When oh when will I have time to take the new "core maths quiz"?

Quiz: Could you pass the new core maths test?

I'm in book hell.

Wonderful letter to the editor re: U.S. math performance

Peter Meyer just sent me the link:

Re “Are You Smarter Than an 8th Grader?,” by Nicholas Kristof (column, April 26):

American kids aren’t inherently less intelligent than kids in Singapore, or so one hopes. That’s the good news. The explanation for the Americans’ continued dismal performance in math therefore lies elsewhere.

Having watched my kids navigate the local public schools for the past 11 years, I know that one of the problems is that educators still seem to be trying to figure out how to teach math. My daughters have been through the Singapore approach, with its traditional emphasis on mastery of number facts and arithmetic procedures; the reform approach, with its confusing inquiry-based philosophy; and now the “can’t we all just agree” Common Core standards approach. Why are we still trying to figure this out?

Math has been taught to children at least since ancient Greece, Rome and Egypt, and those kids grew up to use their mathematical skills to build the Parthenon, aqueducts and pyramids, which are still standing. The math taught in K-12 hasn’t really changed much since Gottfried Leibniz and Isaac Newton invented calculus in the 1600s, so one would think that educators have had enough time to figure out how to teach it.

How about if educators stop experimenting with our kids, adopt whatever approach the Finnish or Singapore schools use, and get on with it?

ELIOT BRENOWITZ

Seattle

The writer is a professor of psychology and biology at the University of Washington.

Our Students' Below-Average Math Abilities | New York Times | May 4, 2015

A say: go with Singapore.

Not Finland.

Math students in other countries can do, plus a brain teaser

From Nicholas Kristoff's column in the Times today:

What is the sum of the three consecutive whole numbers with 2n as the middle number?

A. 6n+3

B. 6n

C. 6n-1

D. 6n-3

More than three-quarters of South Korean kids answered correctly (it is B). Only 37 percent of American kids were correct, lagging their peers from Iran, Indonesia and Ghana.

~~~~~~~~~~

A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?

Only 7 percent of American eighth graders got that one right (the answer is 15 centimeters). In contrast, 53 percent of Singaporean eighth graders answered correctly.

~~~~~~~~~~

How many degrees does a minute hand of a clock turn through from 6:20 a.m. to 8 a.m. on the same day?

A. 680 degrees

B. 600 degrees

C. 540 degrees

D. 420 degrees

Only 22 percent of American eighth-graders correctly answered B, below Palestinians, Turks and Armenians.

~~~~~~~~~~

Correlation isn't causation, but the absence of correlation is meaningful.

Fifteen years of constructivist mathematics programs adopted in virtually every public school in the country, fifteen years of teacher-training in authentic problem solving and guide-on-the-sidery, and here we are.

At a minimum, we can say that constructivist math has not been a blinding success.

~~~~~~~~~~

Back to Kristoff, I love this brain teaser for some reason:

You’re in a dungeon with two doors. One leads to escape, the other to execution. There are only two other people in the room, one of whom always tells the truth, while the other always lies. You don’t know which is which, but they know that the other always lies or tells the truth. You can ask one of them one question, but, of course, you don’t know whether you’ll be speaking to the truth-teller or the liar. So what single question can you ask one of them that will enable you to figure out which door is which and make your escape?
Are You Smarter Than an 8th Grader?

Speaking of millennials

Which I was ....

Education Week reports that a new set of dismal international comparisons--of millenials, this time--is coming out next week. I can't tell whether the test is good, but, then again, I'd just as soon U.S. high school graduates not score lower than high school graduates in every country except France no matter how possibly lousy the test.

[pause]

Yikes.

Here are 3 sample math questions.

Down the rabbit hole:

It's far from the first study to suggest American students are falling behind their international peers. But the analysis of U.S. millennials—those born after 1980, ages 16 to 34 during the study—specifically highlights that the skills gap goes beyond young people who are typically seen as more "at-risk," like immigrants and high school dropouts.

