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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.

On Monday, June 21st, we filed our “Brief of Respondent” in the School District appeal of Judge Spector’s decision. (Sorry to be late in posting it to this blog; our attorney left town after sending me hard copy, but neglected to email an electronic version of the document we filed.) A link to the brief can be found in the left-hand column, below, under “Legal Documents in Textbook Appeal.”

There’s no new information, either in the District’s brief or our response. You might notice that, rather than acknowledge the catalog of unrelated miscellany in the Seattle Public School District’s brief, our attorney, Keith Scully, chose to essentially restate our original case, upon which Judge Spector ruled favorably. He did emphasize certain statements which pertained to claims in the District’s brief.

I think Keith has, once again, done a masterful job.

The District’s Appeal Brief is in — A link to the appeal is shown on the lower left.

The Seattle School District’s first brief in its appeal of Judge Spector’s decision was filed on Friday. To me, it is not surprising that its arguments are weak. I don’t think we could ever have scored this unprecedented victory had our case not been extremely well founded. Nonetheless, one can’t predict what the appeals panel will rule.

Basically, the brief restates the district’s original contention that, because the specified process was followed, any decision made by the board, (I might add — regardless of how it flouted overwhelming evidence) must stand. Also, the brief misstates and misinterprets many aspects of our case. One of the most egregious examples is the contention that the court overstepped its authority by making a decision on curriculum. Not so – the court simply remanded the board’s decision back to the board on the basis of the lack of evidence to support the decision.

We have 30 days to file our response brief (by June 21), and SPS has 15 days after (by July 6) to file its rebuttal. Our attorney tells me that a hearing will be scheduled after all briefs have been filed.

Much more on the initial, successful rollback of Seattle’s Discovery Math program here

Today we received notice of the Seattle School District’s decision to appeal the Decision of Judge Spector which required the SPS board to reconsider its high school math text adoption vote.

I am deeply disappointed that SPS will funnel more resources into this appeal, which, I suspect, will be more costly than following the judge’s instruction to reconsider.

Our attorney tells me: “…. I’ll put in a notice of appearance, and then we wait for the District to complete the record by having the documents and transcripts transmitted to the Court of Appeals. They write the first brief, due 45 days after the record is complete.

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.

“What’s a court doing making a decision on math textbooks and curriculum?” This question and its associated harrumphs on various education blogs and online newspapers came in reaction to the February 4, 2010 ruling from the Superior court of King County that the Seattle school board’s adoption of a discovery type math curriculum for high school was “arbitrary and capricious”.

In fact, the court did not rule on the textbook or curriculum. Rather, it ruled on the school board’s process of decision making–more accurately, the lack thereof. The court ordered the school board to revisit the decision. Judge Julie Spector found that the school board ignored key evidence–like the declaration from the state’s Board of Education that the discovery math series under consideration was “mathematically unsound”, the state Office of the Superintendent of Public Instruction not recommending the curriculum and last but not least, information given to the board by citizens in public testimony.

The decision is an important one because it highlights what parents have known for a long time: School boards generally do what they want to do, evidence be damned. Discovery type math programs are adopted despite parent protests, despite evidence of experts and–judging by the case in Seattle–despite findings from the State Board of Education and the Superintendent of Public Instruction.

Key Curriculum Press is in quite a snit over the Court’s decision about the high school textbooks.

Check out this web page they wrote in response.

Much more on the recent successful community vs. Seattle School District Discovery Math court case here.

Judge Julie Spector’s decision [69K PDF], via Martha McLaren:

THIS MATTER having come on for hearing, and the Court having considered the pleadings, administrative record, and argument in this matter, the Court hereby enters the following Findings of Fact, Conclusions of Law, and Order:

FINDINGS OF FACT

1. On May 6, 2009, in a 4-3 vote, the Seattle School District Board of Directors chose the Discovering Series as the District’s high school basic math materials.

a. A recommendation from the District’s Selection Committee;

b. A January, 2009 report from the Washington State Office of Public Instruction ranking High School math textbooks, listing a series by the Holt Company as number one, and the Discovering Series as number two;

c. A March 11, 2009, report from the Washington State Board of Education finding that the Discovering Series was “mathematically unsound”;

d. An April 8, 2009 School Board Action Report authored by the Superintendent;

e. The May 6, 2009 recommendation of the OSPI recommending only the Holt Series, and not recommending the Discovering Series;

f. WASL scores showing an achievement gap between racial groups;

g. WASL scores from an experiment with a different inquiry-based math text at Cleveland and Garfield High Schools, showing that W ASL scores overall declined using the inquiry-based math texts, and dropped significantly for English Language Learners, including a 0% pass rate at one high school;

h. The National Math Achievement Panel (NMAP) Report;

1. Citizen comments and expert reports criticizing the effectiveness of inquiry-based math and the Discovering Series;

J. Parent reports of difficulty teaching their children using the Discovering Series and inquiry-based math;

k. Other evidence in the Administrative Record;

I. One Board member also considered the ability of her own child to learn math using the Discovering Series.

3. The court finds that the Discovering Series IS an inquiry-based math program.

4. The court finds, based upon a review of the entire administrative record, that there IS insufficient evidence for any reasonable Board member to approve the selection of the Discovering Series.

CONCLUSIONS OF LAW

I. The court has jurisdiction under RCW 28A.645.010 to evaluate the Board’s decision for whether it is arbitrary, capricious, or contrary to law;

2. The Board’s selection of the Discovering Series was arbitrary;

3. The Board’s selection of the Discovering Series was capricious;

4. This court has the authority to remand the Board’s decision for further review;

5. Any Conclusion of Law which is more appropriately characterized as a

Finding of Fact is adopted as such, and any Finding of Fact more appropriately

characterized as a Conclusion of Law is adopted as such.

ORDER

IT IS HEREBY ORDERED:

The decision of the Board to adopt the Discovering Series is remanded for further proceedings consistent with this opinion.

Dated this 4th day of February, 2010.

Melissa Westbrook has more.

Seattle Math Group Press Release:

Judge Julie Spector today announced her finding of “arbitrary and capricious” in the Seattle School Board’s May 6 vote to adopt the Discovering Math series of high school texts despite insufficient evidence of the series’ effectiveness.

Judge Spector’s decision states, “The court finds, based upon a review of the entire administrative record, that there is insufficient evidence for any reasonable Board member to approve the selection of the Discovering series.”

Plaintiffs DaZanne Porter, an African American and mother of a 9th-grade student in Seattle Public Schools, Martha McLaren, retired Seattle math teacher and grandparent of a Seattle Public Schools fifth grader, and Cliff Mass, professor of atmospheric science at the University of Washington, had filed their appeal of the Board’s controversial decision on June 5th, 2009. The hearing was held on Tuesday, January 26th, 2010

Can an algebra textbook be racist?

That’s what was argued Tuesday in a Seattle courtroom. Not overtly racist in that a book of equations and problem sets contains hatred or intolerance of others. But that its existence — its adoption for use in Seattle classrooms — is keeping some folks down.

“We’re on untested ground here,” admitted Keith Scully.

He’s the attorney who advanced this theory in a lawsuit challenging Seattle Public Schools’ choice of the Discovering series of math textbooks last year.

The appeal was brought by a handful of Seattle residents, including UW atmospheric-sciences professor Cliff Mass. It says Seattle’s new math books — and a “fuzzy” curriculum they represent — are harmful enough to racial and other minorities that they violate the state constitution’s guarantee of an equal education.

It also says the School Board’s choice of the books was arbitrary.

Mostly, Mass just says the new textbooks stink. For everyone. But he believes they will widen the achievement gap between whites and some minority groups, specifically blacks and students with limited English skills.

The Scottsdale Unified School District’s administration is scrambling to do damage control after a group of mothers discovered Governing Board President Jann-Michael Greenburg had access to a Google Drive full of personal information, documents, and photos of about 47 people, including children.

An email sent out Wednesday evening by the SUSD’s Communications Office sought to assure families that their personal and educational data is safe. However, the district also solely blamed the discovered digital dossier* site on Mark Greenburg, the father of Jann-Michael Greenburg.

The damage control appears to be too little too late for many parents in the Scottsdale Unified School District, including Amy Carney, a mother of six, who is among those calling for Greenburg to step down.

