Daily Calculus Problem #35

Calculus
Daily Calculus Problem
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Fifth African-American woman to earn a PhD in mathematics

In one week, Baylor University will dedicate a new bust to commemorate Dr. Vivienne Malone-Mayes, their first African-American faculty member (hired in 1966) and the fifth African-American woman to earn a PhD in mathematics. The ceremony will be broadcast live on Baylor’s Facebook page on Tuesday, February 26th! #womeninmath#diversityinmath @bayloruniversity

Source: Facebook Page of Association for Women in Mathematics

Nearly half of US female scientists leave full-time science after first child

Study reveals proportion of people leaving full-time careers in science after the birth of their first child.

This article has been chosen from www.nature.com | By: Holly Else |  Published: 19 FEBRUARY 2019

More than 40% of women with full-time jobs in science leave the sector or go part time after having their first child, according to a study of how parenthood affects career trajectories in the United States. By contrast, only 23% of new fathers leave or cut their working hours.

The analysis (see ‘Parents in science’), led by Erin Cech, a sociologist at the University of Michigan in Ann Arbor, might help to explain the persistent under-representation of women in jobs that involve science, technology, engineering and mathematics (STEM). The study also highlights the impact of fatherhood on a career in science, she says.

Source: Ref. 1

Career versus family

Given that 90% of people in the United States become parents during their working lives, Cech and Mary Blair-Loy, a sociologist at the University of California, San Diego, sought to better understand what happens to scientists’ careers after they start a family.

They used the Scientists and Engineers Statistical Data System, a database provided by the US National Science Foundation that contains information from surveys of the US STEM workforce every two to three years.

From the 2003 data, Cech and Blair-Loy picked the child-free scientists in full-time employment and tracked their familial status in the next wave of the survey, in 2006. This gave them two groups of scientists to compare — 841 who became parents during this period, and 3,365 who remained childless throughout. The researchers also looked at how these individuals’ careers changed between 2003 and 2010.

They report that new parents are significantly more likely to leave a full-time science career for full-time non-science careers than their child-free colleagues1.

Gender imbalance

By the end of the study period, 23% of men and 43% of women who had become parents had left full-time STEM employment. They either went part time, switched to non-STEM careers or left the workforce altogether. This compared to 16% of child-free men and 24% of child-free women. The team controlled for potential confounding differences between people with and without children.

For a subset of the people who had left science, the data set also included an entry on why they had left science. Around half of the new parents in this subset cited family-related reasons, compared with just 4% of people without children.

Taken together, these findings suggest that parenthood is an important driver of gender imbalance in STEM employment, the team says.

But Cech says that this the first time research has shown the proportion of new parents facing difficulties reconciling family life with science. She adds that there is a striking impact on new fathers as well as mothers.

“STEM work is often culturally less tolerant and supportive of caregiving responsibilities than other occupations,” Cech says. “So mothers — and fathers — may feel squeezed out of STEM work and pulled into full-time work in non-STEM fields”.

A ‘structural’ problem

Virginia Valian, a psychologist at the City University of New York, says: “The results showing that fathers also leave STEM reinforces the hypothesis that the problem is a structural one, in which dedicated professionals are not expected to have a personal life, and, indeed, are punished for so doing.”

Ami Radunskaya, a mathematician at Pomona College in Claremont, California, who mentors young female mathematicians, says women can become exhausted from constantly having to prove themselves in a professional environment that is, “at best, challenging to everyone and, at worst, openly sexist”.

“These young women are smart and tenacious,” she says. “When these young women start a family, they realize that this exhaustion and stress is not sustainable.”

Radunskaya suggests several measures that could help to improve the situation. Policies on family leave should send the message that having children is expected and accepted, for example. Senior researchers should mentor junior members of staff, and people should accept the challenges women in science may face. “We need to have candid, non-blaming conversations about [these issues],” she adds.doi: 10.1038/d41586-019-00611-1References

How Reading Novels in Math Class Can Strengthen Student Engagement

This article has been chosen from KQED.ORG | AUTHOR: Kara Newhouse | Published on Mar 18, 2018

Every January, Nashville teacher Joel Bezaire reads The Curious Incident of the Dog in the Night-Time aloud to his students. Sounds pretty standard, right? It would be — for an English class. But Bezaire teaches math. The novel is part of a unit on number sense.

