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103 results found.

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.

Today’s disagreement is about the “math wars.”

The “math wars” is a debate happening in K-12 education about the best way to teach math. Broadly speaking, there are two camps that have conflicting pedagogical approaches:

Explicit instruction focuses on procedural fluency, guided practice, and repetition.

Inquiry-based instruction focuses on conceptual understanding, open-ended problems, and productive struggle.

This is an incredibly high-stakes debate — especially if you have children or loved ones that are currently receiving K-12 math instruction. To explore its contours, we’ve brought on two math education experts

——

Math Forum audio/video.

Brian Conrad, a math professor and director of undergraduate math education at Stanford, is guilty of “academic and professional misconduct” for pointing out errors in the California math framework, claims a letter to the university provost. The letter signed by Duane Habecker, a math administrator, charges that Conrad has “ventured into stochastic terrorism” — encouraging violence — for criticizing the work of Jo Boaler, a Stanford education professor who was one of the authors of the framework

—

More.

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Math Forum audio and video.

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The complaint may appear overly repetitive, but that’s because it’s documenting an ongoing pattern of disregard for accuracy. Each repeated instance of the same inaccuracy matters.

The repetition is evidence, not personal attack, and the inaccuracies remain unaddressed. 4/7

Now, a district math official has accused him of “stochastic terrorism” for this public criticism.

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.

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

When Akihiko Takahashi was a junior in college in 1978, he was like most of the other students at his university in suburban Tokyo. He had a vague sense of wanting to accomplish something but no clue what that something should be. But that spring he met a man who would become his mentor, and this relationship set the course of his entire career.

Takeshi Matsuyama was an elementary-school teacher, but like a small number of instructors in Japan, he taught not just young children but also college students who wanted to become teachers. At the university-affiliated elementary school where Matsuyama taught, he turned his classroom into a kind of laboratory, concocting and trying out new teaching ideas. When Takahashi met him, Matsuyama was in the middle of his boldest experiment yet — revolutionizing the way students learned math by radically changing the way teachers taught it.

Instead of having students memorize and then practice endless lists of equations — which Takahashi remembered from his own days in school — Matsuyama taught his college students to encourage passionate discussions among children so they would come to uncover math’s procedures, properties and proofs for themselves. One day, for example, the young students would derive the formula for finding the area of a rectangle; the next, they would use what they learned to do the same for parallelograms. Taught this new way, math itself seemed transformed. It was not dull misery but challenging, stimulating and even fun.

2006: Math Forum audio video

I am not at all qualified to introduce today’s guest writer, Sergiu Klainerman.

I barely eked out a C+ in high school calculus, while Sergiu is a professor of mathematics at Princeton who specializes in the mathematical theory of black holes. He’s been a MacArthur fellow, a Guggenheim fellow and is a member of the National Academy of Sciences

Mathematics allowed a young Sergiu, who came of age in Ceausescu’s Romania, to escape to a world where right and wrong couldn’t be fudged, and, ultimately, to a life of freedom in the United States. Without math, his life quite literally would not have been possible.

In the piece below he explains how activists are destroying his discipline in the name of progress. Worse, they are robbing poor children of the opportunity to raise themselves up by mastering it — with untold effects on all of us.

Math, with its seemingly unbiased tools — 2 + 2 always equals 4 — has presented a problem for an ideological movement that sees any inequality of outcome as evidence of systemic bias. The problem cannot be that some kids are better at math, or that some teachers are better at teaching it. Like so much else, the basic woke argument against math is that it is inherently racist and needs to be made antiracist. That is accomplished by undermining the notion of right and wrong answers, by getting rid of the expectation that students show their work, by referring to mathematical testing tools as racist, and by doing away with accelerated math classes.

If that sounds like a caricature, I urge you to read this whole document, funded by the Bill and Melinda Gates Foundation, which Sergiu writes about below. As the linguist John McWhorter put it in a powerful piece published yesterday: “to distrust this document is not to be against social justice, but against racism.”

Sergiu wrote me in an email that the situation in his field reminds him of this line from Thomas Sowell: “Ours may become the first civilization destroyed, not by the power of enemies, but by the ignorance of our teachers and the dangerous nonsense they are teaching our children. In an age of artificial intelligence, they are creating artificial stupidity.”

This week, as promised, is education week. Like Shark Week! But dorkier. And, I hope, far more important. This is our first installment.

I’m pleased to publish Sergiu Klainerman:

In my position as a professor of mathematics at Princeton, I have witnessed the decline of universities and cultural institutions as they have embraced political ideology at the expense of rigorous scholarship. Until recently — this past summer, really — I had naively thought that the STEM disciplines would be spared from this ideological takeover.

I was wrong. Attempts to “deconstruct” mathematics, deny its objectivity, accuse it of racial bias, and infuse it with political ideology have become more and more common — perhaps, even, at your child’s elementary school.

This phenomenon is part of what has been dubbed “The Great Awokening.” As others have explained powerfully, the ideology incubated in academia, where it indoctrinated plenty of bright minds. It then migrated, through those true believers, into our important cultural, religious and political institutions. Now it is affecting some of the country’s most prominent businesses.

Unlike the traditional totalitarianism practiced by former communist countries, like the Romania I grew up in, this version is soft. It enforces its ideology not by jailing dissenters or physically eliminating them, but by social shaming, mob punishment, guilt by association, and coerced speech.

When it comes to education, I believe the woke ideology is even more harmful than old-fashioned communism.

Communism had a strong sense of objective reality anchored in the belief that humans are capable of discovering universal truths. It forcefully asserted, in fact, the absolute truth of dialectic materialism, as revealed by its founders Marx, Engels and Lenin. Communist ideology held science and mathematics in the highest regard, even though it often distorted the former for doctrinal reasons.

Mathematics was largely immune to ideological pressure, and thus thrived in most communist countries. Being skilled in math was a source of great societal prestige for school children. And it was a great equalizer: those from socioeconomically disadvantaged families had a chance to compete on equal footing with those from privileged ones.

Related:

Math Forum audio / video

As part of social distancing efforts to slow down the spread of the novel coronavirus, several universities have now transitioned, or begun transitioning, to online teaching models. (My home university of UCLA has not yet done so, but is certainly considering the option. UPDATE: we are transitioning.) As a consequence, I thought it might be an appropriate time to start a discussion on the pros and cons of various technologies for giving talks and lectures online, particularly in the context of mathematical talks where there may be special considerations coming for instance for the need to do mathematical computations on a blackboard or equivalent. My own institution is for instance recommending the use of Zoom for lectures and Respondus for giving finals, and has a limited number of classrooms set up for high quality video and audio casting, as well as a platform for discussion forums and course materials for each class. For smaller meetings, such as one-on-one meetings with graduate students, one can of course improvise using off-the-shelf tools such as Skype. I would be interested in knowing what other options are available and what success lecturers have had with them.

But what will happen to math achievers who do want to take calculus and pursue STEM majors in college? Will they get what they need in untracked classes?

Black students are more likely to wait until 11th or 12th grade to take Algebra 1, according to the U.S. Education Department, he reports in an earlier story. Native Americans have similar patterns.

“Research indicates that forcing students to take Algebra I before they’re ready can be harmful,” writes Sawchuk. “Is it because they’ve correctly assessed students’ ability and put them in the appropriate course?” said Joshua Goodman, an associate professor of public policy at Harvard’s Kennedy School. “Or is it because there’s some amount of discrimination going on?”

Related: Math Forum Audio/Video.

Nearly every state includes measures of college- and career-readiness in their accountability plans under the Every Student Succeeds Act, and the quality of classroom assignments can help gauge whether students are being prepared for success beyond high school.

What is Equity In Motion?

In this series, we look at how issues or equity are playing out in the daily activities of schools and educators. Specifically, do classroom assignments reflect the more rigorous standards for college- and career-readiness?

Math Forum audio and video.

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):

This is just simple math. People compare some “big ticket” item with “small ticket” items and don’t mention how the very large numbers of those small ticket items add up, or how very little the large ticket item would really stretch among the many to whom those small ticket items apply.

So when someone says “if we can afford X, then surely Y isn’t too expensive” take a closer look. Just how much of those “Y” do we have to buy and how much is the total cost?

Related: Math Forum audio and video.

“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 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

For almost 30 years, math enthusiasts have been taking part in festivities on March 14 to honor an infinitely long number beginning with 3.14 – the ratio of a circle’s circumference to its diameter, otherwise known as pi.

The first official Pi Day was March 14, 1988, when physicist Larry Shaw led staff and visitors to San Francisco’s Exploratorium in a celebration of all things pi-related. Since then, it has been celebrated across the globe, with universities, conferences and even pizzerias honoring the day.

To mark Pi Day, here are four findings about math and education in the United States:

Related: Math Forum audio and video.

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.

Yet my children’s experience of school in America is in some ways as indifferent as their swimming classes are good, for the country’s elementary schools seem strangely averse to teaching children much stuff. According to the OECD’s latest international education rankings, American children are rated average at reading, below average at science, and poor at maths, at which they rank 27th out of 34 developed countries. At 15, children in Massachusetts, where education standards are higher than in most states, are so far behind their counterparts in Shanghai at maths that it would take them more than two years of regular education to catch up.