“I am calling for the immediate resignation of our board president Jann-Michael Greenburg. We cannot allow anyone in a leadership position to secretly compile personal documents and information on moms and dads who have dared speak out publicly or on social media about their grievances with the district,’ said Carney, who is running for a seat on the Scottsdale Governing Board in November 2022.

Last year Seattle Public Schools selected new, “inquiry-based” math textbooks. Now there’s a lawsuit against the district over the Discovering Mathematics series of textbooks.

Do you have a child in school who is using the new textbooks? What is your experience with inquiry-based math education? KUOW’s Ross Reynolds is planning a show on Wednesday, February 3 in the 12 o’clock hour. We’d like to hear from you by Wednesday morning. Share your experience with KUOW by filling out the form below, or call 206.221.3663.

Barry Garelick, via email:

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

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

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

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

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

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

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

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

Kids need to be allowed to dream.”

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

— Max Meyer (@mualphaxi) November 18, 2023

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

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

Eliminating 8th grade algebra in the name of equity.

Discovery Math

Singapore Math

There is an intellectual thread that runs through all of these advances: measurement and calculation. Geometric calculations led to breakthroughs in painting, astronomy, cartography, surveying, and physics. The introduction of mathematics in human affairs led to advancements in accounting, finance, fiscal affairs, demography, and economics – a kind of social mathematics. All reflect an underlying ‘calculating paradigm’ – the idea that measurement, calculation, and mathematics can be successfully applied to virtually every domain. This paradigm spread across Europe through education, which we can observe by the proliferation of mathematics textbooks and schools. It was this paradigm, more than science itself, that drove progress. It was this mathematical revolution that created modernity.

Advances in geometry began with the rediscovery of Euclid. The earliest known Medieval Latin translation of Euclid’s *Elements* was completed in manuscript by Adelard of Bath around 1120 using an Arabic source from Muslim Spain. A Latin printed version was published in 1482. After the mathematician Tartaglia translated Euclid’s work into Italian in 1543, translations into other vernacular languages quickly followed: German in 1558, French in 1564, English in 1570, Spanish in 1576, and Dutch in 1606.

Beyond Euclid, the German mathematician Regiomontanus penned the first European trigonometry textbook, *De Triangulis Omnimodis* (*On Triangles of All Kinds*), in 1464. In the sixteenth century, François Viètehelped replace the verbal method of doing algebra with the modern symbolism in which unknown variables are denoted by symbols like x, y, and z. René Descartes and Pierre de Fermat built on Viète’s innovations to develop analytic geometry, where curves and surfaces are described by algebraic equations. In the late seventeenth century, Isaac Newton and Gottfried Leibniz extended the methods of analytic geometry to the study of motion and change through the development of calculus.

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

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

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

Math forum audio/video.

Singapore Math

Connected Math

Discovery Math

Remedial math

Madison’s math review task force.

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

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

Math forum audio/video.

Singapore Math

Connected Math

Discovery Math

Remedial math

Madison’s math review task force.

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

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

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

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

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

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

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

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

Connected Math

Discovery math:

Not, Singapore math, however.

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

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

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

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

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

Related:

Remedial math at the University of Wisconsin.

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

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

http://seattlemathgroup.blogspot.com/.

Discovery Math

Connected math.

Singapore Math

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

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

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

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

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

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

http://seattlemathgroup.blogspot.com/.

Discovery Math

Connected math.

Singapore Math

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

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

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

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

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

Math Forum Audio / Video

Madison’s Math Task Force

21% OF UNIVERSITY OF WISCONSIN SYSTEM FRESHMAN REQUIRE REMEDIAL MATH

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

Related: Singapore Math.

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

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

Math Forum audio video.

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

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

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

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

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

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

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

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

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

Related: math forum audio and video

Alex Davies, Petar Veličković and Pushmeet Kohli:

The practice of mathematics involves discovering patterns and using these to formulate and prove conjectures, resulting in theorems. Since the 1960s, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures^{1}, most famously in the Birch and Swinnerton-Dyer conjecture^{2}, a Millennium Prize Problem^{3}. Here we provide examples of new fundamental results in pure mathematics that have been discovered with the assistance of machine learning—demonstrating a method by which machine learning can aid mathematicians in discovering new conjectures and theorems. We propose a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these observations to guide intuition and propose conjectures. We outline this machine-learning-guided framework and demonstrate its successful application to current research questions in distinct areas of pure mathematics, in each case showing how it led to meaningful mathematical contributions on important open problems: a new connection between the algebraic and geometric structure of knots, and a candidate algorithm predicted by the combinatorial invariance conjecture for symmetric groups^{4}. Our work may serve as a model for collaboration between the fields of mathematics and artificial intelligence (AI) that can achieve surprising results by leveraging the respective strengths of mathematicians and machine learning.

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

Key findings include that classroom and school belonging are distinct and that teachers with more confidence in their ability to teach math had a stronger sense of classroom belonging among their students. The research also found there was no systematic difference in math classroom belonging across racial/ethnic groups or by gender.

“I’m heartened to know that second finding, that teachers’ sense of their efficacy has an impact on kids,” said Madison Metropolitan School District executive director of research and innovation Beth Vaade. “That’s what we want, we want to know as educators that what we do in a classroom is going to be connected to what scholars feel.”

MEP, which is a partnership between the University of Wisconsin-Madison and MMSD, initially hoped to use observations and interviews with students and staff to complement the data from the surveys. But the COVID-19 pandemic prevented that extra step, something researcher and MEP co-director Eric Grodsky called “disappointing.”

Specifically, they explored that feeling in middle school math classrooms. Grodsky said that decision came partly because of the “stereotype threat” surrounding the subject, with the assumption that women and students of color are worse at math creating a psychological threat as soon as they enter a classroom. MMSD STEM director Patti Schaefer said math was an “appealing” subject for this type of research.

“We see math as I’m either a math person or I’m not, a very split way of seeing ourselves in math,” Schaefer said.

To measure belonging, researchers surveyed 1,887 students and 60 teachers at five MMSD middle schools.

Math curriculum/rigor and student performance are not new topics. A few links: Connected Math, Discovery Math, Math Task Force, 21% of University of Wisconsin System Freshman Require Remedial Math, UW-LaCrosse’s Remedial Math Courses and Math forum.

What impact do high school mathematics curricula have on college-level mathematics placement? (Traditional math curriculum students placed higher).

2017: West High Reading Interventionist Teacher’s Remarks to the School Board on Madison’s Disastrous Reading Results

Madison’s taxpayer supported K-12 school district, despite spending far more than most, has long tolerated disastrous reading results.

My Question to Wisconsin Governor Tony Evers on Teacher Mulligans and our Disastrous Reading Results

“An emphasis on adult employment”

Wisconsin Public Policy Forum Madison School District Report[PDF]

WEAC: $1.57 million for Four Wisconsin Senators

Booked, but can’t read (Madison): functional literacy, National citizenship and the new face of Dred Scott in the age of mass incarceration.

California’s new Mathematics Curriculum Framework has become a political hot potato, reports Lawrence Richard on Yahoo News. The state education board will postpone a decision on implementation for 10 months in response to critics who charged it would “de-mathematize math” and prevent high achievers from taking advanced classes.

2007 Math Forum

2017: West High Reading Interventionist Teacher’s Remarks to the School Board on Madison’s Disastrous Reading Results

Madison’s taxpayer supported K-12 school district, despite spending far more than most, has long tolerated disastrous reading results.

My Question to Wisconsin Governor Tony Evers on Teacher Mulligans and our Disastrous Reading Results

“An emphasis on adult employment”

Wisconsin Public Policy Forum Madison School District Report[PDF]

Booked, but can’t read (Madison): functional literacy, National citizenship and the new face of Dred Scott in the age of mass incarceration.

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:

2007 Math Forum

2017: West High Reading Interventionist Teacher’s Remarks to the School Board on Madison’s Disastrous Reading Results

Madison’s taxpayer supported K-12 school district, despite spending far more than most, has long tolerated disastrous reading results.

My Question to Wisconsin Governor Tony Evers on Teacher Mulligans and our Disastrous Reading Results

“An emphasis on adult employment”

Wisconsin Public Policy Forum Madison School District Report[PDF]

Booked, but can’t read (Madison): functional literacy, National citizenship and the new face of Dred Scott in the age of mass incarceration.

