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At Avenues, we have adopted Math in Focus, a Singapore approach, as our math curriculum in the Lower School*. So what is Singapore Math? The math we are teaching is not different math. Two plus two is still four; ten times ten is still one hundred. What is unique about the Singapore approach is the style of teaching and the student goals.

The classroom lessons begin with concrete experience. A kindergartener may use four blue blocks and three red blocks to add 4 + 3. A third grader may use groups of tens and ones counters to make four groups of fifteen in order to multiply 4 x 15. This concrete step engages students and builds deeper understanding of mathematical concepts. From the concrete stage, lessons move toward a pictorial focus. In this stage students use pictures, symbols, diagrams and other two-dimensional representations. Students learn to visualize math concepts and create representations based on the pictures in their minds.

Much more on Singapore Math, here.

Many Math professors, who have looked at the Singapore K-6 Math Books, are strong advocates of them because these books

1. Do an especially good job in training students in Basic Skills and

2. Do an especially good job in providing students with Conceptual Understanding and

3. Provide an especially good background in Arithmetic and Arithmetic word problems, for the learning of Algebraic calculations and for learning how to solve Algebraic word problems.

4. Do an especially good job in training students in non-trivial Arithmetic word problems; while American texts largely avoid non-trivial Arithmetic word problems.

Barry Garelick, via email:

The New York Times ran a story on September 30 about Singapore Math being used in some schools in the New York City area. Like many newspaper stories about Singapore Math, this one was no different. It described a program that strangely sounded like the math programs being promoted by reformers of math education, relying on the cherished staples of reform: manipulatives, open-ended problems, and classroom discussion of problems. The only thing the article didn’t mention was that the students worked in small groups.

Those of us familiar with Singapore Math from having used it with our children are wondering just what program the article was describing. Spending a week on the numbers 1 and 2 in Kindergarten? Spending an entire 4th grade classroom period discussing the place value ramifications of the number 82,566? Well, maybe that did happen, but not because the Singapore Math books are structured that way. In fact, the books are noticeably short on explicit narrative instruction. The books provide pictures and worked out examples and excellent problems; the topics are ordered in a logical sequence so that material mastered in the various lessons builds upon itself and is used to advance to more complex applications. But what is assumed in Singapore is that teachers know how to teach the material–the teacher’s manuals contain very little guidance. Thus, the decision to spend a week on the numbers 1 and 2 in kindergarten, or a whole class period discussing a single number is coming from the teachers, not the books.

The mistaken idea that gets repeated in many such articles is that Singapore Math differs from other programs by requiring or imparting a “deep understanding” and that such understanding comes about through a) manipulatives, b) pictures, and c) open-ended discussions. In fact, what the articles represent is what the schools are telling the reporters. What newspapers frequently do not realize when reporting on Singapore Math, is that when a school takes on such a program, it means going against what many teachers believe math education to be about; it is definitely not how they are trained in ed schools. The success of Singapore’s programs relies in many ways on more traditional approaches to math education, such as explicit instruction and giving students many problems to solve, in some ways its very success represented a slap in the face to American math reformers, many of whom have worked hard to eliminate such techniques being used.

Sally made 500 gingerbread men. She sold 3/4 of them and gave away 2/5 of the remainder. How many did she give away?

This was one of the homework questions in Craig Parsley’s fifth-grade class. The kids are showing their answers on the overhead projector. They are in a fun mood, using class nicknames. First up is “Crackle,” a boy. The class hears from “Caveman,” “Annapurna,” “Shortcut” and “Fred,” a girl.

Each has drawn a ruler with segments labeled by number — on the problem above, “3/4,” “2/5” and “500.” Below the ruler is some arithmetic and an answer.

“Who has this as a single mathematical expression? Who has the guts?” Parsley asks. No one, yet — but they will.

This is not the way math is taught in other Seattle public schools. It is Singapore Math, adopted from the Asian city-state whose kids test at the top of the world. Since the 2007-08 year, Singapore Math has been taught at Schmitz Park Elementary in West Seattle — and only there in the district.

In the war over school math — in which a judge recently ordered Seattle Public Schools to redo its choice of high-school math — Schmitz Park is a redoubt or, it hopes, a beachhead. North Beach is a redoubt for Saxon Math, a traditional program. Both schools have permission to be different. The rest of the district’s elementary schools use Everyday Math, a curriculum influenced by the constructivist or reform methods.

Related: Math Forum Audio / Video.

Next week’s Madison School Board agenda includes a number of pages [PDF] regarding the purchase of Singapore Math materials for elementary schools. Recent activity on this front included the purchase of workbooks without textbooks.

26MB mp3 audio file. Marj Passman, Lucy Mathiak and Maya Cole raised a number of questions regarding the purchase of $69K worth of Singapore Math Workbooks (using Federal tax dollars via “Title 1“) *without* textbooks or teacher’s guides at Monday evening’s Board Meeting. The purchase proceeded, via a 5-2 vote. Ed Hughes and Beth Moss supported the Administration’s request, along with three other board members.

Related Links:

- Math Task Force notes and links
- Math Forum audio / video
- West High School Teachers Letter to Isthmus on the Madison School District’s Math Curriculum

The Madison Math Task Force Report [3.9MB PDF] found that local elementary school teachers used the following curricular materials (page 166):

What, if anything has the Math Task Force report addressed?

Some lawmakers want Utah to follow the lead of a tiny Asian country when it comes to teaching math.

A senate committee Friday morning approved a bill, SB 159, that would allow districts and charter schools to apply for grants to use the Singapore method to teach math. Singapore is one of the highest scoring countries on international math tests.

In Singapore, math students are encouraged to think visually and develop mental strategies to solve problems. They’re discouraged from using paper to compute math problems.

“We seek to create a school system that will produce a significant percentage of the scientists and engineers needed by our country,” said Sen. Howard Stephenson, R-Draper, who is sponsoring the bill.

SB 159 would offer competitive grants to districts that come up with plans for teaching Singapore math in kindergarten through sixth grade and some secondary school classes. The bill would also require districts to train teachers in Singapore math and offer grants to colleges and other groups to train mathematicians to be teachers.

“I believe this will raise the math abilities of everyone in the state,” said Aaron Bertram, chairman of the University of Utah mathematics department.

In 2005, just 45% of the fifth-graders at Ramona Elementary School in Hollywood scored at grade level on a standardized state test. In 2006, that figure rose to 76%. What was the difference?

If you answered 31 percentage points, you are correct. You could also express it as a 69% increase.

But there is another, more intriguing answer: The difference between the two years may have been Singapore math.

At the start of the 2005-06 school year, Ramona began using textbooks developed for use in Singapore, a Southeast Asian city-state whose pupils consistently rank No. 1 in international math comparisons. Ramona’s math scores soared.

“It’s wonderful,” said Principal Susan Arcaris. “Seven out of 10 of the students in our school are proficient or better in math, and that’s pretty startling when you consider that this is an inner-city, Title 1 school.”

Ramona easily qualifies for federal Title 1 funds, which are intended to alleviate the effects of poverty. Nine of every 10 students at the school are eligible for free or reduced-price lunches. For the most part, these are the children of immigrants, the majority from Central America, some from Armenia. Nearly six in 10 students speak English as a second language.

Joanne has more.

It’s also different from American math in that fewer topics are taught in an academic year, giving the instructor the opportunity to teach the concept until it is mastered. “There’s a tendency in the United States to teach a topic, then it’s never seen or heard from again,” said Jeffery Thomas, president of SingaporeMath.com Inc., the official distributor of the math books based in Oregon City, Ore.

The American Institute for Research, one of the largest behavioral and social science research organizations in the world, says Singapore Math is better than American math because Singapore’s textbooks provide a more thorough understanding of concepts, while traditional American math books barely go beyond formulas and definitions. Before someone in Singapore can become a teacher, she must demonstrate math skills superior to her American counterparts, according to the AIR, which is based in Washington, D.C. Additionally, Singapore offers an alternative math framework for low-performing students, but at a slower pace and with greater repetition.

“And that’s what’s so exciting about the program for the kids,” said Luke Felker, Madison Country Day School, “is that through some solid work at the beginning, they begin to realize that they can do a lot of this in their heads.”

Felker says the program also focuses more on depth, than it does covering a variety of math lessons, making it easier for the kids to retain what they learn.

Retired UW professor Richard Askey says the Singapore program is highly successful, but it isn’t the only way to properly teach math.

“It’s possible to do it in other ways,” said Askey. “Japanese elementary schools are not exactly the same as the Singapore, and they’re done carefully.”

Askey says US schools haven’t been teaching math ‘carefully.’

Since the creation of “New Math” in the 1950s and delivery via the SMSG (School Mathematics Study Group) textbooks, the USA’s progressive math education establishments have believed that conceptual understanding is the holy grail of math instruction. Supposedly, once a child has conceptual understanding, math skills will be easier to acquire. Yet after 60 years of placing the cart before the horse, this plan is still not working well, but will anyone notice? The fact is that for most children the acquisition of math skills comes effectively via traditional instruction and practice with some memorization involved. Conceptual understanding comes later.

The Common Core thinkers have it backwards as well. Many school districts downplay the Content Standards and push the eight Standards for Mathematical Practice. This method has yet to demonstrate that it is an effective and efficient way to learn mathematics.

The eight Standards for Mathematical Practice are:

(1) Make sense of problems and persevere in solving them

(2) Reason abstractly and quantitatively

(3) Construct viable arguments and critique the reasoning of others

(4) Model with mathematics

(5) Use appropriate tools strategically

(6) Attend to precision

(7) Look for and make use of structure

(8) Look for and express regularity in repeated reasoning

Notes and links: Singapore Math.

The classrooms at Admiralty are sparsely decorated. When I visit a class of 13-year-olds, there’s a single artwork on the back wall; a paper cut-out of a cherry tree scattering blossom. At the front, where the teacher stands, is a whiteboard, a projector, a Singapore flag and a clock. I am later told that other decorations had been removed to avoid distracting or aiding students during a round of tests.

The subject is English, a second language for most of the children here, who speak either Malay or Chinese at home. At the front of the class, the teacher, Wendy Chen, is showing a film of migrant workers responding to racist comments. It’s a controversial subject: foreign labourers who work in construction, manufacturing and domestic service are often targets of racial prejudice in Singapore. Chen strips the language down to its constituent parts, asking the 13-year-old students to look at the use of the pronouns “we” and “they”. She hands out a newspaper cutting, again about migrant workers, and asks them to analyse it. “Underline who, what, when, where, how,” she instructs briskly.

The atmosphere is industrious. Throughout the day, the children work quietly at their tasks with relatively little chatter. Corporal punishment is permitted as a last resort — for boys only — at Singapore schools. When the teachers need to command attention, they strike an insistent note rather than raising their voices. One teacher, as she senses her class flagging, begins to pepper her instructions with the phrase “my dears”. Further absorbing discipline, many of the children join police or military cadet organisations, and can be seen dressed in uniform and standing to attention in the schoolyard after class. For the boys, who face two years’ national service after graduating from high school, it’s a particularly useful preparation.

Math Forum Audio and Video

A school maths question posted on Facebook by a Singaporean TV presenter has stumped thousands, and left many asking if that’s really what is expected of Singaporean students.

The question asks readers to guess the birthday of a girl called Cheryl using the minimal clues she gives to her friends, Albert and Bernard.Cheryl’s Birthday was initially reported to be an examination question for 11-year-olds.

Students stressed by tough examinations is a perennial issue here, and Cheryl’s Birthday reignited concerns that the education system was too challenging.

Kenneth Chang and Alex Bellos.

Related: The infliction of Connected Math on our children is worth a deep dive.

The countries that outperform the United States in math and science education have some things in common. They set national priorities for what public school children should learn and when. They also spend a lot of energy ensuring that every school has a high-quality curriculum that is harnessed to clearly articulated national goals. This country, by contrast, has a wildly uneven system of standards and tests that varies from place to place. We are also notoriously susceptible to educational fads.

Editorial, *New York Times*, September 18, 2006

The countries that outperform the United States in math and science education have some things in common. They set national priorities for what public school children should learn and when. They also spend a lot of energy ensuring that every school has a high-quality curriculum that is harnessed to clearly articulated national goals. This country, by contrast, has a wildly uneven system of standards and tests that varies from place to place. We are also notoriously susceptible to educational fads.

One of the most infamous fads took root in the late 1980’s, when many schools moved away from traditional mathematics instruction, which required drills and problem solving. The new system, sometimes derided as “fuzzy math,’’ allowed children to wander through problems in a random way without ever learning basic multiplication or division. As a result, mastery of high-level math and science was unlikely. The new math curriculum was a mile wide and an inch deep, as the saying goes, touching on dozens of topics each year.

Much more, here.

My mom cried during the SpaceX launch. She’s a math teacher.

“So many people in the education world want to get rid of advanced math for equity. I’m sick of it. Without math, this [launch] can’t happen.

Kids need to be allowed to dream.”

Spot on, mom 🇺🇸pic.twitter.com/LsGvs9WM5O

— Max Meyer (@mualphaxi) November 18, 2023

The less we teach CPS kids math, the more math they have to discover on their individual journeys of learning!

— Mayor Brandon Johnson (Power to the Parody!) (@maybemayorbj) November 21, 2023

Eliminating 8th grade algebra in the name of equity.

Discovery Math

Singapore Math

A few years ago she shifted her approach, turning to more direct explanation after finding a website on a set of evidence-based practices known as the science of math.

“I could see how the game related to multiplication, but the kids weren’t making those connections,” said Stark, a math teacher in the suburbs of Kansas City. “You have to explicitly teach the content.”

As American schools work to turn around math scores that plunged during the pandemic, some researchers are pushing for more attention to a set of research-based practices for teaching math. The movement has passionate backers, but is still in its infancy, especially compared with the phonics-based “science of reading” that has inspired changes in how classrooms across the country approach literacy.

Math forum audio/video.

Singapore Math

Connected Math

Discovery Math

Remedial math

Madison’s math review task force.

