Research in math rarely generates much controversy, but the recent back and forth over the work of Rochelle Gutierrez and others is something of an exception. That work discusses the cultural roots of math, specifically the way it operates as a gendered space that perpetuates male and white privilege. Even though many professional organizations in math have supported Gutierrez and her work, people continue to demonize her.
Suffice it to say that I stand with Gutierrez. See here for more information.
(For an added bonus, check out The Liberated Mathematician.)
Dashiell Hammett tells this classic story in terse, punchy sentences that take the reader around San Francisco and through a twisty plot with Sam Spade, private eye. Spade is worldly, jaded, at times childish, and always chauvinistic. Despite his shortcomings, his ability to assess people and their motivations is remarkable, his insights and intuitions not perfect, but close enough to do the job. In the end we see that, for Hammett, Spade’s flaws are reflections of the world in which he lives.
It took me a long time to read Have His Carcase. Sayers’ detailed style is, perhaps, a little slow for the contemporary ear. On the other hand, it speaks to the real pace of most police work. They laboriously check every lead, slowly eliminating possibilities till they narrow it down to the real killer. It’s not exciting, but it is satisfying because it works.
In The New Jim Crow, Michelle Alexander traces the history of racialized control in the US – from slavery, to Jim Crow, to mass incarceration – pointing out the similarities and differences, particularly between the Jim Crow of the early and mid-20th century and the mass incarceration of African-American and Latino men in the present day.
Jim Crow – which had replaced slavery as the method of reinforcing white supremacy in the US – was a system of laws and practices that made black people into second class citizens unable to vote, to serve on juries, to live in white neighborhoods, to go to school with white children, to use the same bathrooms as white people, or to participate in white society in a myriad of other ways. When it began to crumble in the face of the civil rights movement in the 1950s and 1960s, there was a period of relative hope for racial equality for African-Americans that included more decent-paying jobs, educational opportunities, and more.
The time of promise was short-lived. Alexander argues that the War on Drugs is the mechanism that was and is used to replace Jim Crow by imprisoning of huge numbers of men of color and reinforcing what she calls the “caste system” in the United States. The War on Drugs was initiated by President Reagan in 1982 despite the fact that at the time “less than 2 percent of the American public viewed drugs as the most important issue facing the nation.” Money for drug enforcement skyrocketed. “Department of Defense antidrug allocations increased from $33 million in 1981 to $1,042 million in 1991. During that same period, DEA antidrug spending grew from $86 to $1,206 million, and FBI antidrug allocations grew from $38 to 181 million.”
Because “police can stop, interrogate, and search anyone they choose for drug investigations, provided they get ‘consent,’” racial biases have free rein. In fact, police are allowed to rely on race as a factor in selection whom they stop and search (even though people of color are no more likely to be guilty of drug crimes than whites) – effectively guaranteeing that those who are swept into the system are primarily black and brown.
“Human Rights Watch reported in 2000 that, in seven states, African-Americans constitute 80 to 90 percent of all drug offenders sent to prison. In at least fifteen states, blacks are admitted to prison on drug charges at a rate from twenty to fifty-seven times greater than that of white men.” In that same year, African-Americans were admitted to prison at a level “more than twenty-six times the level in 1983. The number of 2000 drug admissions for Latinos was twenty-two times the number of 1983 admissions.” (Emphasis in the original.) By comparison, “the number of white drug admissions was eight times the number admitted in 1983.”
After arrest, prosecutors can overwhelm defendants with extra charges for which they have no evidence in an often successful attempt to get them to accept a lesser, but still felonious conviction. Because of harsh sentencing laws, “drug offenders in the United States more time under the criminal justice system’s formal control – in jail or prison, on probation or parole – than drug offenders anywhere else in the world.”
Predictably, the prison population exploded: “In 1972, fewer than 350,000 people were being held in prisons and jails nationwide, compared with more than 2 million today .” They are disproportionately black and Latino. “One in every 14 black men was behind bars in 2006, compared with 1 in 106 white men. For young black men, the statistics are even worse. One in 9 black men between the ages of twenty and thirty-five was behind bars in 2006, and far more were under some form of penal control – such as probation or parole.”
This despite the fact that crime rates in the US remained flat or even fell during this time. Moreover, study after study show that crime rates are roughly equal across racial groups. It is not that black and Latino men are more likely to commit crime. It is that they are more likely to be targeted for arrest, more likely to be convicted, and tend to have longer sentences when convicted.