George Zacharopoulos, Francesco Sella & Roi Cohen Kadosh:

Formal education has a long-term impact on an individual’s life. However, our knowledge of the effect of a specific lack of education, such as in mathematics, is currently poor but is highly relevant given the extant differences between countries in their educational curricula and the differences in opportunities to access education. Here we examined whether neurotransmitter concentrations in the adolescent brain could classify whether a student is lacking mathematical education. Decreased γ-aminobutyric acid (GABA) concentration within the middle frontal gyrus (MFG) successfully classified whether an adolescent studies math and was negatively associated with frontoparietal connectivity. In a second experiment, we uncovered that our findings were not due to preexisting differences before a mathematical education ceased. Furthermore, we showed that MFG GABA not only classifies whether an adolescent is studying math or not, but it also predicts the changes in mathematical reasoning ∼19 mo later. The present results extend previous work in animals that has emphasized the role of GABA neurotransmission in synaptic and network plasticity and highlight the effect of a specific lack of education on MFG GABA concentration and learning-dependent plasticity. Our findings reveal the reciprocal effect between brain development and education and demonstrate the negative consequences of a specific lack of education during adolescence on brain plasticity and cognitive functions.

2007 Math Forum

My Question to Wisconsin Governor Tony Evers on Teacher Mulligans and our Disastrous Reading Results

“An emphasis on adult employment”

Wisconsin Public Policy Forum Madison School District Report[PDF]

We need to get racial politics out of the equation before it’s too late.

Among all human endeavors, mathematics stands alone in terms of its beauty, universality, and innumerable applications. Though its role is often obscured by esoteric language, mathematics is behind almost all of humanity’s major advances in science and engineering.

Bridges stand, planes fly, rockets carry us into space, and MRIs can see into our brains thanks to precise mathematical calculations performed by powerful computers, invented by mathematicians such as Alan Turing and John von Neumann. Behind tasks performed by computers—predicting the weather, performing complex financial transactions, or encrypting billions of messages each day—lie sophisticated mathematical algorithms. Artificial intelligence, for example, is but a happy marriage between powerful computers and abstract mathematical models that sort and analyze massive amounts of data.

Before our discipline became the universal global enterprise it is today, great mathematical discoveries passed from ancient civilizations to medieval ones and then to modern ones. One can argue that the preeminence of each civilization was, in part, due to their sophisticated understanding and use of mathematics. This is particularly clear in the case of the West, which forged ahead in the 17th century with the discovery of calculus, one of the greatest scientific breakthroughs of all time.

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

Democratic Virginia state Senator J. Chapman Petersen is one of many parents voicing concerns about a new racial equity push that would eliminate certain advanced placement classes in the state’s mathematics curriculum.

The Virginia Mathematics Pathway Initiative (VMPI) would replace the traditional mathematics progression of Algebra 1, Geometry, and Algebra 2 courses with courses that teach so-called “essential” topics. Under the plan, all students would take the same courses through the tenth grade but would then be allowed to enroll in classes that correspond with their post-graduation career plans.

A major goal of the VMPI is to combat disparities in educational outcomes between racial and ethnic minorities. However, many Northern Virginia parents are mobilizing to reject the program, claiming that the new “pathway” will inhibit higher-achieving students and discourage academic exploration and performance among all kids, including the racial minorities the program is designed to help.

Related: Connected Math Discovery Math

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

This is my second post investigating whether a terminal degree is practically ~necessary for groundbreaking scientific work of the 20th century.

Mathematics seems like a great field for outsiders to accomplish groundbreaking work. In contrast to other fields, many of its open problems can be precisely articulated well in advance. It requires no expensive equipment beyond computing power, and a proof is a proof is a proof.

Unlike awards like the Nobel Prize or Fields Medal, and unlike grants, a simple list of open problems established in advance seems immune to credentialism. It’s a form of pre-registration of what problems are considered important. Wikipedia has a list of 81 open problems solved since 1995. ~146 mathematicians were involved in solving them (note: I didn’t check for different people with the same last name). I’m going to randomly choose 30 mathematicians, and determine whether they got a PhD on or prior to the year of their discovery.

The categories will be No PhD, Partial PhD, PhD, evaluated in the year they solved the problem. In my Boyle’s desiderata post,

^{2}⁄_{15}(13%) of the inventors had no PhD. I’d expect mathematics to exceed that percentage.

In February, before the COVID-19 pandemic locked down cities and closed borders, I spent four days with about 50 mathematicians at the Oberwolfach Research Institute for Mathematics in the Black Forest of southern Germany. Most weeks of the year the institute hosts small gatherings focused on different areas of mathematics. I planned to insinuate myself among the professional mathematicians: break bread with them, take a far-back seat at their lectures, eavesdrop on their hallway conversations, and try to figure out how a close gathering like this one promotes mathematical discovery.

There’s no easy way to get to Oberwolfach. I arrived on a Monday by the recommended route, which is to fly to Frankfurt, then take a two-hour train trip south to the hamlet of Wolfach, then a 30-minute cash-only taxi ride along the river Wolf. Eventually I spied the institute itself, perched midway up a steep hill and backed by an expanse of evergreen forest.

Remoteness is the point.

Math is a deeply frustrating subject for many elementary and high school students. But Seattle public schools are gearing up to accuse math of a litany of more serious crimes: imperialism, dehumanization, and oppression of marginalized persons.

The district has proposed a new social justice-infused curriculum that would focus on “power and oppression” and “history of resistance and liberation” within the field of mathematics. The curriculum isn’t mandatory, but provides a resource for teachers who want to introduce ethnic studies into the classroom vis a vis math. According to Education Week:

Discovery Math and the Seattle Public Schools.

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

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

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

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

Related: Discovery, Connected and Singapore Math.

Madison’s math task force.

21% of University of Wisconsin System Freshman Require Remedial Math

.

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

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

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

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

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

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

Related: Connected math

A question of culture

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

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

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

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

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

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

Related: Math Forum.

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

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

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

Related: Math Forum

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

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

Related: Math Forum

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

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

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

Related (deja vu):

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

Related:

James Wollack

and Michael Fish:

Major Findings

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

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

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

2014: “

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

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

He advocated earlier intervention in high school.

”

Related: Math Forum audio/video.

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

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

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

Related: Math Forum audio/video

Madison’s 2009 (!) Math Task Force

21% OF UNIVERSITY OF WISCONSIN SYSTEM FRESHMAN REQUIRE REMEDIAL MATH

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

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

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

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

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

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

…..

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

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

Related: Math Forum audio/video

Madison’s 2009 (!) Math Task Force

21% OF UNIVERSITY OF WISCONSIN SYSTEM FRESHMAN REQUIRE REMEDIAL MATH

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

Madison School District Administration (PDF):

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

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

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

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

Madison School District Administration (PDF):

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

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.

Hidden truths permeate our world; they’re inaccessible to our senses, but math allows us to go beyond our intuition to uncover their mysteries. In this survey of mathematical breakthroughs, Fields Medal winner Cédric Villani speaks to the thrill of discovery and details the sometimes perplexing life of a mathematician. “Beautiful mathematical explanations are not only for our pleasure,” he says. “They change our vision of the world.”

Vladimir Voevodsky had no sooner sat himself down at the sparkling table, set for a dinner party at the illustrious Institute for Advanced Study in Princeton, New Jersey, than he overturned his empty wine glass, flipping bowl over stem and standing the glass on its rim—a signal to waiters that he would not be imbibing. He is not always so abstemious, but Voevodsky, that fall of 2013, was in the midst of some serious work.

Founded in 1930, the Institute has been called “the earthly temple of mathematical and theoretical physics,” and is a hub for all manner of rigorous intellectual inquiry. Einstein’s old house is around the corner. In the parking lot a car sports a nerdy bumper sticker reading, “Don’t Believe Everything You Think”—which might very well be aimed directly at Voevodsky. Because during the course of some professional soul-searching over the last decade or so, he’d come to the realization that a mathematician’s work is 5 percent creative insight and 95 percent self-verification. And this was only reinforced by a recent discovery around the time of the dinner party: He’d made a big mistake.