While it’s easy to envision using math picture books in elementary school classrooms, literature for older grades poses a bigger challenge. Can reading fit into the curriculum as the books get longer and the math gets more complex?

Bezaire thinks it can, and so does another teacher, Sam Shah, of Brooklyn. The two occupy opposite ends of the secondary math spectrum — seventh-grade pre-algebra and 12th-grade calculus, respectively — and both have found ways to strengthen student engagement through reading.

Joel Bezaire and class read The Curious Incident of the Dog in the Night-Time. (Courtesy of Joel Bezaire)

Novel study in pre-algebra

During Bezaire’s Curious Incident unit, each period begins with a typical 20-minute math lesson, followed by a 15-minute discussion of the previous day’s reading. For the rest of the 55-minute period, he reads a new chapter aloud. As he reads, Bezaire often pauses to dig deeper into the story’s math. Sometimes, the concepts align directly with the day’s pre-algebra lesson. For example, on the day when they learn about prime numbers, the class also reads why the main character, Christopher, chose primes as his system for labeling chapters.

“The literary hook for this lesson is strong, and kids are really into learning more about primes thanks to the context of the story,” said Bezaire. “The lessons don’t always line up this nicely, but so much of what Christopher writes about regarding mathematics is about flexibility with numbers that it’s a really nice match.”

After class students complete written reflections about the book, with different types of questions serving multiple pedagogical goals.

Mathematical questions, which often relate to puzzling out the novel’s two mysteries, allow students to practice problem-solving strategies in a context with more buy-in than the usual practice worksheets. They also encourage deeper thinking about the reasoning behind a math strategy. For example, after students test Christopher’s method for mental math with large multiplication, they are asked how easy or hard it was and when it might be most useful.

Questions related to plot and language, Bezaire said, help his less confident math students. “Students who more easily self-identify as ‘English types’ immediately get a little more comfortable in math class if they experience those types of (literary) questions regularly.”

Others questions invite students to connect personally with the text. For instance, one question asks students to share the meaning of their name. Another asks them to consider how it might affect their interactions if they could not read facial expressions, like Christopher, who has autism. These questions allow Bezaire to learn about his students in ways that equations cannot. They also improve students’ patience and understanding with each other, he said.View image on Twitter

View image on Twitter

Joel Bezaire@joelbezaire

If any MS math teacher is interested in trying my curriculum for the novel The Curious Incident of the Dog in the Night-Time (https://prealgebraone.wordpress.com/novel-studies/ ) I have a set of 20 novels I can send you. I’ve accumulated way too many extras and would love to pass them on. #mtbos1024:56 PM – Jan 9, 201843 people are talking about thisTwitter Ads info and privacy

“Context and prior knowledge are critical components in fostering comprehension, regardless of the topic,” according to Faith Wallace, co-author of Teaching Math Through ReadingReading literature is one of several ways to build that context and background knowledge. “When math is integral to the story students can learn the concepts in a natural way, become inquisitive, engage in thoughtful conversation, and more,” said Wallace.

The combination of mathematical, literary and personal reflection, along with students’ genuine interest in the story, leads to higher student engagement, Bezaire said. Year after year, his students who previously kept quiet raised their hands during discussions of The Curious Incident. “Very often, this continues into the rest of the year after our novel study is done,” he said. “Often when middle school students get momentum in a certain class, they are hardy enough to allow it to continue even when the unit of study changes.”

Calculus Book Club

Two years ago, when a schedule change created extra periods in Sam Shah’s multivariable calculus course, he instituted a class book club. The students started with the satirical science fiction novel Flatland by Edwin Abbott and later read several nonfiction texts about mathematicians and mathematical ideas. Book club meetings took place during a block of 30 to 40 minutes a few times per month, with a rotating pair of students leading each discussion.

In the first year, Shah said, his biggest challenge was deciding how much to chime into the discussions. It’s as important to create a relaxed atmosphere for the meetings as it is to keep students focused on the text, he said.

During the second year of book club, he made an effort to intervene less often. “When I reflected upon what my goal was … it wasn’t to teach kids how to do close readings and feel like drudgery. The readings were picked to inspire kids to think, to have strong feelings about, to be curious about something mathematical that showed up, to see and think about math differently.”

That’s what the readings did.