Once convicted, discrimination that is remarkably similar to Jim Crow segregation is legal and encouraged. A system of laws and practices denies felons the right to participate in society, even though they have “paid their debt.” “The vast majority of convicted offenders will never integrate into mainstream, white society. They will be discriminated against, legally, for the rest of their lives – denied employment, housing, education, and public benefits.” Felons cannot vote or serve on juries. Felons cannot apply for federal low-income housing. They are not eligible for most financial aid for college. It is legal in almost all states to deny jobs to the formerly-incarcerated, and they are barred from obtaining many licenses to open businesses of their own. Even in states where convicted felons are eligible for some of these right, they are shackled by legal fees and paperwork requirements that make exercising those rights all but impossible.
Alexander is clear and thorough and thoughtful. The statistics she cites are useful and compelling. Her arguments are logical and compassionate. If at times I felt overwhelmed by the book, it speaks only to its power.
Her goal is not to propose remedies, though she does begin to discuss them at the book’s end. Instead, I think her goal is to show how the system of mass incarceration is one of the biggest, if not the biggest civil rights issue of our time. In this, I think she succeeds.
When she does discuss remedies, she brings in the vision of Dr. Martin Luther King Jr., who called for a shift from civil rights to human rights. Alexander, in turn, suggests that we unify across racial lines, not by ignoring our differences or pretending that we don’t see the color of each other’s skins, but by recognizing and acknowledging the humanness that we all possess. We can no longer accept the “racial bribes” we are often given, the crumbs that put most whites, even if they live in abject poverty, above most people of color. Some people of color benefit, too, but at the expense of everyone else. Alexander argues that a more just and better world could exist if we reject those bribes and form a coalition that recognizes the common human needs we share and are systematically denied. Together we could be more powerful and build a society that benefits all the people, rather than just a few.
As I read this book, I repeatedly thought that a similar analysis needs to be done of many of our institutions so that we can understand and deconstruct the ways that all our institutions disadvantage people of color, women, and others. I thought particularly of the ways that higher education pushes out people of color and poor folks, sending them the message that they don’t belong there. Perhaps someone is already working on these books. I hope they are, because I believe that knowing and understanding these issues can help us create a more just society.
In Silence of the Lambs, Thomas Harris uses straightforward clear prose to tell the story of an aspiring FBI agent, Clarice Starling, assigned to help track down a serial killer by interviewing the brilliant sociopath, Hannibal Lecter. When the serial killer kidnaps the daughter of a US Senator, the chase is on to rescue the daughter before she dies a gruesome and lonely death.
The novel is part procedural, but the best moments are personal. The dynamic between Starling and Lecter is brilliantly rendered. I found myself waiting for more.
I never saw the Academy Award-winning movie adaption. The book is good enough on it’s own.
As part of my research, I’ve stumbled across the work of Michelle Pacansky-Brock and what she calls “humanizing” online learning. She has created an infographic summarizing “How to Humanize Your Online Class“:
Pacansky-Brock’s work dovetails nicely with the work of Drs. Luke Wood, Frank Harris III, and Khalid White. In their book, Teaching Men of Color in the Community College (there’s also an online course with the same name), they stress teacher-student relationships that include positive messaging, authentic care, and intrusive interventions. They also point to the importance of high expectations and high support in the context of relevant content, critical reflection, collaboration, and performance monitoring. While that’s a lot to take in, I thought Michael Smedshammer’s approach in his Online Teaching Conference presentation, Five Ways to Leverage Your LMS to Improve Student Equity, put it succinctly: “Put relationships before pedagogy” and use “intrusive pedagogy.”
For me, this means it’s the teacher’s responsibility to reach out to our students. We cannot just offer to meet with students or put the invitation out there. We need to schedule times with our students and seek them out if they don’t show up. This is especially important for those students who need the most help and may be most embarrassed to asked for it.
In my own experience as an online and hybrid teacher building the relationships is the most difficult part, particularly because it’s one of the strengths I bring to my face-to-face classroom. Online and hybrid instructors typically see our students much less often than our in-the-classroom colleagues. We have to create human presence through the internet. When I started teaching online, I not only didn’t know how to be “present” remotely, I wasn’t very comfortable with trying. It felt completely alien and weird and the opposite of personal. I had to learn to get over myself. No matter how accomplished I was in the classroom, I had to adapt to the new environment. I had to get out of my comfort zone and do the things that my students needed. The resulting experiments have not been perfect, but I’ve learned a lot.
Here’s some concrete ways you can make your presence more real for your students online. You can use these to show who you are and to demonstrate your passion for your subject and for teaching. (Many of these ideas are gleaned from Pacansky-Brock and Smedshammer, as well as Fabiola Torres):
- Embed video of yourself in your syllabus
- Use icebreakers
- Offer online office hours using Zoom or Google Hangouts
- Use a texting service like Remind:
Email is old-fashioned. There’s no better way to reach your students than on their phones. I now require my online and hybrid students to sign up to receive texts from me. Even though I give them the option to talk to me about why they don’t want to get those texts, not one student has asked to get out of the requirement. Far from being intrusive, most students seem to appreciate my texts and see it as sign that I care about their success.
