunity? Sadly, dear parents and other adults, Lake Wobegone does not exist.

NOW They Notice That Teachers Will Go Missing

The most experienced teachers are retiring. Report Foresees Mass Teacher Retirements. No kidding. Back in the 1980's, the government noticed that baby boomers would start retiring in 2008, increased the percentage of social security withholding, and created the social security trust fund to hold the money. The point is not the current political debates about social security; the point is the foresight displayed. Our schools, as the educators of the nation's future, should be experts in foresight and preparation, but no.

As recently as 2003, according to a National Commission on Teaching and America's Future (NCTAF) report, retirement was not considered a factor. In fact, one chapter of the report is entitled, “It's Not About Retirement.”

The skeptical often ask: But don’t high retirement rates contribute to the high rate of teacher attrition? Not as much as we might think. More people are leaving teaching for non-retirement reasons (see figure 6) and available new entrants could easily offset the number of retirees if teacher turnover and attrition were not so high.

It is true that a large number of teachers currently in the classroom were hired in the late 1960s and the 1970s and that they are now approaching retirement. It is also true that retirement rates have been increasing each year. But the number of retiring teachers is far below the total number of teachers hired into our schools from all sources (see Table 2). Over the next 10 years, about 700,000 teachers are projected to retire, accounting for about 28 percent of hiring needs during that period.8 Teachers leaving the profession for reasons other than retirement (e.g., low pay, lack of professional support, poor school leadership) outnumber those retiring by almost 3-to-1. These reasons also drive some experienced teachers into early retirement.

In the end, the combined number of new entrants and re-entrants greatly exceeds the retirement rate. Even without drawing on potential re-entrants from the reserve pool of former teachers and those with teaching degrees who never entered teaching, our teacher preparation system could easily accommodate the current retirement rate. It is the high attrition rate among those who are not retiring that is fueling the teacher shortage.

For at least the last twenty-five years, schools have been rejecting mid-career expert teachers who move from one district to another. If, and that's a big if, a district hires an out-of-district teacher, the most credit for experience the teacher will get on the salary scale is a mere five years, if that.


So the expert essentially takes a big pay cut in proportion to experience. The more experience, the bigger the pay cut. Even so, districts have been routinely rejecting the expert teacher in order to save the extra few thousand that paying for a mere 5 years would cost.


So why the alarm now?

...a third of experienced teachers could retire. The problem is most dire in 18 states where half of all public school teachers are over age 50....To complicate matters, the report says, attrition rates among new teachers are as high as ever, with over a third of teachers leaving the profession within their first five years.

And what is the result? The old teachers are leaving, the new teachers are quitting, and the mid-career teachers are missing, working as insurance agents, receptionists, or tax preparers or whatever. What few mid-career teachers are left in the schools will be overwhelmed. Teachers with experience will be at a premium.

What should be done?

The first answer is usually to recruit more. But the problem is not so much recruiting as retention.

Districts are able to hire an adequate number of teachers, it says, but many turn over within three to five years, leaving schools with massive gaps to fill each fall. According to Carroll, attrition rates among career changers and alternative-pathway recruits are often the highest.

The report cited earlier agrees.

But in fact, we dramatically increased the supply of teachers during the late 1990s (see Table 2). The problem is that the teacher attrition rate has been increasing even faster. We are losing teachers faster than we can replace them. Teacher retention has become a national crisis.

How about emphasizing retention?

With the supply of new teachers “collapsing at both ends,” as the report describes, schools need to make a new effort toward retention.

To help solve the problem, the report suggests restructuring district staffing practices, by hiring retirees for flexible, part-time positions within schools and by replacing one-classroom-one-teacher models with cross-generational collaborative-learning teams. Such teams, NCAFT believes, could serve as an internal support network for new teachers, keep experienced teachers on staff to share their expertise, and provide a diverse set of experiences for students to learn from.

“We need to break out of the idea of classrooms altogether,” Carroll said. “It’s not one teacher per classroom, but a team that works with 150 or 200 students.” In NCTAF’s conception, learning teams would be led by National Board-certified or otherwise highly accomplished teachers and would incorporate community members, including adjunct content experts, and representatives from neighborhood agencies.