This is not for lack of investment. America spends more on educating its children than all but a handful of rich countries. Nor is it due to high levels of inequality: the proportion of American children coming from under-privileged backgrounds is about par for the OECD. A better reason, in my snapshot experience of American schooling, is a frustrating lack of intellectual ambition for children to match the sporting ambition that is so excellently drummed into them in our local swimming pool and elsewhere.

My children’s elementary school, I should say, is one of America’s better ones, and in many ways terrific. It is orderly, friendly, well-provisioned and packed with the sparky offspring of high-achieving Washington, DC, commuters. Its teachers are diligent, approachable and exude the same relentless positivity as the swimming instructors. We feel fortunate to have them. Yet the contrast with the decent London state school from which we moved our eldest children is, in some ways, dispiriting.

After two years of school in England, our six-year-old was so far ahead of his American peers that he had to be bumped up a year, where he was also ahead. This was partly because American children start regular school at five, a year later than most British children; but it was also for more substantive reasons.

Related: Connected Math, Discovery Math and the Math Forum (audio and video).

Reading requires attention as well. (MTEL)

Locally, Madison has long tolerated disastrous reading results despite spending more than most, now around $18k per student.

And, National Council on teacher quality links are worth a look.

If we could snap our fingers and change the way math and science are taught in U.S. schools, most of us would. The shortcomings of the current approach are clear. Subjects that are vibrant in the minds of experts become lifeless by the time they’re handed down to students. It’s not uncommon to hear kids in Algebra 2 ask, “When are we ever going to use this?” and for the teacher to reply, “Math teaches you how to think,” which is true — if only it were taught that way.

To say that this is now changing is to invite an eye roll. For a number of entrenched reasons, from the way teachers are trained to the difficulty of agreeing on what counts in each discipline, instruction in science and math is remarkably resistant to change.

That said, we’re riding the next big wave in K-12 science and math education in the United States. The main events are a pair of highly visible but often misunderstood documents — the Common Core math standards and the Next Generation Science Standards (NGSS) — that, if implemented successfully, will boldly remake the way math and science are taught. Both efforts seek to recast instruction in the fundamental ideas and perspectives that animate the two fields.

“What we did in reorganizing the content of school mathematics was long overdue,” said Phil Daro, one of three lead authors of the Common Core math standards.

The changes go beyond the contentious new methods of teaching arithmetic that have grabbed headlines and threatened to blunt the momentum of Common Core math. Both documents developed out of decades of academic research on how children learn, and they reflect similar priorities. They exhibit an elegant rethinking of the basic structure of knowledge, along with new assertions of what’s important for students to be able to do by the time they finish high school.

Related: Connected Math; Math Forum audio and video.

Wayne State University has subtracted mathematics from the list of classes all students must take to graduate.

Up until now, students had to take one of three different math classes before they could earn their degree.

Now, depending on their major, students may be able to squeak through college without taking math. The university is leaving it up to the individual departments to decide whether math will be a required part of a degree’s curriculum.

That means the nursing program will be responsible for setting one level of math students must pass in order to graduate, while the journalism department could set a completely different standard.

“We felt the math requirement was better left to the various programs and majors to decide and to decide what levels of mathematics would be needed,” Monica Brockmeyer, associate provost for student success, told the Free Press.. “We still continue to support mathematics at Wayne State.”

Indeed, in a note sent out late last month to students announcing the change, the university said it “strongly encouraged” students to take mathematics as an elective. The note said two of the foundation classes are still important to take for students looking to go into STEM fields and that the Mathematics in Today’s World class “does an excellent job in introducing students to many important applications of mathematics.”

Related: Math Forum.

Teachers pack their items outside of Everest College, in City of Industry, California, one of the shuttered Corinthian Colleges.

Last year, I met fifteen former students and graduates of Corinthian Colleges who had taken a remarkable action to protest the collection of their student debt. Corinthian, a for-profit institution that was, at the time, facing a financial meltdown and several lawsuits over alleged fraud in its recruitment process, had recently started shutting down or selling off its campuses. The students, calling themselves the Corinthian Fifteen, had organized a “debt strike,” refusing to repay their student loans even at the risk of going into default. Their argument was that the Department of Education shouldn’t collect on loans that students were misled into incurring, especially since they earned a degree that was all but worthless or, in some cases, found that their college had shut down before they could graduate.

Related: connected math and the math forum audio/video.

The nation’s high school seniors have shown no improvement in reading achievement and their math performance has slipped since 2013, according to the results of a test administered by the federal government last year.

The results of the National Assessment of Educational Progress, or NAEP, also show a longer-term stagnation in 12th-grade performance in U.S. public and private schools: Scores on the 2015 reading test have dropped five points since 1992, the earliest year with comparable scores, and are unchanged in math during the past decade.

“These numbers are not going the way we want,” said William J. Bushaw, executive director of the National Assessment Governing Board, an independent panel established by Congress to oversee NAEP policy. “We have to redouble our efforts to prepare our students.”

The sobering news, released Wednesday, comes at the same time the nation is celebrating its highest-ever graduation rate, raising questions about whether a diploma is a meaningful measure of achievement.

Eighty-two percent of high school seniors graduated on time in 2014, but the 2015 test results suggest that just 37 percent of seniors are academically prepared for college coursework in math and reading — meaning many seniors would have to take remedial classes if going on to college.

Related: Math Forum audio/video links.

Katherine Beals & Barry Garelick:

“In general, there is no more evidence of “understanding” in the explained solution, even with pictures, than there would be in mathematical solutions presented in a clear and organized way. How do we know, for example, that a student isn’t simply repeating an explanation provided by the teacher or the textbook, thus exhibiting mere “rote learning” rather than “true understanding” of a problem-solving procedure?

“Math learning is a progression from concrete to abstract. The advantage to the abstract is that the various mathematical operations can be performed without the cumbersome attachments of concrete entities—entities like dollars, percentages, groupings of pencils. Once a particular word problem has been translated into a mathematical representation, the entirety of its mathematically relevant content is condensed onto abstract symbols, freeing working memory and unleashing the power of pure mathematics. That is, information and procedures that have been become automatic frees up working memory. With working memory less burdened, the student can focus on solving the problem at hand. Thus, requiring explanations beyond the mathematics itself distracts and diverts students away from the convenience and power of abstraction. Mandatory demonstrations of “mathematical understanding,” in other words, can impede the “doing” of actual mathematics.”

Related: Math Forum: audio/video.

I notice that the kid didn’t write them as (x,y) but wrote them as x,y. I wonder how come he did that? Or, more precisely, I wonder if he doesn’t see much of a difference between (x,y) and x,y or if three is some other reason for leaving off the parentheses.

Related: Math Forum audio & video.

Mathematicians often deal in abstractions that are quite beyond the ken of non-mathematicians. For instance, in 1637, the Frenchman Pierre de Fermat conjectured that there is no whole-number solution for the equation An + Bn = Cn where N is greater than two. He famously wrote in the margin of a book that he had a proof for it, but he never wrote it down.

Most people think Fermat was mistaken, for the proof became a sort of holy grail of mathematicians. And it wasn’t until 1995 that the British professor Andrew Wiles published a proof of Fermat’s conjecture, using many 20th century techniques that were unavailable to Fermat. The proof runs 109 pages, and—trust me on this—if you don’t have a Ph.D. in math, you won’t understand a word of it.

Related: Math Forum audio/video and Connected Math.

Scientific American writes about rescuing the enormous theorem (classification of finite simple groups) before the proof vanishes. How can a proof vanish?

In mathematics and theoretical computer science, we read research papers primarily to find research questions to work on, or find techniques we can use to prove new theorems. What happens to a research area then when researchers go elsewhere?

In a response to a question about how can one contribute to mathematics, Bill Thurston notes that our knowledge of mathematics can deteriorate over time.

Related: Math Forum and “connected math“.

New waves of Indians and Chinese are taking America’s business-school entrance exam, and that’s causing a big problem for America’s prospective M.B.A.s.

Why? The foreign students are much better at the test.

Asia-Pacific students have shown a mastery of the quantitative portion of the four-part Graduate Management Admission Test. That has skewed mean test scores upward, and vexed U.S. students, whose results are looking increasingly poor in comparison. In response, admissions officers at U.S. schools are seeking new ways of measurement, to make U.S. students look better.

Domestic candidates are “banging their heads against the wall,” said Jeremy Shinewald, founder and president of mbaMission, a New York-based M.B.A. admissions-consulting company. While U.S. scores have remained consistent over the past several years, the falling percentiles are “causing a ton of student anxiety,” he said.

we continue to play in the “C” (D?) leagues.

Madison’s disastrous reading scores.

Math forum audio and video. Math task force.

Madison School Board Accountabilty Commentary.

Before Common Core I was a typical math teacher. I had my curriculum maps and and state standards which read like a skill and drill check list that I marked off one by one whether the kids understood them or not. I used really “great” methods and math terminology like “butterfly method”, “keep switch flip”, “leave opposite opposite”, and so many more that I would love to forget. I moved to Kentucky the year that KCAS (Kentucky’s Common Core) was adopted and thought “how different could it be?” The answer to that question can be answered easily with a quick peak inside my classroom today.

Today, my classroom is cognitively busy and alive with excitement about numbers. We no longer focus on skills, timed tests, facts, or catchy phrases to make students remember things that have no meaning to them. Today, we do math talks, counting circles, estimating, and reasoning instead of direct instruction. We take the time to understand numbers and their meanings rather than memorizing facts. I don’t drill random formulas and information into students heads so that they can remember it long enough to pass a test rather than understanding it to a depth that can be applied to real life.