“What I appreciated most is how humanizing our conversations were of mathematics — in terms of who was doing it — and how much curiosity students brought to the mathematical ideas they were exposed to.”

One student, for example, used The Calculus of Friendship by Steven Strogatz as the model for her final course project, in which she explored her identity and mathematical experiences using calculus concepts.

Although another schedule change this year forced Shah to drop book club from calculus, he has continued the club outside class with interested students.

“If you have the time, it’s a magical way to get kids to see mathematics through a number of different lenses,” he said.

Shah created a list of titles that would work well in a math book club, and Bezaire’s curriculum for The Curious Incident of the Dog in the Night-Time is available on his website. MindShift asked the two teachers to share their advice for educators who want to try incorporating literature into their own math classrooms.

Tips for Curious Incident

  • Lay the groundwork for the unit by communicating with parents, other teachers, administrators, students before diving in. There may be resistance: the book has been removed from some schools because of profanity.
  • Stock up on throat lozenges or tea with honey. “I speak out loud in front of classes for a living, and it’s still a stretch for me to read the book out loud four times per day,” Bezaire said.
  • Pre-read each day’s reading passage to find teachable moments: clues, red herrings and math worth expanding on. Make notes in your copy of the novel to make things easier the second year.

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Tips for math book club

  • Bring snacks and drinks. Make the class feel like it is embarking upon something special and different.
  • Don’t grade anything. Let it be fun and non-stressful.
  • Don’t talk too much.
  • Have all kids come with two to four discussion points to share at the start of each book club. This allows everyone to know what others found interesting and see if there were any topics that the discussion leaders should definitely address.
  • Plan and lead the first book club to set an example of the structure and style.

For a Black Mathematician, What It’s Like to Be the ‘Only One’

Fewer than 1 percent of doctorates in math are awarded to African-Americans. Edray Goins, who earned one of them, found the upper reaches of the math world a challenging place.

Article from New York Times, By Amy Harmon, Feb. 18, 2019.

BALTIMORE — It was not an overt incident of racism that prompted Edray Goins, an African-American mathematician in the prime of his career, to abandon his tenured position on the faculty of a major research university last year.

The hostilities he perceived were subtle, the signs of disrespect unspoken.

There was the time he was brushed aside by the leaders of his field when he approached with a math question at a conference. There were the reports from students in his department at Purdue University that a white professor had warned them not to work with him.

One of only perhaps a dozen black mathematicians among nearly 2,000 tenured faculty members in the nation’s top 50 math departments, Dr. Goins frequently asked himself whether he was right to factor race into the challenges he faced.

That question from a senior colleague on his area of expertise, directed to someone else? His department’s disinclination to nominate him to the committee that controls hiring? The presumption, by a famous visiting scholar, that he was another professor’s student?

What about the chorus of chortling that erupted at a lunch with white and Asian colleagues when, in response to his suggestion that they invite underrepresented minorities as seminar speakers, one feigned confusion and asked if Australians qualified.

“I can give you instance after instance,” Dr. Goins, 46, said as he navigated the annual meeting of the nation’s mathematicians in Baltimore last month. “But even for myself I question, ‘Did it really happen that way, or am I blowing it out of proportion? Is this really about race?’”

Black Americans receive about 7 percent of the doctoral degrees awarded each year across all disciplines, but they have received just 1 percent of those granted over the last decade in mathematics. Like many who see in that disparity a large pool of untapped talent, Dr. Goins has long been preoccupied with fixing what is known as the “leaky pipeline.”

Redress the racial disparities that exist at every level of math education, the logic goes, and racial diversity among those who grapple with math’s biggest problems will follow.

To that end, Dr. Goins delivers guest lectures to underrepresented middle and high school math students, organizes summer research programs for underrepresented math undergraduates, mentors underrepresented math graduate students, and heads an advocacy group that was formed in 1969 after the American Mathematical Society, the professional association for research mathematicians, rejected a proposal to address the dearth of black and Hispanic members.