[snip]

The ETS study, to be released this week, compares millennials in 22 industrialized countries, including the United States, who took part in the Program for the International Assessment of Adult Competencies, or PIAAC, in 2012, the last time it was given. The Organization for Economic Cooperation and Development, which runs the school-based Program for International Student Assessment, also runs the PIAAC, which is given directly to adults in their homes. Unlike the PISA, which measures academic content skills, the PIAAC measures practical, career-oriented literacy and numeracy skills, and, as of 2012, "problem-solving in technology-rich environments."

[snip]

Across the board, young Americans fared poorly compared to those in the other countries studied. They tied for last, with Italy and Spain, in math skills. In problem-solving, they again performed at the bottom of the pack, with Ireland, Poland, and the Slovak Republic. U.S. millennials also had lower literacy scores than peers in 15 out of 22 countries, tied with a few, and outperformed only peers in Italy and Spain.

[snip]

. . . the skills gaps persisted among students who are least likely to be considered academically at risk. Those who performed in the top 10 percent of all Americans in their age group still performed worse than the top performers in 15 other countries, including Germany and the Republic of Korea.

While a higher proportion of U.S. millennials versus those in other countries had earned a college degree, those with a four-year degree in the United States still showed lower math skills than those with college degrees in any country studied but Poland and Spain.^* Moreover, the percentages of Americans who demonstrated the lowest-level math skills increased from 2003 to 2012, regardless of what level of education they had achieved.

[snip]

Even those with a master's or doctoral degree demonstrated lower numeracy skills than their counterparts in all but a few countries. The average U.S. math score for millennials with a postbaccalaureate degree, 308, was not only below the average for countries studied who are in the Organization for Economic Cooperation and Development, but was below the average score for young adults with just a bachelor's degree in several countries, and near the score for top-performing students with less than a bachelor's degree in a few countries.

[snip]

American millennials with a high school diploma or less performed lower than those with a secondary credential in every country but France.

[snip]

. . . in the United States, native-born millennials showed a greater decline in skills from the 2003 to 2012 cohorts than did their immigrant peers.

[snip]

Racial and ethnic performance gaps continued, with 12 percent of white and Asian young adults in America showing advanced levels of math skill, versus only 3 percent of Hispanic and 1 percent of black millennials. Yet on average, OECD countries had about 15 percent of all millennials performing at an advanced level, and white and Asian students in the United States performed below their counterparts in most other countries studied.

From the department of unintentional irony:

While a higher proportion of U.S. millennials versus those in other countries had earned a college degree, those with a four-year degree in the United States still showed lower math skills than those with college degrees in any country studied but Poland and Spain.

If a higher proportion of U.S. millennials finish college, then you would expect college-educated U.S. millennials as a group to have a lower average math score than college-educated millennials elsewhere. [Copy edit courtesy of Glen]

I wonder how the numeracy skills of U.S. education reporters stack up compared to those of education reporters in France and Spain.
.

The law of universal linearity

Interesting discussion

I was struck by this passage:

In terms of implementing this in practice, I think that college is way too late, and also quite difficult because college math (and STEM) courses tend to be mostly about transmitting massive amounts of boring technical content and technical skills, leaving little to no room for actual ideas or ways of thinking. Nevertheless, I do think it would be an interesting experiment to have students keep something akin to a "vocabulary notebook" where they record the meaning (as opposed to the formal definition) of the various kinds of expressions they run in to. For example, a fraction ab is supposed to mean "a number which when multiplied by b gives a"; it is short and illuminating work to figure out from this (using distributivity of multiplication over addition, which we definitely want numbers to satisfy) that ab+cd=ad+bcbd, that there is no number meant by a0, and that 00 can mean any number). This of course, presupposes that somebody takes the time and makes sure that the language in which these meanings are explained is coherent, so it would be a lot of work to design a course around this method.