However, out-of-district teachers have become invisible. Many of these teachers were highly successful, went on to get their Master's degrees, love to teach, only to become virtually unemployable. No Child Left Behind may mandate highly qualified teachers, but these teachers have three strikes against them: education, experience, and possibly no certification in a new state.

These teachers are not asking for “alternative certification.” They just want recognition for what they have already accomplished. These highly qualified, but uncertified teachers, may be found in private schools all over the country. Sometimes a charter school will pick them up, but as more and more charter and private schools accept the conventional wisdom that somehow a teaching credential is an indication of quality, these teachers are nowhere. They want to teach, but society has thrown them away as just so much garbage.

The Limits of Educational Software

So if you control for the variables you know help students achieve, your study of (fill in the blank) shows no significant gain due to (fill in the blank). In this case the blank is filled by the darling of grant funders everywhere, technology, specifically education delivered by computers.

For the second year in a row, a controversial $14.4 million federal study testing the effectiveness of reading and math software programs has found few significant learning differences between students who used the technology and those taught using other methods.
...snip...
“These studies are intended to wash out all the variation in school environments, teacher quality, resources­—all the things that we, in fact, know make a difference when it comes to student learning,” said Margaret A. Honey, a technology expert who is the president of the New York Hall of Science.

In other words, students who do well with the educational software were doing well anyway, probably because of the school environment or teacher quality or other known predictor of student achievement.

Technology is way over-rated. Consider the mathematical concept of place value. Teachers can design an activity that involves students boxing objects into groups of ten, and then packing ten boxes into a case, then stacking ten cases on a crate. I have such an activity with pinto beans. Students keep a columnar tally as they fill each “box” with beans. One rule of the game is that there can be no partially filled boxes, cases, or crates.

Subtraction is modeled with the same manipulatives. Students must often unpack a crate or a case or a box do complete the subtraction. If, for example, students must open a case in order to subtract boxes, they must empty the case entirely and stack all ten boxes with however many full boxes they already have, all the while keeping a columnar tally. If students have 2 crates, 4 cases, 3 boxes and 6 loose beans and want to “fill an order” (subtract) 4 boxes, they must empty a case. Now they have 2 crates, 3 cases, 13 boxes and 6 loose beans. We do not worry about conforming to the standard algorithm when we model on paper the actual mathematics of the task.

I once had a group of education students do the same activity on computer using a Java applet. Among other features, the applet used a rope tool to surround 10 loose objects and a box tool to pack into full boxes. I asked the students to compare the educational soundness of each activity. They quickly observed the “magical” aspect of the computer version. The concrete activity was real. Students could easily see how boxes were filled because they physically filled the boxes. The computer converted a lassoed group of objects to a box by some mystical means. At least, it may seem mystical to a child of the target age group.

Computers compromise sensory experience. No matter how 3D the graphics, the display is essentially two dimensional relying almost exclusively on the visual. Brain scientists might say the concrete activity forms more neural pathways by utilizing more of the five senses.

Paradoxically, some computer animation looks amazingly real. I often wonder how unhealthy a reliance on computers might be. At least in the days of Captain Kangaroo, small children could easily distinguish the real from the unreal. At a age when children are known to confuse reality and fantasy, can it really be a good idea to deliberately smudge the line between the two? Could computer animation undermine the development of analytical ability when the child's own senses cannot be trusted? When painted pictures of squirrels on cardboard placard danced around on Captain Kangaroo, no child was led to conclude that squirrels actually do hip-hop. The cardboard squirrel was obviously unreal. Can the same be said for the squirrel in the famous commercial doing a fist pump after causing a car accident? Will our children think less critically and be more vulnerable to scams?

Charter School Misconceptions

A post about charter schools is sure to scare up the usual litany of misconceptions. As long as ideology drives the debate, then nothing anybody says matters. Each ideologue cherishes their own set of misconceptions.