Barry Garelick, via a kind email:

A video about how the Common Core is teaching young students how to do addition problems is making the rounds on the internet: http://rare.us/story/watch-common-core-take-56-seconds-to-solve-96/

Much ballyhoo is being made of this. Given the prevailing interpretation of Common Core math standards, the furor is understandable. The purveyors of these standards claim that they neither dictate nor prohibit any pedagogical approach, but the wave of videos and articles sweeping the internet like the one above suggest the opposite may be true: that, in fact, the Common Core math standards are dictating how teachers are to teach math.

I believe that CC math, while not dictating particular teaching styles, has given the math reform movement that has been raging for slightly more than two decades in the United States a massive dose of steroids. Reform math has manifested itself in classrooms across the United States mostly in lower grades, in the form of “discovery-oriented” and “student-centered” classes, in which the teacher becomes a facilitator or “guide on the side” rather than the “sage on the stage” and students work so-called “real world” or “authentic problems.” It also has taken the form of de-emphasizing practices and drills, requiring oral or written “explanations” of problems so obvious they need none, finding more than one way to do a problem, and using cumbersome strategies for basic arithmetic functions. The big reason behind all of this is that math reformers believe such practices will result in students understanding how numbers work—as opposed to just “doing” math. In fact, reformers tend to mischaracterize traditionally taught math as teaching only the “doing” and not the understanding; that it is rote memorization of facts and procedures and that students do not learn how to think or problem solve.

Barry Garelick, via a kind email:

All my classes were getting ready to take their first quiz later in the week. My second period class was the second-year Algebra 1 class. We were working on systems of linear equations covering the various ways of solving two equations with two unknowns.

I was preparing for my second period class by looking over the upcoming quiz and identifying the questions that most students would likely get wrong. As I reached the disturbing conclusion that this would be almost all the questions, Sally, the District person who talked to the math teachers about Common Core the day before school began, stuck her head in the door and asked if I had done any of the activities she had talked about that day. These were discovery-oriented projects that lead students to explore certain topics (specifically: probability, repeating decimals, and solving systems of equations) while allowing teachers to do formative assessments. Which means evaluating students by observing them “communicate and defend their thinking”.

The mathematics of ancient Iraq, attested from the last three millennia BCE, was written on clay tablets in the Sumerian and Akkadian languages using the cuneiform script, often with numbers in the sexagesimal place value system (§1.2). There have been many styles of interpretation since the discovery and decipherment of that mathematics in the late nineteenth and early twentieth centuries CE (§1.1), but this book advocates a combination of close attention to textual and linguistic detail, as well as material and archaeological evidence, to situate ancient mathematics within the socio-intellectual worlds of the individuals and communities who produced and consumed it (§1.3)

Iraq—Sumer—Babylonia—Mesopotamia: under any or all of these names almost every general textbook on the history of mathematics assigns the origins of ‘pure’ mathematics to the distant past of the land between the Tigris and Euphrates rivers. Here, over five thousand years ago, the fi rst systematic accounting techniques were developed, using clay counters to represent fixed quantities of traded and stored goods in the world’s earliest cities (§2.2). Here too, in the early second millennium bce, the world’s first positional system of numerical notation—the famous sexagesimal place value system—was widely used (§4.2). The earliest widespread evidence for ‘pure’ mathematics comes from the same place and time, including a very accurate approximation to the square root of 2, an early form of abstract algebra, and the knowledge, if not proof, of ‘Pythagoras’ theorem’ defining the relationship between the sides of a right-angled triangle (§4.3). The best-known mathematical artefact from this time, the cuneiform tablet

Plimpton 322, has been widely discussed and admired, and claims have been made for its function that range from number theory to trigonometry to astronomy. Most of the evidence for mathematical astronomy, however, comes from the later fi rst millennium bce (§8.2), from which it is clear that Babylonian astronomical observations, calculational models, and the sexagesimal place value system all had a deep impact on the later development of Old World astronomy, in particular through the person and works of Ptolemy. It is hardly surprising, then, that ever since its discovery a century ago the mathematics of ancient Iraq has claimed an important role in

the history of early mathematics.

Ariel Starra, Melissa E. Libertus & Elizabeth M. Brannon:

The uniquely human mathematical mind sets us apart from all other animals. How does this powerful capacity emerge over development? It is uncontroversial that education and environment shape mathematical ability, yet an untested assumption is that number sense in infants is a conceptual precursor that seeds human mathematical development. Our results provide the first support for this hypothesis. We found that preverbal number sense in 6-month-old infants predicted standardized math scores in the same children 3 years later. This discovery shows that number sense in infancy is a building block for later mathematical ability and invites educational interventions to improve number sense even before children learn to count.

Two math-notebook pages recently authenticated as belonging to Abraham Lincoln suggest the 16th president, who was known to downplay his formal education, may have spent more time in school than usually thought.

And the Illinois State University math professors behind the discovery say the work shows Lincoln was no slouch, either.

Math professors Nerida Ellerton and Ken Clements said Friday at the university in Normal that they’d recently confirmed that the two pages were part of a previously known math notebook from Lincoln’s childhood. It was found in the archives of Houghton Library at Harvard University, where it remains.

The book, known as a cyphering book in Lincoln’s day, is a sort math workbook in which Lincoln wrote math problems and their answers. It’s the oldest known Lincoln manuscript.

For many young people who aspire to be scientists, the great bugbear is mathematics. Without advanced math, how can you do serious work in the sciences? Well, I have a professional secret to share: Many of the most successful scientists in the world today are mathematically no more than semiliterate.

During my decades of teaching biology at Harvard, I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail. This mistaken assumption has deprived science of an immeasurable amount of sorely needed talent. It has created a hemorrhage of brain power we need to stanch.

I speak as an authority on this subject because I myself am an extreme case. Having spent my precollege years in relatively poor Southern schools, I didn’t take algebra until my freshman year at the University of Alabama. I finally got around to calculus as a 32-year-old tenured professor at Harvard, where I sat uncomfortably in classes with undergraduate students only a bit more than half my age. A couple of them were students in a course on evolutionary biology I was teaching. I swallowed my pride and learned calculus.

I was never more than a C student while catching up, but I was reassured by the discovery that superior mathematical ability is similar to fluency in foreign languages. I might have become fluent with more effort and sessions talking with the natives, but being swept up with field and laboratory research, I advanced only by a small amount.

Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.

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.

Laurie Rogers, via a kind email:

Many of America’s public schools have incorporated “student-centered learning” models into their math programs. An adoption committee in Spokane appears poised to recommend the adoption of yet another version of a “student-centered” program for Grades 3-8 mathematics.

It’s critically important that American citizens know what that term means. Aspects of the Common Core State Standards initiatives are leading many districts to adopt new curricular materials that have “student-centered learning” as a centerpiece.

In Spokane Public Schools, student-centered learning (also known as “inquiry-based” learning or “discovery-based” learning or “standards-based” learning) has been the driver of curriculum adoptions for nearly 20 years. This approach has not produced graduates with strong skills in mathematics. Spokane now suffers from a dearth of math skills in most of its younger citizens.

Nor is Spokane alone with this problem. Student-centered learning has largely replaced direct instruction in the public-school classroom. It was pushed on the country beginning in the 1980s by the National Council of Teachers of Mathematics, the federal government, colleges of education, and various corporations and foundations. Despite its abject failure to produce well-educated students, student-centered learning is coming back around, again pushed by the NCTM, colleges of education, the federal government and various corporations and foundations.

In a previous blog post, I made the claim that much of the math curriculum is ordered based on historical precedent rather than conceptual dependencies. Some parts of the math curriculum we have in place is based on the order of discovery (not always, but mostly) and while other parts are taught out of pure habit: This is how I was taught, so this is how I’m going to teach. I don’t think this needs to be the case. In fact, I think that this is actually a detriment to students. If we want to produce a generation of mathematicians and scientists who are going to solve the difficult problems of today, then we need to address some of the recent advances in those fields to prepare them. Students should not have to “wait until college” to hear about “Topology” or “Quantum Mechanics”. We need to start developing the vocabulary for these subjects much earlier in the curriculum so that students are not intimidated by them in later years.

TWO plus two equals four: nobody would argue with that. Mathematicians can rigorously prove sums like this, and many other things besides. The language of maths allows them to provide neatly ordered ways to describe everything that happens in the world around us.