---

I did in fact once successfully disabuse a(n Honors Calculus) student of "the Law of Universal Linearity" using these ideas. The particular instance concerned manipulating the Fibonacci sequence, and the student had made the error of writing something like Fx+Fx=F2x. What I did is explain the stuff above and had the student apply them by analyzing the meaning of the various expressions he had written down was, and then ask whether that equality was justified based on what he knew the expressions meant. That seemed to make an impression on the student, but I personally believe it was an impression made ten years too late...

down and out in the UK

Erica Meltzer sends a link:

Jane Mitchell was the daughter of a lorry driver. Reflecting on her education during the 1940s, she wrote: "I enjoyed the mental drill and exercise I was put through, even the memorising from our geography book of the principal rivers and promontories of the British Isles . . . It never occurred to me to question the purposes or methods of what we were made to do at school. The stuff was there to be learned, and I enjoyed mopping it up."

Jane went on to become a classics lecturer at Reading University. It is hard to imagine a child of her background taking so academic a career route today. Then again, it is hard to imagine that such a child today would receive the rigorous education she enjoyed.
Child-Centered Learning Has Let My Pupils Down by Matthew Hunter | Standpoint June 2012

Reading the whole thing now.

Terri W is of two minds

re: Fill-in-the-blank has a really bad idea

I'm of two minds whenever I hear of particularly dumb ideas being floated in the school systems.

On the one hand, I'm thinking, "Cool, this gives my kids a leg up over the competition."

Then on the other hand, I realize that the overwhelming vast majority of the next generation of citizens are being educated with these cockamamie ideas and I think: "We are so hosed."

I'm on both sides of that fence with just one (typical) kid!

C. is now an official Math Victim of U.S. schools (including his Catholic high school, sad to say). And, at the same time, he's way out in front in the verbal realm compared to most h.s. seniors in America (also thanks to his Catholic high school, as well as to family background).

Speaking of 'official,' C. has just now reached the point of maturity at which he realizes, without being told by his mother: Holy ****, I don't know any math. 

He has two weeks left in high school. He came home the other day, said he'd had a talk with his math teacher (statistics!), who had convinced him he needed to take math in college. So he was wanting to know whether NYU has remedial math courses.

K-12 kids don't know, while they're K-12 kids, that they're going to be sorry they didn't learn math or writing or science or whatever else they didn't learn. I remember Glen, I think it was, once saying that we have to advocate for our children's future selves: for the selves they're going to be, eventually.

That's exactly right.

why Americans need precision teaching: we're hyper

One consequence of the recent expansion of human genetic variability is that a number of culturally relevant SNPs are also local and cross-culturally variable in frequencies. For example, long (e.g., 7-repeat) allelic versions of dopamine receptor gene 4 (DRD4) have been linked to attention deficit hyperactivity disorder and novelty seeking. Importantly, these versions of the gene are quite common among Caucasian Americans, but they are virtually absent among Asians. Chen et al. (1999) hypothesize that long allelic versions of DRD4 provide a selective advantage in new, challenging environments because they are increasingly predominant as a function of the distance by which different ethnic groups immigrated in historic and evolutionary times (for alternative possibilities, see Cochran & Harpending 2009). Findings such as these strongly suggest that to fully understand the origins of cultural differences in psychological processes, genetic processes must be taken into account.
Shinobu Kitayama1 and Ayse K. Uskul. Culture, Mind, and the Brain: Current Evidence and Future Directions. Annu. Rev. Psychol. 2011. 62:419–49.Chen C, Burton M, Greenberger E, Dmitrieva J. 1999. Population migration and the variation of dopamine D4 receptor (DRD4) allele frequencies around the globe. Evol. Hum. Behav. 20:309–24.

Years ago, John Ratey and I argued in Shadow Syndromes that Americans had a higher genetic propensity to have attention deficit hyperactivity disorder, and we were right.