Faculty members in the University of California (UC) system have begun to speak out against their campuses’ adoption of lower math standards in order to bolster diversity, equity, and inclusion (DEI).

The controversy surrounds a policy enacted by a UC committee in 2020, which changed the admissions requirements for high school applicants in order “to expand course offerings beyond the traditional sequence of math courses that may lead students into the ‘race to calculus,’ to be more inclusive of new and innovative advanced math courses (e.g., data science), and to address equity issues.”

Math forum audio/video.

Singapore Math

Connected Math

Discovery Math

Remedial math

Madison’s math review task force.

*“The result of the educative process is capacity for further education.” — John Dewey*

A couple of weeks ago, Armand Domalewski wrote a guest post for Noahpinion about how the new California Math Framework threatened to dumb down math education in the state — for example, by forbidding kids from taking algebra before high school:

Well, I’m going to write another post about this subject, because the direction in which math education is trending in America under “progressive” guidance just frustrates me so deeply.

A few days after Armand’s post, the new California Math Framework was adopted. Some of the worst provisions had been thankfully watered down, but the basic strategy of trying to delay the teaching of subjects like algebra remained. It’s a sign that the so-called “progressive” approach to math education championed by people like Stanford’s Jo Boaler has not yet engendered a critical mass of pushback.

And meanwhile, the idea that teaching kids less math will create “equity” has spread far beyond the Golden State. The city of Cambridge, Massachusetts recently removed algebra and all advanced math from its junior high schools, on similar “equity” grounds.

It is difficult to find words to describe how bad this idea is without descending into abject rudeness. The idea that offering children fewer educational resources through the public school system will help the poor kids catch up with rich ones, or help the Black kids catch up with the White and Asian ones, is unsupported by any available evidence of which I am aware. More fundamentally, though, it runs counter to *the whole reason that public schools exist in the first place*.

The idea behind universal public education is that all children — or almost all, making allowance for those with severe learning disabilities — are fundamentally *educable*. It is the idea that there is some set of subjects — reading, writing, basic mathematics, etc. — that essentially all children can learn, if sufficient resources are invested in teaching them.

Related: Madison’s various one size fits all schemes:

Connected Math

Discovery math:

Not, Singapore math, however.

Some years ago, shortly before I left the Financial Times, I gave a talk at a literary event in Oxford. Put up your hand, I said to the audience, if you are useless at maths — whereupon the arms of around a third of them shot into the air. At the time, I wrote a column saying something had gone badly wrong when so many people in one of the most intellectually rarefied towns on the planet were not only dunces at maths but wore their inadequacy as if it were a charming quirk.

This week, the prime minister made the same point when he railed against the country’s “anti-maths mindset”. Rishi Sunak’s solution is to force all teenagers to study the subject until they are 18; mine was to roll my sleeves up and become a maths teacher myself.

The difference between our approaches is that mine did no harm. I tried my hardest to get teenagers to learn probability and algebra but after a year, with the relief that comes from deciding to do what you love, I switched to teaching economics and business instead. Sunak’s scheme may be equally well intentioned, but coercing students to go on doing what they hate will be ruinously expensive, counterproductive and borderline cruel.

Sunak, whose formative experience of maths was from his own school days at Winchester, would have done well to visit me as I entirely failed to teach standard-form maths to a Year 10 bottom set in an inner London comp. He would have witnessed a struggling student asking the million-dollar question: “Miss, why are we doing this?” There was no earthly reason. None of them would ever need standard form again. Surely Sunak would have seen that his first task was to do something about the 30 per cent of students nationally who fail to get the lowest pass at maths GCSE.

These teenagers are now required to retake the exam over and over until they pass or turn 18 — with the result that 100,000 students each year will have spent two years notching up successive failures, leaving most of them at 18 feeling they are not only failures at maths, but at life.

Related:

Remedial math at the University of Wisconsin.

“used surveys in early 2020 to assess how students felt in their math classes and what teachers thought about their own efforts to help students feel like they belong”

Much more on the successful citizen lawsuit overturning the Seattle School District’s use of Discovery Math, here.

http://seattlemathgroup.blogspot.com/.

Discovery Math

Connected math.

Singapore Math

Local links: Math Task Force, Math Forum Audio/Video and West High School Math Teachers letter to Isthmus.

A new study finds that high school students identify more with math if they see their math teacher treating everyone in the class equitably, especially in racially diverse schools. The study by researchers at Portland State University, Loyola University Chicago and the University of North Texas was published in the journal *Sociology of Education*. Dara Shifrer, associate professor of sociology at Portland State and former middle school math teacher, led the study.

Who can do well in math? How you answer that question may depend on where you live. Whereas people in East Asian countries tend to believe that hard work can lead anyone to succeed at math, people in the United States are more likely to believe that people need natural talent in the subject to succeed. This perception means that students in the U.S. may be particularly susceptible to racial and gender stereotypes about who is and is not “good at math.”

“Americans don’t realize what strange stereotypes we have about math,” says Shifrer. “It really sets kids up for failure here.”

The fact that some high school students are more likely to give up on math than others has important implications for their individual futures and for the lack of diversity in STEM (science, technology, engineering and math) careers.

Much more on the successful citizen lawsuit overturning the Seattle School District’s use of Discovery Math, here.

http://seattlemathgroup.blogspot.com/.

Discovery Math

Connected math.

Singapore Math

Local links: Math Task Force, Math Forum Audio/Video and West High School Math Teachers letter to Isthmus.

On RussianMathTutors.com, a site promoting a Soviet-era style of math instruction, a sample question involves Masha, a mom who bakes a batch of unmarked pies: three rice, three bean and three cherry. The student must determine how Masha can find a cherry pie “by biting into as few tasteless pies as possible.”

While Masha is biting pies, American parents are eating it up.

In the smarter, faster, better quest that is child-rearing in the United States, goal-oriented moms and dads eager to give their children an academic edge have long looked beyond U.S. borders for math education. Singapore math promotes concept mastery and critical thinking. Japanese math espouses the discipline of daily study. Now, another turbocharged math style is having its moment. Russian math, which uses reasoning and abstract concepts to build understanding, is lighting up parent group chats as the country emerges from a pandemic that left children zoning out over Zoom and schools prioritizing social-emotional recovery over homework.

“I always think for students it’s great to aim higher,” said Andrea Campbell, a mother from Newcastle, Calif. Her three children have studied with $20-an-hour instructors from Russian Math Tutors for the past two years as they pursue math competitions. “For math, you can’t do enough.”

Math Forum Audio / Video

Madison’s Math Task Force

21% OF UNIVERSITY OF WISCONSIN SYSTEM FRESHMAN REQUIRE REMEDIAL MATH

(2009) What impact do high school mathematics curricula have on college-level mathematics placement?

Related: Singapore Math.

Sumit Agarwal, Andrea Presbitero, André F. Silva, and Carlo Wix:

We study credit card rewards as an ideal laboratory to quantify the cross-subsidy from naive to sophisticated consumers in retail financial markets. Using granular data on the near universe of credit card accounts in the United States, we find that sophisticated consumers profit from reward credit cards at the expense of naive consumers who lose money both in absolute terms and relative to classic cards. We estimate an aggregate annual cross-subsidy of $15.5 billion. Notably, our results are not driven by income—while sophisticated high-income consumers benefit the most, naive high-income consumers pay the most. Banks lure consumers into the use of reward cards by offering lower interest rates than on comparable classic cards and bank profits are highest for borrowers in the middle of the credit score distribution. We show that credit card rewards transfer wealth from less to more educated, from poorer to richer, from rural to urban, and from high to low minority areas, thereby widening existing spatial disparities.

Math Forum audio video.

Benjamin Franklin Elementary in Connecticut overhauled the way it taught — and the way it ran the classroom. Every minute counted

It’s just after lunchtime, and Dori Montano’s fifth-grade math class is running on a firm schedule.

In one corner of the classroom, Ms. Montano huddles with a small group of students, working through a lesson about place value: Is 23.4 or 2.34 the bigger number? Nearby, other students collaborate to solve a “math mystery.” All the while, Ms. Montano watches the time.

At 1:32 p.m., she presses a buzzer, sending students shuffling: “Ladies and gentleman, switch please!”

This is what pandemic recovery looks like at Benjamin Franklin Elementary in Meriden, Conn., where students are showing promising progress in math, a subject that was hit hard during the shift to remote learning, even more so than reading.

The school’s math progress may not look like much: a small improvement amounting to a single decimal point increase from spring 2019 to the spring of this year, according to state test results.

But by pandemic standards, it was something of a minor miracle, holding steady when test scores nationally have fallen, particularly among low-income, Black and Hispanic students, the children that Franklin serves. About three in four students at the school qualify for free or reduced lunch, and a majority are Hispanic, Black or multiracial.

The groundwork was laid before the pandemic, when Franklin overhauled how math was taught.

It added as much as 30 minutes of math instruction a day. Students in second grade and above now have more than an hour, and fourth and fifth graders have a full 90 minutes, longer than is typical for many schools. Students no longer have lessons dominated by a teacher writing problems on a white board in front of the class. Instead, they spend more time wrestling with problems in small groups. And, for the first time, children who are behind receive math tutoring during the school day.

Related: math forum audio and video

At the heart of the wrangling lies a broad agreement about at least one thing:

The way California public schools teach math isn’t working. On national standardized tests, California ranks in the bottom quartile among all states and U.S. territories for 8th grade math scores.

Yet for all the sound and fury, the proposed framework, about 800-pages long, is little more than a set of suggestions. Its designers are revising it now and will subject it to 60 more days of public review. Once it’s approved in July, districts may adopt as much or as little of the framework as they choose — and can disregard it completely without any penalty.

“It’s not mandated that you use the framework,” said framework team member Dianne Wilson, a program specialist at Elk Grove Unified. “There’s a concern that it will be implemented unequally.”

K-12 Math links:

“Discovery math” (Seattle lawsuit)

What impact do high school mathematics curricula have on college-level math placement?

Connected Math.

Singapore Math

Math forum

California is on the verge of politicizing K-12 math in a potentially disastrous way. Its proposed *Mathematics Curriculum Framework* is presented as a step toward social justice and racial equity, but its effect would be the opposite—to rob all Californians, especially the poorest and most vulnerable, who always suffer most when schools fail to teach their students. As textbooks and other teaching materials approved by the State would have to follow this framework and since teachers are expected to use it as a guide, its potential to steal a promising future from our children is enormous.

The proposed framework would, in effect, de-mathematize math. For all the rhetoric in this framework about equity, social justice, environmental care and culturally appropriate pedagogy, there is no realistic hope for a more fair, just, equal and well-stewarded society if our schools uproot long-proven, reliable and highly effective math methods and instead try to build a mathless Brave New World on a foundation of unsound ideology. A real champion of equity and justice would want all California’s children to learn *actual* math—as in arithmetic, algebra, geometry, trigonometry and calculus—not an endless river of new pedagogical fads that effectively distort and displace actual math. The proposed framework:

- Promotes fringe teaching methods such as “trauma-informed pedagogy.” [ch. 2, p. 16]
- Distracts from actual mathematics by having teachers insert “environmental and social justice” into the math curriculum. [ch. 1, p. 35]
- Distracts from actual mathematics by having teachers develop students’ “sociopolitical consciousness.” [ch. 2, p. 39]
- Distracts from actual mathematics by assigning students—as schoolwork—tasks it says will solve “problems that result in social inequalities.” [ch. 7, p. 29]
- Urges teachers to take a “justice-oriented perspective at any grade level, K–12” and explicitly rejects the idea that mathematics itself is a “neutral discipline.” [ch. 2, p. 29]
- Encourages focusing on “contributions that historically marginalized people have made to mathematics” rather than on those contributions themselves which have been essential to the academic discipline of mathematics. [ch. 2, p. 31]
- “Reject[s] ideas of natural gifts and talents” and discourages accelerating talented mathematics students. [ch. 1, p. 8]
- Encourages keeping all students together in the same math program until the 11th grade and argues that offering differentiated programs causes student “fragility” and racial animosity. [ch.1, p. 15]
- Rejects the longstanding goal of preparing students to take Algebra I in eighth grade, on par with high-performing foreign countries whose inhabitants will be future competitors of America’s children—a goal explicitly part of the 1999 and 2006 Math Frameworks. [ch. 9, p. 43]

We, the undersigned, disagree. Mathematics is a discipline whose language is universally accessible with good teaching. The claim that math is not accessible is an insult to the millennia of non-Western mathematicians and erases the contributions of cultures around the world to mathematics as we now know it. Large numbers of students in developing countries are currently succeeding in advanced mathematics, and American industries have been put in the position of having to encourage them to come to the United States to work.

K-12 Math links:

“Discovery math” (Seattle lawsuit)

What impact do high school mathematics curricula have on college-level math placement?

Connected Math.

Singapore Math

Math forum

America has a maths problem. Its pupils have ranked poorly in international maths exams for decades. In 2018, American 15-year-olds ranked 25th in the oecd, a club of mostly rich countries. American adults ranked fourth-from-last in numeracy when compared with other rich countries. As many as 30% of American adults are comfortable only with simple maths: basic arithmetic, counting, sorting and similar tasks. American employers are desperate for science, technology, engineering and mathematics skills: nuclear engineers, software developers and machinists are in short supply. And while pupils’ maths scores are bad enough now, they could be getting worse. On the National Assessment of Educational Progress (naep), a national exam, 13-year-old pupils’ scores dropped five points in 2020 compared with their peers’ in 2012. The status quo does not add up. But teachers and academics cannot agree on where to go next.

K-12 Math links:

“Discovery math” (Seattle lawsuit)

What impact do high school mathematics curricula have on college-level math placement?

Connected Math.

Singapore Math

Math forum

If everything had gone according to plan, California would have approved new guidelines this month for math education in public schools.

But ever since a draft was opened for public comment in February, the recommendations have set off a fierce debate over not only how to teach math, but also how to solve a problem more intractable than Fermat’s last theorem: closing the racial and socioeconomic disparities in achievement that persist at every level of math education.