I really do understand the reason so many parents seem to get upset about the “new math” associated with Common Core. After all, it is change and change is difficult but here is what I know. I have talked to tons of adults and not one has told me that they have to take skill and drill tests daily at work or risk being fired. When I ask what they have to do at work I get a lot of answers but there is always a common theme, in real life we are no longer asked to use math as a check list of skills that we either know or don’t know. Instead real life is about using the math to solve real problems, to be a critical thinker, to reason, and actually understand what is happening around them. Those are all the things along with many more that Common Core has brought to my classroom.

Much more on the Common Core, here.

Related: Math Forum Audio & Video.

Many of the graduates entering college from New York’s Hampton Bays High School in 2011 weren’t ready for higher education math.

At neighboring Suffolk County Community College, 68 percent of the first-year students from Hampton Bays had to take remedial math.

“These numbers were horrifying to us and created a real sense of urgency,” says Denise Sullivan, the assistant superintendent for curriculum at the Hampton Bays Schools.

Sullivan approached the college president to discuss the problem and forged an innovative partnership.

In an uncommon move, Sullivan and the chair of the mathematics department at the college created a high school course that mirrors the remedial class that students deficient in math have to take when they start college.

The college was “thrilled.” “Nobody else was taking this approach,” Sullivan says. The college had found that only 20 percent of the students who entered in need of developmental courses went on to graduate.

Related: Math Forum audio & video.

“When you look at the data, there’s something not working, clearly,” she said. “And if you know being on track in ninth grade is key to a student’s success then it’s our obligation to change that.”

She said the district will be strengthening the quality and consistency of algebra instruction across schools so that courses in each school approach the class the same. After the district’s review of high school curriculum is complete, the ninth-grade algebra requirement and graduation requirements could change.

Like Madison, districts across the state are looking at ways to improve rates at which students pass algebra and are also developing new curriculum that includes algebraic concepts as early as kindergarten, said Department of Public Instruction spokesman Tom McCarthy.

Signe Carney, who has taught math at Memorial High School for 18 years, said part of the reason for the algebra failure rate is that “people are OK with saying, ‘I’m bad at math,’ and they will never say they can’t read. People think they can or can’t, and if they think they can’t, they won’t succeed.”

Another factor is that algebraic concepts build on each other, so it’s hard to catch up if students miss days, she said.

Related:

What impact do high school mathematics curricula have on college-level mathematics placement? by James Wollack & Michael Fish @ UW Center for Placement Testing.

Math Forum Audio & Video (2008!).

Americans could use a crash course in math.

According to a new study from the Brookings Institution, jobs in science, technology, engineering and math are vacant for more than twice as long as other positions — largely because employers can’t find people with the math and science skills to fill them.In fact, high school graduates with science, technology, engineering and math (STEM) skills are in greater demand than college grads without them.

Related: Math Forum Audio & Video and wisconsin2.org.

But they don’t appear to do much financial training in Shanghai?

One of the report’s most interesting conclusions was that the best way of teaching financial literacy is not necessarily by instruction in the classroom. Far more important as indicators of proficiency were mathematical skills and personal experience with financial products.

So Chinese children, who score very highly on fundamental maths and science, are more likely to understand money-related concepts than those taught directly about banks, credit and interest rates. Countries such as the US or Slovak Republic, which had much higher levels of in-class teaching than Shanghai, performed worse when tested.

Andreas Schleicher, OECD education director, said: “The volume of exposure to financial literacy in the classroom has no relationship with performance. That is very different for maths or science teaching.”

The data also suggest having a bank account or managing phone credits gives a youngster much more opportunity – and motivation – to learn about financial concepts. On average, students in the 13 core OECD economies who held a bank account scored 33 points higher than those who did not.

Madison math forum audio and video and math task force.

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.

What could be so horrible? Grade-school math.

As schools around the U.S. implement national Common Core learning standards, parents trying to help their kids with math homework say that adding, subtracting, multiplying and dividing has become as complicated as calculus.

They’re stumped by unfamiliar terms like “rectangular array” and “area model.” They wrestle with division that requires the use of squares, slashes and dots. They rage over impenetrable word problems.

Related: Math Forum audio & video.

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.

The economic returns to education are well documented. It is also well-known that college graduates with certain majors will earn more than others and find it easier to land a job. But surprisingly, the courses students take in high school also make a difference, when the courses are mathematics. Even among workers with the same level of education, those with more math have higher wages on average and are less likely to be unemployed. These findings suggest that even students ending their formal education after high school can increase their future earnings by investing in more math courses while in high school.

High school graduates earn more money in general than high school dropouts. This well-known fact is a powerful incentive to finish high school. But is it just the diploma that counts, or do the particular courses students take while in high school matter for their future job prospects? Students can opt for a variety of courses, from vocational tracks to advanced placement classes for college credit, during their final four years of required education.

Most high school graduates choose a curriculum that is far more rigorous than the minimum requirements. This is most evident in mathematics courses. For example, in 2009, 75 percent of high school graduates completed math coursework at the level of Algebra II or above. Most of these students could have stopped at Algebra I and satisfied the minimum high school requirements. Only six states required Algebra II for graduation as of 2006. About 11 required Algebra I, six required geometry, and the remaining 27 required only that students complete a minimum of three years of mathematics at any level.

The fact that so many students take a rigorous math curriculum is not surprising given that a minimum of Algebra II is necessary for adequate college preparation. But an analysis of detailed high school transcript data and employment outcomes suggests that a more rigorous high school math curriculum benefits even those who do not go to college. While math may be difficult for many, our findings indicate that the payoffs for all students may be substantial.

Unsurprising, particularly when one encounters young people unable to comprehend cell phone costs, student loan terms or simply make change.

Related: Math Forum audio / video and Connected Math.

Donna St. George, via a kind reader’s email:

For another semester, Montgomery County high school students flunked their final exams in math courses in startlingly high numbers, according to new figures that show failure rates of 71 percent for Geometry and 68 percent for Algebra 1.

The numbers add to a phenomenon that goes back more than five years and came to widespread public attention this spring, setting off a wave of concern among parents as well as elected officials in the high-performing school system.

Latest math-exam figures show high failure rates persist in the high-performing school system.

The new figures, for exams given in June, show that failure rates worsened in Algebra 1 and Geometry; improved in Precalculus and Bridge to Algebra 2; and stayed fairly even in Algebra 2, Honors Precalculus, Honors Algebra 2 and Honors Geometry.

Overall, 45 percent of high school students in eight math courses failed their June finals — about 14,000 students out of roughly 31,000 enrolled.

Exactly what explains steep failure rates for exam-takers has been an issue of debate in recent months.

In a memo to the school board, School Superintendent Joshua P. Starr released a preliminary figure on test-skipping: As many as 500 students were no-shows for the Algebra 1 exam in June, accounting for one-sixth of the 2,912 students who failed the test.

Starr said student motivation was one of a half-dozen issues under study as a newly created math work group seeks to understand the failure problem and suggest ways to turn it around. Other possible causes cited include alignment between the curriculum and the exam, school system practices and policies, and the “cognitive demands” of the exam.

Related: Math Forum audio & video along with a number of connected matharticles.

2004 (!) Madison West High School math teacher letter to Isthmus on dumbing down the curriculum.

If I was a Seattle Public School parent, I would be getting angry now.

Why? Most Seattle students are receiving an inferior math education using math books and curriculum that will virtually insure they never achieve mastery in key mathematical subjects and thus will be unable to participate in careers that requires mathematical skills.

There are so many signs that a profound problem exists in this city. For example,

Parents see their kids unable to master basic math skills. And they bring home math books that are nearly indecipherable to parents or other potential tutors.

Nearly three quarters of Seattle Community College students require remediation in math.

Over one hundred Seattle students are not able to graduate high school because they could not pass state-mandated math exams.

Minority and economically disadvantaged students are not gaining ground in math.

Much more on Seattle’s math battles, here.

Related:

Community college students are needlessly assigned to remedial math classes to learn lessons they won’t use during their studies, according to new research from a Washington, D.C. group.

And the study also found that many high school graduates are not learning subjects they will need to use in their careers.

The study was produced by the Washington, D.C.-based National Center on Education and the Economy and funded by the Bill and Melinda Gates Foundation.

“What these studies show is that our schools do not teach what their students need,” the authors wrote, “while demanding of them what they don’t need; furthermore, the skills that we do teach and that the students do need, the schools teach ineffectively. Perhaps that is where we should begin.”

Related: Math forum audio/video.

I am moved to respond to Sol Garfunkel’s “Opinion” article.1 I am a long-time high school mathematics teacher in a public school. I started teaching around the time of SMSG and have been in the trenches throughout several of the math wars. I know Dr. Garfunkel’s fine work in creating interesting modeling projects and his outspoken opinion that using technology to solve problems that apply the mathematics we are teaching will better concretize students’ understanding of the underlying mathematics. It sounds like a fine idea, but the reality is often very different.