Americans need precision teaching because it's fast, and it's efficient:

Morningside Academy offers a money-back guarantee for progressing 2 years in 1 in the skill of greatest deficit. In twenty-five years, Morningside Academy has returned less than one percent of school-year tuition.

zip

deathless

We point out simply that not only do U.S. students on average perform better internationally than reported in a myriad of policy papers, but as Boe and Shin demonstrate, the majority of U.S. students (white students) actually rank near the very top on international tests.
Into the Eye of the Storm
October 2007
B. Lindsay Lowell Georgetown University
Hal Salzman The Urban Institute

Right.

That's why my high-IQ, culturally-advantaged, non-hyperactive, W-H-I-T-E, rising-5th grade son placed into the second-semester 3rd grade textbook in Singapore Math back when he was age 9. (placement test here).

In the real world, a gap that big by age 9 does not get smaller.

It gets bigger.


non-poor students doing fine in Princeton

momof4 boils it down

on another thread, momof4 writes:

As far as I can tell, the best-performing countries don't expect their kids to discover multiplication, reading or anything else on their own; teachers explicitly teach the material.

Until this moment, I had never thought of it quite this starkly -- but now that I am thinking of it quite this starkly, my sense is that momof4 is probably right.

From time to time high-performing countries seem to decide they need to be more creative, which seems to mean sending teams of teachers to the U.S. to observe our cr**** math curricula,^* but these initiatives never seem to last.


^*I'm not going to take the time now to track down the links.

the return of Exo!

Synchronicity is real.

Heck, maybe ESP is real.

I can't tell you how many times, now, I've thought "WHERE is so-and-so," so-and-so being a ktm Commenter who hasn't commented in a long time. The next thing I know, I read the site and there s/he is!

Just this week, I was thinking, "I miss Exo."

And presto chango, here is Exo!

pop quiz: what do Americans keep ignoring about Finland's school success?

Answer: The Scandinavian country is an education superpower because it values equality more than excellence.

I give up.

non-poor students doing fine in Princeton

From the Princeton Alumni Weekly, an interview with Earl Kim, Class of '93, now superintendent of Montgomery Township Schools:

When, exactly, did public education become a blood sport? Granted, there were vicious battles over busing in the 1970s. But now the whole American system of public education, which once made us so proud, seems to have become suspect. Perhaps it’s all those reports that show how far our students now lag behind their peers in places like Finland and Singapore — though Kim points out that once you adjust for poverty, we are still doing fine...

Affluent suburban schools, in my experience, don't have much truck with data. My own affluent suburban school district, for instance, grades itself on a strictly pass-fail basis. Percent passing the state tests, percent failing the state tests. Percent passing AP exams, percent failing AP exams. We have many more passes than fails, and we are doing fine.

The question is: what does "doing fine" actually mean in the larger scheme of things?

The Global Report Card, which ranks US schools against schools in 25 developed countries, puts Montgomery Township schools at the 76th percentile in math, 83rd in reading.

As to Finland and Singapore, here are the numbers for Montgomery Township:

Mind you, these aren't apples-to-apples comparisons. Montgomery Township is affluent and well-educated; assuming I understand the website, affluent children with well-educated parents in Montgomery Township are not being compared to affluent children with well-educated parents in Finland, Singapore, and Canada. Affluent children with well-educated parents in Montgomery Township are being compared to all students in Finland, Singapore, and Canada.

If Montgomery Township students are in, say, the 90th percentile of US students in math (they may be higher), is it "fine" for them to be in the 56th percentile in math in Singapore?

Maybe so.

Princeton trivia: Ben Bernanke served on the Montgomery Township Board of Education.

Robyne Camp says PISA may be coming to my town

How are we doing?

Glenn Ellison on schools and the gender gap in math

I had read this research in Choke -- didn't know the author of the study was also the author of Hard Math for Middle School.

ABSTRACT
This paper uses a new data source, American Mathematics Competitions, to examine the gender gap among high school students at very high achievement levels. The data bring out several new facts. There is a large gender gap that widens dramatically at percentiles above those that can be examined using standard data sources. An analysis of unobserved heterogeneity indicates that there is only moderate variation in the gender gap across schools. The highest achieving girls in the U.S. are concentrated in a very small set of elite schools, suggesting that almost all girls with the ability to reach high math achievement levels are not doing so.