Charter schools are private schools, or at least, a variation on private schools. Less money goes to public education when charter schools are operating, with the result that public funding can be reduced.

The word “public” in the phrase “public school” means publicly funded. Parents do not pay tuition. In fact, charters schools sponsored by a public entity such as a traditional public school or the county office of education, usually operate on 85% of the per-pupil funding of the traditional public school. The sponsoring entity retains 15% of the funding, ostensibly to pay for stuff charter school parents do not use, such as busing. Some of the 15% also pays for support, such as having the charter school payroll handled along with the payroll for the public entity.

Critics of charter schools recognize the public nature of charter schools when they worry that a churchgoing principal of a charter school is deceptively running a private religious school on the public dime. No one similarly charges the churchgoing principal of a traditional public school. Now I will admit that some founders may have hoped that they could get public funds for their private religious schools by going charter. Even if they successfully secure their charter, the religious aspect immediately goes by the wayside. Typical religious private or parochial schools have weekly chapels; charters cannot.

Charter schools do not have to accept every student. Public schools must take everyone.

The charter for every single charter school by law must contain the standard non-discrimination clause. Many states mandate the exact language of this clause. Charter schools take every student they can on a first-come, first-served basis. Some fortunate charters have waiting lists, but most take all comers. Their funding is based on enrollment numbers just like traditional public schools. Would that our public schools were as desirable as the need for a lottery at some charters indicates.

Charter schools “skim the cream.” Charter schools can expel disruptive students. Public schools cannot.

Public schools routinely kick out extremely disruptive students.  My local school board has expulsion hearings about twice a week.  Because actual expulsion would put the expelled students on the street with way too much free time, such students are not actually expelled in the classic sense, but are sent to alternative education, community schools, the county independent study program or charter schools. Some charter schools specialize in these students.

Charter school are less likely to offer special education services because it costs too much money and the schools are too small.

I do agree that there are fewer special services.  Yet charter schools may have special ed teachers, and if an aide has been assigned to a student, the aide will accompany the student to charter school classes just as readily as to classes in a public school.  Public schools, while providing many more social services than when I was a child, are failing to provide other basic services because of cost.  The most conspicuous example is the school nurse.  In my day, every school had a full-time nurse who had her own office with a couple beds.  Today, one nurse may be responsible for multiple schools.

Charter school teachers are unprepared and unqualified. If qualified, they tend to be inexperienced novices because charter schools pay less than traditional public schools.

What every teacher knows is that public schools tend to hire newer, less experienced teachers over more experienced teachers because of cost. What often happens is that the more experienced teachers will work at a charter school for less pay. Such a situation happens when teachers move their household to a new district. These out-of-district teachers find themselves virtually unemployable in the public schools.

Most credentialed private schools require their teachers to be certified if only to avoid paying the fine for hiring uncertified teachers. I have seen private schools lay off uncertified teachers for the year they are renewing the schools credential. I have also seen private schools pay the fine as the cost of keeping an excellent uncertified teacher.

Half of the teaching staff of many urban or rural traditional public schools may be uncertified. Funny thing is certification is a very poor predictor of teacher quality. Certification only certifies the teacher has completed the state-mandated indoctrination, usually at a college of education. Most colleges of education give short shrift to proven educational philosophies such as Montessori or Waldorf, among others.

Charter schools lack oversight and accountability.

I also agree that sometimes oversight can be a problem. Regardless of the official accountability mechanisms in place, practically speaking, parents handle academic oversight ad hoc. They expect results for their extra effort, or they pull their children. Some charter schools have had their charters pulled for financial hanky-panky.

Charter schools cheat on tests so their scores will look good.

In the beginning charter scores tended to be better than the traditional public schools. Over the years considerable regression toward the mean has occurred so that now there is no significant difference in scores on the aggregate. Teaching to the test plagues charter schools AND traditional public schools.

The existence of charter schools threatens the existence of traditional public schools.

Charter schools are public schools.  If traditional public schools want to diffuse the so-called threat of charter schools, they could do so by providing a superior alternative.  If parents thought they were getting a superior result in the traditional public school, they would not expend the extra time, effort and personal cost to send their children to a charter school. They would happily send their children to the local public schools.

