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There Is No Such Thing as “White” Math

Sergiu Klainerman:

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.

Math Forum audio / video

Rethinking High School Math

Joanne Jacobs:

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.

Checking In: Are Math Assignments Measuring Up?

Keith Dysarz:

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.

Just teach my kid the math

James Tanton:

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

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

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

Related: Math Forum

Connected math

Natasha Singer & Danielle Ivory:

Singapore Math

How Silicon Valley Plans to Conquer the Classroom

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

Madison Teacher / Student Relationships and Academic Outcomes?

Karen Rivedal:

“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.

Déjà vu: Madison elementary school students explore the district’s new math curriculum

Amber Walker:

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):

Math. It’s not just for breakfast any more.

David Burkehead:

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.

Michelle Obama at WWDC: Bad Math Teachers Drove My Daughters Out of STEM

Slashdot.org:

“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.”

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

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.

Why Singapore’s kids are so good at maths

aJeevan Vasagar:

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.

Singapore Math.

Math Forum Audio and Video

K-12 Math Rigor? Are High School Graduates Capable Of Basic Cost/Benefit Calculations…

Kevin Carey:

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.

PDF Report link.

Related: Math Forum audio/video

21% OF UNIVERSITY OF WISCONSIN SYSTEM FRESHMAN REQUIRE REMEDIAL MATH

Singapore Math

Madison’s 2009 (!) Math Task Force

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?

Big bang for just a few bucks: The impact of math textbooks in California

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.

PDF Report link.

Related: Math Forum audio/video

21% OF UNIVERSITY OF WISCONSIN SYSTEM FRESHMAN REQUIRE REMEDIAL MATH

Singapore Math

Madison’s 2009 (!) Math Task Force

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

The Economist’s Washington correspondent wonders why his offspring are being taught swimming so well and maths so badly

James Astill:

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.

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.

Meet the New Math, Unlike the Old Math

Kevin Hartnett:

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 drops math as general ed requirement

David Jesse:

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.

Approved Textbooks

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.

Commentary On K – 12 Math Preparation

Vauhini Vara:

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.

U.S. high school seniors slip in math and show no improvement in reading

Emma Brown

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.

Explaining Your Math: Unnecessary at Best, Encumbering at Worst

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.

Naming Coordinates, Feedback and Revision – Math Mistakes

Math Mistakes:

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.

The Man Behind Modern Math

John Steele Gordon:

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.

“the widespread denial of educational mediocrity”

Laura Waters:

What’s more troubling is that many middle-class families take this propaganda as gospel and reject efforts to maintain meaningful oversight and accountability.

The Problem Is Us
Now, New Jersey may be an extreme example. We’re die-hard local control fanatics who cherish our small towns and district identities. As such, we adhere to what Rotherham calls the “middle class politics of education” which “means leaving suburban schools alone to rise and fall as they might. This has led to widespread mediocrity and pockets of excellence…and neutering accountability systems to mask uncomfortable bad news about school performance.”

Will Our Understanding of Math Deteriorate Over Time?

Lance Fortnow:

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“.

Young Adults Look to Parents for Financial Education

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.

No One Can Figure Out 1917 Multiplication Wheel

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.

A Math Teacher on Common Core

Brooke Powers:

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.

On Remedial Math

Ron Schacter

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.

Math Forum Audio & Video (2008!).

Deja Vu on Madison Math: Algebra: The most-failed class for Madison freshmen

Molly Beck:

“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.

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

Connected Math.

Everyday Math

America’s Math Crisis

Dick Resch

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.

Dumping Everyday Math? The Future of Seattle Elementary Math Education Will Be Decided on Wednesday

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.

2+2=What? Parents rail against Common Core math

Michael Rubinkam:

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.

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

Solve math problems with logic

Manila Standard Today:

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 Surprising Impact of High School Math on Job Market Outcomes

Jon James:

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.

Grades are in: June’s final exams in math show more failure in Montgomery County Schools

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.

Failing Math Curriculum in Seattle Public Schools

Cliff Mass:

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:

Study: Schools And Colleges Are Teaching The Wrong Type Of Math

John O’Connor:

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.

“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.”

Susan Schwartz Wildstrom:

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.

Chris Rickert via several kind readers:

It’s Time to Turn the Page on Math in Seattle Schools

Rick Burke:

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.

In L.A., inexperienced teachers more likely to be assigned to students behind in math, study says

Teresa Watanabe:

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.

UW-La Crosse gets $50K from the Gates Foundation to improve remedial math

channel3000:

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.

Tyrany of Low Expectations: Will lowered test scores bring about broader change in Madison schools?

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.

Hold district accountable for deceit, academic failure and questionable activity
“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.