[snip]

[T]he highest-scoring boys and the highest-scoring girls appear to be drawn from very di fferent pools. Whereas the boys come from a variety of backgrounds, the top-scoring girls are almost exclusively drawn from a remarkably small set of super-elite schools: as many girls come from the top 20 AMC schools as from all other high schools in the U.S. combined. This suggests that almost all girls with extreme mathematical ability are not developing their talent to the degree necessary to do very well on the Olympiad contests.

[snip]

The nonrepresentativeness of the schools these girls come from is startling: the median CGMO [China Girls' Math Olympiad] team member comes from a school at the 99.3rd percentile among AMC participating schools, i.e. from one of the top 20 or so schools in the country. Only three come from schools that are not in the 99th percentile in most measures. And even those three are from schools that had at least one other student qualify for the 2008 USAMO and are at least in the 93rd percentile in terms of the number of high-scorers on the AMC 12. The male IMO team members, in contrast, come from a much broader set of schools. Some are from super-elite schools and most come from schools that do very well on the AMC 12, but the median student is just from a 93rd percentile school. The majority of the IMO team members had no schoolmates qualify to take the USAMO, whereas all CGMO team members had at least one schoolmate qualify and most had at least four.

[snip]

It may also be worth noting that almost all of the CGMO team members are Asian-American, which suggests that even within the super-elite schools the U.S. educational system may be missing the opportunity to bring many talented girls up to the highest level.
The Gender Gap in Secondary School Mathematics at High Achievement Levels: Evidence from the American Mathematics Competitions
Glenn Ellison MIT and NBER and Ashley Swanson MIT

Should We Be Worried? (YES)

Core Standards Are Very Different
The new standards are supposed to be internationally benchmarked. Yet Common Core’s eighth-grade math standards don’t match Finland (0.21), Japan (0.17) or Singapore (0.13), primarily because these countries stress performing procedures. On language arts and reading, alignment ranges from 0.09 with Finland to 0.37 with New Zealand.

Should we be worried? Common Core Standards represent “a change for the better” when it comes to “higher order cognitive demand,” Porter concludes, but the “answer is less clear” when it comes to the topics that are covered.

Personally, I would say the "answer" is perfectly clear!

How Big a Change are the Common Core Standards?

slower math students in Singapore

from the Air report on math education in Singapore:

The topic structure in Singapore’s framework is efficient because topics are not taught and retaught as students move through the primary grades. Instead of repeating topics that students have already learned, teachers simply reintroduce them as a foundation on which to build new mathematical content. This practice, however, may not be suitable for students who have more difficulty with mathematics. The Singapore system recognizes that students who have trouble with mathematics may not attain mastery by following Singapore’s regular program of mathematics instruction and that these students may need special assistance to attain competence.

Beginning in grades 5 and 6, Singapore identifies its weaker students on the basis of a general examination of mathematics and language competency. These students receive special assistance and are taught according to a special fifth- and sixth-grade mathematics framework. This special framework mandates that students in the slower track

• receive approximately 30 percent more mathematics instruction than students in the regular track, and

• be exposed to the same mathematical content as students in the regular track, although at a slower pace.

The mathematics framework for students needing compensatory assistance adds review material to strengthen students’ understanding of previously taught content. For example, topics on numbers and geometry taught in grade 4 are repeated at a faster pace in grade 5. The introduction of some new concepts such as ratios, rates, and averages, which are normally introduced in grade 5, are delayed until grade 6 for the weaker students (Ministry of Education, 2001a). What is important, however, is that because slower students spend extra time studying mathematics, topics usually taught in grades 5 and 6 do not have to be completely sacrificed to make room for repetition.6

To support the framework for slower students, Singapore has developed a Learning Support Program to help educators identify these students and provide them with extra help (Ministry of Education 2003c). Mathematics Support Teachers (MST), who receive on-the-job supervision and specialized training to ensure that they are professionally competent, deliver compensatory assistance.