- Post weekly or more frequent videos in your course:
Encourage students and let them see your normal or even geeky self. Torres calls these “learning nudges.” You can use QuickTime or iMovie or any number of other applications.
- Respond to student work with a video — this is really easy inside Canvas. There should be a button to press under the box for assignment comments that allows you record and post a private video right inside the LMS.
Before the 13th century AD, math was done in sentences, sometimes called “rhetorical math.” The symbols we currently associate with math began to emerge in the Arab world during the 13th, 14th, and 15th centuries. By the 16th century, French thinkers were developing a fully symbolic system.
The advent of symbolic algebra changed the way we think about, learn, and do math. It also changed the kinds of problems that were doable by the lay mathematician with a basic education. Electronic calculators made arithmetic with large numbers more accessible, but didn’t fundamentally shift the way we think about math or learn it. (There is still plenty of debate in math education circles about the appropriate use of calculators in the curriculum.)
Today, computer technology is slowly altering math and math education, but especially in math education that potential is only beginning to be realized. Much of what we do with computers in math education mimics books, except in more color and with occasional hyperlinks. While there are folks taking advantage of multimedia presentation (think video, interactive sliders, etc. – for instance, the folks at Desmos are doing some great work), I have yet to see computers fundamentally and broadly change the way we teach math in the way that symbolic manipulation on paper did.
One option is to let the internet provide the kind of instructions that we’re used to seeing from teachers. Sites such as Khan Academy and publishers like XYZ Textbooks provide videos with multiple examples worked out slowly and carefully. Students can watch them on their own time, as many times as they want, stopping and starting and rewinding as they need. In class, teachers can clear up misconceptions and extend ideas already developed at home.
This “flipped classroom” model, however, assumes students can access the internet at home, an assumption that is often wrong and disadvantages those with the least (Is Digital Equity the Civil Rights Issue of the Day?). Add to that the fact that desk tops are giving way to small screens and it’s clear we must make sure we are making mobile-native, or at least mobile-friendly, education sites and activities. Even then, folks living in or on the edge of poverty often lose their access.
With this as context, consider Keith Devlin’s Mathematics Education for a New Era. In it, Devlin pulls together a career as a math educator and a love of video games to suggest a way for math and math education to evolve for the 21st century and beyond.
Devlin starts by discussing what he calls eleven principles of an ideal learning environment – like “the learning environment should be as similar as possible to the environment in which people will use what they learn” and “there should be sufficient ‘cost’ to getting something wrong to motivate correction, but not so great that it leads to the student losing heart and giving up” – ideas I think most people would agree with. With that basis, he tries to show how video games fit the principles very closely, even to the point of calling the next chapter “Euclid Would Have Taught Math This Way.” Part of this argument involves discussing the 36 principles of education that go into video games according to James Paul Gee (professor of education at Arizona State University) in his book, What Video Games Have to Teach Us About Learning and Literacy. Devlin goes on to discuss various aspects of math education and finishes by advocating for a math pedagogy that is part “flipped” and all carefully thought out to create optimal learning for each individual student, taking advantage of whatever methods are best for what’s being taught.
I find Devlin’s ideas compelling. Use computers and computer games to do the things they are good at: repetition and drilling (when appropriate); motivation and story. Continue to respect the relationships between teachers and students in a thoughtful system that supports students in the ways that they most need it. He is not arguing that that video games should be the sole way to teach math, or even that it is the best way. Instead, he believes that well-designed math education video games could be a powerful addition to school, home, textbooks, and the rest of the math educational apparatus.
He also makes some useful observations and distinctions for math teachers (like myself):
- The phrase “’do math’ is all too frequently taken to mean mindless manipulating symbols, without the full engagement that comes with genuine mathematical thinking.” In fact, Devlin points out, “skills are much more easily acquired when encountered as a part of mathematical thinking.” But he reminds us, “mathematical thinking is not something the human mind finds natural.”
- Anyone trying to teach math should design situations for students that promote mathematical thinking and expect to need to help them, while always remembering that “attempts to understand what it all means at too early a stage can slow the learning process.” In fact, “full conceptual understanding, while desirable, is not strictly necessary in order to be able to apply mathematics successfully.” Often what is needed in the short term is “functional understanding”:
Calculus is in many ways a cognitive technology – a tool you use without knowing much, if anything, about how it works. For example, few people know how an automobile engine or a computer works, but that does not prevent those people from becoming skillful drivers or computer users. Successful use of a technology does generally does not require an understanding of how or why it works.