The California guidelines, which are not binding, could overhaul the way many school districts approach math instruction. The draft rejected the idea of naturally gifted children, recommended against shifting certain students into accelerated courses in middle school and tried to promote high-level math courses that could serve as alternatives to calculus, like data science or statistics.

The draft also suggested that math should not be colorblind and that teachers could use lessons to explore social justice — for example, by looking out for gender stereotypes in word problems, or applying math concepts to topics like immigration or inequality.

Just read this NYT piece on proposed California state education standards that demand that teachers change curriculums to bring racial identity politics into everyday math lessons. So I click the draft standards and the first section cited this CRT paper. https://t.co/tGoJ3nmsB9 pic.twitter.com/qCTEtqzG3T

— Lee Fang (@lhfang) November 6, 2021

K-12 Math links:

“Discovery math” (Seattle lawsuit)

https://www.schoolinfosystem.org/?s=Discovery+math

What impact do high school mathematics curricula have on college-level math placement?

https://www.schoolinfosystem.org/pdf/2009/05/wollack_fishwmc2009.pdf

https://www.schoolinfosystem.org/?s=Connected+math

https://www.schoolinfosystem.org/?s=singapore+math

Math forum

https://www.schoolinfosystem.org/?s=Math+forum+audio+video

Idaho can develop effective non-Common Core standards for mathematics and English/reading if its Legislature requires the development of K-12 standards in mathematics and in English/reading with the following features and guiding policies:

In mathematics:

Standards for all basic arithmetical operations (addition, subtraction, multiplication, short and long division) and standard algorithms are taught at the same grade levels as in Singapore Math’s original series for the elementary grades. Here are articles about the original Singapore Mathematics program for K-5/6 after it began to be taught in 3 elementary schools in the North Middlesex Regional School District in Massachusetts:

Boston.com

PR News Wire

ChristianBook

Singapore math study

Standards that enable all children in public elementary schools to be prepared via their mathematics curriculum to enroll in and complete a traditional Algebra I course in grade 7 or 8 before going on to advanced science and math in high school.

Standards/lessons from Dolciani-authored or co-authored mathematics textbooks in grade 8 and above, where possible.

There are a lot of good points being made in this thread. I have had a theory that it is in part related to the funding available for lab equipment and computers. During the latter half of the 20th century, in Russia you were very lucky to get access to a “real” computer.

I spent some time in 1992 in Protvino, RU, a science city of (at the time) some 20,000 scientists and engineers. The city hadn’t been listed on any official map from the USSR, even though it had existed since 1958; it was devoted to a large synchrotron. I was really struck by the contrast between the super-abundance of material resources to get the job done in the US and EU, vs. the creativity and thought by the Russians. At the risk of oversimplifying, I noticed that because of the traditional scarcity of equipment, Russian students and scientists had to

thinkrather thanexperiment, whether with computers or accelerators; it was often all that was available to them.

For instance, there was much more of an effort in Protvino to repurpose equipment than to have new equipment machined as I had seen at FermiLab or CERN. The rank and file Russian engineers that I saw in the ’90s were using a home-grown knockoff of the Intel 8088 series. The managers got imported IBM XTs. At the same time in the US working on the SSC, on my desk I had a SuperSPARC minicomputer, a Mac, and an HP 80486 Windows machine, as well as access to a twin Hypercube.

As a result, “computer experiments” like Monte Carlo simulation were not used very often in Protvino except by those for whom it was essential (and often not even then – such experiments were usually pushed down so far in the queue that they never got executed). Rather, there was much more emphasis on closed-form or approximate analytical solutions. Coding up a simulation and having a computer torture it until it confessed the results you wanted certainly takes talent, but it is arguably a different kind of talent than thinking deeply about the problem itself. Thinking about the simulation often leads to thinking that improves the computing methods and hardware used. Thinking about the problem itself gives insight into the nature of the problem itself and its connections with other areas of study.

Related: Connected Mathd Singapore Math

1965 Madison School District Math 9 Textbook Committee

Madison’s most recent Math Task Force

Remedial Math at the UW-Madison.

About a thousand years ago, the Muslim world flourished with math, science, medicine, culture and economics.

It’s unrecognisable now, but Baghdad in the 8th to 13th centuries was an intellectual centre, a hub of learning that hosted the greatest collection of knowledge in a grand library known as the House of Wisdom. Muslim scholars gave the world devices that could read the stars, surgical instruments, and algebra, named after the Arabic word “al-jabr”, which translates to the “reunion of broken parts” in English.

But as religious conservatism and fundamentalism slowly took hold, the scientific method was tossed in the trunk, argues Pakistani nuclear physicist Pervez Amirali Hoodbhoy, while regular conflict in the Middle East didn’t exactly help push things forward.

Centuries later and over 7,000 kilometres away from the Middle East, an Islamic institution holds a sturdy belief that a conservative, religious education system doesn’t need to prohibit modern, cutting-edge technology. In fact, quite the opposite: Madrasah Alsagoff Al-Arabiah has fully embraced the cult of Apple — so much so that it has scored the official title of being an Apple Distinguished School. It’s a rare title attained by just 400 schools around the world, including Nanyang Girls’ High School and Singapore American School.

Before he was denounced as a thief and cast out of the hedge fund industry, before he was a Goldman Sachs banker or a math prodigy, Ke Xu was a little boy in Hubei province, China, who loved puzzles. His parents, junior government clerks, didn’t have much money, so Xu would scour the house to find old algebra and science textbooks. He spent hours with the series 100,000 Whys, children’s brainteasers with a Maoist flavor. The commune wants to build 40 tractors—how many wheels should it buy?

When Xu was 16, his head teacher identified him as a gifted student and recommended him for a scholarship at the Raffles Institution in Singapore, a prestigious British-style boarding school with the Latin motto Auspicium melioris aevi (Hope of a better age). Xu mastered English and cruised through his classes, if not the school’s extracurricular activities. Cricket was a mystery he could never solve.

Mr. Jones, now 22 years old, walked out with a gray Accord sedan with heated leather seats. He also took home a 72-month car loan that cost him and his then-girlfriend more than $500 a month. When they split last year and the monthly payment fell solely to him, it suddenly took up more than a quarter of his take-home pay.

He paid $27,000 for the car, less than the sticker price, but took out a $36,000 loan with an interest rate of 1.9% to cover the purchase price and unpaid debt on two vehicles he bought as a teenager. It was particularly burdensome when combined with his other debt, including credit cards, he said.

Just 18% of U.S. households had enough liquid assets to cover the cost of a new car, according to a Wall Street Journal analysis of 2016 data from the Fed’s triennial Survey of Consumer Finances, a proportion that hasn’t changed much in recent years.

Even a conservative car loan often won’t do it. The median-income U.S. household with a four-year loan, 20% down and a payment under 10% of gross income—a standard budget—could afford a car worth $18,390, excluding taxes, according to an analysis by personal-finance website Bankrate.com.

Related: Discovery, Connected and Singapore Math.

Madison’s math task force.

21% of University of Wisconsin System Freshman Require Remedial Math

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Chinese high school students generally outperform their western peers at math — at least, that’s what many in the country believe.

That assumption was shattered Monday, when China placed a mediocre sixth at the 2019 Romanian Master of Mathematics (RMM), a major math competition for pre-university students. The U.S. won the championship for best team, while the highest individual prize went to an Israeli candidate.

Math competitions like the RMM are serious business in China, where participation can give students a leg up in university admissions.

China’s defeat on Monday prompted social media users to ask if recent Ministry of Education curbs on math competitions were misguided.

Since the ministry requested that universities limit preferential admissions for math competition participants, interest in the subject has fallen, one Weibo user said, in a comment that received 2,200 likes.“Chinese parents still take a utilitarian approach toward education.”

Others said the government should avoid a one-size-fits-all approach and encourage participation from truly talented students.

Related: Connected math

A question of culture

When I was a grad student at UC Berkeley (in the late 1980s), it was under- stood, among my American classmates, that the Eastern Europeans were simply better. They weren’t genetically superior; indeed, many of my Amer- ican classmates, myself included, were themselves descended from Eastern European immigrants. And we knew that we weren’t stupid. Many of us had excelled at mathematical olympiads, even at the international level. But at Berkeley, the Eastern Europeans — students and faculty alike — were known for their intensity.

American-dominated seminars might last for one polite hour; in contrast, a Russian or Rumanian seminar would go on for an entire argumentative evening. Some of us joked that the Russians really came from the planet Krypton, attaining super powers when they came to live among us.

All joking aside, we fledgling mathematicians understood that the single most important thing was not raw intelligence or knowledge (Americans tend to lag behind in the latter compared to all international students). What mattered was passion. The way to become successful in mathematics, like almost every endeavor, is to care about it, to love it, to obsess over it. And in this, Eastern Europeans had a clear superiority, a cultural advantage. They had been trained, from an early age, to love mathematics more intensely.

For many years, dating from at least the Sputnik era, America has suf- fered from an educational inferiority complex. We try to catch up, hunting for the secret ingredients that other nations use. Should we adopt the Sin- gapore curriculum? Put our kids in after-school Kumon programs? Teach them meditation? Yoga?

There’s nothing wrong with any of this; examining the practices of oth- ers’ is bound to be enriching. But it’s not the ingredients that really matter.

There is no single magical special sauce. What you need is a culture of in- tellectual inquiry, and one that fits.

Related: Math Forum.

It is astounding to me that mathematics – of all school subjects – elicits such potent emotional reaction when “reform” is in the air. We’ve seen the community response to the Common Core State Standards in the U.S., the potency of the Back to Basics movement in Alberta, Canada, and the myriad of internet examples of the absolute absurdity of “new math.”

At face value, the strong reactions we see can be interpreted as paradoxical. Parents might openly admit they themselves did not understand mathematics, that they actively hate mathematics even, but insist that we don’t dare do anything different for their child in math class! Parents’ befuddlement over their child’s third-grade homework might be seen as a wrong of the new curriculum, not as evidence of the failing of their own mathematics education, that they weren’t provided the flexibility and agility of thought to see simple arithmetic in multiple lights.

It seems that previous generations were seduced to equate familiarity with understanding. For instance, our standard arithmetic algorithms are somewhat bizarre – they are the end result of a human process of codifying arithmetical thinking, designed with the extra goal of using as little of precious 17th-century ink as possible. But if one does them often enough, their routine begins to feel comfortable and familiar.

Related: Math Forum

Project Baltimore analyzed 2017 state test scores released this fall. We paged through 16,000 lines of data and uncovered this: Of Baltimore City’s 39 High Schools, 13 had zero students proficient in math.

Digging further, we found another six high schools where one percent tested proficient. Add it up – in half the high schools in Baltimore City, 3804 students took the state test, 14 were proficient in math.

Related: Math Forum

MMSD highlighted the success of the new math curriculum in its annual report, released last July. The report said the first cohort of schools using Bridges saw an eight-point increase in math proficiency scores and nine-point gains in math growth in one school year on the spring Measures of Academic Progress (MAP) exam for third through fifth grade students.

By comparison, fifth grade MAP proficiency scores across the district increased eight points in the last four years.

“(Bridges) focuses on developing the students’ understanding of math concepts,” Davis said. “It is not about how students can memorize certain skills, but really around their ability to problem solve and look at math in more complex ways…and explain their reasoning to their teachers and peers.”

Related (deja vu):

“I have two daughters now who are perfectly good in math, but they had one or two bad math teachers and they are done. That’s what happens to girls. They walk away from tech and science. And there’s something going on that is not just about the girls. There’s something going on with how these subjects are taught.”

Related:

James Wollack

and Michael Fish:

Major Findings

- CORE-Plus students performed significantly less well on math placement test and ACT-M than did traditional students
- Change in performance was observed immediately after switch
- Score trends throughout CORE-Plus years actually decreased slightly
Inconsistent with a teacher learning-curve hypothesis

- CORE-AP students fared much better, but not as well as the traditional-AP students
Both sample sizes were low

2012: “An increasing number of freshmen in the UW System need remedial math when they start college, according to UW officials.”

2014: “

The UW’s freshman math remediation rate of 21% is below the national average of 25% to 35%, according to Cross.

UW Regent Jose Vasquez bristled at the UW System taking on “a problem that is really our cohort’s problem,” referring to K-12. “The problem was not created by the university and I’m not convinced we can solve it within the university.”

He advocated earlier intervention in high school.

”

Related: Math Forum audio/video.

and: Foundations of Reading Results (Wisconsin Education Schools), or MTEL arrives.

The problem, from a regulatory standpoint, is that they borrow a lot of money to obtain the degree — over $78,000 on average, according to the university. The total tuition is $62,593. And because it’s a graduate program, students can also borrow the full cost of their living expenses from the federal government, regardless of their credit history.

After accounting for basic living expenses, the average Harvard A.R.T. Institute graduate has to pay 44 percent of discretionary income just to make the minimum loan payment.

Related: Math Forum audio/video

Madison’s 2009 (!) Math Task Force

21% OF UNIVERSITY OF WISCONSIN SYSTEM FRESHMAN REQUIRE REMEDIAL MATH

DEJA VU: REPORT OF THE 1965 MADISON SCHOOL DISTRICT MATH 9 TEXTBOOK COMMITTEE.

More regulation simply makes things worse. Why not make sure that students can adequately assess the cost and benefits of their choices?

Cory Koedel and Morgan Polikoff, via a kind Dan Dempsey email:

Textbooks are one of the most widely used educational inputs, but remarkably little is known about their effects on student learning. This report uses data collected from elementary schools in California to estimate the impacts of mathematics textbook choices on student achievement. We study four of the most popular books in the state from 2008-2013 and find that one—Houghton Mifflin California Math—consistently outperforms the other three. The superior performance of California Math persists up to four years after adoption and shows up in grades 3, 4, and 5.