Or so they once thought. Gregory Chaitin, a mathematics researcher at IBM’s T. J. Watson Research Center in Yorktown Heights, New York, has shown that mathematicians can’t actually prove very much at all. Doing maths, he says, is just a process of discovery like every other branch of science: it’s an experimental field where mathematicians stumble upon facts in the same way that zoologists might come across a new species of primate.

Mathematics has always been considered free of uncertainty and able to provide a pure foundation for other, messier fields of science. But maths is just as messy, Chaitin says: mathematicians are simply acting on intuition and experimenting with ideas, just like everyone else. Zoologists think there might be something new swinging from branch to branch in the unexplored forests of Madagascar, and mathematicians have hunches about which part of the mathematical landscape to explore. The subject is no more profound than that.

One of the most frustrating aspects of working on the improvement of math education is dealing with an educational establishment that makes decisions based on fads and opinions rather than empirical facts.

Now, let us accept that there are different approaches to teaching mathematics, with a major divide between the “reform, discovery approaches” and the more “traditional, direct instruction” approaches. Reform/discovery approaches became the rage among the educational community in the 1990s and I believe it is a major, but not sole, reason that math performance has lagged.

As a scientist, it would seem to me that the next step is clear: test a variety of curriculum approaches in the classroom, insuring the class demographics are similar, and find out what works best. In short, do a carefully controlled experiment with proper statistics and find the truth in an empirical way. But what frustrates me is that such experimentation is virtually never done by the educational bureaucracy. They seem to go from fad to fad and student progress suffers. Reform math, Integrated Math, Teach for America, Whole Language, and many more.

Biology used to be about plants, animals and insects, but five great revolutions have changed the way that scientists think about life: the invention of the microscope, the systematic classification of the planet’s living creatures, evolution, the discovery of the gene and the structure of DNA. Now, a sixth is on its way – mathematics.

Maths has played a leading role in the physical sciences for centuries, but in the life sciences it was little more than a bit player, a routine tool for analysing data. However, it is moving towards centre stage, providing new understanding of the complex processes of life.

The ideas involved are varied and novel; they range from pattern formation to chaos theory. They are helping us to understand not just what life is made from, but how it works, on every scale from molecules to the entire planet – and possibly beyond.

The biggest revolution in modern biology was the discovery of the molecular structure of DNA, which turned genetics into a branch of chemistry, centred on a creature’s genes – sequences of DNA code that specify the proteins from which the gene is made. But when attention shifted to what genes do in an organism, the true depth of the problem of life became ever more apparent. Listing the proteins that make up a cat does not tell us everything we want to know about cats.

The Washington State Court of Appeals has reversed an earlier decision in King County Superior Court that found Seattle’s choice of a new high-school math series was arbitrary and capricious.

The appellate court found no basis for the Superior Court’s conclusion in February 2010 that the Seattle School board “was willful and unreasoning in coming to its decision” when it chose the Discovering Math series of textbooks for algebra and geometry in high school math.

The school district has been using the series since the start of the 2009 school year.

Some parents have criticized the Discovering Math series, saying it is inferior to other series and that its emphasis on verbal descriptions makes it difficult for some students to understand, especially those for whom English is a second language.

Much more on the Seattle Discovery Math lawsuit, here.

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.

have an article in this Sunday’s Ideas section of the Boston Globe entitled Hard to find: Why it’s increasingly difficult to make discoveries – and other insights from the science of science. It discusses a scientific paper of mine published recently inScientometrics, which is the journal of the “science of science”. The journal article entitled Quantifying the Ease of Scientific Discovery (also freely available on the arXiv), discusses how to think mathematically about how scientific discovery becomes more difficult over time.

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).

Thanks to all the people who have written, expressing your support and dedication to this effort, and also to those who have so generously made financial donations. We are many, many people nationwide standing in solidarity in our commitment to make effective math education accessible to all students.

I apologize to those who have looked for news recently on this blog: I’ve been following other math ed news, but little has been happening directly regarding our lawsuit, so I haven’t sat down to give updates.

In the last 6 weeks, there has been an outpouring of support for our lawsuit and its outcome, as well a surge of determination to deflect the tide of inquiry-based math instruction that has flooded so many of our schools. I’ve been very moved by letters from parents who have struggled (heroically, and often poignantly, it seems to me) to support their children in developing strong math skills despite curricula that they found confusing, unintelligible, and deeply discouraging. I strongly believe that, whether the Seattle School District’s appeal of Judge Spector’s decision succeeds or fails, the continuing legal action will only heighten public awareness of the tragic and devastating results of the nationwide inquiry-based math experiment. The public NEEDS TO KNOW about this debacle. I think/hope that our lawsuit and its aftermath are helping this to happen.

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.

Martha McLaren, DaZanne Porter, and Cliff Mass:

Today Cliff Mass and I, (DaZanne Porter had to be at a training in Yakima) accompanied by Dan Dempsey and Jim W, had our hearing in Judge Julie Spector’s King County Superior Courtroom; the event was everything we hoped for, and more. Judge Spector asked excellent questions and said that she hopes to announce a decision by Friday, February 12th.

The hearing started on time at 8:30 AM with several members of the Press Corps present, including KIRO TV, KPLU radio, Danny Westneat of the Seattle Times, and at least 3 others. I know the number because, at the end, Cliff, our attorney, Keith Scully, and I were interviewed; there were five microphones and three cameras pointed towards us at one point.

The hearing was brief; we were done by 9:15. Keith began by presenting our case very clearly and eloquently. Our two main lines of reasoning are, 1) that the vote to adopt Discovering was arbitrary and capricious because of the board’s failure to take notice of a plethora of testimony, data, and other information which raised red flags about the efficacy of the Discovering series, and 2) the vote violated the equal education rights of the minority groups who have been shown, through WASL scores, to be disadvantaged by inquiry based instruction.

Realistically, both of these arguments are difficult to prove: “arbitrary and capricious” is historically a very, very difficult proof, and while Keith’s civil rights argument was quite compelling, there is no legal precedent for applying the law to this situation.

The School District’s attorney, Shannon McMinimee, did her best, saying that the board followed correct procedure, the content of the books is not relevant to the appeal, the books do not represent inquiry-based learning but a “balanced” approach, textbooks are merely tools, etc., etc. She even denigrated the WASL – a new angle in this case. In rebuttal, Keith was terrific, we all agreed. He quoted the introduction of the three texts, which made it crystal clear that these books are about “exploration.” I’m blanking on other details of his rebuttal, but it was crisp and effective. Keith was extremely effective, IMHO. Hopefully, Dan, James, and Cliff can recall more details of the rebuttal.

A lawsuit challenging the Seattle School District’s math curriculum went to trial Monday in King County Superior Court.

A group of parents and teachers say the “Discovering Math” series adopted last year does a poor job, especially with minority students who are seeing an achievement gap widen.

A spokeswoman for the Seattle School District, Teresa Wippel, says it has no comment on pending litigation.

KOMO-TV reports the district has already spent $1.2 million on Discovering Math books and teacher training.

On Tuesday, January 26th, at 8:30 AM, King County Superior Court Judge Julie Spector will consider an appeal by a group of Seattle residents (including yours truly) regarding the selection by Seattle Public Schools of the Discovering Math series in their high schools. Although this issue is coming to a head in Seattle it influences all of you in profound ways.

In this appeal we provide clear evidence that the Discovery Math approach worsens the achievement gap between minority/disadvantaged students and their peers. We show that the Board and District failed to consider key evidence and voluminous testimony, and acted arbitrarily and capriciously by choosing a teaching method that was demonstrated to produce a stagnant or increasing achievement gap. We request that the Seattle Schools rescind their decision and re-open the textbook consideration for high school.

To improve science and mathematics education for American children, the White House is recruiting Elmo and Big Bird, video game programmers and thousands of scientists.

President Obama will announce a campaign Monday to enlist companies and nonprofit groups to spend money, time and volunteer effort to encourage students, especially in middle and high school, to pursue science, technology, engineering and math, officials say.

The campaign, called Educate to Innovate, will focus mainly on activities outside the classroom. For example, Discovery Communications has promised to use two hours of the afternoon schedule on its Science Channel cable network for commercial-free programming geared toward middle school students.

Science and engineering societies are promising to provide volunteers to work with students in the classroom, culminating in a National Lab Day in May.

This site continues to mention math curricula challenges from time to time, and as long as I am around, and have community math experiences, it will continue to do so.