But most parents do not have the luxury of, in their perception, sacrificing their child's short window of academic opportunity to political or ideological considerations.  If motivated parents believe the local traditional public school compares unfavorably to the local charter school, it is quite understandable they would choose the charter school or even other alternatives, such as private schools, or homeschooling.

There are excellent traditional public schools and there are failing traditional public schools. And there are merely satisfactory traditional public schools. There are excellent charter public schools and there are failing charter public schools. And there are merely satisfactory charter public schools. As Dr. P.L. Thomas observed, "Evidence on charter schools, public schools, and private schools all produce a RANGE of quality. There is no evidence that "charterness," "publicness," or "privateness" is the reason for any differences, be it positive or negative." Here is another effort to debunk the persistent myth that from the beginning the entire purpose of charter schools has been to destroy public education.

Charter School Good News, Bad News

A new study of charter schools will vindicate some and disappoint others.

In the last seventeen years since the first charter school opened in 1992, 4000 charter schools educate over one million students. So far most studies have managed to harden preconceived notions.

Supporters argue that charter schools can improve student achievement and attainment, serve as laboratories for innovation, provide choice to families that have few options, and promote healthy competition with traditional public schools (TPSs). Critics worry that charter schools perform no better (and, too often, worse) than TPSs, that they may exacerbate stratification by race and ability, and that they harm the students left in TPSs by skimming away financial resources and motivated families.

The study sought to answer four questions:

(1) What are the characteristics of students transferring to charter schools? (2) What effect do charter schools have on test-score gains for students who transfer between TPSs and charter schools? (3) What is the effect of attending a charter high school on the probability of graduating and of entering college? (4) What effect does the introduction of charter schools have on test scores of students in nearby TPSs?

Characteristics of Charter School Students

Charter schools do NOT skim the cream.

We find no systematic evidence to support the fear that charter schools are skimming off the highest-achieving students. The prior test scores of students transferring into charter schools were near or below local (districtwide or statewide) averages in every geographic location included in the study.

...snip...

...students entering charter schools often have pretransfer achievement levels lower than those of local public school students who have similar demographic characteristics.

My own experience with charter schools supports the study's finding. Many parents pull their children from the traditional public school and enroll them in a charter school precisely because their children are not doing so great. Far from picking and choosing their students, charter schools will accept every child. In fact, the charter school law of most states requires charter schools to include in their charter document language that explicitly forbids exclusion on all the typical grounds.

Effect on Test-Score Gains

Because the study's authors could not locate baseline scores for kindergarten age children, they hesitate to overgeneralize. They have more confidence in data gathered from charter schools that begin accepting students at later ages.

In five out of seven locales, these nonprimary charter schools are producing achievement gains that are, on average, neither substantially better nor substantially worse than those of local TPSs.

Older studies consistently found superior results for charter school students, but those studies may have been flawed, or the exploding growth of charter schools has been accompanied by that bugaboo, regression toward the mean. Poor performance of charter school students has been associated with virtual delivery of education, but the authors have no confidence in forming any generalizations. More work must be done to identify possible idiosyncratic characteristics of students or their parents who choose virtual delivery. The educational implications of the technology itself also merit further research.

Likelihood of Attending College

Charter school students are significantly more likely to attend or graduate from college than students from traditional public schools. Given the flat difference in test scores, perhaps parents of charter school students have higher expectations for college attendance. Certainly, charter school parents are more likely to have invested substantial time and effort in their children's education, if only the daily grind to drive the kids to school every day.

Charter schools do not necessarily have to provide the one-stop comprehensive education experience usually expected of a traditional public school. Parents often make the extra effort and pay the extra expense to supplement the charter school program.

Charter School Effect on Neighboring Traditional Public Schools

None, one way or another.

There is no evidence in any of the locations that charter schools are negatively affecting the achievement of students in nearby TPSs. But there is also little evidence of a positive competitive impact on nearby TPSs.