The textbook impacts we identify are educationally meaningful and come at an extremely low cost. With regard to cost, textbooks are relatively inexpensive and tend to be similarly priced. The implication is that the marginal cost of choosing a more effective textbook over a less effective alternative is essentially zero. In terms of achievement impacts, our findings suggest non-trivial gains in student achievement are attainable simply by choosing more effective curriculum materials. The effect sizes we document are on par with what one could expect from a hypothetical policy that substantially increases the quality of the teaching workforce. But whereas there is much uncertainty about whether commensurate increases in teacher quality are attainable, and how they might be attained—at least in the near term—choosing a more effective textbook is a seemingly straightforward policy option for raising student achievement.

A critical factor limiting the capacity of school administrators to choose more effective textbooks is that there is virtually no evidence on how different textbooks affect student achievement. The fundamental problem limiting the development of an evidence base is that very few states track school and district textbook adoptions. This point bears repeating: most states do not know which curriculum materials are being used in which schools and districts. Without these data, it is not possible to perform evaluations of textbook efficacy. Thus, in most states, decisionmakers who wish to incorporate into their adoption decisions evidence on how textbooks affect student achievement are simply out of luck.

…..

Our work makes several important contributions. First, we have assembled a dataset of textbook adoptions in California, the largest U.S. state with the greatest number of schools. We have received funding to continue collecting these data moving forward. We will continue to analyze the data and go on to study other subjects and other grades. We also plan to make the data available to interested researchers so that others can pursue new lines of inquiry. There are many questions in this area of great import that do not have to do with impacts on student achievement—

for instance, is there equitable access to current curriculum materials? How do charter and traditional public schools differ in their adoption patterns? We hope these newly available data can spawn a new wave of data-driven research on textbook adoptions and their effects. The current research literature is sorely lacking in quantitative analyses of textbooks in schools.Second, our work again demonstrates a method (previously demonstrated by Bhatt, Koedel, and Lehmannxiv) that can be applied in other states, grades, and subjects. We believe at this point that the method is suf ciently well developed that it can be widely applied. By doing this—studying textbook effects across multiple settings—we can begin to develop a better understanding of what is working, where, and for whom. In addition to California, we have collected data on textbook adoptions in Texas, Illinois, New York, and Florida. Whether the data we have are suf ciently complete to allow this kind of investigation in each setting is unclear, but we will try.

Related: Math Forum audio/video

Madison’s 2009 (!) Math Task Force

21% OF UNIVERSITY OF WISCONSIN SYSTEM FRESHMAN REQUIRE REMEDIAL MATH

DEJA VU: REPORT OF THE 1965 MADISON SCHOOL DISTRICT MATH 9 TEXTBOOK COMMITTEE.

Madison School District Administration (PDF):

Project Description: MMSD has provided funding to support coursework in the content and teaching knowledge of middle school teachers of math. Toward that goal, a partnership was formed back in 2010 between the District, the UW-Madison School of Education, the UW- Madison Department of Mathematics, and the University of Wisconsin Extension – Office of Education Outreach and Partnerships. MMSD will continue this for the 2016-17 school year and continue to offer math coursework for teachers to participate. The courses consists of a five course sequence (Number, Ratio, Geometry, Algebra, and Experimentation, Conjecture & Reasoning) with two courses being offered each semester. MMSD will continue to provide some financial support for teachers in each class with priority determined by; 1) middle school teacher working with an existing condition of employment, 2) middle school math teachers, and 3) teachers who began the program in previous years.

NOTE: There is a significant reduction in the estimate of this program from the 2015-2016 school year to the 2016-2017 school year. As a reminder, the change for this program and financial support moving forward was shared with the Board April 2016. The model continues the five course MSMS Program using non-credit courses for teachers currently enrolled in the program. This reduces the annual operating budget to $27,000. In addition, the full-time Math teacher leader’s responsibilities have been repositioned to provide support and professional development for middle school math teachers and for algebra teachers.

Talent management has been working with principals to select best candidates for current and future hiring. Middle school math teachers are now provided with standards aligned curricular resources and job embedded coaching.

Related: Singapore Math, Math Forum, Connected Math, Discovery Math.

Madison School District Administration (PDF):

The University of Wisconsin System is exempt from complying with the requirements of the District’s Contract Compliance Plan.

As Britain struggles to work out whether it is better off in or out of the EU, it might pay heed to the devastating analysis that shows the really frightening obstacles to a thriving future lie at home. The OECD, the Paris-based think-tank, last month ranked British teenagers bottom of 23 developed countries in literacy, and 22nd out of 23 in numeracy.

That was not the first blow. Another OECD survey in May put British 15-year-olds 20th in the world in maths and science (above the US at 28th, it must be said); Singapore was top, followed by Hong Kong and South Korea. International rankings are controversial, not least because they sometimes compare cities or regions against whole countries; Shanghai’s glittering record hardly reflects the performance of China’s rural poor. Still, the tables help monitor a country’s progress, or lack of it — and point to teaching techniques that can be borrowed.

Singapore, the land of many math geniuses, may have discovered the secret to learning mathematics (pdf). It employs a teaching method called productive failure (pdf), pioneered by Manu Kapur, head of the Learning Sciences Lab at the National Institute of Education of Singapore.

Students who are presented with unfamiliar concepts, asked to work through them, and then taught the solution significantly outperform those who are taught through formal instruction and problem-solving. The approach is both utterly intuitive—we learn from mistakes—and completely counter-intuitive: letting kids flail around with unfamiliar math concepts seems both inefficient and potentially damaging to their confidence.

But I would suggest an even more important vote will occur on Wednesday, one that will decide the future of tens or hundreds of thousands of Seattle students over the next decade: the Seattle School Board’s vote on the future elementary math curriculum.

As I have noted in previous blogs, Seattle Public Schools is now using a grossly inferior math curriculum, Everyday Math. Most school districts in the area (and around the country) have dropped it because it fails to provide basic competency in elementary-level mathematics, crippling students’ ability to learn algebra and higher mathematics later in their career. Everyday Math is a prime example of “fuzzy math,” with students spending much their their time inventing their own algorithms, writing long essays, using calculators, and doing group projects. Everyday Math is a wonderful example of the tendency to jump on the latest fad, which may sound good, but fails in the classroom.

So you would think the district would be doubly sure not to make a serious mistake again.

Last month, a committee established by the district provided their recommendation of a possible new curriculum. Their rankings were:

1. EnVision Math

2. Go Math!

3. Math in Focus (MIF), which is a U.S. version of Singapore Math.As I explained in my last blog of the subject, their evaluation was a great disappointment. Math in Focus, based on the extraordinarily successful Singapore Math approach, was downgraded because it advanced student’s too rapidly (compared to the latest fad, the Common Core standards). Go Math! is glossy and weak. EnVision, their top choice, is glossy and full of excessive reading and writing, making it a poor choice for students who do not have strong English skills. But better than Everyday Math for sure.

Much more on Everyday Math, here.

Related: Math Forum audio/video.

Locally, Madison has also used Everyday Math.

Here’s a modest test result to bolster the argument of those who say the American educational system isn’t so terrible. On a new creative problem-solving test taken by students in 44 countries and regions, U.S. 15-year-olds scored above the international average and rank at number 18 in the world. That’s much better than the below-average performance of U.S. students on the PISA (Program for International Student Assessment) reading and math tests conducted by the Organization for Economic Cooperation and Development (OECD).

“We think teaching through problem solving is already more developed in the US than in other countries,” said the OECD’s Pablo Zoido, in explaining why US students have higher problem-solving scores than expected.

Still, Asian countries and regions dominate the top 10 spots in creative problem solving, with Singapore, Korea and Japan taking first, second and third place. Canada, Australia and Finland were the only non-Asian nations to make it into the top 10. Shanghai, which topped the PISA charts in math and reading, was relatively weaker in problem solving at number 6.

The children of cleaners in Asian cities such as Shanghai and Singapore are better at maths than the offspring of doctors and lawyers in the US and UK, according to an analysis of the global Pisa test rankings published on Tuesday.

The international league table, first released by the OECD in December, had shown 15-year-olds in Shanghai to be top in maths, while the UK languished in 26th place and the US in 36th.

But fresh scrutiny has revealed that the state-educated children of British professionals are on average a whole school year behind the children of “elementary” workers in Shanghai in maths ability, and around three months behind the same group in Singapore. The gap is even wider between US professionals and Asian cleaners or caterers.

For more than a decade, Singapore, along with South Korea, Taiwan, Japan, Shanghai, Hong Kong and Finland, has been at or near the top of international leagues tables that measure children’s ability in reading, maths and science. This has led to a considerable sense of achievement in Finland and East Asia and endless hand-wringing and head-scratching in the West.

What then do Singaporean teachers do in classrooms that is so special, bearing in mind that there are substantial differences in classroom practices between – as well as within – the top-performing countries? What are the particular strengths of Singapore’s instructional regime that helps it perform so well? What are its limits and constraints?

Is it the right model for countries seeking to prepare students properly for the complex demands of 21st century knowledge economies and institutional environments more generally? Is Singapore’s teaching system transferable to other countries? Or is its success so dependent on very specific institutional and cultural factors unique to Singapore that it is folly to imagine that it might be reproduced elsewhere?

An educational and enrichment workshop was recently conducted by the Galileo Enrichment Learning Program where the multi-awarded mathematician and Singapore Math advocate Dr. Queena Lee-Chua together with her son Scott, shared with the participants the fundamentals of Singapore Math and demonstrated how this fun learning approach is used to solve word problems.

Multi-awarded mathematician and Singapore Math advocate Dr. Queena Lee-Chua shared with the participants the fundamentals of Singapore Math and demonstrates how this fun-learning approach is used to solve word problems.

The workshop, held at Nuvali Evoliving AVR, Sta. Rosa City, Laguna, was organized by Galileo Sta. Rosa, attended by parents and their kids, as well as by teachers from different pre-schools and elementary schools in and outside Manila. It was indeed an enlightening and engaging time for everyone as the mother and son tandem proved to the audience that complex mathematical problems can be solved with simple math logic.

Much more on Singapore Math, here.

Related: Math Forum Audio/Video.

Fourth- and eighth-grade students in the United States continue to lag behind students in several East Asian countries and some European nations in math and science, although American fourth graders are closer to the top performers in reading, according to test results released on Tuesday.

Fretting about how American schools compare with those in other countries has become a regular pastime in education circles. Results from two new reports, the Trends in International Mathematics and Science Study and the Progress in International Reading Literacy Study, are likely to fuel further debate.

South Korea and Singapore led the international rankings in math and fourth-grade science, while Singapore and Taiwan had the top-performing students in eighth-grade science. The United States ranked 11th in fourth-grade math, 9th in eighth-grade math, 7th in fourth-grade science and 10th in eighth-grade science.

Related: www.wisconsin2.org.

Arthur Levine, via a kind Erich Zellmer email:

Parents nationwide are familiar with the wide academic achievement gaps separating American students of different races, family incomes and ZIP Codes. But a second crucial achievement gap receives far less attention. It is the disparity between children in America’s top suburban schools and their peers in the highest-performing school systems elsewhere in the world.

Of the 70 countries tested by the widely used Program for International Student Assessment, the United States falls in the middle of the pack. This is the case even for relatively well-off American students: Of American 15-year-olds with at least one college-educated parent, only 42% are proficient in math, according to a Harvard University study of the PISA results. That is compared with 75% proficiency for all 15-year-olds in Shanghai and 50% for those in Canada.

Compared with big urban centers, America’s affluent suburbs have roughly four times as many students performing at the academic level of their international peers in math. But when American suburbs are compared with two of the top school systems in the world–in Finland and Singapore–very few, such as Evanston, Ill., and Scarsdale, N.Y., outperform the international competition. Most of the other major suburban areas underperform the international competition. That includes the likes of Grosse Point, Mich., Montgomery County, Md., and Greenwich, Conn. And most underperform substantially, according to the Global Report Card database of the George W. Bush Presidential Center.

Related: The Global Report: Compare US School Districts to the World.

I read with interest Nathan Comps’ article on the forthcoming 2012-2013 Madison School District budget. Board Vice President Marj Passman lamented:

“If Singapore can put a classroom of students on its money, and we can’t even put our money into children, what kind of country are we?” asks Passman, Madison school board vice president. “It’s going to be a horrible budget this year.”

Yet, according to the World Bank, Singapore spends 63% less per student than we do in America on primary education and 47% less on secondary education. The US spent $10,441/student in 2007-2008 while Madison spent $13,997.27/student during that budget cycle. Madison’s 2011-2012 budget spends $14,858.40/student.

The Economist on per student spending:

Those findings raise what ought to be a fruitful question: what do the successful lot have in common? Yet the answer to that has proved surprisingly elusive. Not more money. Singapore spends less per student than most. Nor more study time. Finnish students begin school later, and study fewer hours, than in other rich countries.

In Finland all new teachers must have a master’s degree. South Korea recruits primary-school teachers from the top 5% of graduates, Singapore and Hong Kong from the top 30%.

Rather than simply throwing more money (Madison taxpayers have long supported above average K-12 spending) at the current processes, perhaps it is time to rethink curriculum and just maybe, give Singapore Math a try in the Madison schools.

Related:

- 60% to 42%: Madison School District’s Reading Recovery Effectiveness Lags “National Average”: Administration seeks to continue its use
- Singapore Math and Math Forum.
- Singapore school statistics (PDF)
- When A Stands for Average: Students at the UW-Madison School of Education Receive Sky-High Grades. How Smart is That?
- Alabama, unlike Wisconsin, participated in the 2011 global TIMSS examinations. Perhaps one day, Wisconsin will have the courage to compare our students to the world.

Via the Global Report Card. The average Madison student performs better than 23% of Singapore students in Math and 35% in reading.

Madison schools aren’t failing, by any stretch of the imagination, for many students.

In fact, if you’re a white, middle-class family sending your children to public school here, your kids are likely getting an education that’s on a par with Singapore or Finland — among the best in the world.

However, if you’re black or Latino and poor, it’s an unquestionable fact that Madison schools don’t as good a job helping you with your grade-point average, high school graduation, college readiness or test scores. By all these measures, the district’s achievement gap between white and minority students is awful.

These facts have informed the stern (and legitimate) criticisms leveled by Urban League President Kaleem Caire and Madison Prep backers.