Dr. Goins’s own journey through the pipeline was propelled by a magnet program that offered Advanced Placement calculus for the first time at his majority-black south Los Angeles high school. In 1990, having aced the A.P. calculus BC exam, he became the first student from the school ever to gain admission to the prestigious California Institute of Technology, just 20 miles away.Attendees gathered for the Joint Mathematics Meetings in Baltimore last month.CreditJared Soares for The New York Times

Attendees gathered for the Joint Mathematics Meetings in Baltimore last month.CreditJared Soares for The New York Times

The 10 black students in his incoming class were the largest group Caltech had ever enrolled, he learned when he wrote a paper on the little-known history of being black at Caltech for a summer research project. Only three of the others graduated with him four years later.

Most of his classmates, Dr. Goins quickly realized, had arrived with math training that went far beyond his own. In his freshman year, he sometimes called his high school calculus teacher for help with the homework. In his sophomore year, he watched from his dormitory television as the 1992 Los Angeles riots erupted a few blocks from his mother’s home. But he also came to excel in applied math, which traffics in real-world problems, and, later, to immerse himself in “pure math,” which seeks to elucidate the questions intrinsic to mathematics itself.

Dr. Goins won two math prizes at Caltech, and in 1999 he received a Ph.D. from Stanford’s math department — one of three African-Americans that have ever done so, according to an informal count by William Massey, a Princeton professor who received the second. In 2004, after holding a visiting scholar position at the Institute for Advanced Study in Princeton and another at Harvard, Dr. Goins joined the faculty of Purdue in West Lafayette, Ind.

“You are such an inspiration to us all,” Talitha Washington, a black mathematician who is now a tenured professor at Howard University, wrote on his Facebook page when he received tenure in the spring of 2010.

Yet having emerged at the far end of the pipeline, Dr. Goins found himself unwilling to stay. Last fall, in a move almost unheard-of in the academic ecosystem, he traded his full professor post at Purdue, where federal resources are directed at tackling science’s unsolved problems and training a new generation of Ph.D.’s, for a full professorship at Pomona, a liberal arts college outside Los Angeles that prioritizes undergraduate teaching.

“Edray,” he recalled one colleague telling him, “you are throwing your career away.”

In an essay that has been widely shared over the last year, Dr. Goins sought to explain himself. He extolled the virtues of teaching undergraduates and vowed to continue his research. But he also gave voice to a lament about the loneliness of being black in a profession marked by extraordinary racial imbalance.

“I am an African-American male,” Dr. Goins wrote in a blog published by the American Mathematical Society. “I have been the only one in most of the universities I’ve been to — the only student or faculty in the mathematics department.”

“To say that I feel isolated,” he continued, “is an understatement.”

Experiences similar to Dr. Goins’s are reflected in recent studies by academic institutions on attrition among underrepresented minorities and women across many disciplines. Interviews with departing faculty of color indicated that “improving the climate” would be key to retaining them, according to a 2016 University of Michigan report.Officials at Columbia, which has spent over $85 million since 2005 to increase faculty diversity, with disappointing results, suggested last fall that progress would hinge partly on majority-group faculty members adjusting their personal behavior.

“In most cases, faculty are not consciously or purposely trying to make colleagues feel unwelcome or excluded,” said Maya Tolstoy, dean of Columbia’s arts and science faculty. “But it happens.”

At the Baltimore conference, Dr. Goins delivered a keynote address titled “A Dream Deferred: 50 Years of Blacks in Mathematics.”CreditJared Soares for The New York TimesImage

And at the recent math meeting, where Dr. Goins delivered a keynote address titled “A Dream Deferred: 50 Years of Blacks in Mathematics,” his presence kindled conversations about racial slights in the math world. The presumption of competence and authority that seems to be automatically accorded other mathematicians, for instance, is often not applied to them, several black mathematicians said.

“Who do they make eye contact with? Not you,” said Nathaniel Whitaker, an African-American who heads the department of mathematics and statistics at the University of Massachusetts at Amherst.

Michael Young, a mathematician at Iowa State University, said he almost gave up on graph theory a few years ago after an encounter with some of the leaders of the field at a math institute at the University of California, Los Angeles.

“A couple of them were at a board writing something,” he recalled. “I went over and asked, ‘What are you guys working on?’”

“We’re too far in to catch you up,” he said he was told.

The ethos characterized as meritocracy, some said, is often wielded as a seemingly unassailable excuse for screening out promising minority job candidates who lack a name-brand alma mater or an illustrious mentor. Hiring committees that reflect the mostly white and Asian makeup of most math departments say they are compelled to “choose the ‘best,’” said Ryan Hynd, a black mathematician at the University of Pennsylvania, “even though there’s no guideline about what ‘best’ is.”