Charter schools receive money on the same basis as traditional public schools—according to enrollment. What may surprise some people is that charter schools are often required to educate their students on 85% of the public funding allowed per child enrolled. The other 15% goes to the sponsoring school district supposedly for infrastructure costs that do not benefit the charter school. An example of an infrastructure benefit the charter school does receive may be payroll services for its employees. An example of an infrastructure benefit the charter school does not receive may be school bus service. The charter school must pay a share of the transportation costs even though none of its students takes the bus.

I know of situation where, at one time, the sponsoring traditional public school had 150 students while its charter school had 600 students. Thus the traditional public school got funding as if they had 240 students without the costs of the additional 90 students (6.67 charter school students equals 1 traditional public school student). Mountain Oaks Charter School started out as the independent study department of the Calaveras County Office of Education.

The researchers identified possible shortcomings and recommended further research.

Finally, one of the most important implications of our work for future research on charter schools is the need to move beyond test scores and broaden the scope of measures and questions examined. Our estimates of positive charter-school effects on high-school graduation and
college entry are more encouraging than most of the test score–based studies to date (including our own test-score results). Future studies of charter schools should seek to examine a broad and deep range of
student outcome measures and to provide evidence on the mechanisms producing positive long-term impacts.

No Surprise Algebra-For-All Fails

“Algebra-for-All Policy Found to Raise Rates Of Failure in Chicago”

Math educators, with good reasons, have long recommended that students be required to study algebra. Many districts mandate algebra in the ninth grade. California, one-upping everyone else, currently requires eighth graders to take algebra. Japanese children begin studying algebra in the fifth grade. So how's it working out?

Findings from a study involving 160,000 Chicago high school students offer a cautionary tale of what can happen, in practice, when school systems require students to take algebra at a particular grade level.

160,000 is a lot of students, and normally the bigger the sample from the population, the more reliable the conclusions. Researchers studied eleven “waves” of students entering ninth grade from 1994 to 2005.

(Researchers) compared changes within schools from cohort to cohort during a period before the policy took effect with a period several years afterward. They also compared schools that underwent the changes with those that already had an “algebra for all” policy in place.

What did the researchers find?

The policy change may have yielded unintended effects, according to researchers from the Consortium on Chicago School Research, based at the University of Chicago. While algebra enrollment increased across the district, the percentages of students failing math in 9th grade also rose after the new policy took effect.

By the same token, the researchers say, the change did not seem to lead to any significant test-score gains for students in math or in sizeable increases in the percentages of students who went on to take higher-level math courses later on in high school.

Not much upside. More students failed, test scores were flat, and the percentage of students motivated to take advanced math course did not rise, but, gee, “algebra enrollment increased.” The district says more students will fail when required to take harder courses without supports in place. Yet the district made attempts to include supports over the last seven or eight years.

Steps include developing curricular materials introducing students to algebra concepts in grades K-8, requiring struggling 9th graders to take double periods of algebra, and providing more professional development in math to middle and high school teachers..

One of the researchers thinks that test scores did not improve because teachers may have “watered down” the content since “math classes included children with a wider range of ability levels following the change.”

But Japanese elementary schools are not tracked. All children study exactly the same material with such predictability that some observers have quipped that every child in Japan is on the same page of the textbook on any given day. I have successfully taught Algebra 1 to high school special education students, or to give due credit, special education students have successfully learned Algebra 1 under my guidance.

The problem is with issuing mandates without a coherent, integrated societal commitment to the foundations of education, mathematics in particular. I have seen Montessori preschool students exploring algebra with manipulatives. I have often said that lots of profound math can be learned without any resort to pencil and paper. Children do not necessarily need numerals to understand number.

There is one other thing. Japanese children from kindergarten age regularly take abacus lessons the way American children take piano or ballet. Generating a sum with the abacus is different than generating a sum using the written algorithm. The very process of thinking about number and computation in more than one way leads to greater mathematical flexibility. Japanese students can therefore more readily absorb and manifest algebraic thinking. That's my hypothesis anyway and maybe the Gates Foundation or somebody else will provide me a grant to test it.