I try to visit Madison’s wonderful Farmer’s Market weekly. This past weekend, I purchased some fabulous raspberries from an older Hmong couple. Their raspberries are the best. Unfortunately, while I made my purchase, they asked how much change I was due, something I saw repeated with other buyers. They periodically have a younger person around to handle the transactions, or a calculator.

Purchasing tickets at high school sporting events presents yet another opportunity to evaluate high schooler’s basic, but ESSENTIAL math skills. A Dane County teenager could not make change from $10 for three $2 tickets recently. I have experienced this at local retail establishments as well.

Unfortunately, the “Discovery” approach to math does not appear work….

Barry Garelick, via email:

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

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

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

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

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.

In the process of researching where the U.S. ranks internationally in science and math education, I discovered that one of the Democratic presidential candidates (the one who’s governor of a Southwestern state) keeps citing our nation’s current rank as No. 29 (or, on a good day, No. 28) after our having been No. 1 throughout the world.

Apparently neither statistic is true, however, which suggest that it may be Bill Richardson himself who needs a bit of remedial math.

This is not the first time our national educational system has been politicized. Fifty years ago, a global scientific effort called the International Geophysical Year (IGY) encompassed 11 Earth sciences: aurora and airglow, cosmic rays, geomagnetism, gravity, ionospheric physics, longitude and latitude determinations (precision mapping), meteorology, oceanography, seismology and solar activity.

The Soviet Union celebrated IGY by launching the first artificial satellite (Sputnik) one month into the event on Oct. 1, 1957. We countered with the discovery of the Van Allen radiation belts and the discovery of mid-ocean submarine ridges, which was an important confirmation of plate tectonics.

Immediately following the successful orbiting of Sputnik, attendant paranoia regarding U.S. loss of the space race converted our collaboration with the country into a major retooling of the nation’s school curricula. The focus would now be on science and mathematics.

It’s impossible to deny a general decline in these areas nationally versus India and a handful of other countries that emphasize science, technology, engineering and mathematics (STEM) education on a cultural level. In recent years, Minnesota has been adamant and resolute about creating and maintaining collaboration between the private and public sectors to improve these areas of learning among K-12 students statewide.

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.

Mathematics education seems to be very subject to passing trends – surprisingly more so than many other subjects. The most notorious are, of course, the rise of New Math in the 60s and 70s, and the corresponding backlash against it in the late 70s and 80s. It turns out that mathematics education, at least in the US, is now subject to a new trend, and it doesn’t appear to be a good one.

To be fair the current driving trend in mathematics education is largely an extension of an existing trend in education generally. The idea is that we need to cater more to the students to better engage them in the material. There is a focus on making things fun, on discovery, on group work, and on making things “relevant to the student”. These are often noble goals, and it is something that, in the past, education schemes have often lacked. There is definitely such a thing as “too much of a good thing” with regard to these aims, and as far as I can tell that point was passed some time ago in the case of mathematics.

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.

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

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

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

Last week, a reclusive Russian topologist named Grigory Perelman seemed to be playing to type, or stereotype, when he refused to accept the highest honor in mathematics, the Fields Medal, for work pointing toward the solution of Poincaré’s conjecture, a longstanding hypothesis involving the deep structure of three-dimensional objects. He left open the possibility that he would also spurn a $1 million prize from the Clay Mathematics Institute in Cambridge, Mass.

Unlike Brando turning down an Academy Award or Sartre a Nobel Prize, Dr. Perelman didn’t appear to be making a political statement or trying to draw more attention to himself. It was not so much a medal that he was rejecting but the idea that in the search for nature’s secrets the discoverer is more important than the discovery.

“I do not think anything that I say can be of the slightest public interest,” he told a London newspaper, The Telegraph, instantly making himself more interesting. “I know that self-promotion happens a lot and if people want to do that, good luck to them, but I do not regard it as a positive thing.”

Nadejda Lobastova has more. Poincaré Conjecture

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

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

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

- Ben Feller:

*Science and math have zoomed to the top of the nation’s education agenda. Yet Amanda Cook, a parent of two school-age girls, can’t quite see the urgency.*

“In Maine, there aren’t many jobs that scream out ‘math and science,'” said Cook, who lives in Etna, in the central part of the state. Yes, both topics are important, but “most parents are saying you’re better off going to school for something there’s a big need for.”

Nationwide, a new poll shows, many parents are content with the science and math education their children get – a starkly different view than that held by national leaders. - Celia R. Baker:

*Dissatisfaction with math curriculum in Alpine School District might seem like a local issue. It isn’t.*

Alpine’s math wars made the area ground zero for the explosion of charter, home and private schools in Utah, and the discord continues to drive legislation regarding school choice.

Eagle Mountain resident Doug Cannon, father of seven, became concerned about Alpine’s math curriculum soon after the district adopted the “Investigations” math program in its elementary schools in 2001.

The textbook series is meant to improve students’ understanding of math through discovery of math concepts. As originally implemented, it downplayed rote learning and memorization of traditional algorithms such as times tables.

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

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

Interesting thread on discovery learning, with notes from Alan Siegel’s study of videotaped Japanese Math lessons:

Discovery learning is fashionable in math reform circles, writes Seebach. The Japanese are supposed to be the models. But the Japanese teach traditionally — with “beautifully designed and superbly executed” lessons.

The videotape shows, Siegel says, that “a master teacher can present every step of a solution without divulging the answer, and can, by so doing, help students learn to think deeply. In such circumstances, the notion that students might have discovered the ideas on their own becomes an enticing mix of illusion intertwined with threads of truth.”

The latest state audit of Seattle Public Schools didn’t tell me anything I didn’t already know: The district is stuck in a culture of lax indifference when it comes to taxpayers’ money.

Despite the last decade’s phalanx of highly paid budget and money managers overseeing the district, few inroads have been made in transforming this culture.

Let’s start with the audit’s biggest discovery for the 2008-09 school year. The district overpaid at least 83 employees to the tune of $228,860. The district says the number of accidentally overpaid employees could be as high as 144.

Repayment plans have been set up for most of the employees. But others left the district, requiring costly measures, including collection agencies, to recover the money. Expect this debacle to reverberate as tax implications and impacts to the state retirement system unfold.

There’s a great deal of citizen activism underway in Seattle, including: a successful lawsuit that overturned the District’s adoption of Discovery Math, a recall drive for 5 of the 7 school board members and a lawsuit regarding the New Student Assignment Plan. Melissa Westbrook offers additional comments.

Spending and governance questions are not unique to Seattle.

Blacks for Political and Social Action of Dane County, Inc.:

In the midst of these challenges, the Madison Metropolitan School District heard its superintendent-designee, Matthew Gutiérrez, was rescinding his acceptance of the position to remain as superintendent of the Seguin, Texas school district. This lack of a permanent superintendent can have an incredibly negative impact on African American students. The initiative known as “Black Excellence” began under the leadership of former superintendent Jennifer Cheatham. Cheatham has been gone for almost a year. Nothing about the current leadership suggests that Black Excellence is a district priority. African American children in Wisconsin experience the widest achievement disparities in the nation in reading and mathematics. Our eighth graders are performing 47 points below their White counterparts in mathematics. Our fourth graders are performing 39 points below their White counterparts in reading. Where is the collective outrage over these disparities? Who on the current school board is demanding improvement?

The racial problems of MMSD run long and deep: Issues of achievement, disproportionate assignment to special education, lack of access to honors and advanced placement classes, disproportionate levels of suspensions and expulsions, and disproportionate graduation rates (59% Black vs. 88% White). In the midst of this there is an inverse relationship between the percentage of teachers of color and that of students. Eighty-eight percent of the teachers are White in a district with a student population that is 43% White. And, we have had repeated instances of White teachers using racial epithets and other disrespect toward Black students and their parents (e.g. a White teacher mistakenly sent a text to a Black parent about how the parent and her child were so dumb).

African Americans in Madison have been more than patient when it comes to improving their status — education, employment, housing, and every other measure of health and well-being. There have been over 40 years of reports, task forces and initiatives. Post-pandemic Madison will be a “new” Madison. We have learned a lot in the midst of crisis. We know that far too many of our community members are one paycheck away from poverty — loss of housing, food, health care, childcare, schooling, etc. What is the place for African Americans in this new Madison?