Our problems in teaching mathematics begin in elementary school. Sadly, many teachers working with our children at the start of their mathematical journeys are not themselves comfortable with the mathematics they are trying to teach. They often only know one way to teach an idea and they may not fully understand how that method works and why it gives the right answers. Such a teacher confronted with an alternate creative method (perhaps suggested by a clever child or a seasoned colleague) may reject the alternative rather than trying to see how and why two methods produce the same result. Beyond stifling the creativity of students and discouraging them from trying to see how the mathematics works, such an approach is not fertile ground for applications and modeling projects in which creative exploration and possibly unorthodox methods are encouraged as a means of truly understanding what is happening. Teachers who lack confidence in their own understanding of the ideas may not want to include these sorts of activities in their classrooms.

Related: Math Forum audio & video.

Days are getting longer, the weather is warmer. The smell of spring is in the air. But if you inhale deeply down by JSCEE, there’s another smell. It’s the smell of math. After years of sideways movement, the stars are aligned for systemic changes to math instruction in Seattle Public Schools.

When you look at Seattle kids’ math achievement against other urban districts, Seattle might seem to be doing OK. As a district-level statistic, we’re not too bad. But closer inspection of disaggregated data and the view from inside the system prompt a cry for help. Seattle still has a large number of struggling students and a persistent achievement gap which we can’t shake. Outside tutoring has become commonplace, with math as the most frequent remediation subject. However, recent national and state developments have identified common ground and outcome-proven methods which can serve as a model for Seattle.

This brings us around to a community support initiative for math education. Seattle has a math-focused School Board, and Seattle’s new superintendent, Jose Banda, came to Seattle from proven math success with a diverse student population in Anaheim. Recent news reports are that staff at JSCEE are planning a K-8 math instructional materials adoption soon. Examples of success are scattered through Seattle classrooms and it’s time for those successes to take root across the district.

Related: Math forum audio/video and Seattle’s “Discovery Math” lawsuit.

A new study has found that inexperienced teachers in the Los Angeles Unified School District are disproportionately more likely to be assigned to lower-performing math students, perpetuating the achievement gap.

The study also found that L.A. Unified teachers “vary substantially” in their effectiveness, with top teachers able to give students the equivalent of eight additional months of learning in a year compared with weaker instructors.

Such findings raise “deep concerns,” said Drew Furedi, the district’s executive director of talent management, who oversees teacher training. “For us, it’s a call to action.”

The study by the Strategic Data Project, which is affiliated with Harvard University’s Center for Education Policy Research, analyzed the performance of about 30% of L.A. Unified teachers and presented findings based primarily on students’ standardized math test scores from 2005 through 2011 in grades three through eight. The study’s authors acknowledged that test scores were only one measure of teacher effectiveness.

….

The study also found:

Teacher effects vary substantially in LAUSD, more than in many other districts. The difference between a 25th and 75th percentile elementary math teacher is over one-quarter of a standard deviation, which is roughly equivalent to a student having eight additional months of instruction in a calendar year.

Teach for America and Career Ladder teachers have higher math effects on average than other novices in their first year by 0.05 and 0.03 standard deviations respectively, which is roughly equivalent to one to two months of additional learning. These differences persist over time

The performance of math teachers improved quickly in the first five years, then leveled off.

Those with advanced degrees were no more effective than those without, although L.A. Unified pays more to teachers pursuing such degrees.

Long-term substitute teachers — who have been employed more frequently to fill in amid widespread layoffs — have positive effects in teaching middle-school math

View the complete 1.4MB PDF study, here.

Related: Math forum audio/video.

The University of Wisconsin-La Crosse has received a $50,000 grant to help incoming students who need remedial math courses.

The UW System says one in five incoming freshmen needs remedial math. And for under-represented minority students, that figure is double.

To bring those students up to speed faster, the La Crosse campus is using the grant money to develop an online math course. The program will be available to high school students who want to evaluate how ready they are for college, and for non-traditional students who’ve been away from school and need a refresher before coming back.

Remarkable. Are we making no progress? Perhaps it is time to revisit the math forum audio and video.

Related: What impact do high school mathematics curricula have on college-level mathematics placement? by James Wollack and Michael fish.

New spending approved by the Oshkosh school board would cover a gap in math tutoring services that has left four schools with inadequate help for struggling students since last year.

About 13 percent of Oshkosh elementary school students perform below grade level in math, said Director of Curriculum Shelly Muza.

That’s better than the average Wisconsin district, which has about 25 percent of elementary students performing below grade level. But budget cuts in the 2009-10 academic year stripped Oakwood, Carl Traeger, Lakeside and Green Meadow schools of math support services after the board decided to fund the $295,000 program with federal Title I dollars – money given only to schools with higher rates of poverty – instead of general fund dollars.

The remaining math intervention teachers who work one-on-one with struggling students can barely keep up. The equivalent of 4.25 full-time teachers are split between about 570 students in 12 elementary schools, said Muza.

Two relate links: Math Forum Audio, Video & Links; Math Task Force.

Respondents focus their brief on arguing that no reasonable school board would adopt “inquiry-based” high school mathematics textbooks instead of “direct instruction” textbooks. There are “dueling experts” and other conflicting evidence regarding the best available material for teaching high school math, and the Seattle School Board (“the Board”) gave due consideration to both sides of the debate before reaching its quasi legislative decision to adopt the Discovering series and other textbooks on a 4-3 vote.

The trial court erred by substituting its judgment for the Board’s in determining how much weight to place on the conflicting evidence. Several of the “facts” alleged in the Brief of Respondents (“BR”) are inaccurate, misleading, or lack any citation to the record in violation of RAP l0.3(a)(4). The Court should have an accurate view of the facts in the record to decide the important legal issues in this case. The Board is, therefore, compelled to correct any misimpressions that could arise from an unwary reading of respondents’ characterization of the facts.

Much more on the successful citizen lawsuit overturning the Seattle School District’s use of Discovery Math, here. http://seattlemathgroup.blogspot.com/. Clusty Search: Discovery Math.

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

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.

via a kind reader. Related: Connected Math, Math Forum audio/video, the successful Seattle Discovery Math lawsuit and the Madison School District Math Task Force (SIS links).

If you are a parent in cities such as Bellevue, Issaquah or Seattle, your kids are being short-changed–being provided an inferior math education that could cripple their future aspirations–and you need to act. This blog will tell the story of an unresponsive and wrong-headed educational bureaucracies that are dead set on continuing in the current direction. And it will tell the story of how this disaster can be turned around. Parent or not, your future depends on dealing with the problem.

Let me provide you with a view from the battlefield of the math “wars”, including some information that is generally not known publicly, or has been actively suppressed by the educational establishment. Of lawsuits and locking parents out of decision making.

I know that some of you would rather that I only talk about weather, but the future of my discipline and of our highly technological society depends on mathematically literate students. Increasingly, I am finding bright students unable to complete a major in atmospheric sciences. All their lives they wanted to be a meteorologist and problems with math had ended their dreams. Most of them had excellent math grades in high school. I have talked in the past about problems with reform or discovery math; an unproven ideology-based instructional approach in vogue among the educational establishment. An approach based on student’s “discovering” math principles, group learning, heavy use of calculators, lack of practice and skills building, and heavy use of superficial “spiraling” of subject matter. As I have noted before in this blog, there is no competent research that shows that this approach works and plenty to show that it doesn’t. But I have covered much of this already in earlier blogs.

Related: Math Forum audio / video.

For entertainment value read the Discovering Math Q&A in this article in the Seattle Times. The Discovering Math guy (1) doesn’t always answer the question asked, (2) answers but doesn’t address the topic properly – see the question on if Discovering Math is “mathematically unsound” and (3) sounds like he works for the district.

Here’s one example:

The Discovering books have been criticized by parents, but they’ve been the top pick of a couple of districts in our area, including Seattle and Issaquah. Any thoughts on why the textbooks seem to be more popular with educators than with parents?

Ryan: I think because (parents) lack familiarity — this doesn’t look like what I was taught. I don’t know how you get students to a place where more is required of them by repeating things that have been done in the past. That’s not how we move forward in life.

What?

Much more on the successful community lawsuit vs. the Seattle School District’s implementation of Discovery Math. Math Forum audio / video.

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.

The local school district’s increasing use of reform math programs lead to the creation of a “Math Task Force“. The District Administration’s response is outlined in this 2.6MB PDF document:

The purpose of this report is to describe the recomrnendations in response to the Madison Metropolitan School District Mathematics Task Force Report: Review of Mathematics Curriculum and Related Issues, submitted to the Board of Education June, 2008.

Administrative Recommendations Summary The materials included in this packet update and replace those distributed to the Board of Education in April 2009. Included in the materials is a proposed budget.

Middle School Mathematics Specialists (see Recommendations 1-5)

The Superintendent and UW-Madison Deans of Letters and Sciences and the School of Education commissioned a representative and collaborative group to design a professional development plan for this initiative. The group was convened in June and has since met four times during the summer to research and design a professional development plan to support middle school mathematics teachers.

The Middle School Math Partnership committee has tentatively planned five courses for the professional development proposal. Those courses are Number and Generalization, Rational Number and Proportional Reasoning, Geometry, Measurement and Trigonometry, and Algebra and Functions. The courses would be spread out over two years and be co-facilitated by UW and MMSD staff.

Research, data gathering and design will continue through 2009-2010 with the initial cohort of middle school teachers beginning in summer 2010. Upon completion of an initial draft, the plan will be presented to district teachers for further input and refinement.

