The Disagreement

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

Explicit instruction focuses on procedural fluency, guided practice, and repetition.
Inquiry-based instruction focuses on conceptual understanding, open-ended problems, and productive struggle.

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

——

Commentary.

Math Forum audio/video.

Sharon Lurye:

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.

Wesley Crocket:

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.

Lucy Kellaway:

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.

Summer Allen:

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.

Joanne Jacobs:

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

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

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

Related: Math Forum Audio/Video.

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.

Discovery Math

Connected Math

Singapore Math

Core Plus

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

Kevin Carey:

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

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

PDF Report link.

Related: Math Forum audio/video

Connected Math

Discovery Math

Singapore Math

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.

PDF Report link.

Related: Math Forum audio/video

Connected Math

Discovery Math

Singapore Math

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.

American Inst. of Mathematics:

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

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

Vauhini Vara:

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

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

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

Emma Brown

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

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

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

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

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

Related: Math Forum audio/video links.

Katherine Beals & Barry Garelick:

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

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

Related: Math Forum: audio/video.

John Steele Gordon:

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

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

Related: Math Forum audio/video and Connected Math.

Manila Standard Today:

An educational and enrichment workshop was recently conducted by the Galileo Enrichment Learning Program where the multi-awarded mathematician and Singapore Math advocate Dr. Queena Lee-Chua together with her son Scott, shared with the participants the fundamentals of Singapore Math and demonstrated how this fun learning approach is used to solve word problems.
Multi-awarded mathematician and Singapore Math advocate Dr. Queena Lee-Chua shared with the participants the fundamentals of Singapore Math and demonstrates how this fun-learning approach is used to solve word problems.
The workshop, held at Nuvali Evoliving AVR, Sta. Rosa City, Laguna, was organized by Galileo Sta. Rosa, attended by parents and their kids, as well as by teachers from different pre-schools and elementary schools in and outside Manila. It was indeed an enlightening and engaging time for everyone as the mother and son tandem proved to the audience that complex mathematical problems can be solved with simple math logic.

Much more on Singapore Math, here.
Related: Math Forum Audio/Video.

Cliff Mass:

If I was a Seattle Public School parent, I would be getting angry now.
Why? Most Seattle students are receiving an inferior math education using math books and curriculum that will virtually insure they never achieve mastery in key mathematical subjects and thus will be unable to participate in careers that requires mathematical skills.
There are so many signs that a profound problem exists in this city. For example,
Parents see their kids unable to master basic math skills. And they bring home math books that are nearly indecipherable to parents or other potential tutors.
Nearly three quarters of Seattle Community College students require remediation in math.
Over one hundred Seattle students are not able to graduate high school because they could not pass state-mandated math exams.
Minority and economically disadvantaged students are not gaining ground in math.

Much more on Seattle’s math battles, here.
Related:

• Connected Math
• Madison Math Forum Audio/Video

John O’Connor:

Community college students are needlessly assigned to remedial math classes to learn lessons they won’t use during their studies, according to new research from a Washington, D.C. group.
And the study also found that many high school graduates are not learning subjects they will need to use in their careers.
The study was produced by the Washington, D.C.-based National Center on Education and the Economy and funded by the Bill and Melinda Gates Foundation.
“What these studies show is that our schools do not teach what their students need,” the authors wrote, “while demanding of them what they don’t need; furthermore, the skills that we do teach and that the students do need, the schools teach ineffectively. Perhaps that is where we should begin.”

Related: Math forum audio/video.

Rick Burke:

Days are getting longer, the weather is warmer. The smell of spring is in the air. But if you inhale deeply down by JSCEE, there’s another smell. It’s the smell of math. After years of sideways movement, the stars are aligned for systemic changes to math instruction in Seattle Public Schools.
When you look at Seattle kids’ math achievement against other urban districts, Seattle might seem to be doing OK. As a district-level statistic, we’re not too bad. But closer inspection of disaggregated data and the view from inside the system prompt a cry for help. Seattle still has a large number of struggling students and a persistent achievement gap which we can’t shake. Outside tutoring has become commonplace, with math as the most frequent remediation subject. However, recent national and state developments have identified common ground and outcome-proven methods which can serve as a model for Seattle.
This brings us around to a community support initiative for math education. Seattle has a math-focused School Board, and Seattle’s new superintendent, Jose Banda, came to Seattle from proven math success with a diverse student population in Anaheim. Recent news reports are that staff at JSCEE are planning a K-8 math instructional materials adoption soon. Examples of success are scattered through Seattle classrooms and it’s time for those successes to take root across the district.

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

Teresa Watanabe:

A new study has found that inexperienced teachers in the Los Angeles Unified School District are disproportionately more likely to be assigned to lower-performing math students, perpetuating the achievement gap.
The study also found that L.A. Unified teachers “vary substantially” in their effectiveness, with top teachers able to give students the equivalent of eight additional months of learning in a year compared with weaker instructors.
Such findings raise “deep concerns,” said Drew Furedi, the district’s executive director of talent management, who oversees teacher training. “For us, it’s a call to action.”
The study by the Strategic Data Project, which is affiliated with Harvard University’s Center for Education Policy Research, analyzed the performance of about 30% of L.A. Unified teachers and presented findings based primarily on students’ standardized math test scores from 2005 through 2011 in grades three through eight. The study’s authors acknowledged that test scores were only one measure of teacher effectiveness.
….
The study also found:
Teacher effects vary substantially in LAUSD, more than in many other districts. The difference between a 25th and 75th percentile elementary math teacher is over one-quarter of a standard deviation, which is roughly equivalent to a student having eight additional months of instruction in a calendar year.
Teach for America and Career Ladder teachers have higher math effects on average than other novices in their first year by 0.05 and 0.03 standard deviations respectively, which is roughly equivalent to one to two months of additional learning. These differences persist over time
The performance of math teachers improved quickly in the first five years, then leveled off.
Those with advanced degrees were no more effective than those without, although L.A. Unified pays more to teachers pursuing such degrees.
Long-term substitute teachers — who have been employed more frequently to fill in amid widespread layoffs — have positive effects in teaching middle-school math

View the complete 1.4MB PDF study, here.
Related: Math forum audio/video.