Related, Madison K-12 experiments:

Madison’s taxpayer supported K-12 school district, __despite spending far more than most__, has long __tolerated disastrous reading results__.

My __Question to Wisconsin Governor Tony Evers__ on Teacher Mulligans and our Disastrous Reading Results

In early March, British leaders planned to take a laissez-faire approach to the spread of the coronavirus. Officials would pursue “herd immunity,” allowing as many people in non-vulnerable categories to catch the virus in the hope that eventually it would stop spreading. But on March 16, a report from the Imperial College Covid-19 Response Team, led by noted epidemiologist Neil Ferguson, shocked the Cabinet of the United Kingdom into a complete reversal of its plans. Report 9, titled “Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand,” used computational models to predict that, absent social distancing and other mitigation measures, Britain would suffer 500,000 deaths from the coronavirus. Even with mitigation measures in place, the report said, the epidemic “would still likely result in hundreds of thousands of deaths and health systems (most notably intensive care units) being overwhelmed many times over.” The conclusions so alarmed Prime Minister Boris Johnson that he imposed a national quarantine.

Subsequent publication of the details of the computer model that the Imperial College team used to reach its conclusions raised eyebrows among epidemiologists and specialists in computational biology and presented some uncomfortable questions about model-driven decision-making. The Imperial College model itself appeared solid. As a spatial model, it divides the area of the U.K. into small cells, then simulates various processes of transmission, incubation, and recovery over each cell. It factors in a good deal of randomness. The model is typically run tens of thousands of times, and results are averaged—a technique commonly referred to as an ensemble model.

In a tweet sent in late March, Ferguson—then still one of the leading voices within the U.K.’s Scientific Advisory Group for Emergencies (SAGE), tasked with handling the coronavirus crisis—stated that the model was implemented in “thousands of lines of undocumented” code written in C, a widely used and high-performing computing language. He refused to publish the original source code, and Imperial College has refused a Freedom of Information Act request for the original source, alleging that the public interest is not sufficiently compelling.

As Ferguson himself admits, the code was written 13 years ago, to model an influenza pandemic. This raises multiple questions: other than Ferguson’s reputation, what did the British government have at its disposal to assess the model and its implementation? How was the model validated, and what safeguards were implemented to ensure that it was correctly applied? The recent release of an improved version of the source code does not paint a favorable picture. The code is a tangled mess of undocumented steps, with no discernible overall structure. Even experienced developers would have to make a serious effort to understand it.

I’m a virologist, and modelling complex processes is part of my day-to-day work. It’s not uncommon to see long and complex code for predicting the movement of an infection in a population, but tools exist to structure and document code properly. The Imperial College effort suggests an incumbency effect: with their outstanding reputations, the college and Ferguson possessed an authority based solely on their own authority. The code on which they based their predictions would not pass a cursory review by a Ph.D. committee in computational epidemiology.

Related, Madison K-12 experiments:

Madison’s taxpayer supported K-12 school district, __despite spending far more than most__, has long __tolerated disastrous reading results__.

My __Question to Wisconsin Governor Tony Evers__ on Teacher Mulligans and our Disastrous Reading Results

Natasha Singer & Danielle Ivory:

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

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

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

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

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

Common ground

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

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

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

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

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

Related: Math Forum

Professor Vlahos concludes that elites (which he defines more broadly than “the One Percent”) are acting to their own advantage, as elites have done in other times moving towards the point when things fell apart (for example, at the end of Classical times in 6th through the 8th Centuries or after the Black Death in the 14th Century or after the World Wars in the 20th Century).

He further thinks that over what could be a long period of time our current elites have set the stage, by monopolizing resources, for a catastrophic event (perhaps climate change) to change how the cards are dealt.

Professor Vlahos came to that conclusion while teaching graduate courses on how global systems subside. He states that he initially focused on climate change, but came to see such events (like the, probably climate related, Plague of Justinian in the 6th Century) as being a trigger for a course of events that were already in trail.

There have been thinkers who have considered these matters before.

In 1930, the Spanish philosopher, José Ortega y Gasset, published a book called The Revolt of the Masses, which dealt with the “mass-ification” of society, which included “señorito satisfecho” (“Little Mr. Satisfied” or the bureaucrat).

In 1995, the late historian, Christopher Lasch, wrote a book called The Revolt of the Elites, which presciently predicted the perception on the part of many Americans that elites “‘dangerously isolated’ from the rest of the country” mind set and lacked a sense of “noblesse oblige.”

I am vastly less qualified than the people I have cited, but let me offer my own opinion.

English 10, connected math and discovery math.

Last October, Madison Superintendent Jen Cheatham signed a resolution agreement with the U.S. Department of Education’s Office for Civil Rights regarding OCR’s compliance review of access to advanced coursework by Hispanic and African-American students in the District. The resolution agreement was presented at the December 5, 2016 Instruction Workgroup meeting (agenda item 6.1):

http://www.boarddocs.com/wi/mmsd/Board.nsf/goto?open&id=AFL2QH731563The description of the resolution agreement by Dylan Pauly & Jen Cheatham starts around 2 (h) 16 (m)

https://www.youtube.com/watch?v=iaW0YclXc8c&feature=em-share_video_userThe OCR resolution agreement was included on the agenda (item 9.3) of the December 12, 2016 full board meeting as part of the Instruction Workgroup “report out” without discussion.

When OCR does a compliance review, it issues a resolution letter to the subject institution which describes OCR’s review and OCR’s findings. The resolution agreement (signed by the institution) then sets forth what the institution agrees to do to address the issues in the resolution letter.

Adele Rapport (PDF), via a kind reader:

According to the Superintendent, the District did not have a unified cuniculum prior to the 2013-201 4 school year. The Distiict recently reported to OCR that it is implementing “a multi-year, multi-phased plan to engage in course alignment. The end result will be courses that share a common course plan, common titles and course descriptions in the high school course guides, syllabi using common templates and common end-of-course summative assessments.” As summarized below. the District’s cum~nt approach to AL services is the product of several programs and initiatives as well as a recently concJuded audit by WDPI.