But they doesn’t take into account some recent glimmers of hope that shouldn’t be discounted or overlooked. Programs like AVID/TOPS support first-generation college-bound students in Madison public schools and are showing some successes. Four-year-old kindergarten is likely to even the playing field for the district’s youngest students, giving them a leg up as they enter school. And, the data surrounding increasing numbers of kids of color participating in Advanced Placement classes is encouraging.

Stepping back from the local district and looking at education through a broader lens, it’s easy to see that No Child Left Behind and Race to the Top have aimed to legislate, bribe and punish their way toward an unrealistic Lake Wobegon world where all the students are above average.

Remarkable. Are there some excellent teachers in Madison? Certainly. Does Madison’s Administration seek best in the world results? A look at the math task force, seemingly on hold for years, is informative. The long one size fits all battle and the talented and gifted complaint are worth contemplating.

Could Madison be the best? Certainly. The infrastructure is present, from current spending of $14,963/student to the nearby UW-Madison, Madison College and Edgewood College backed by a supportive community.

Ideally, Madison (and Wisconsin) should have the courage to participate in global examinations (Florida Students Take Global Examinations, Wisconsin’s Don’t). Taxpayers and parents would then know if Troller’s assertions are fact based.

You’ve heard this a million (10 to the power of 6) times, but it is frightening. In the 2009 (41 X 49) Program for International Student Assessment US 15-year-olds ranked 25th (4! + 1) among 34 (square root of 1156) countries in math falling behind Canada, New Zealand, Finland, and Asian countries such as China, South Korea, Japan, Singapore, and Hong Kong.

To counter this sad trend, stop by The Math Salon at Mosaic Coffeehouse on February 28th from 4-6 PM:

Educators at a small private Christian school in Olde Town Augusta are seeing results with a math curriculum imported from halfway around the world.

For the past three years, Heritage Academy has used Singapore Math as its basal math curriculum for kindergarten through sixth grade.

In the first year the school adopted Singapore Math, all of its kindergarten and first-grade pupils met or exceeded proficiency standards on the Iowa Tests of Basic Skills, as did 80 percent of second-graders.

Why use math from Singapore?

Related: Math Forum Audio/Video.

American teenagers made modest progress on an international exam, but still performed below average in mathematics compared with their peers in other industrialized countries, according to results released Tuesday by the U.S. Department of Education.

The test, called the Program for International Student Assessment, has been given every three years since 2000 to 15-year-old students. Last year, when the test was administered, 60 countries participated. It’s coordinated worldwide by the Paris-based Organization of Economic Cooperation and Development.

The results for American students drew a lukewarm response from U.S. education officials as they seek to boost test scores among high-school and college students. “We’re in the middle of the pack; that’s not where we want to be,” said Stuart Kerachsky, deputy commissioner at the National Center for Education Statistics, an arm of the Department of Education that administers the PISA test in the U.S.

Korea and Finland top OECD’s latest PISA survey of education performance:

Korea and Finland top the OECD’s latest PISA survey of reading literacy among 15-year olds, which for the first time tested students’ ability to manage digital information.

The survey, based on two-hour tests of a half million students in more than 70 economies, also tested mathematics and science. The results for 65 economies are being released today.

The next strongest performances were from Hong Kong-China, Singapore, Canada, New Zealand and Japan. Full results here.

The province of Shanghai, China, took part for the first time and scored higher in reading than any country. It also topped the table in maths and science. More than one-quarter of Shanghai’s 15-year-olds demonstrated advanced mathematical thinking skills to solve complex problems, compared to an OECD average of just 3%.

By the time they get to kindergarten, children in this well-to-do suburb already know their numbers, so their teachers worried that a new math program was too easy when it covered just 1 and 2 — for a whole week.

“Talk about the number 1 for 45 minutes?” said Chris Covello, who teaches 16 students ages 5 and 6. “I was like, I don’t know. But then I found you really could. Before, we had a lot of ground to cover, and now it’s more open-ended and gets kids thinking.”

The slower pace is a cornerstone of the district’s new approach to teaching math, which is based on the national math system of Singapore and aims to emulate that country’s success by promoting a deeper understanding of numbers and math concepts. Students in Singapore have repeatedly ranked at or near the top on international math exams since the mid-1990s.

Franklin Lakes, about 30 miles northwest of Manhattan, is one of dozens of districts, from Scarsdale, N.Y., to Lexington, Ky., that in recent years have adopted Singapore math, as it is called, amid growing concerns that too many American students lack the higher-order math skills called for in a global economy.

From: Oliver Kim

Date: September 26, 2010 5:17:44 AM EDT

To: fitzhugh@tcr.org

Subject: Thank you from Singapore

Dear Mr. Fitzhugh,

Thank you for publishing my essay on the Maginot Line in this year’s fall issue of The Concord Review. Receiving your letter was at once joyous and humbling.

From the rise of the standardized test as a measure of academic success, to the subordination and disappearance of the long-form essay in the high school curriculum, the humanities appear to be losing ground in education. In light of the numerous competitions and accolades available to students of math and the hard sciences, options for students of the humanities, especially history, are comparatively few. The Concord Review stands alone as an exemplar for quality writing by lovers of history.

Thanks to your hard work, my school has all freshman students write a long-form historical essay based on the model of the essays that appear in The Concord Review. All students of AP European History are required to do the same, and, even in those classes that do not require long-form essays, The Concord Review is employed as a standard of quality and academic rigor. Though I cannot speak for my whole school, I can say that, anecdotally, this project has sparked historical curiosity and illuminated unexplored talents in my classmates.

Again, thank you for publishing my essay. I hope that the Review will find a solution to its financial woes and continue inspiring future generations of historians.

Warm regards,

Oliver Kim

Singapore American School [Class of 2011]

The Concord Review.

Two primary school pupils from Hong Kong won the top awards in one of Asia’s most prestigious maths competitions.

It’s the first time that any Hong Kong pupil has won a grand champion award at the International Mathematics Contest which was held in Singapore last month. About 1,000 pupils competed in the event which sees teams from the mainland, Hong Kong, Taiwan, Indonesia, South Korea, Malaysia, the Philippines, Singapore and Thailand battling it out in algebra, geometry, statistics and measurements.

Nine-year-old boy Li Ka-wing scored the highest marks in the Primary Three category and 11-year-old girl Lam Ho-yan was the best pupil for the Primary Five exams.

They both train at the Hong Kong Mathematical Olympiad School in Kowloon which offers intensive maths coaching.

“Each year, there are good results. However this year, it was very special,” the school’s principal, Pinky Lam Sui-ping, said. Every year, thousands of Hong Kong pupils applied to compete in the event by sitting online tests, she said.

I know that I’m inviting trouble with this, but something that Reader wrote in a comment on another thread piqued my interest. I would like to discuss only a narrow question. Please don’t expand the discussion.

Writing about Everyday Math and Singapore, Reader wrote: “The fact is, the newer curricula stress more problem solving and discovery. That is, it’s doing more than a lot of older curricula.”

Here’s my question: can problem-solving be taught?

I mean this in the nicest possible way and I don’t have an answer myself. I’m not sure, I’m asking. Can people be taught or trained in problem-solving techniques or is it a talent that some people just natively have more than others? Problem solving requires a certain amount of creativity, doesn’t it? It can require a flexibility of perspective, curiosity, persistence, and pattern recognition. Can these things be taught or trained?

Related: Math Forum audio/video links.

America’s future math teachers, on average, earned a C on a new test comparing their skills with their counterparts in 15 other countries, significantly outscoring college students in the Philippines and Chile but placing far below those in educationally advanced nations like Singapore and Taiwan.

The researchers who led the math study in this country, to be released in Washington on Thursday, judged the results acceptable if not encouraging for America’s future elementary teachers. But they called them disturbing for American students heading to careers in middle schools, who were outscored by students in Germany, Poland, the Russian Federation, Singapore, Switzerland and Taiwan.

On average, 80 percent to 100 percent of the future middle school teachers from the highest-achieving countries took advanced courses like linear algebra and calculus, while only 50 percent to 60 percent of their counterparts in the United States took those courses, the study said.

The winter 2009-2010 issue of “American Educator”, has a number of interesting articles. Here are two of interest for people interested in mathematics education.

Daniel Willingham “Is It True That Some People Just Can’t Do Math”

Patsy Wang-Iverson, Perla Myers, and Edmund Lim W.K. “Beyond Singapore’s Mathematics Textbooks – Focused and Flexible Supports for Teaching and

Learning”

The first has a number of useful references as well as comments. Here is one. There have been many papers written in Madison on student’s lack of understanding of the equal sign. I once asked Liping Ma if this was a problem in China. She said that as far as she knew it was not. There is confirmation of this in one of the references.

Four questions asked of sixth grade students in the U.S. and China.

The second article in American Educator has comments on curriculum, teacher induction and education and support while teaching. There is also a one page supplemental article on teacher professional development and evaluation by Susan Sclafani and Edmund Lim W.K.

In addition there have been two very interesting books on school mathematics education written by mathematicians. The first is “Arithmetic for Parents: A Book for Grownups about Children’s Mathematics” by Ron Aharoni, Sumizdat, 2007. An article by Aharoni about his experience teaching mathematics in an elementary school in Israel can be read here. This is a good introduction to his book, and more useful details are in the

book.

The second is “And All the Children Are Above Average: A Review of The End of Ignorance: Multiplying Our Human Potential” by John Mighton, a Canadian mathematician and playwright. The paperback version of this book was published by Vintage Canada. You can read about Mighton here. and there is also information about his math program JUMP here. This program was developed after Mighton learned a number of things while tutoring students who had significant problems in learning elementary mathematics. A review of this book by David Kirshner appeared in the Journal for Research in Mathematics Education in the January, 2010 issue.

Superintendent Dan Nerad [64K PDF]:

MMSD has begun a three-year implementation plan to achieve an equitable and balanced mathematics program at tbe elementary level. The plan was developed and refined through collaboration with teachers, Instructional Resource Teachers and principals over the course of the past several years. The plan includes the materials described below (details via this 64K PDF),

With the attached order, MMSD has provided each classroom teacher in the District with a Learning Mathematics in the Primary/Intermediate Grades instructional guide and the set of teacher resources from the Investigations program. The third component of the teacher materials is Teaching Student Centered Mathematics by John Van de Walle, which is in place in most classrooms but will continue to be ordered using ELM or Title I funds, as necessary. Additional professional resources have been or are being purchased at the building level to create a library available for all staff to access as needed. Those resources include Primary Mathematics textbooks and teacher guides, Thinking Mathematically and Children’s Mathematics by Thomas Carpenter, Teaching Number series from Wright, among other recommended titles.

MMSD has provided all Title I schools with the Primary Mathematics (Singapore) workbooks and Extra Practice workbooks for the 2009-2010 school year. All manipulatives have been ordered for Title I schools over tbe past two years and are in place. Non-Title I schools have been and will continue to use ELM funds to purchase tbe student components for the implementation of a balanced mathematics classroom.

Related:

Barry Garelick, via email:

By way of introduction, I am neither mathematician nor mathematics teacher, but I majored in math and have used it throughout my career, especially in the last 17 years as an analyst for the U.S. Environmental Protection Agency. My love of and facility with math is due to good teaching and good textbooks. The teachers I had in primary and secondary school provided explicit instruction and answered students’ questions; they also posed challenging problems that required us to apply what we had learned. The textbooks I used also contained explanations of the material with examples that showed every step of the problem solving process.

I fully expected the same for my daughter, but after seeing what passed for mathematics in her elementary school, I became increasingly distressed over how math is currently taught in many schools.

Optimistically believing that I could make a difference in at least a few students’ lives, I decided to teach math when I retire. I enrolled in education school about two years ago, and have only a 15-week student teaching requirement to go. Although I had a fairly good idea of what I was in for with respect to educational theories, I was still dismayed at what I found in my mathematics education courses.

In class after class, I have heard that when students discover material for themselves, they supposedly learn it more deeply than when it is taught directly. Similarly, I have heard that although direct instruction is effective in helping students learn and use algorithms, it is allegedly ineffective in helping students develop mathematical thinking. Throughout these courses, a general belief has prevailed that answering students’ questions and providing explicit instruction are “handing it to the student” and preventing them from “constructing their own knowledge”–to use the appropriate terminology. Overall, however, I have found that there is general confusion about what “discovery learning” actually means. I hope to make clear in this article what it means, and to identify effective and ineffective methods to foster learning through discovery.

Garelick’s part ii on Discovery learning can be found here.

Related: The Madison School District purchases Singapore Math workbooks with no textbooks or teacher guides. Much more on math here.

Via a Barry Garelick email:

“The article describes my experience tutoring my daughter and her friend when they were in sixth grade, using Singapore Math in order to make up for the train wreck known as Everyday Math that she was getting in school. I doubt that the article will change the minds of the administrators who believe Everyday Math has merit, but it wasn’t written for that purpose. It was written for and dedicated to parents to let them know they are not alone, that they aren’t the only ones who have shouted at their children, that there are others who have experienced the tears and the confusion and the frustration. Lastly it offers some hope and guidance in how to go about teaching their kids what they are not learning at school.”

University of Wisconsin-Madison math lecturer Gabriele Meyer advocates the use of Singapore math in this 3 minute mp3 audio file. Much more on Madison’s math program here.

Related: the politics (and spin) of calculator use.

If there were a math-and-science Olympics for elementary and middle schoolers, USA students could hold their heads high — they’re consistently better than average. In math, it turns out, they’re improving substantially, even as a few powerhouse nations see their scores drop.

But at the end of the day, the USA never quite makes it to the medal podium, a dilemma that has educators and policymakers divided, with some saying factors outside school play a key role in both achievement and productivity in general.

For the first time since 2003, the results of the Trends in International Mathematics and Science Study, or TIMSS, a battery of international math and science tests among dozens of nations, are out — and they paint a somewhat mixed picture of achievement: On the one hand, the USA ranks consistently above international averages in both subjects.

On the other hand, several nations consistently outscore our fourth- and eighth-graders, with a few countries turning in eye-popping performances.