And Ken Ono, a prominent mathematician in Dr. Goins’s field, number theory, and a vice president of the mathematical society, said that a part of Dr. Goins was always likely to be wondering, “‘Do they see me as the token African-American, or do they see me as a number theorist?’”

“And honestly, to tell the truth, I think that answer would vary from individual to individual,” Dr. Ono said.

Most tenured math faculty members at research institutions do not leave, regardless of their race. “I’ve done well and am really enjoying myself,” wrote Chelsea Walton, a black mathematician at the University of Illinois, in a comment on Dr. Goins’s blog post.

But because role models of the same race are seen as critical to luring talented students from underrepresented minorities into a Ph.D. program, it is a blow to lose even one, Dr. Ono said. For the representation of African-Americans in math departments to reach parity with their 13-percent share of the country’s adult population, their ranks would have to increase more than tenfold. (The number of women, also notoriously low among math faculty, would need to triple.) “It’s a loss to our mathematical community that Edray may never advise graduate students again,” said Dr. Ono, who is Japanese-American.

Dr. Goins’s isolation, he himself was the first to note, was also forged by an early career failure. Near the end of his graduate studies at Stanford, he set out to prove a conjecture using techniques suggested by the solution to a 350-year-old problem, Fermat’s last theorem, which had rocked the mathematical world a few years earlier.

Dr. Goins is one of about a dozen black mathematicians among nearly 2,000 tenured faculty members in the nation’s top 50 math departments.CreditJared Soares for The New York Times

It was an ambitious undertaking whose success would probably have snagged him job offers from the most elite math departments in the country. But the conjecture was grounded in a highly technical area populated by the field’s top talent. And despite guidance from Richard Taylor, a white mathematician then at Harvard who had assisted in solving Fermat’s theorem, Dr. Goins was unable to publish the paper he produced four years later.

Several mathematicians familiar with Dr. Goins’s efforts said they did not see racial discrimination as playing a role. It is not all that unusual, they said, for such an ambitious undertaking to end in an unsatisfying result. But it also can require deep reserves of self-confidence and a professional network to bounce back.

Dr. Goins’s colleagues at Purdue said his receipt of tenure and subsequent promotion to full professor signaled the university’s willingness to overlook a sparse research portfolio in light of his extraordinary work with undergraduates, as well as the summer programs he organized for minority students.

“While these areas are not necessarily ‘traditional’ markers for excellence at major research universities, they were valued,” Greg Buzzard, the head of Purdue’s math department, who is white, said in a statement.

But Dr. Goins said he was looking for something else.

“I just never really felt respected,” he said.

At the math meeting last month, Dr. Goins’s essay was not immune from criticism.

Some black mathematicians questioned the utility of dwelling on perceived slights, many of which are unconscious or made out of ignorance.

Some who know Dr. Goins noted his sensitivity. Insults that others might shrug off, they said, might stick with him.

For Bobby Wilson, a mathematician at the University of Washington, offenses related to race “just start to wash over you.” He added: “That doesn’t mean it’s right or good.”

Over dinner one evening, another black mathematician told Dr. Goins that he was worried that his blog account of the difficulties he faced might discourage black graduate students who hope to pursue careers in academic research.

Maybe, it was suggested, he should have kept it to himself.

Dr. Goins, taking that in, was silent. His reply came only the next day.

“I didn’t write it to tell people what should happen,” he said. “I wrote it to tell people what could happen.”

Amy Harmon is a national correspondent covering the intersection of science and society. She has won two Pulitzer Prizes, one for her series “The DNA Age,” and another as part of a team for the series “How Race Is Lived in America.” @amy_harmon • Facebook

Operator K-Theory in Geometry, Topology and Representation Theory

As the university of Kyoto has announced a conference in ” Operator K-Theory in Geometry, Topology and Representation Theory” will be held
to mark the occasion of Gennadi Kasparov’s 70th birthday:

  • Operator K-Theory in Geometry, Topology and Representation Theory (Gennadi Kasparov 70)
  • Venue : Kyoto University, Kyoto, Japan
  • Dates : June 10-14, 2019

The link of announcement: Gennadi Kasparov 70