In 2008 The District received a $5.3 million Smaller Learning Communities grant from the Department. With these funds the District began, in its words, “to rethink and reconceptualize the high school experience.” As a result of this process, the Distri<.:t in October 2010 announced the "Dual Pathways Plan," with goals that included aligning the curriculum among all four high schools: closing the achievement gap between white students and students of color: and remedying what the District concedes was unequal access for students to advanced courses. The District proposed we meet these goals by implementing two different pathways for high school students: a "preparatory pathway" and an "accelerated pathway". In March, 2011, The WDPI concluded an investigation of the District's TAG program by determining that the District had failed to comply with four State of Wisconsin requirements for TAG programs: (1) establish a TAG plan and hire a TAG coordinator: (2) identify TAG students in multiple domain areas, including intellectual, academic, creative. leadership and the arts: (3) provide access to TAG programming without cost and allow parents to participate in identification and programming. The District subsequently adopted and implemented a corrective action plan to address findings of WDPI's audit. On February 6, 2015, WDPI concluded monitoring the implementation of the District's corrective action plan, finding the District in compliance with all relevant statutory requirements for TAG programs in Wisconsin. Also in 2011, in response to unfavorable feedback from parents and community members regarding the Dual Pathways proposal, the District modified the proposal and enacted a more modest series of reforms focusing on curriculum alignment. The District began to scale back its use of prerequisites for advanced high school courses, implementing a system of "recommended skills and experiences." The District also increased its advanced course offerings for the ninth and tenth grade, and expanded its assessment of elementary and middle school students for advanced kaming opportunities by broadening its reliance on qualitative factors like teacher recommendations. ...... The District offers honors ond AP courses to provide enriched academic opportunities for students. The District does not offer an International Baccalaureate program. Students can take honors courses at the middle school level, and both honors and AP courses at the high school level. None of the high schools offers weighted grades or credits for honors or AP courses. The District's offoring of honors and AP courses varies among schools, and neither the alternative high school (Shabazz City High School) nor the non-traditional high school (Innovative and Alternative Education) which focuses on expeliential learning, offers such courses. The District offored 13 different AP courses in multiple sections during the 2013-14 school year and 24 different AP courses during the 2015-16 school year. Recognizing that its AP course offerings vary across its four high schools, the District recently completed a three-year plan for course vetting and course alignment that includes AP coursework. Pursuant to this plan, the District plans to standardize across all four high schools AP courses that do not have prerequisites. In addition, the Dist1ict's Director of CuITiculum and Instruction said the District has the goal to have a standard set of AP courses across all four high schools: the schools will not necessarily offer all of the same courses, but the AP courses each offers will be drawn from the same set of AP courses. The District will gauge student interest in AP courses in deciding where to offer the courses. However, the District will ensure that core AP courses such as Physics and English will be offered at all four high schools. The AL Direclor noted that a first step in offering higher level math courses at all high schools is to ensure that Algebra 1 is the same at all school. The Director of Curriculum and Management confirmed that the District is realigning the math curriculum. ...... The magnitude of the racial disparity in AP enrollment is worse for math and science AP courses. There were only 18 math and 17 science AP enrollments by African-American students, a rate of 1.2 math and 1.1 science AP enrollments per 100 African-American students. There were only 44 math and 38 science AP enrollments by Hispanic students, a rate of 3.9 math and 3.3 science AP enrollments per 100 Hispanic students. By comparison, there were 526.5 math and 368 science AP enrollments by white students, a rate of 14.9 math and 10.4 science AP enrollments per 100 white students. Thus, in the 2013-14 school year, enrollments by white students in AP math and AP science courses were 12.4 and 9.5 times greater respectively, than enrollments by African-American students, and 3.8 and 3.2 times greater, respectively, than enrollmentw by Hispanic students. ...... Further the data provided by the District show that there was underepresentation of African American and Hispanic students in AP courses at each high school in the District. During the 2013-2014 school year, the disparity between African-American students' participation and all other students' participation was statistically significant in 12 of 15 AP courses offered at East High School, 5 of 13 courses at LaFollette High School, 13 of 17 courses at Memorial High School and 9 of 14 courses at West High School. The disparity between Hispanic student enrollment and all other students' enrollment was statistically significant in 2 of 15 AP courses offered at East High SchooL 0 of 13 courses at LaFollette High School. 6 of 17 courses at Memorial High School and 8 of 14 courses at West High School. In addition. African-American students underrepresentation in AP math ws statistically significant in all 12 of the AP math offerings that were offered at every District high school (in the three courses of Calculus AB, Calculus BC and Statistics) and Hispanic students underrepresentation in AP math was statistically significant in 3 of the same 12 AP math offerings. As for participation in AP science, African-American students' underrepresentation was statistically significant in 8 of 12 offerings of AP science (in the three courses of Physics C, Chemistry, Biology and Environmental Science), and Hispanic students' underrepresentation was statistically significant in 3 of the same 12 AP science offerings.

Related:

Small Learning Communities English 10

Madison’s Long Term, Disastrous Reading Results.

Scores on Algebra 1 Regents exam plummeted by 14 percentage points at south Queens schools that used a controversial new curriculum teachers have blasted as “a complete disaster,” a superintendent revealed this week

Josephine Van Ess, superintendent of Queens South High Schools, told parent leaders Wednesday that the 29 high schools under her watch, all but one of which used the Illustrative Mathematics curriculum, saw their average pass rate plunge from 59% to 45%.

The commercial curriculum — which forces teachers to give scripted lessons on a rigid schedule, expects students to “discover” solutions with little instruction, and frustrates kids lacking prerequisite skills — is partly to blame.

—-

More.

“Connected Math”

“Discovery Math”

“Singapore Math”

Math forum audio / video

When high school teacher Rachel King welcomed a new cohort of 10th graders to her classroom in the fall of 2021, she made a discovery: a number of her students had never completed their coursework from the previous year.

At the time, the 36-year-old taught English at The Urban Assembly Institute of Math and Science for Young Women in downtown Brooklyn. It was her 13th year teaching and her third at the all-girls middle and high school, which serves predominantly Black and Latino children from low-income households.

When schools first shifted to remote learning in March 2020, it quickly became clear that students were struggling to log on to their classes and complete assignments. Thousands lacked access to devices, WiFi, or a quiet place to work. As worry spread that many could get left behind, education department officials announced new academic guidelines. Attendance and testing requirements would be waived for the remainder of the year. No student would fail a course.

For instance I never learned that a man named Oswald Avery, in the 1940s, puzzled over two cultures of *Streptococcus* bacteria. One had a rough texture when grown in a dish; the other was smooth, and glistened. Avery noticed that when he mixed the smooth strain with the rough strain, every generation after was smooth, too. Heredity in a dish. What made it work? This was one of the most exciting mysteries of the time—in fact of all time.

Most experts thought that protein was somehow responsible, that traits were encoded soupily, via differing concentrations of chemicals. Avery suspected a role for nucleic acid. So, he did an experiment, one we could have replicated on our benches in school. Using just a centrifuge, water, detergent, and acid, he purified nucleic acid from his smooth strep culture. Precipitated with alcohol, it became fibrous. He added a tiny bit of it to the rough culture, and lo, that culture became smooth in the following generations. This fibrous stuff, then, was “the transforming principle”—the long-sought agent of heredity. Avery’s experiment set off a frenzy of work that, a decade later, ended in the discovery of the double helix.

In his “Mathematician’s Lament,” Paul Lockhart describes how school cheapens mathematics by robbing us of the questions. We’re not just asked, hey, how much of the triangle takes up the box?

Huh, 39, has now been awarded the Fields Medal, the highest honor in mathematics, for his ability to wander through mathematical landscapes and find just the right objects — objects that he then uses to get the seemingly disparate fields of geometry and combinatorics to talk to each other in new and exciting ways. Starting in graduate school, he has solved several major problems in combinatorics, forging a circuitous route by way of other branches of math to get to the heart of each proof. Every time, finding that path is akin to a “little miracle,” Huh said.

One might say the same of his path into mathematics itself: that it was characterized by much wandering and a series of small miracles. When he was younger, Huh had no desire to be a mathematician. He was indifferent to the subject, and he dropped out of high school to become a poet. It would take a chance encounter during his university years — and many moments of feeling lost — for him to find that mathematics held what he’d been looking for all along.

That poetic detour has since proved crucial to his mathematical breakthroughs. His artistry, according to his colleagues, is evident in the way he uncovers those just-right objects at the center of his work, and in the way he seeks a deeper significance in everything he does. “Mathematicians are a lot like artists in that really we’re looking for beauty,” said Federico Ardila-Mantilla, a mathematician at San Francisco State University and one of Huh’s collaborators. “But I think in his case, it’s really pronounced. And I just really like his taste. He makes beautiful things.”

“When I found out that he came to mathematics after poetry, I’m like, OK, this makes sense to me,” Ardila added.

What are the consequences of closing virtually every American school and shifting to online education for months at a time?

It’s a question that education experts have been asking since the emergence of COVID-19, and one whose answers are gradually becoming clearer. With federal sources reporting that 99 percent of students have now returned to classrooms, newly available data are showing how students were affected by spending long stretches of the last two school years at home. And the signs are not good.

Perhaps the most disturbing news yet was found in a working paper released last month by the National Bureau of Economic Research, which found that state test scores dropped significantly in both reading and math during the pandemic. In a discovery that will reopen questions about the wisdom of keeping schools closed, economist Emily Oster and her co-authors found that learning loss was far worse in districts that kept classes fully remote, and that declines in reading scores were greater in districts serving predominantly poor and non-white students.

Oster, a Brown University professor and popular author, has won both adulation and criticism in the COVID era as an advocate for school reopenings. One study she co-authored, examining the spread of coronavirus in 250 Massachusetts districts last winter, helped persuade officials at the Centers for Disease Control to reduce the recommended social distancing requirement in schools from six feet to three.

The data clearly indicate that being able to read is not a requirement for graduation at (Madison) East, especially if you are black or Hispanic”

My Question to Wisconsin Governor Tony Evers on Teacher Mulligans and our Disastrous Reading Results

“An emphasis on adult employment”

Wisconsin Public Policy Forum Madison School District Report[PDF]

WEAC: $1.57 million for Four Wisconsin Senators

Friday Afternoon Veto: Governor Evers Rejects AB446/SB454; an effort to address our long term, disastrous reading results

When A Stands for Average: Students at the UW-Madison School of Education Receive Sky-High Grades. How Smart is That?

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