In collaboration with the above group, a National Science Foundation Targeted Partnership proposal, Professional Learning Partnership K-20 (PLP K-20), was submitted on August 20, 2009. A UW-Madison and MMSD team of nearly 30 members worked during the summer to craft a proposal focused on systemic and sustainable mathematics professional development. The vision described in the proposal creates “a lasting interface to coordinate material, human, social, and cyber resources” among the UW-Madison and District. The principal investigator of the NSF proposal is Eric Wilcots. Co-Pl’s include Provost Deluca, Superintendent Nerad, Dean Sandefur and Dean Underwood.

Background notes and links:

- Math Forum audio & video links.
- West High School Math Teacher letter to Isthmus.
- UW-Madison Math Faculty (35 signatures) open letter to the Madison School District about the Math Coordinator Position.
- Madison School District 8th Grade Math Data.

Again, it will be interesting to see what, if any substantive changes occur in the local math programs.

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?

Nineteen years ago, Jennifer Courter set out on a career path that has since provided her with a steady stream of lucrative, low-stress jobs. Now, her occupation — mathematician — has landed at the top spot on a new study ranking the best and worst jobs in the U.S.

“It’s a lot more than just some boring subject that everybody has to take in school,” says Ms. Courter, a research mathematician at mental images Inc., a maker of 3D-visualization software in San Francisco. “It’s the science of problem-solving.”

The study, to be released Tuesday from CareerCast.com, a new job site, evaluates 200 professions to determine the best and worst according to five criteria inherent to every job: environment, income, employment outlook, physical demands and stress. (CareerCast.com is published by Adicio Inc., in which Wall Street Journal owner News Corp. holds a minority stake.)

The findings were compiled by Les Krantz, author of “Jobs Rated Almanac,” and are based on data from the U.S. Bureau of Labor Statistics and the Census Bureau, as well as studies from trade associations and Mr. Krantz’s own expertise.

According to the study, mathematicians fared best in part because they typically work in favorable conditions — indoors and in places free of toxic fumes or noise — unlike those toward the bottom of the list like sewage-plant operator, painter and bricklayer. They also aren’t expected to do any heavy lifting, crawling or crouching — attributes associated with occupations such as firefighter, auto mechanic and plumber.

The study also considers pay, which was determined by measuring each job’s median income and growth potential. Mathematicians’ annual income was pegged at $94,160, but Ms. Courter, 38, says her salary exceeds that amount.

Related:

- The Madison School District is holding public meetings tonight (LaFollette High School) and tomorrow (Memorial High School) on the recent Math Task Force Report.
- Math Forum audio/video
- West High School Math Teachers Letter to Isthmus
- Madison and Wisconsin Math Data, 8th Grade by Richard Askey
- UW-Madison Math Faculty letter to the Madison School District
- Math report commentary by TJ Mertz, more here

Parents and citizens have another opportunity to provide input on this matter when Brian Sniff, Madison’s Math Coordinator and Lisa Wachtel, Director of Madison’s Teaching & Learning discuss the Math Report at a Cherokee Middle School PTO meeting on January 14, 2009 at 7:00p.m.

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.”

The students swapped stories of little sisters, brothers and cousins who were taking above-grade-level math and getting good grades, yet did not seem to have a firm grasp of the material. The curriculum is being “narrowed and shallowed,” Walstein said. “The philosophy is that they squeeze you out the top like a tube of toothpaste. That’s what Montgomery County math is.”

Several students nodded their heads. This thesis has become Walstein’s obsession: In its drive to be the best, please affluent parents and close the achievement gap on standardized tests, the county is accelerating too many students in math, at the expense of the curriculum — and the students. The average accelerated math student “thinks he’s fine. His parents think he’s fine. The school system says he’s fine. But he’s not fine!” Walstein declares on one occasion. On another, Walstein is even less diplomatic. ” ‘We have the best courses and there’s no achievement gap and everything is wonderful,’ ” he says, parroting the message he believes county administrators are trying to project.

“The problem is, they’re lying!”

Math Forum audio / video links.

1997 saw the height of the Math Wars in California.

On the one side stood educrats, who advocated mushy math – or new-new math. They sought to de-emphasize math skills, such as multiplication and solving numeric equations, in favor of pushing students to write about math and how they might solve a problem. Their unofficial motto was: There is no right answer. (Even to 2 +2.)

They were clever. They knew how to make it seem as if they were pushing for more rigor, as they dumbed down curricula. For example, they said they wanted to teach children algebra starting in kindergarten, which seemed rigorous, but they had expanded the definition of algebra to the point that it was meaningless.

On the other side were reformers, who wanted the board to push through rigorous and specific standards that raised the bar for all California kids. Miraculously, they succeeded, and they took pride in the state Board of Education’s vote for academic standards that called for all eighth-graders to learn Algebra I.

Math Forum Audio, Video and links.

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.

Next fall, 26 of the sharpest fifth-grade minds at Potomac Elementary School will study seventh-grade math. The rest of the fifth grade will learn sixth-grade math. Fifth-grade math will be left to the third- and fourth-graders.

Public schools nationwide are working to increase the number of students who study Algebra I, the traditional first-year high school math course, in eighth grade. Many Washington area schools have gone further, pushing large numbers of students two or three years ahead of the grade-level curriculum.

Math study in Montgomery County has evolved from one or two academic paths to many. Acceleration often begins in kindergarten. In a county known for demanding parents, the math push has generated an unexpected backlash. Many parents say children are pushed too far, too fast.

Sixty Montgomery math teachers complained, in a November forum, that students were being led into math classes beyond their abilities.

Related links:

- Math Forum Audio, Video and Links.
- West High School Math teachers letter to Isthmus

One train leaves Station A at 6 p.m. traveling at 40 miles per hour toward Station B. A second train leaves Station B at 7 p.m. traveling on parallel tracks at 50 m.p.h. toward Station A. The stations are 400 miles apart. When do the trains pass each other?

Entranced, perhaps, by those infamous hypothetical trains, many educators in recent years have incorporated more and more examples from the real world to teach abstract concepts. The idea is that making math more relevant makes it easier to learn.

That idea may be wrong, if researchers at Ohio State University are correct. An experiment by the researchers suggests that it might be better to let the apples, oranges and locomotives stay in the real world and, in the classroom, to focus on abstract equations, in this case 40 (t + 1) = 400 – 50t, where t is the travel time in hours of the second train. (The answer is below.)

“The motivation behind this research was to examine a very widespread belief about the teaching of mathematics, namely that teaching students multiple concrete examples will benefit learning,” said Jennifer A. Kaminski, a research scientist at the Center for Cognitive Science at Ohio State. “It was really just that, a belief.”

Dr. Kaminski and her colleagues Vladimir M. Sloutsky and Andrew F. Heckler did something relatively rare in education research: they performed a randomized, controlled experiment. Their results appear in Friday’s issue of the journal Science.

The Advantage of Abstract Examples in Learning Math by Jennifer A. Kaminski, Vladimir M. Sloutsky, Andrew F. Heckler.

I wonder what has become of the Madison School District’s Math Task Force?

Math Forum audio, video, notes and links.

Talk with Terry Millar long enough and it’s bound to happen: The mathematics professor will begin drilling you in math. He’ll slip in a question such as “What is pi?” and before you know it you’re being coached to a whole new level of mathematical understanding.

Linda McQuillen refers to it as having Millar “attend to her mathematics” and as his long-time collaborator she’s well acquainted with the experience.

“Traveling with him [to meetings] and when we’d do presentations for various audiences, on the cab rides to and from the airport, we were always doing mathematics,” laughs McQuillen, a retired math teacher and a former leader of the Madison school district’s math goals. “The problem is, Terry can do it verbally and I can’t. He’s just amazing.”

If Millar’s enthusiasm for teaching math can be overwhelming, it’s also true he has put the energy to good use. For well over a decade, Millar has worked to improve math and science instruction for students at all levels by bringing together the knowledge of university mathematicians and scientists with the teaching and curricular expertise of educators.

Terry Millar and Linda McQuillen participated in the Math Forum. Check out the notes, audio and video here.

The National Mathematics Advisory Panel was convened by President Bush in April 2006 to address concerns that many of today’s students lack the math know-how needed to become tomorrow’s engineers and scientists. The 24-member panel of mathematicians and education experts announced recommendations to improve instruction and make better textbooks and even called on researchers to find ways to combat “mathematics anxiety.”

Larry R. Faulkner, panel chairman and former president of the University of Texas at Austin, said the country needs to make changes to stay competitive in an increasingly global economy. He noted that many U.S. companies draw skilled workers from overseas, a pool he said is drying out as opportunities in other countries improve.

“The question is, are we going to be able to get the talent?” Faulkner said in a briefing before the report’s release. “And it’s not just a question of economic competitiveness. In the end, it’s a question of whether, as a nation, we have enough technical prowess to assure our own security.”

Google News. Math Forum audio / video.

Joanne rounds up a few more links.

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.

A group of Prince William County parents is mounting a campaign to repeal a new elementary school math curriculum, using an Internet discussion group and an online petition to gather support and fuel criticism.

The group, whose members include parents from such elementary schools as Westridge, Ashland and Springwoods as well as teachers from various schools, plans to present the Prince William County School Board in February with its petition, which has about 500 names. Parents in the group, whose Web site ( http://www.pwcteachmathright.com) lists several of their complaints, say that the Investigations curriculum is putting their children behind grade level and is too convoluted.