I realize all of this is a pretty big pill to swallow for many of us, especially those, like me, raised on endless worksheets of drill, without motivation except a task master with a real or metaphorical ruler ready to slap the idle hand. But computers are changing many aspects of our life, for better or worse, and I don’t think that’s going to stop. Instead let’s figure out how to use them well, for the good of the generations to come. I think that’s what Devlin is trying to do. If it’s not the “right” answer, then it’s a pretty good try.
I’ll leave you with a long quote from the book’s opening chapter that I think captures some of Devlin’s vision and passion:
When people made the first attempts to fly, the most successful machines for transport were wheeled vehicles, and the only know examples of flying creatures were birds and insects, both of which fly by flapping wings. . . but that doesn’t work for humans. The key to human flight was to separate flying from flapping wings, and to achieve flight by another means more suited to machines built from wood or metal. . . .
Putting symbolic expressions in a math ed game environment is to confuse mathematical thinking with its static, symbolic representation on a sheet of paper, just as the early aviators confused flying with the one particular representation of flying which they had observed. To build truly successful math ed video games we have to separate the activity – a form of thinking – from its familiar representation in terms of symbolic expressions.
Mathematical symbols were introduced to do mathematics first in the sand, then on parchment and slate, and still later on paper and blackboards. Video games provide an entirely different representational medium. As a dynamic medium, video games are far better suited in many ways to representing and doing middle-school mathematics than are symbolic expressions on a page. We need to get beyond thinking of video games as an environment that delivers traditional pedagogy – a new canvas on which to pour symbols – and see them as an entirely new medium to represent mathematics.
Jay Fitger is a middle-aged professor of English and creative writing at Payne (pun intended) University, by his own admission a “second-tier,” liberal arts college. Though fully-tenured, he is sagging under the pressures of a writing career in neutral, a personal life in reverse, and the general neglect of the liberal arts in academia.
Nevertheless, numerous students and colleagues request letters of recommendation from him for things ranging from administrative positions at the college to jobs in paintball emporiums to $400 scholarships. Fitger completes these letters and does mention the recommendee, but feels free to add whatever else he wants. Personal issues, critique of the institution to which he writes, and praise of the traditional letter as opposed to the electronic form are common themes.
A representative sample:
Dear Committee Members,
This letter recommends Ms. Stella Castle to your graduate institution in the field of public policy. And to begin the recommendation on the proper footing: no, I will not fill out the inane computerized form that is intended to precede or supplant this letter; ranking a student according to his or her placement among the “top 10 percent,” “top 2 percent,” or “top 0.000001percent” is pointless and absurd. No faculty member will rank any student, no matter how severely lacking in ability or reason, below “top 10 percent.” This would be tantamount to describing the candidate in question as a witless beast. A human being and his or her caliber, intellect, character, and promise are not reducible to a check mark in a box. Faced with a reductionist formula such as yours, I despair for the future, consoling myself with the thought that I and others of my generation, with its archaic modes of discourse, won’t live to see the barren cyberworld the authors of your recommendation form are determined to create.
Even if you sympathize with Fitger’s sentiments, it’s hard to see how such a letter can help Ms. Castle regardless of what praise he heaps on her after this first paragraph.
In my own life as an academic, I have known my share of Fitgers. They are pompous, self-centered, and not very nice. The (mostly unacknowledged) privilege they enjoy is matched only by the degree to which they feel persecuted and powerless. It is a potent brew. In Dear Committee Members, Julie Shumacher has captured them in all their delicious irony. I see it as a cautionary tale: there but through compassion, love, and hopefully humility go I.
I am currently on sabbatical till January, 2018. During my sabbatical my primary work-related responsibility is to complete a research project.
In my research project I’m trying to pull together three areas that I have worked in over the course of my career as a community college math teacher: math education, multicultural education, and online education. My initial research has found that, while there is literature in the overlap of pairs of these (math and multicultural, math and online, multicultural and online), there is little where the three areas intersect.
If further research confirms that little or no work has been done in these area, then this niche needs to be filled. The importance of better math education is well-documented. As our college student population increasingly diversifies, the need for the still majority-white teaching profession to understand how to better communicate with students of all backgrounds is more crucial than ever. And, though I don’t think technology is the answer to all educational problems, we would be foolish to think that online education is going away; on the contrary, the private-sector is pushing that way, legislatures have visions of the savings it can produce, and students are demanding the flexibility of learning on their own time and from where ever they happen to be.
I’d love to collaborate with others on what I think is a critical confluence of research and practice. If you’d like to work together, or if you know of work in the intersection of math education, multicultural education, and online education, I’d like to here from you. Please comment here or contact me at: email@example.com.