In the United States, we expect all students to meet the standards in state frameworks, but the standards do not help teachers address the needs of slower students. In fact, U.S. standards do not acknowledge that students learn at different rates. No Child Left Behind addresses the needs of failing schools, but it does not directly require that failing students receive help. Although some research evidence supports the belief that students benefit when the curriculum is adjusted to match their ability levels (Loveless, 1999), a distinct alternative curriculum would raise concerns in the United States about potential harm to students from ability grouping. Singapore’s approach differs from traditional ability grouping in that Singapore establishes a framework that requires students to master the same content as other students, not a watered-down curriculum as often happens in U.S. ability grouped classrooms. Singapore also provides extra assistance from an expert teacher.

What the United States Can Learn From Singapore’s World-Class Mathematics System: An Exploratory Study (and what Singapore can learn from the United States)

Apparently teachers in Singapore do not deliver 10-minute mini lessons followed by 40 minutes of one-on-one work with the students who are "struggling."

39,947 Chinese undergraduates

With China sending more students to American colleges than any other country, the competition for spots at the top schools has soared. During the 2009-10 academic year, 39,947 Chinese undergraduates were studying in the United States, a 52 percent increase from the year before and about five times as many as five years earlier, according to the Institute of International Education, a U.S. organization.

Coaching and Much More for Chinese Students Looking to U.S.

By DAN LEVIN
Published: May 29, 2011
NY Times

The admissions people at SUNY Binghamton told us they have undergraduate students from over 100 countries.

equation

from Science Daily:

Texas A and M University researchers ... have found that not fully understanding the "equal sign" in a math problem could be a key to why U.S. students underperform their peers from other countries in math.

"About 70 percent of middle grades students in the United States exhibit misconceptions, but nearly none of the international students in Korea and China have a misunderstanding about the equal sign, and Turkish students exhibited far less incidence of the misconception than the U.S. students," note Robert M. Capraro and Mary Capraro of the Department of Teaching, Learning, and Culture at Texas A&M.

[snip]

The problem is students memorize procedures without fully understanding the mathematics, he notes.

"Students who have learned to memorize symbols and who have a limited understanding of the equal sign will tend to solve problems such as 4+3+2=( )+2 by adding the numbers on the left, and placing it in the parentheses, then add those terms and create another equal sign with the new answer," he explains. "So the work would look like 4+3+2=(9)+2=11.

"This response has been called a running equal sign...

[snip]

The Texas A&M researchers examined textbooks in China and the United States and found "Chinese textbooks provided the best examples for students and that even the best U.S. textbooks, those sponsored by the National Science Foundation, were lacking relational examples about the equal sign."

Students' Understanding of the Equal Sign Not Equal, Professor Says
August 11, 2010

They had me until that last line.

How do Everyday Math and Terc teach the equal sign?

not puzzling, and not a paradox, either

Barry spotted this Thursday session (pdf file) at the NCTM's upcoming 2011 Annual Meeting:

The Chinese Paradox: How Traditional China Trumps U.S. Reform Attempts
(General Interest) Session

Using video of urban Chinese math classes and professional development, the speaker will explain the puzzling paradox for how seemingly traditional Chinese educational methods—large, teacher-centered, lecture-based classes; exam-driven curricula; and so on—produce students who excel over their U.S. peers, despite the United States’s recent reform attempts initiated by NCTM.

Thomas Ricks
Louisiana State University, Baton Rouge

The success of large, teacher-centered, lecture-based classes where students learn exam-driven curricula is not a puzzling paradox to me.


seemingly?

I'm wondering about that word seemingly.

seemingly traditional Chinese educational methods

I'm wondering whether Thomas Ricks is going to resolve the paradox by arguing that Chinese educational methods are only seemingly traditional.

I hope not.



Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series)