The group’s formation comes right after the school system presented a year-long study of the curriculum that showed 80 percent of second-graders and 70 percent of first-graders are proficient on all 10 subtests of the Stanford Diagnostic Mathematics Test. The school system wants to continue studying the program and incorporate data from student performance on the state Standards of Learning exams.

School Board member Julie C. Lucas (Neabsco) said in an interview that she wants to examine the program inside a classroom to assess its effectiveness. She added that she has been hearing positive reviews from at least one principal in her district but that she wants to withhold making public comments until she visits schools.

The Investigations program has been undergoing a phased-in implementation since the School Board adopted its materials in 2006. In the 2006-07 academic year, kindergarten through second grade started the program; this year, third-graders began it; and next year, fourth-graders will use the material.

Investigations teaches children new ways of learning mathematics and solving problems. For instance, a student may not need to learn how to add 37 and 23 by stacking the figures on top of each other, and carrying the numbers. They may learn to add up the tens and then combine the seven and three to arrive at 60.

Related:

- Math Forum Audio / Video
- Madison School District’s Math Task Force
- Clusty Search: Math Investigations
- Teaching Math Right website:

*Why this website?*

…Because our children – ALL children – deserve a quality mathematics education in PWCS!!

In 2006 PWCS directed mandatory implementation of the elementary school mathematics curriculum TERC – “Investigations in Number, Data, and Space” in all PWCS elementary schools. The traditional, proven, successful mathematics program was abandoned for a “discovery learning” program that has a record of failure across the country.

Of all the VA Department of Education approved elementary math text/materials, “Investigations” least adequately supports the VA Standards of Learning. Yet it was somehow “the right choice” for PWCS children. Parents of 2nd and 3d graders are already realizing the negative impact of this program in only a year and a half’s worth of “Investigations.” Children subjected to this program end up two years behind where they should be in mathematics fluency and competency by the end of 5th grade. PWCS is committed to experimenting with our children’s future. We think our children and our tax dollars deserve better.

Improvement in math and science education is a priority in Madison, as it is across the nation.

Science, technology, engineering and math (STEM) training is not only of growing importance to our technology-dependent society, these disciplines also represent esthetically compelling advances in human knowledge that all students should have the opportunity to appreciate.

Since 2003, UW Madison and the Madison School District have been involved in a unique partnership, funded by the National Science Foundation, to reform science and math education from kindergarten through graduate school.

Preliminary results are encouraging. This five-year endeavor, SCALE — System-wide Change for All Learners and Educators — has partners that include three universities and large school districts in Madison, Los Angeles, Denver and Providence, R.I. The NSF made exploring new forms of partnership its key feature.

Improving STEM education has proven resistant to traditional “you do your thing, I ‘ll do mine ” approaches. SCALE ‘s successes underscore the wisdom of NSF ‘s emphasis on partnership.

SCALE incorporates research on student learning and teacher professional development. SCALE puts premiums on increasing teachers ‘ STEM subject matter knowledge and boosting their teaching skills.

In one preliminary study, teachers showed a significant increase in content knowledge after attending SCALE science professional development institutes in Los Angeles.

SCALE partners believe the most important resource in a school is its teachers, an idea that has not always been central to reform. However, the final measure of effectiveness is increased student understanding and performance. In 2009-2010, a randomized study involving 80 elementary schools in Los Angeles will provide definitive data on SCALE ‘s impact on student performance in science.

Links:

- UW Math Professor Terry Millar appeared at the Math Forum (audio/video).
- Additional SIS links
- Professor Millar’s webpage at the Wisconsin Center for Education Resarch.
- Clusty Search.

Math Excellence in Columbia Missouri Public Schools:

To: Columbia Public Schools Board of Education and Superintendent Phyllis Chase

An increasing number of parents and community leaders have expressed concern about the various math curricula currently used in the Columbia Public Schools (CPS). These experimental math programs go by the names of Investigations (TERC), Connected Math (CMP) and Integrated Math (Core Plus) and they emphasize “self-discovery” over mathematical competency. We are concerned because these curricula have been discredited and abandoned in other regions of the country after they failed to deliver demonstrable results. The failed curricula are currently the only method of instruction in the elementary grades and middle schools. At higher grade levels, CPS has actively discouraged students from enrolling in math courses that place more emphasis on widely accepted standard methods. And, while implementing and evaluating these programs, the Columbia School District did not provide open access to meetings or adequately consider the concerns of professional mathematicians, parents and community leaders.

Therefore, we, the undersigned, would like to express our deep concern with the following issues and to propose that the Columbia School District adopt the following goals:

1. Protect the right of students to become computationally fluent in mathematics. We expect students to receive direct instruction in standard algorithms of all mathematical operations and laws of arithmetic so that they can master the skills that allow fast, accurate calculation of basic problems. This goal cannot be met with the current Investigations/TERC math curriculum for lower grade levels.

2. Ensure that math instruction is flexible enough to allow for various learning styles and is age and grade-level appropriate. The elementary level should focus on math standards that will build a solid base of mathematical skills for ALL students. Middle school curricula should build a bridge between the fundamental arithmetic learned in elementary school and the more abstract concepts taught in high school. At both the elementary and middle school levels the curricula should allow teachers the flexibility to meet the needs of all types of learners. This goal cannot be met with the Connected Math program currently used in middle and junior high schools.

Related: Columbia Parents’ blog site, which offers a number of useful posts. [RSS]

Math Forum Audio / Video.

Via a reader.

KitchenTableMath and Text Savvy aren’t happy with the Education Department’s advice to parents on teaching children math:

Try to be aware of how your child is being taught math, and don’t teach strategies and shortcuts that conflict with the approach the teacher is using.

There are many reasons parents might be interested in their children’s math program(s), including this discussion of math scores. Math Forum audio / video.

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.

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

But they strongly believe that their math textbooks should include actual math.

Donald’s “Connected Mathematics” book at Harbour Pointe Middle School in Mukilteo asks him to arrange a list of 20 cities in order of their populations, all in the tens of millions.

Yes, he concedes, he must recognize differences among numbers, but it’s a pretty low-level task for a bright sixth-grader, about as challenging as alphabetizing words.

But check out the next activity: Locate the cities on a map.

“That’s not math,” Donald protests. “That’s geography.”

The Chacon-Taylor children and their parents, Hugh Taylor and Monique Chacon-Taylor, are among Snohomish County families raising questions about the effectiveness of widely used math textbooks that encourage discovery and writing about math, but de-emphasize basics such as multiplication and long division.

They’ve joined other Washington parents in an organization called Where’s the Math? that’s calling on the state Office of Superintendent of Public Instruction (OSPI) to rewrite its K-12 math standards, select more effective textbooks and re-examine the math content of the Washington Assessment of Student Learning (WASL)

The calls for rethinking the state’s math education come amid signs that the present system is failing large numbers of students. Just 51 percent of 10th-graders and 59 percent of fourth-graders passed the math section of the WASL in the spring. About 29,000 juniors haven’t passed the WASL math test, which they must do to graduate in spring 2008..

The Madison School District uses Connected Math in middle school. Many links and notes on math, including the recent Math Forum audio/video.

Problem: Find the slope and y-intercept of the equation 10 = x – 2.5.

Solution: The equation 10 = x – 2.5 is a specific case of the equation y = x – 2.5, which has a slope of 1 and a y-intercept of –2.5.

This problem comes from a 7th grade math quiz that accompanies a widely used textbook series for grades 6 to 8 called Connected Mathematics Program or CMP.[1] The solution appears in the CMP Teacher’s Guide and is supported by a discussion of sample student work.

Richard Askey, a mathematician at the University of Wisconsin at Madison, reported, “I was told about this problem by a parent whose child took this quiz. The marking was exactly as in the text.”[2] Students instructed and graded in this way learn incorrect mathematics, and teachers who know better may be undermined by their less informed peers, armed with the “solution.” This example is far from the only failing of CMP. Among other shortcomings, there is no instruction on division of fractions in the entire three year CMP series, and the other parts of fraction arithmetic are treated poorly.[3]

Is CMP just an anomaly? Unfortunately not. CMP is only one of more than a dozen defective K-12 math programs funded by the National Science Foundation. More specifically, the NSF programs were created and distributed through grants from the Education and Human Resources (EHR) Division within the NSF. In contrast to the NSF’s admirable and important role in supporting fundamental scientific research, the EHR has caused, and continues to cause, damage to K-12 mathematics education.

Notes and links on math curriculum. Audio / Video from the recent math forum.

Connected Math is widely used within the Madison School District resulting in no small amount of supplementing by teachers, students and parents.

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.

After a number of parents and teachers objected, the school board of Olympia, Washington, has ignored an administrative recommendation to adopt a constructivist math program for their middle schoolers:

Connected Math and the Madison School District was discussed at a recent math forum (audio / video).

UW Emeritus Math Professor Dick Askey wrote a followup article on test scores and the local math curriculum.

The MMSD is currently looking for a “Coordinator of Mathematics“.

Clusty Connected Math Search.

At a meeting on February 22 (*audio / video*), representatives of the Madison Metropolitan School District presented some data [820K pdf | html (*click the slide to advance to the next screen*)] which they claimed showed that their middle school math series, Connected Mathematics Project, was responsible for some dramatic gains in student learning. There was data on the percent of students passing algebra by the end of ninth grade and data from the state eighth grade math test for eight years. Let us look at the test data in a bit more detail.