Joanne has more along with Gerald Bracey:

First, comparing nations on average scores is a pretty silly idea. It’s like ranking runners based on average shoe size or evaluating the high school football team on the basis of how fast the average senior can run the 40-yard dash. Not much link to reality. What is likely much more important is how many high performers you have. On both TIMSS math and science, the U. S. has a much higher proportion of “advanced” scorers than the international median although the proportion is much smaller than in Asian nations.

Second, test scores, at least average test scores, don’t seem to be related to anything important to a national economy. Japan’s kids have always done well, but the economy sank into the Pacific in 1990 and has never recovered. The two Swiss-based organizations that rank nations on global competitiveness, the Institute for Management Development and the World Economic Forum, both rank the U. S. #1 and have for a number of years. The WEF examines 12 “pillars of competitiveness,” only one of which is education. We do OK there, but we shine on innovation.

Innovation is the only quality of competitiveness that does not show at some point diminishing returns. Building bigger and faster airplanes can only improve productivity so much. Innovation has no such limits. When journalist Fareed Zakaria asked the Singapore Minister of Education why his high-flying students faded in after-school years, the Minister cited creativity, ambition, and a willingness to challenge existing knowledge, all of which he thought Americans excelled in.

Malcolm Gladwell, Outliers

New York: Little, Brown, 2008, pp. 247-249

“Rice Paddies and Math Tests”

Every four years, an international group of educators administers a comprehensive mathematics and science test to elementary and junior high students around the world. It’s the TIMSS…and the point of the TIMSS is to compare the educational achievement of one country with another’s.

When students sit down to take the TIMSS exam, they also have to fill out a questionnaire. It asks them all kinds of questions, such as what their parents’ level of education is, and what their views about math are, and what their friends are like. It’s not a trivial exercise. It’s about 120 questions long. In fact, it is so tedious and demanding that many students leave as many as ten or twenty questions blank.

Now, here’s the interesting part. As it turns out, the average number of items answered on that questionnaire varies from country to country. It is possible, in fact, to rank all the participating countries according to how many items their students answer on the questionnaire. Now, what do you think happens if you compare the questionnaire rankings with the math rankings on the TIMSS? They are exactly the same. In other words, countries whose students are willing to concentrate and sit still long enough to focus on answering every single question in an endless questionnaire are the same countries whose students do the best job of solving math problems.

The person who discovered this fact is an educational researcher at the University of Pennsylvania named Erling Boe, and he stumbled across it by accident. “It came out of the blue,” he says. Boe hasn’t even been able to publish his findings in a scientific journal, because, he says, it’s just a bit too weird. Remember, he’s not saying that the ability to finish the questionnaire and the ability to excel on the math test are related. He’s saying that they are the same: if you compare the two rankings, they are identical.

Think about this another way. Imagine that every year, there was a Math Olympics in some fabulous city in the world. And every country in the world sent its own team of one thousand eighth graders. Boe’s point is that we could predict precisely the order in which every country would finish in the Math Olympics without asking a single math question. All we would have to do is give them some task measuring how hard they were willing to work. In fact, we wouldn’t even have to give them a task. We should be able to predict which countries are best at math simply by looking at which national cultures place the highest emphasis on effort and hard work.

So, which places are at the top of both lists? The answer shouldn’t surprise you: Singapore, South Korea, China (Taiwan), Hong Kong, and Japan. [Mainland China doesn’t yet take part in the TIMSS study.] What those five have in common, of course, is that they are all cultures shaped by the tradition of wet-rice agriculture and meaningful work. They are the kind of places where, for hundreds of years, penniless peasants, slaving away in the rice paddies three thousand hours a year, said things to one another like “No one who can rise before dawn three hundred and sixty days a year fails to make his family rich.”

Dr. Gary W. Phillips & John A. Dossey [2.5MB PDF Report]:

Students in six major U.S. cities are performing on par or better in mathematics than their peers in other countries in grades 4 and 8, according to a new study by the American Institutes for Research (AIR). However, students from five other major cities are not faring as well, and overall, U.S. student performance in mathematics falls off from elementary to middle school grades — and remains behind many industrialized nations, particularly Asian nations.

The AIR study offers the first comparison between students from large U.S. cities and their international peers. The study compares U.S. 4th grade students with their counterparts in 24 countries and 8th grade students with peers in 45 countries.

“Globalization is not something we can hold off or turn off…it is the economic equivalent of a force of nature… like the wind and water” (Bill Clinton)

If you are a student today competing for jobs in a global economy, the good jobs will not go to the best in your graduating class–the jobs will go to the best students in the world. Large urban cities are intimately connected to the nations of the world. Large corporations locate their businesses in U.S. cities; foreign students attend U.S. schools; and U.S. businesses export goods and services to foreign nations. Large urban cities need to know how their students stack up against peers in the nations with which the U.S. does business. This is especially important for students in the fields of science, technology, engineering, and mathematics. The students in these fields will allow our future generation to remain technologically innovative and economically competitive.

This report provides a comparison of the number of mathematically Proficient students in Grades 4 and 8 in 11 large cities in the United States with their international peers.

This comparison is made possible by statistically linking the National Assessment of Educational Progress (NAEP) in 2003 and the Trends in International Mathematics and Science Study (TIMSS) in 2003 when both assessments were conducted in the United States in the same year and in the same grades.

After the statistical linking was completed, it was possible to compare the most recent NAEP results (from 2007) to the most recent TIMSS results (from 2003). How the United States compares to the overall international average.

At Grade 4, five countries (Singapore, Hong Kong SAR, Chinese Taipei, Japan, and the Flemish portion of Belgium) performed significantly better than the United States (Figure 1). However, the United States (at 39% proficiency) performed better than the international average (27% proficiency) of all 24 countries (Figure 13).

At Grade 8, eight countries (Singapore, Hong Kong SAR, Republic of Korea, Chinese Taipei, Japan, Belgium (Flemish), Netherlands, and Hungary) performed significantly better than the United States (Figure 1). However, the United States (at 31% proficiency) performed better than the international average (21% proficiency) of all 44 countries (Figure 14).

….

Because of the persistent requests of urban school districts, the U .S . Congress authorized NAEP to assess, on a trial basis, six large urban school districts beginning in 2002 . Since then, more districts have been added, resulting in 11 school districts in 2007 (and plans are underway to include even more districts in the future) . The urban school chiefs in these 11 large school districts, which voluntarily participated in the 2007 NAEP, recognized the global nature of educational expectations and the importance of having reliable external data against which to judge the performance of their students and to hold themselves accountable . They should be commended for their visionary goal of trying to benchmark their local performance against tough national standards. National standards provide a broad context and an external compass with which to steer educational policy to benefit local systems . The purpose of this report is to further help those systems navigate by providing international benchmarks.

Clusty Search: Gary W. Phillips and John A. Dossey.

Greg Toppo has more:

Even if the findings are less-than-stellar, he says, they should help local officials focus on improving results.

“In that sense, I think it could be a very positive thing to use in-house, in the district, to keep their nose to the grindstone,” says Kepner, a former middle- and high-school math teacher in Iowa and Wisconsin.”If they can show they’re improving, they might be able to attract more companies to a system that’s on the move.”

Phillips says the findings prove that in other countries “it is possible to do well and learn considerably under a lot of varied circumstances — in other words, being low-income is not really an excuse when you look around the rest of the world.”

March 7, 2008 Meeting [rtf / pdf]. Well worth reading for those interested in the use of Connected Math and Core Plus, among others, in our schools.

A few interesting items:

- Mitchell Nathan proposed a change to the name of the Work Group to more authentically describe its intent. There was consensus to accept the change in designation for the Work Group from “Curriculum Review and Research Findings” to “Learning from Curricula.”
- “Addresses the misconception that there is one curriculum. There are a number of curricula at play, with the exception of the narrowing down at the middle school level, but teachers are also drawing from supplementary materials. There are a range of pathways for math experiences. The work plan would give an overview by level of program of what exists. “
- “Could say that variety is good for children to have places to plug into. Could expand on the normative idea of purchasing commercial curricula vs. richer, in-house materials. Standards tell the teachers what needs to be taught. Published materials often are missing some aspect of the standards. District tries to define core resources; guides that help people with classroom organization.”
*Fascinating, given the move toward one size fits all in high school, such as English 9 and 10.* - “Want to include a summary of the NRC report that came out in favor of Connected Math but was not conclusive—cannot control for teacher effects, positive effects of all curricula, etc. “
- “Would like to give some portrayal of the opportunities for accelerated performance — want to document informal ways things are made available for differentiation. “
- “Include elementary math targeted at middle school, e.g., Math Masters. There is information out there to address the Math Masters program and its effect on student achievement.”
- “Data are available to conclude that there is equity in terms of resources”
- “District will have trend data, including the period when Connected Math was implemented, and control for changes in demographics and see if there was a change. No way to link students who took the WKCE with a particular curriculum experience (ed: some years ago, I recall a teacher asked Administration at a PTO meeting whether they would track students who took Singapore Math at the Elementary level: “No”). That kind of data table has to be built, including controls and something to match teacher quality. May recommend that not worth looking at WKCE scores of CM (Connected Math) student or a case study is worth doing. “
- The Parent Survey will be mailed to the homes of 1500 parents of students across all grades currently enrolled in MMSD math classes. The Teacher Survey will be conducted via the district’s web site using the Infinite Campus System.
- MMSD Math Task Force website

Math Forum audio / video and links.

The most noticeable change is a dramatic increase in students taking accelerated math classes in the middle years, an initiative that seems to have spread to every school system in the region. Educators view math acceleration as a gateway to advanced study in high school and, in turn, to college. Higher-level math classes have helped middle schools cultivate a community of students similar to those in honors and Advanced Placement high school classes.

At Samuel Ogle Middle School in Bowie, the number of students taking Algebra I, a high-school-level course, has doubled from 60 to 120 in the past two years.

Barry Garelick references Montgomery County’s experiment with Singapore Math. About Singapore Math. More here.

Why do some countries, like Singapore, Korea, and the Czech Republic, do so much better than the United States in math? I’ve heard all sorts of reasons; diversity and poverty top the list. But after some 15 years conducting international research, I am convinced that it’s the diversity and poverty of U.S. math standards—not the diversity and poverty of U.S. students—that are to blame.

The single most important result of the Third International Mathematics and Science Study (TIMSS) is that we now know that student performance is directly related to the nature of the curricular expectations. I do not mean the instructional practices. I mean the nature of what it is that children are to learn within schools. (In the U.S., the curricular expectations are usually referred to as standards; in other countries they are known by various names.) After all, what is more central to schooling than those things we, as a society, have chosen to pass on to our children?

The TIMSS research has revealed that there are three aspects of math expectations, or standards, that are really important: focus, rigor, and coherence. Let’s take a brief look at each.

Greg Barlow, an Air Force officer in the defense secretary’s office at the Pentagon, was helping his 8-year-old son, Christian, one recent night with a vexing problem: What is 674 plus 249?

The Prince William County third-grader did not stack the numbers and carry digits from one column to the next, the way generations have learned. Applying lessons from his school’s new math textbook, “Investigations in Number, Data, and Space,” Christian tried breaking the problem into easier-to-digest numbers.

But after several seconds, he got stumped. He drew lines connecting digits, and his computation amounted to an upside-down pyramid with numbers at the bottom. His father, in a teacherly tone, nudged him toward the old-fashioned method. “How would you do that another way?” Barlow asked.

In Prince William and elsewhere in the country, a math textbook series has fomented upheaval among some parents and teachers who say its methods are convoluted and fail to help children master basic math skills and facts. Educators who favor the series say it helps young students learn math in a deeper way as they prepare for the rigors of algebra.

The debate over “Investigations in Number, Data, and Space,” a Pearson School series used in thousands of elementary classrooms, including some in Arlington, Fairfax, Loudoun and Howard counties, is one of the newer fronts in the math wars. Such battles over textbooks and teaching methods are fueled in part by the anxieties of parents who often feel powerless over their children’s education, especially in subjects they know.

The curriculum, introduced in the 1990s and updated in a second edition issued last fall, offers one answer to the nation’s increasingly urgent quest for stronger elementary math education. The nonprofit organization TERC, based in Cambridge, Mass., developed “Investigations” with support from the National Science Foundation.

Related Links:

- 35 of 37 UW Math Department members open letter to the Madison School District.
- Math Forum Audio / Video & Links
- West High School Math Teacher Letter
- UW Math Professor Emeritus Dick Askey reviews Madison School District Math performance information.
- NCTM Press Release
**NCTM Report**: Curriculum Focal Points. 18.9MB Full PDF report- Joanne notes that Kitchen Table Math compares NCTM’s new curriculum focal points to the sequence of topics in Singapore Math.

The idea that more time in school produces better results could get a small boost today with the release of international data from the Brookings Institution. The study finds adding 10 minutes of math instruction to an eighth-grader’s day translates into a jump in math skills.

The findings come as a handful of states and school districts experiment with packing more minutes into the school day and, in a few cases, more days into the year.

The study, which examined eighth-grade math scores in 20 countries, found that five of seven that added instructional minutes from 1995 to 2003 showed improved skills. Of the 13 countries that subtracted time, 10 got worse results. The three exceptions were Latvia, the Netherlands and the USA.

Most U.S. eighth-graders got 45 minutes of daily math instruction in 2003, down from 49 in 1995, but their scores on the Trends in Mathematics and Science Survey improved slightly. Researcher Tom Loveless says that is an anomaly, and more time in class could help boost scores. But even 450 more minutes of math, or two weeks’ worth, would shrink the gap between the USA and top-scorer Singapore by less than 5%, he says.

Students’ success in mathematics, and algebra specifically, hinges largely on their mastering a focused, clearly defined set of topics in that subject in early grades, the draft report of a federal panel concludes.

The long-awaited report of the National Mathematics Advisory Panel is still very much in flux. Members of the White House-commissioned group staged their 10th, and what was supposed to be their final, meeting in a hotel here Nov. 28, though they indicated that numerous revisions to the document are yet to come.