All that was presented was data from MMSD and there was a very sharp rise in the percent of students scoring at the advanced and proficient level in the last three years. To see if something was responsible for this other than an actual rise in scores consider not only the the Madison data but the corresponding data for the State of Wisconsin.

The numbers will be the percent of students who scored advanced or proficient by the criteria used that year. The numbers for Madison are slightly different than those presented since the total number of students who took the test was used to find the percent in the MMSD presented data, and what is given here is the percent of all students who reached these two levels. Since this is a comparative study, either way could have been used. I think it is unlikely that those not tested would have had the same overall results that those tested had, which is why I did not figure out the State results using this modification. When we get to scores by racial groups, the data presented by MMSD did not use the correction they did with all students (* All 8th grade students in both cases*)

MMSD | Wisconsin | |

Oct 97 | 40 | 30 |

Feb 99 | 45 | 42 |

Feb 00 | 47 | 42 |

Feb 01 | 44 | 39 |

Feb 02 | 48 | 44 |

Nov 02 | 72 | 73 |

Nov 03 | 60 | 65 |

Nov 04 | 71 | 72 |

This is not a picture of a program which is remarkably successful. We went from a district which was above the State average to one with scores at best at the State average. The State Test was changed from a nationally normed test to one written just for Wisconsin, and the different levels were set without a national norm. That is what caused the dramatic rise from February 2002 to November 2002. It was not that all of the Middle Schools were now using Connected Mathematics Project, which was the reason given at the meeting for these increases.

It is worth looking at a breakdown by racial groups to see if there is something going on there. The formats will be the same as above.

Hispanics |
||

MMSD | Wisconsin | |

Oct 97 | 19 | 11 |

Feb 99 | 25 | 17 |

Feb 00 | 29 | 18 |

Feb 01 | 21 | 15 |

Feb 02 | 25 | 17 |

Nov 02 | 48 | 46 |

Nov 03 | 37 | 38 |

Nov 04 | 50 | 49 |

Black (Not of Hispanic Origin) |
||

MMSD | Wisconsin | |

Oct 97 | 8 | 5 |

Feb 99 | 10 | 7 |

Feb 00 | 11 | 7 |

Feb 01 | 8 | 6 |

Feb 02 | 13 | 7 |

Nov 02 | 44 | 30 |

Nov 03 | 29 | 24 |

Nov 04 | 39 | 29 |

Asian |
||

MMSD | Wisconsin | |

Oct 97 | 25 | 22 |

Feb 99 | 36 | 31 |

Feb 00 | 35 | 33 |

Feb 01 | 36 | 29 |

Feb 02 | 41 | 31 |

Nov 02 | 65 | 68 |

Nov 03 | 55 | 53 |

Nov 04 | 73 | 77 |

White |
||

MMSD | Wisconsin | |

Oct 97 | 54 | 35 |

Feb 99 | 59 | 48 |

Feb 00 | 60 | 47 |

Feb 01 | 58 | 48 |

Feb 02 | 62 | 51 |

Nov 02 | 86 | 81 |

Nov 03 | 78 | 73 |

Nov 04 | 88 | 81 |

I see nothing in the demography by race which supports the claim that Connected Mathematics Project has been responsible for remarkable gains. I do see a lack of knowledge in how to read, understand and present data which should concern everyone in Madison who cares about public education. The School Board is owed an explanation for this misleading presentation. I wonder about the presentations to the School Board. Have they been as misleading as those given at this public meeting?

Several westside PTO’s hosted a candidate forum Wednesday evening. The candidates discussed a wide variety of questions, including referendums, the budget process, strings, local education media coverage and differences with their opponents. Listen to the entire event (34.6MB mp3 audio file), or click on the links below to review specific questions & answers.

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.

American Inst. of Mathematics:

The list below groups open textbooks by course title. All the books have been judged to meet the evaluation criteria set by the AIM editorial board.

Related: Connected Math, math forum audio/video and English 10.

This statistical capitulation was a dismaying read for anyone still wedded to the idea — apparently a quaint one — that gathering statistical information might help us understand and improve our world. But the Guardian’s cynicism can hardly be a surprise. It is a natural response to the rise of “statistical bullshit” — the casual slinging around of numbers not because they are true, or false, but to sell a message.

Politicians weren’t always so ready to use numbers as part of the sales pitch. Recall Ronald Reagan’s famous suggestion to voters on the eve of his landslide defeat of President Carter: “Ask yourself, ‘Are you better off now than you were four years ago?’” Reagan didn’t add any statistical garnish. He knew that voters would reach their own conclusions.

The British election campaign of spring last year, by contrast, was characterised by a relentless statistical crossfire. The shadow chancellor of the day, Ed Balls, declared that a couple with children (he didn’t say which couple) had lost £1,800 thanks to the government’s increase in value added tax. David Cameron, the prime minister, countered that 94 per cent of working households were better off thanks to recent tax changes, while the then deputy prime minister Nick Clegg was proud to say that 27 million people were £825 better off in terms of the income tax they paid.

Could any of this be true? Yes — all three claims were. But Ed Balls had reached his figure by summing up extra VAT payments over several years, a strange method. If you offer to hire someone for £100,000, and then later admit you meant £25,000 a year for a four-year contract, you haven’t really lied — but neither have you really told the truth. And Balls had looked only at one tax. Why not also consider income tax, which the government had cut? Clegg boasted about income-tax cuts but ignored the larger rise in VAT. And Cameron asked to be evaluated only on his pre-election giveaway budget rather than the tax rises he had introduced earlier in the parliament — the equivalent of punching someone on the nose, then giving them a bunch of flowers and pointing out that, in floral terms, they were ahead on the deal.

Each claim was narrowly true but broadly misleading. Not only did the clashing numbers confuse but none of them helped answer the crucial question of whether Cameron and Clegg had made good decisions in office.

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

Using panel data on more than 100,000 American households over seven years, they tracked purchases of toilet paper, which has the great benefit of being non-perishable and steadily consumed (it’s hard to go without, but we also don’t use more just because we happen to have more in the house). That’s nearly 3 million toilet paper purchases.When Orhun and Palazzolo compared households with similar consumption rates shopping at comparable stores — and controlling for two-ply TP — they found that the poor were less likely than wealthier households to buy bigger packages, or to time their purchases to take advantage of sales. By failing to do so, they paid about 5.9 percent more per sheet of toilet paper — a little less than what they saved by buying cheaper brands in the first place (8.8 percent).

Perhaps this sounds like a subtle discovery about minor household goods. But it supports a larger point about poverty: It’s expensive to be poor. Or, to state the same from another angle: Having more money gives people the luxury of paying less for things.

In the case of toilet paper, or any number of other storable goods like canned tomatoes, rice or paper towels, shoppers have to pay more up front to reap savings over time.And the poor often can’t afford to do that — to pay $24 for a 30-pack instead of $5 for a four-pack.Then, because they can’t stock up, they can’t afford to wait until the next sale comes around. When the toilet paper runs out, they have to run to the store for another small quantity of it — whatever it costs in that moment. Because they can’t use one money-saving strategy, they can’t use the other, either.

The use of connected math has not helped. More, here.

Philip Greenspun, via a kind reader:

Based on what people said at the forum, the core driver of mediocrity seems to be the dual function of the American school. A home-schooled child studies for three hours per day. A Russian child studies for about four hours, from just after breakfast until just before lunch (with 10-minute breaks, but no recess). Children are parked at an American school for 6-7 hours per day and thus necessarily much of the time is spent on stuff other than learning. This leads to the school becoming a place for “social/emotional development” during 2-3 hours per day. The “social/emotional” aspects were the foremost concerns of the parents at the forum. One mother described how the first 20 minutes out of a 25-minute parent/teacher conference were spent discussing a child’s social life during recess. This was not a complaint, just a response to the question of how such conferences were going. When asked what was on their mind, nearly every other parent led with “social/emotional.” It makes sense if you step back from the situation and ask “What is urgent for a parent?” Of course we would all like our children to be well-educated at age 25 (or 30?) when they are done with the master’s degree that is now our entry-level credential. But the immediate (and therefore urgent) goal is to see one’s child smiling. If a child comes home in tears because of something that happened at recess it would be a rare parent who would say “let’s talk about how what you learned writing this history essay is going to affect your performance in college.”

As this was a new principal and the forum was a place for open discussion, I asked if anyone had read The Smartest Kids in the World, which was a New York Times bestseller and recommended heavily by Amazon, The Economist, and various newspapers. Everyone in the room was either employed by a school or interested enough to take time to show up at this forum, but nobody had read the book. So I mentioned that the Russian system (not much better results than ours, but absurdly cheap to run by comparison) and the Finnish system had schools and teachers concentrate on the single mission of academics. Day care, sports, and social/emotional were handled by people other than teachers in venues other than school. Then I asked if there were state regulations that would prevent the town from setting up a Russian-style system in which teachers taught until lunch and then a separate set of employees took over for the lunch+afternoon social/emotional/daycare shift. That way parents could concentrate on academics when talking with teachers. The principal responded that “children aren’t built that way” (i.e., the American way of alternating academic and daycare activities for 6-7 hours is the only possible way to run a school).

Mediocre math standards are not a new issue.