The panel spent most of a day debating and rewriting a 68-page draft of the report. The draft makes recommendations and findings on curricular content, learning processes, training and evaluation of teachers, instructional practices, assessment, and research as those topics apply to math in grades pre-K through 8.

“International and domestic comparisons show that American students have not been succeeding in the mathematical part of their education at anything like a leadership level,” the report says. “Particularly disturbing is the consistent finding that American students achieve in mathematics progressively more poorly at higher grades.”

The 19-member panel has reviewed an estimated 18,000 research documents and reports as part of its work, which began in 2006. But its draft document also bemoans the paucity of available research in several areas of math—including instruction and teacher training. Government needs to do more, it says, to support research with “large enough samples of students, classrooms, teachers, and schools to identify reliable effects.”

The draft attempts to define the core features of a legitimate school algebra course as opposed to one, the panelists said, that presents watered-down math under that course title. Topics in an algebra course should include concepts such as symbols and expressions, functions, quadratic relations, and others, it notes.

The working report also spells out specific concepts in math that are too often neglected in pre-K through grade 8 math instruction generally, such as fractions, whole numbers, and particular elements of geometry and measurement.

“We don’t spend enough time on them and we don’t assess them,” panel member Camilla Persson Benbow, an educational psychologist at Vanderbilt University in Nashville, Tenn., said of fractions. “[They’re] really not well mastered by schoolchildren.”

In arguing in behalf of a more focused curriculum in elementary and middle schools, the panel lists several “benchmarks for critical foundations” in prekindergarten through 8th grade math, leading to algebra. The goal is to develop fluency with fractions, whole numbers, and other topics. The panel drew from a diverse assortment of documents, including the 2006 “Curriculum Focal Points,” published by the National Council of Teachers of Mathematics, as well as Singapore’s national standards and a number of U.S. state math standards.

National Mathematics Advisory Panel Website

“Math Power: How to Help Your Child Love Math Even If You Dont’,” the only

book by a mathematician written for parents of children aged 1-10, is

about to go out of print for the second time. Both times the publisher

sold its trade books to another publisher just as it was published, so

none of the four publishers made any effort to publicize it. This time,

however, I have a good offer to buy the remaining copies. I really want

it to get into as many libraries as possible — and many hands. There

are many copies left.

If you can get a library to offer me a thank you note and give me the

address, I will send that library an autographed copy free for the tax

deduction. If you want an autographed copy, I will be glad to send you a

copy for $10. The price on the cover is $19.95, and it’s fine to resell

them at this time. If you can find an outlet or use them yourself, I can

send a box of 18 books for $140. (No autographs on those books because

they will be inside the box.) There are MANY boxes available.

“Math Power” had excellent reviews from both sides of the “Math Wars” when

it first appeared in 1997, and another from “The Library Journal,” but

without some publisher publicity, books don’t sell. It may be that math

is not a popular subject in this culture; there is other evidence.

Singapore’s National Institute of Education (NIE) and Vietnam’s National Institute of Education Management have signed a Memorandum of Understanding to set up a centre to train education professionals in Hanoi.

Vietnam’s Deputy Prime Minister and Minister of Education and Training Professor Dr Nguyen Thien Nhan and Singapore’s Education Minister and Second Finance Minister Tharman Shanmugaratnam witnessed the signing.

The Centre will focus on leadership training for Vietnam’s school principals, professional development for educational administrators and English language training.

Singapore Mathematics & Mathematics Education Academic Group.

Via a reader, interested in this issue:

Jessica Blanchard:

When Seattle elementary-schoolers open their math textbooks this fall, they’ll all be on the same page — literally.

In an attempt to boost stagnant test scores, elementary teachers will start using the same math textbooks and materials and covering lessons at the same time as their colleagues at other Seattle elementary schools, the School Board decided Wednesday.

“It’s clear to me that the math adoption is long overdue, and Seattle desperately needs a consistent and balanced approach,” board member Brita Butler-Wall said.

Lessons will now be taught using the conceptual “Everyday Math” books, which help students discover algorithms on their own and explore multiple ways to solve problems, and the more traditional “Singapore Math” books, which help hone students’ basic computation skills through repetition and problem solving. Teachers will follow the district’s guidelines for the order the lessons would be taught.

The Madison School District’s Math Task Force was introduced to the School Board last night. Watch the video or listen to the mp3 audio.

Background Links:

- Madison School Board Discusses Independent Math Review: Audio / Video.
- Math Forum Audio / Video
- UW Math Professor Dick Askey on the MMSD’s math scores; related: State test scores adjusted to match last year
- Isthmus Take Home Test on Curriculum
- Connected Math in Olympia, WA
- Lee Sensenbrenner on Connected Math
- The Politics of K-12 Math and Academic Rigor
- New Math Curriculum Draws Complaints

6th Grade Textbooks: Connected (left) and Singapore Math.

UPDATE: A reader emailed this:

I noticed that there were 10 student books in the 6th grade pile for CMP. That was surprising since there are only 8 in publication. Then I looked at the teacher editions and noticed there were 10 as well. There are two copies of both How Likely is It? and Covering and Surrounding.

The statement, “A quick look at the size of the Connected Math textbooks compared to the equivalent Singapore Math course materials illustrates the publisher and author interests in selling these large volumes irrespective of curriculum quality and rigor (not to mention the much larger potential for errors or the lost trees….)” is following the picture in one of the discussions. Taking a look at the Singapore Math website It appears that in addition to the 2 textbooks pictured and student workbooks pictured, there are Intensive Practice books, Extra Practice Books, and Challenging Word Problems books, as well as other resources. Also, the white book on the bottom of the pile appears to be an answer key. There are also teacher guides for 6A and 6B that are not in the picture.

I’m not suggesting the statement above is false, I would just like to point out that the picture being used is not an accurate comparison. I hope you find this information valuable.

Connected Math textbooks for one year and the equivalent Singapore Math version.

Brandon Lorenz:

A recent meeting at Central Middle School attracted about 50 people to discuss concerns with the district’s Connected Mathematics Project, a new constructivist approach that was introduced in sixth, seventh and eighth grades this year.

Another meeting for parents is scheduled for Dec. 13 at Horning Middle School.

Such new math programs rely on more hands-on activities and problem-solving skills than traditional programs.

Speaking with Zaborowski, Lynn Kucek said she was worried the math program would make it more difficult for her daughter, who does well in other subjects, to get into college.

More on Connected Math and the recent Math Forum.

It says the typical state math curriculum runs a mile wide and an inch deep, resulting in students being introduced to too many concepts but mastering too few, and urges educators to slim down those lessons.

Some scholars say the American approach to math instruction has allowed students to fall behind those in Singapore, Japan and a dozen other nations. In most states, they say, the math curriculum has swelled into a thick catalogue of skills that students are supposed to master to attain “proficiency” under the federal No Child Left Behind mandate.

Math Forum audio / video

Look around the business world and two things stand out: the modern economy places an enormous premium on brainpower; and there is not enough to go round.

But education inevitably matters most. How can India talk about its IT economy lifting the country out of poverty when 40% of its population cannot read? [MMSD’s 10th Grade Reading Data] As for the richer world, it is hard to say which throw more talent away—America’s dire public schools or Europe’s dire universities. Both suffer from too little competition and what George Bush has called “the soft bigotry of low expectations”.

Thursday’s meeting between Madison School Superintendent Art Rainwater, the MMSD’s Brian Sniff and the UW Math department included two interesting guests: UW-Madison Chancellor John Wiley [useful math links via the Chancellor’s website] and the Dean of the UW-Madison Education School. Wiley and the Ed School Dean’s attendance reflects the political nature of K-12 curriculum, particularly math. I’m glad Chancellor Wiley took time from his busy schedule to attend and look forward to his support for substantial improvements in our local math program.

*Typical of many math textbooks in the U.S., this one is thick, multicolored,and full of games,puzzles,and activities,to help teachers pass the time, but rarely challenge students. Singapore Math’s textbook is thin, and contains only mathematics — no games. Students are given briefexplanations, then confronted with problems which become more complex as the unit progresses.*

Barry Garelick [232K PDF]:

It was another body blow to education. In December of 2004, media outlets across the country were abuzz with news ofthe just-released results of the latest Trends in International Mathematics and Science Study (TIMSS) tests. Once again despite highly publicized efforts to reform American math education (some might say because of the reform efforts) over the past two decades, the United States did little better than average (see Figure 1). Headquartered at the International Study Center at Boston College and taken by tens of thousands of students in more than three dozen countries, TIMSS has become a respected standard of international academic achievement. And in three consecutive TIMSS test rounds (in 1995, 1999,and 2003), 4th- and 8th-grade students in the former British trading colony of Singapore beat all contenders, including math powerhouses Japan and Taiwan. United States 8th graders did not even make the top ten in the 2003 round; they ranked 16th. Worse, scores for American students were, as one Department of Education study put it,”among the lowest of all industrialized countries.”

Critics of “Fuzzy” Methods Cheer Educators’ Findings; Drills Without Calculators. Taking Cues from Singapore.

John Hechinger:

The nation’s math teachers, on the front lines of a 17-year curriculum war, are getting some new marching orders: Make sure students learn the basics.

In a report to be released today, the National Council of Teachers of Mathematics, which represents 100,000 educators from prekindergarten through college, will give ammunition to traditionalists who believe schools should focus heavily and early on teaching such fundamentals as multiplication tables and long division.

The council’s advice is striking because in 1989 it touched off the so-called math wars by promoting open-ended problem solving over drilling. Back then, it recommended that students as young as those in kindergarten use calculators in class.

Those recommendations horrified many educators, especially college math professors alarmed by a rising tide of freshmen needing remediation. The council’s 1989 report influenced textbooks and led to what are commonly called “reform math” programs, which are used in school systems across the country.

Francis Fennell, the council’s president, says the latest guidelines move closer to the curriculum of Asian countries such as Singapore, whose students tend to perform better on international tests. There, children focus intensely on a relative handful of topics, such as multiplication, division and algebra, then practice by solving increasingly difficult word and other problems. That contrasts sharply with the U.S. approach, which the report noted has long been described as “a mile wide and an inch deep.”

If school systems adopt the math council’s new approach, their classes might resemble those at Garfield Elementary School in Revere, Mass., just north of Boston. Three-quarters of Garfield’s students receive free and reduced lunches, and many are the children of recent immigrants from such countries as Brazil, Cambodia and El Salvador.

Three years ago, Garfield started using Singapore Math, a curriculum modeled on that country’s official program and now used in about 300 school systems in the U.S. Many school systems and parents regard Singapore Math as an antidote for “reform math” programs that arose from the math council’s earlier recommendations.

The Singapore Math curriculum differs sharply from reform math programs, which often ask students to “discover” on their own the way to perform multiplication and division and other operations, and have come to be known as “constructivist” math.

Links:

- 35 of 37 UW Math Department members open letter to the Madison School District.
- Math Forum Audio / Video & Links
- West High School Math Teacher Letter
- UW Math Professor Emeritus Dick Askey reviews Madison School District Math performance information.
- NCTM Press Release
**NCTM Report**: Curriculum Focal Points. 18.9MB Full PDF report- Joanne notes that Kitchen Table Math compares NCTM’s new curriculum focal points to the sequence of topics in Singapore Math.

Strong parent and teacher views on the MMSD’s math strategy may well spill over to non-support for referendums and incumbent board members, particularly in light of increasing UW Math Department activism on this vital matter.

R. James Milgram 15MB e-book pdf:

It has long been felt that the mathematical preparation of pre-service teachers throughout the country has been far too variable, and often too skimpy to support the kind of outcomes that the United States currently needs. Too few of our K – 12 graduates are able to work in technical areas or obtain college degrees in technical sub jects. This impacts society in many and increasingly harmful ways, and it is our failure in K – 8 mathematics instruction that is at the heart of the problem.

This is especially true when we compare outcomes in the United States with outcomes in countries that do a better job of teaching mathematics, countries such as Poland, Hungary, Bulgaria, Romania, Singapore, China, and Japan, to name a few.

It has also been increasingly recognized that if we are to improve our performance in K – 8 mathematics instruction, pre-service teachers should take focused, carefully designed courses directly from the mathematics departments, and not, as is often the case, just a single math methods course taught in the Education School. A focused two year sequence in the basic mathematics teachers have to know is the minimal mathematics sequence that pre-service teachers need in order to to successfully teach students in K – 8.

Video and audio from Wednesday’s Math Forum are now available [watch the 80 minute video] [mp3 audio file 1, file 2]. This rare event included the following participants:

- Dick Askey (UW Math Professor)
- Faye Hilgart, Madison Metropolitan School District
- Steffen Lempp (MMSD Parent and UW Math Professor)
- Linda McQuillen, Madison Metropolitan School District
- Gabriele Meyer (MMSD Parent and a UW Math Department Lecturer)
- Dr. Terry Millar of the Wisconsin Center for Education Research
The conversation, including audience questions was lively.

The books are distributed by an Oregon-based company known as SingaporeMath.com, which counts a private school in Madison as the first of its growing number of clients.

The biggest difference between math instruction in Singapore – a city-state with a population of about 4.4 million – and the United States is a simple premise: Less is more.

Students in Singapore are introduced to roughly half the number of new math topics a year as students in the United States are. Experts and policy analysts say Singapore’s emphasis on depth over breadth is a formula for success.

The thicker the textbooks and the greater the volume of math topics introduced a year, the less likely American students and teachers are to achieve similar results, says Alan Ginsburg, director of the policy and program studies service at the U.S. Department of Education.

More on the Connected Math / Singapore Math textbook photos.

Madison Country Day School was the first US school to purchase Singapore Math textbooks, in 1997, according to this article.