KSTP:

The results of a new survey released Monday by U.S. Bank stated that many college-age young adults say they have no idea how to keep a budget.

What’s more, they look to their parents for financial education and advice.

The study’s key findings show college students don’t fully understand credit and credit scores. They have a good perspective on saving, the study found, but they need help understanding investments and retirement savings.

According to the survey results, parents are most often mentioned as students’ financial role models.

“They really felt unprepared to talk about the future or to save for the future, had no knowledge of retirement savings whatsoever and many didn’t know that their parents would have to pay back their loan if they didn’t pay their student loan back,” Christine Hobrough, U.S. Bank region market manager in the Twin Cities, said.

Related: Connected Math and the now 10 year old math forum.

NPR:

Math teacher Sherry Read’s classroom is a total mess. The students are gone for the summer, and light fixtures dangle from the ceiling. The floor has a layer of dust. Down the hallway, workers make a racket while they renovate the school, which dates back to the 1890s. They’re working in what has become an archaeological site.

A construction crew at the Oklahoma City school made a startling discovery earlier this month. They found old chalkboards with class lessons that were written almost a century ago, and chalk drawings still in remarkably good condition. So Read doesn’t mind the mess. In fact, she’s amazed.

Related: Math Forum and Connected Math.

Chris Rickert via several kind readers:

Wisconsin has a “long way to go in all our racial/ethnic groups,” said Adam Gamoran, director of the Wisconsin Center for Education Research at UW-Madison.

My hope is that, given Wisconsin’s overwhelmingly white population, proficiency problems among white students will spur more people to push for policies inside and outside of school that help children — all children — learn.

“I hate to look at it that way, but I think you’re absolutely right,” said Kaleem Caire, president and CEO of the Urban League of Greater Madison. “The low performance of white students in our state may just lead to the type and level of change that’s necessary in public education for black and other students of color to succeed as well.”

Indeed, Gamoran said Massachusetts’ implementation of an evaluation system similar to the one Wisconsin is adopting now has been correlated with gains in reading and math proficiency and a narrowing of the racial achievement gap in math. But he emphasized that student achievement is more than just the schools’ responsibility.

Madison has known for a while that its schools are not meeting the needs of too many students of color.

The issue of low expectations and reduced academic standards is not a new one. A few worthwhile, related links:

- April 2004 West High School Math Teacher Letter

*Moreover, parents of future West High students should take notice: As you read this, our department is under pressure from the administration and the math coordinator’s office to phase out our “accelerated” course offerings beginning next year. Rather than addressing the problems of equity and closing the gap by identifying minority math talent earlier, and fostering minority participation in the accelerated programs, our administration wants to take the cheaper way out by forcing all kids into a one-size-fits-all curriculum.*

It seems the administration and our school board have re-defined “success” as merely producing “fewer failures.” Astonishingly, excellence in student achievement is visited by some school district administrators with apathy at best, and with contempt at worst. But, while raising low achievers is a laudable goal, it is woefully short-sighted and, ironically, racist in the most insidious way. Somehow, limiting opportunities for excellence has become the definition of providing equity! Could there be a greater insult to the minority community? - 2009: 60% to 42%: Madison School District’s Reading Recovery Effectiveness Lags “National Average”: Administration seeks to continue its use
- 2006: Math Forum audio, video and links
- 2005: 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
- “They’re all rich, white kids and they’ll do just fine” — NOT!
- 2006: Connected Math
- 2005: English 10
- 2009: Action Needed, Please Sign on…. Math Teacher Hiring in the Madison School District
- Madison will spend $374,700,000 to educate 24,861 students during the 2012-2013 school year. $15,071/student.
- wisconsin2.org.

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:

“Where ignorance is bliss, ignorance of ignorance is sublime.” – Paul Dunham

Laurie Rogers, via a kind email:

Last week, I went to a Spokane Public Schools math presentation at Indian Trail Elementary School. It was billed as a forum in the school newsletter and on the reader board outside of the school. It was not, in any way, a forum. It was a tightly controlled 20-minute presentation that offered no data, little information, allowed for no parent input and was patronizing in tone.

At one point, parents were asked to define math to the person next to us. (The principal said he would not offer his definition.) We also were told to describe to our neighbor a math experience we’d had. These conversations ended right there, thus being pointless. We watched a video of several small children talking about the importance of math. The kids were cute, but the video was long. It was made clear to us that math is hard, parents don’t get it (see slide 7 of the presentation), “traditional math” is no longer useful, and math is intimidating to all. Printed materials reinforced the idea of parent incompetence, with students supposedly “taking the lead” and teaching their parents.

Parents were warned to stay positive about math, however, despite our supposed fear and lack of skill, and we also were told what a “balanced” program looks like – as if that’s what Spokane actually has.

Related: Math Forum audio & video.

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.

Via a kind reader’s email:

Culturally Relevant/Cultural Relevance 40

Standards 24

Content 21

Measure (including measurement) 28

DPI 2

TAG 17

Special Education 8

ELL 2 (it comes up 45 times, but the other 43 were things like ZELLmer)

inclusion 0

differentiation 0

science 2

mathematics 0

literacy 4

reading 7 (of these, three were in the appendix with the existing ‘plan’)

African American 7

Hmong 1 (and not in any of the action plans)

Latino or Latina 0

Hispanic 0

Spanish speaking or Spanish speakers 0

Anyone see a problem here?????

The free Adobe Reader includes a text search field. Simply open the proposed document (773K PDF) and start searching.

The Proposed Strategic Plan, along with some comments, can be viewed here.

Interested readers might have a look at this Fall, 2005 Forum on Poverty organized by Rafael Gomez (audio/video). Former Madison School Board member Ray Allen participated. Ray mentioned that his daughter was repeatedly offered free breakfasts, even though she was fed at home prior to being dropped off at school. The event is worth checking out.

I had an opportunity to have lunch with Madison Superintendent Dan Nerad last summer. Prior to that meeting, I asked a number of teachers and principals what I should pass along. One of the comments I received is particularly relevant to Madison’s proposed Strategic Plan:

Curriculum: greater rigorDiscipline: a higher bar, much higher bar, consistent expectations district wide, a willingness to wrestle with the negative impact of poverty on the habits of mind of our students and favor pragmatic over ideological solutionsTeacher inservice: at present these are insultingly infantileLeadership: attract smart principals that are more entrepreneurial and less bureaucratic, mindful of the superintendent’s “inner circle” and their closeness to or distance from the front lines (the classrooms)

I know these are general, but they are each so glaringly needy of our attention and problem solving efforts.

Notes and links on Madison’s Strategic Planning Process.

One of the most interesting things I’ve observed in my years of local school interaction is the extensive amount of pedagogical and content development that taxpayers fund within the Madison School District. I’ve always found this unusual, given the proximity of the University of Wisconsin, MATC and Edgewood College, among other, nearby Institutions of Higher Education.

The recent Math Task Force, a process set in motion by several school board elections, has succeeded in bringing more attention to the District’s math curriculum. Math rigor has long been a simmering issue, as evidenced by this April, 2004 letter from West High School Math Teachers to Isthmus:

Moreover, parents of future West High students should take notice: As you read this, our department is under pressure from the administration and the math coordinator’s office to phase out our “accelerated” course offerings beginning next year. Rather than addressing the problems of equity and closing the gap by identifying minority math talent earlier, and fostering minority participation in the accelerated programs, our administration wants to take the cheaper way out by forcing all kids into a one-size-fits-all curriculum.

It seems the administration and our school board have re-defined “success” as merely producing “fewer failures.” Astonishingly, excellence in student achievement is visited by some school district administrators with apathy at best, and with contempt at worst. But, while raising low achievers is a laudable goal, it is woefully short-sighted and, ironically, racist in the most insidious way. Somehow, limiting opportunities for excellence has become the definition of providing equity! Could there be a greater insult to the minority community?

The fact the Madison’s Teaching & Learning Department did not get what they want tonight is significant, perhaps the first time this has ever happened with respect to Math. I appreciate and am proud of the Madison School Board’s willingness to consider and discuss these important issues. Each Board member offered comments on this matter including: Lucy Mathiak, who pointed out that it would be far less expensive to simply take courses at the UW-Madison (about 1000 for three credits plus books) than spend $150K annually in Teaching & Learning. Marj Passman noted that the Math Task Force report emphasized content knowledge improvement and that is where the focus should be while Maya Cole noted that teacher participation is voluntary. Voluntary participation is a problem, as we’ve seen with the deployment of an online grading and scheduling system for teachers, students and parents.

Much more on math here, including a 2006 Forum (audio / video).

Several years ago, the late Ted Widerski introduced himself at an event. He mentioned that he learned something every week from this site and the weekly eNewsletter. I was (and am) surprised at Ted’s comments. I asked if the MMSD had an internal “Knowledge Network”, like www.schoolinfosystem.org, but oriented around curriculum for teachers? “No”.

It would seem that, given the tremendous local and online resources available today, Teaching & Learning’s sole reason for existence should be to organize and communicate information and opportunities for our teaching staff via the web, email, sms, videoconference, blogs, newsletters and the like. There is certainly no need to spend money on curriculum creation.

“Men more frequently require to be reminded than informed.”

Listen to tonight’s nearly 50 minute Madison School Board math discussion via this 22MB mp3 audio file.

schoolinfosystem.org