The problems with CMP go far beyond failing to reach parents. One big problem is that the edifice of mathematics is so huge. Think of how long it took mathematicians to discover all of it. When one tries to use the discovery paradigm as the sole model for math lessons, all of the time available is spent in discovery process of basic concepts. There isn’t time for more than a cursory look at any topic. There isn’t any work on hard problems related to basic concepts. There isn’t time to master computational aspects of basic concepts. Everyone learns 1/2 + 1/4, but no one learns how to find the least common denominator of 1/14 and 1/35. The people who promote a constructivist approach to math set up a false dichotomy between traditional math which teaches one to memorize formulas and tables of computations, and discovery math which teaches one to really understand how math works. I actually had a TAG resource teacher say this to me very patronizingly. “We don’t teach math anymore the way that YOU learned it. Now children really understand math when they learn it.” Excuse me, but traditional math was never like that. Tradtional math presents concepts AND teaches understanding of concepts. One learns formulas AND why they work. One also does large numbers of progressively more difficult computations to become skilled at them. The problem with traditional math is that large numbers of students don’t understand the concepts as presented and try to get by with memorizing and manipulating formulas which they don’t understand. They also don’t master the computational aspects and try to make up for this deficit by using calculators inappropriately.

Newsweek International Edition columnist Fareed Zakaria interviewed Singapore Minister of Education Tharman Shanmugaratnam to understand why he believes Singapore students score tops in math and science on international tests, but lacks leaders in business, academia, math and science in the professional world.

Shanmugaratnam’s sees driving ambition, creativity, and adventuresomeness as lacking in Singapore students — characteristics that are not measured in global testing. He says, “Most of all, America has a culture of learning that challenges conventional wisdom, even if it means challenging authority. ”

Funding and academic-private partnerships are another factor in U.S. favor, he says. Foundations are critical for funding research in the U.S. “For example, you could not imagine American advances in biomedical sciences without the Howard Hughes Foundation,” says Shanmugaratnam.

But Shanmugaratnam is not all praise for U.S. education system. “[It] as a whole has failed. Unless you are comfortably middle class or richer,” he explained, “you get an education that is truly second-rate by any standards…. In Singapore we get the poor kid who is very bright and very hungry, and that’s crucial to our success.”

A year’s worth of Connected Math textbooks and teacher guides are on the left while the equivalent Singapore Math texts are on the right.

Friedman’s latest ,where he demonstrates how other countries are “eating our kid’s lunch in math” is well worth reading, as are these www.schoolinfosystem.org math posts. UW Math Professor Dick Askey has much more to say on K-12 math curriculum.

A few observations from a layperson who couldn’t be farther from a math expert’s perspective on this (in other words, I’m not a math expert):

- Children must be able to read effectively to use the voluminous Connected Math curriculum,
- The Connected Math curriculum has very extensive teacher instructions, while the Singapore curriculum is rather thin in this area. Does it follow that teachers using Singapore Math have far more freedom with respect to their instruction methods, or is the intention to make sure that teachers teach Connected Math in a scripted way?
- The Connected Math texts require more dead trees and I assume cost more than the Singapore texts directly and indirectly (transportation, packaging and the overhead of dealing with more pieces)
- The voluminous Connected Math texts have far more opportunities for errors, simply based on the amount of text and illustrations included in the books.
- Madison Country Day School uses Singapore Math.

There’s quite a bit of discussion on Connected Math and Singapore Math around the internet. Maybe it’s time to follow the www.heymath.net people (from India, China and Great Britain) and virtualize this while eliminating the textbooks?

Post your comments below.

A reader forwarded this article: Jay Mathews, writing in the Washington Post:

So when I found a new attack on the National Council of Teachers of Mathematics (NCTM), the nation’s leading association for math teachers, by a group of smart advocates, I saw a chance to bring some clarity to what we call the Math Wars. For several years, loosely allied groups of activist teachers and parents with math backgrounds have argued that we are teaching math all wrong. We should make sure that children know their math facts — can multiply quickly in their heads and do long division without calculators, among other things — or algebra is going to kill them, they say. They blame the NCTM, based in Reston, Va., for encouraging loose teaching that leaves students to try to discover principles themselves and relies too much on calculators.

The model method is a very powerful problem-solving strategy extensively used in the Primary Mathematics curriculum in Singapore, sometimes referred to as “Singapore Math” by other countries. Model Method help students visualize and simplify a math problem in a pictorial way. It was developed and popularized by Mr Hector Chee, a Singapore teacher, in 1990s.

Versatile and used in various topics

It is used to teach a wide range of Mathematics topics taught in the Primary Mathematics curriculum in Primary schools (elementary schools). Some of these include arithmetic, fractions, percentage, decimals, average, ratio and of course various problem sums testing these topics. It provides the pictorial perspective of the Mathematical problems and also provides easy analysis of ‘parts whole’ and comparison between quantities

The Madison School Board has scheduled [PDF] a 2:00p.m. meeting tomorrow, Sunday 30 September for an “Initial exchange of proposals and supporting rationale for such proposals in regard to collective bargaining negotiations regarding the Collective Bargaining Agreements (CBA) for MMSD Madison Teachers, Inc. (MTI) Teachers, Substitute Teachers, Educational Assistants, Supportive Educational Employees (SEE), and School Security Assistants (SSA), held as a public meeting pursuant to Wis. Stat. §111.70(4)(cm)”.

The School Board along with other Madison area governments have moved quickly to negotiate or extend agreements with several public sector unions after a judicial decision overturning parts of Wisconsin’s Act 10. The controversial passage of Act 10 changed the dynamic between public sector organizations and organized labor.

I’ve contemplated these events and thought back to a couple of first hand experiences:

In the first example, two Madison School District teacher positions were being reduced to one. Evidently, under the CBA, both had identical tenure so the choice was a coin toss. The far less qualified teacher “won”, while the other was laid off.

In the second example, a Madison School District teacher and parent lamented to me the poor teacher one of their children experienced (in the same District) and that “there is nothing that can be done about it”.

In the third example, a parent, after several years of their child’s “mediocre” reading and writing experiences asked that they be given the “best teacher”. The response was that they are “all good”. Maybe so.

Conversely, I’ve seen a number of teachers go far out of their way to help students learn, including extra time after school and rogue curricula such as phonics and Singapore Math.

I am unaware of the School Board meeting on a Sunday, on short notice, to address the District’s long time reading problems.

A bit of background:

Exhibit 1, written in 2005 illustrating the tyranny of low expectations” “When all third graders read at grade level or beyond by the end of the year, the achievement gap will be closed…and not before”.

Exhibit 2, 60% to 42%: Madison School District’s Reading Recovery Effectiveness Lags “National Average”: Administration seeks to continue its use.

Ripon Superintendent Richard Zimman’s 2009 Madison speech to the Madison Rotary Club is worth reading:

“Beware of legacy practices (most of what we do every day is the maintenance of the status quo), @12:40 minutes into the talk – the very public institutions intended for student learning has become focused instead on adult employment. I say that as an employee. Adult practices and attitudes have become embedded in organizational culture governed by strict regulations and union contracts that dictate most of what occurs inside schools today. Any impetus to change direction or structure is met with swift and stiff resistance. It’s as if we are stuck in a time warp keeping a 19th century school model on life support in an attempt to meet 21st century demands.” Zimman went on to discuss the Wisconsin DPI’s vigorous enforcement of teacher licensing practices and provided some unfortunate math & science teacher examples (including the “impossibility” of meeting the demand for such teachers (about 14 minutes)). He further cited exploding teacher salary, benefit and retiree costs eating instructional dollars (“Similar to GM”; “worry” about the children given this situation).

William Rowe has commented here frequently on the challenges of teacher evaluation schemes.

This being said, I do find it informative to observe the Board’s priorities in light of the District’s very serious reading problems.

This article is worth reading in light of local property taxes and spending priorities: The American Dream of upward mobility has been losing ground as the economy shifts. Without a college diploma, working hard is no longer enough.

Unlike his parents, John Sherry enrolled in college after graduating from high school in Grand Junction, a boom-bust, agriculture-and-energy outpost of 100,000 inhabitants on Colorado’s western edge. John lasted two years at Metropolitan State University in Denver before he dropped out, first to bag groceries at Safeway, later to teach preschool children, a job he still holds. He knew it was time to quit college when he failed statistics two semesters in a row. Years passed before John realized just how much the economic statistics were stacked against him, in a way they never were against his father.

Greg Sherry, who works for a railroad, is 58 and is chugging toward retirement with an $80,000-a-year salary, a full pension, and a promise of health coverage for life. John scrapes by on $11 an hour, with few health benefits. “I feel like I’m working really hard,” he says, “but I’m not getting ahead.”

This isn’t the lifestyle that John’s parents wished upon their younger child. But it reflects the state of upward–or downward–mobility in the American economy today.

Related: Wisconsin State Tax Based K-12 Spending Growth Far Exceeds University Funding.

TJ Mertz comments on collective bargaining, here and here.

Madison School Board Member Ed Hughes: Didn’t See That One Coming: How the Madison School Board Ended Up Back in Collective Bargaining.

The Capital Times: Should local governments negotiate with employees while the constitutionality of the collective bargaining law is being appealed?

New city statistics are showing a steep decline in parent involvement in New York public schools, giving potential ammunition to critics who say the Department of Education under Mayor Michael Bloomberg has been unresponsive to families.

City officials attributed part of the plummet to a new data-collection system. But critics, including some possible mayoral contenders, said the numbers in the annual Mayor’s Management Report were hard evidence of long-held frustrations by public-school parents.

I wonder if Madison PTO attendance patterns have changed? During the 2000’s, most meetings that I observed or participated in typically had no more than 12 to 15 parents. Often less than 10 appeared.

One meeting sticks out. More than 50 parents attended a Thoreau PTO meeting which attempted to bring Singapore Math to the school. That was a spectacular failure, unfortunately.

Poor numeracy is blighting Britain’s economic performance and ruining lives, says a new charity launched to champion better maths skills.

The group, National Numeracy, says millions of people struggle to understand a payslip or a train timetable, or pay a household bill.

It wants to challenge a mindset which views poor numeracy as a “badge of honour”.

It aims to emulate the success of the National Literacy Trust.

Related:

Natasha Singer & Danielle Ivory:

Silicon Valley is going all out to own America’s school computer-and-software market, projected to reach $21 billion in sales by 2020. An industry has grown up around courting public-school decision makers, and tech companies are using a sophisticated playbook to reach them, The New York Times has found in a review of thousands of pages of Baltimore County school documents and in interviews with dozens of school officials, researchers, teachers, tech executives and parents.

Related: Madison’s long term, disastrous reading results and

“Kids aren’t going to be able to take risks and push themselves academically, without having a trusting support network there,” said Lindsay Maglio, principal of Lindbergh Elementary School, where some teachers improved on traditional get-to-know-you exercises in the first few weeks of school by adding more searching questions, and where all school staff are engaged in community-building lessons in small-group sessions with students taking place at set periods throughout the year.

While noting that getting to know their students is already “something we do feel strongly about,” fourth-grade teacher Beth Callies, now in her 11th year at Lindbergh, said she saw value in a districtwide strategy emphasizing it. “It’s a good push to remind us,” Callies said.

Beyond asking her students to describe themselves through traditional questions such as choosing what animal or what TV show they would like to be, and where they would like to take a vacation and why, Duernberger also invited them to free-associate this year by responding to the line: “I wish my teacher knew this about me.”

Common ground

The students’ answers, which they also read to each other in a follow-up exercise, were as varied as their life stories. Students said they liked to go camping, had two brothers, worked hard, could read-upside down, and had two dogs at home before mom gave one away.Teachers have been encouraged to mine a book by educator Zaretta Hammond known as “Culturally Responsive Teaching and the Brain” for new techniques and deeper understanding of the issue. At Lindbergh, Maglio built time into the school day for all staff to meet once a week for 40 minutes with students in small groups “to build community and work on trust,” with possible lessons on topics such as resolving conflicts or bullying.

“It’s really based off the issues that kids are having, so there’s not a set structure (for the weekly sessions),” Maglio said. “We just need to think about being more purposeful in how we plan for all our students. It might be working for 80 percent of students, but we need to think more about the ones we may be struggling to reach.”

Madison has long tolerated disastrous reading results, despite spending more than most – now nearly $20,000 per student.

A Project Baltimore investigation has found five Baltimore City high schools and one middle school do not have a single student proficient in the state tested subjects of math and English.

We sat down with a teen who attends one of those schools and has overcome incredible challenges to find success.

Related: Math Forum

Two interesting notes, among many, I’m sure from Monday evening’s Madison School Board meeting:

- Johnny Winston, Jr. introduced a motion for the Administration to look at acquiring land in Fitchburg for a new school. This motion passed 5-1, with Bill Keys voting no (and Juan Jose Lopez absent).
- Ruth Robarts advocated curriculum changes as a means to attract more families to certain schools. She mentioned the use of Singapore Math (Note that some Madison residents are paying a chunk of money to send their children to Madison Country Day School, which uses Singapore Math).

Speaking of Math, Rafael Gomez is organizing a middle school math forum on February 22, 2006, from 7 to 8:00p.m.

Local news commentary:

- Channel3000:

*The Madison Metropolitan School Board met for hours Monday discussing overcrowding options for the looming referendum* - WKOW-TV:

*After nearly five hours of discussion, the Madison School Board decided to put off asking tax payers for a new school in April and says voters may have to head to the polls this fall instead.* - Susan Troller:

*That potential option was added to the mix regarding how the Madison School District could deal with growth and overcrowding on the west side following a special School Board meeting Monday night.*

Board Vice President Johnny Winston, Jr. led a motion to ask district administrators to explore land sites and options for a possible new school in the rapidly developing areas south of the Beltline in Fitchburg, including land currently in the Verona and Oregon school districts.

Board member Lawrie Kobza supported Winston’s motion and said she may be willing to support a new elementary school in the south Fitchburg area as part of a long-range plan for the district. Kobza does not support an addition at Leopold, saying the school already has more than 650 students, which the district has deemed its maximum acceptable capacity. - Sandy Cullen:

*The Madison School Board voted Monday to direct district administrators to investigate purchasing land for a future school in south Fitchburg as a long-term solution to crowding at Leopold Elementary School, while board members continue to explore a more immediate solution to the problem.*

schoolinfosystem.org