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Andrew Hacker’s The Math Myth and Other STEM Delusions simply continues to promote the misguided path he got on several years ago, and it’s difficult to see how it could lead us anywhere productive. Hacker started the business of attacking school mathematics in a New York Times op-ed where he argued, in sync with gimmicky T-shirts claiming the same, that algebra was unnecessary, or perhaps even detrimental to our future. In a national scene where mathphobia is rampant and most people’s memories of school mathematics remain unpleasant at best, he struck a chord. Then, of course, come book contracts and even more adulation.
Thoughtful people have already responded authoritatively to the various errors in Hacker’s argument -- see here for another scathing review. A short and quick reply is here. For this audience of college and university educators, some of whom might be tempted by Hacker’s bravado and wonder about implications for higher education, I’d like to also point out that Hacker seems to forget why we educate our young. Even if as students years ago we may have had difficulty in certain subjects, as parents we want to ensure that our children go beyond what we ourselves have achieved. We expect that what they learn will be beneficial to their growth and future opportunities. We also hope that they will gain certain personal characteristics that, together with their knowledge and skills, will help them build a better future for our society and the world.
The Western tradition starts this conversation in ancient Greece with Socrates arguing that virtue is central to the education of the young. Aristotle teaches us that the ultimate goal of education should be happiness -- the durable contentment of a creative and intellectual life. St. Augustine shows us that we should not depend on teachers to teach us everything, that there is much to be learned from the internal wisdom of the heart, which itself is cultivated by our moral compass. Rousseau argues that children need to be exposed to the world as they grow to learn to live within the society to which they belong. Locke and Mill teach us that education should be well-rounded, cultivating an intellectually capable mind aware of the complexities of the world.
Mathematics educators agree. We know that in mathematics, as in any other knowledge system that builds on itself, the procedures that work so well are only part of the package. That in the center is the student, but always situated in the midst of a society that is constantly evolving. That students learn best when encouraged and supported by knowledgeable teachers who help them explore and understand underlying concepts. That intellectual stimulation and growth are possible and enjoyable for all children. That in our classrooms, we can help students sharpen their ability to persist in the face of apparent failure. That today’s students need to learn to tackle complex and ill-defined problems requiring both individual and collaborative effort.
And to these ends, we have been working to improve what we do. Mathematics teachers, mathematics education researchers and mathematicians are working together in classrooms, in math circles, in conferences and workshops, in curricular reform efforts and in policy discussions. We are working to create meaningful mathematical experiences for students to encourage critical thinking, foster creative reasoning and enhance problem-solving abilities. (See here and here for two collections of mathematics lesson plans and modules that were developed by or in collaboration with researchers. See here for a college-level initiative for revamping the mathematics curriculum.)
We are working to engender the sense of wonder and accomplishment that mathematics -- when done right -- naturally inspires. We are working to develop and support a coherent set of curricular standards that will help tomorrow’s adults live up to the expectations of this nation from its children. We are working to discover and share with parents, teachers and educators what works well in the classroom even if it is not typical, and what doesn’t work even if it “just makes sense” and “it’s the way I learned things.” (How many people believe that the point of multiplication tables is to torture students till they can recite them at the speed of light? Linda Gojak, past president of the National Council of Teachers of Mathematics, is one among many educators speaking out about fluency in mathematics and how it is no longer acceptable to equate it with “fast and accurate.”)
Admittedly, we mathematics instructors don’t always help our own cause. People remember how their middle school math teacher made them feel, and I don’t need to tell you that it’s generally not a good memory. (I was lucky -- mine made me feel like there wasn’t a problem I couldn’t solve if I put in the time and effort.) But dropping mathematics from the required K-12 curriculum would be a perfect example of the cliché of throwing out the baby with the bathwater. (While I myself have argued elsewhere that we might just do that, my tongue was decidedly set in my cheek, and my concern was the essence of what is lost in most mainstream experiences of school mathematics. Now, can I get a book contract, too?)
The current state of mathematics education in the United States is certainly not ideal. Yet the fact is that teachers, parents, mathematicians, mathematics education researchers and policy makers are working on it. Furthermore, this is definitely a problem worth working on. It is tough, it is messy and there are many nuances to the issue and many implications to any avenue of resolution.
Hacker writes of high school graduates unable to perform simple numeracy tasks. I’d venture to guess that more than a handful of high school grads are also incapable of understanding IRS publications, may occasionally be unable to interpret correctly the user manuals of their DVD players and can’t foresee all repercussions of a ballot measure they are willing to vote for or against. But we do not blame all of these insufficiencies on K-12 English teachers. Nor do we suggest replacing English courses with courses on reading ballot measures or user manuals. What do we do? We demand that English Language Arts curricula be developed that are more sensitive to the range of literacy demands of our daily lives.
Hacker gets it right at least in one instance; quantitative literacy is crucial in today’s society. And it should be one of the essential outcomes we expect from our education system, as I argueelsewhere. However, the role of mathematics in our education system goes beyond quantitative literacy. (And conversely, quantitative literacy as a goal itself should not be limited to the mathematics classroom. Most science and social studies classrooms offer excellent contexts for quantitative literacy.)
During this election year, I offer you another analogy. Today there are many, including some reading this, who worry that the American democratic machine is not producing the results they would like. So shall we give up on democracy? I’d like to believe that the overwhelming majority would agree with me when I say no. Instead, we continue working to improve our system; we continue to fight for broader access; we continue to work to further political and social justice.
Mathematics education is perhaps not on the same level of importance and urgency, but the solutions are the same. We must work to improve the system. We must fight for broader access. And we must work to further political and social justice.
Today mathematics acts as a gateway (or a gatekeeper, depending on your perspective) in terms of who has access to the lucrative STEM jobs that many aspire to. Students who learn mathematics as far as their school contexts allow have many more opportunities open to them when they graduate from high school. Knowing the fundamental building blocks of mathematics today leads well-prepared high school graduates to a range of rigorous paths of college-level study in many disciplines. And those are also the students who will become the adults who will create the new mathematical, statistical and computational tools we will need in the future.
What would happen if we dropped mathematics? Which schools and school districts would not be offering those “now optional” advanced mathematics courses? Which students would be deprived of the opportunity to learn, and, can I suggest, find meaning, confidence and opportunity through advanced mathematics? And which students would be able to move forward with those STEM careers that many parents dream of?
People can succeed without mathematics in their lives. You can also choose to never try sushi, to vacation only within the continental United States despite being able to afford international travel, to never wear flip-flops or learn to ride a bike, and still lead a happy and productive life. But nobody’s job prospects are affected by their decision to avoid sushi (unless you want to be a sushi chef, which would be odd if you didn’t like sushi to start with). And having the choice to decline comes out of privilege. Can this nation afford to make such a decision for all its children? When people choose to drop mathematics later in their academic paths, we can say they made a decision knowing their options and the opportunities they are letting go. But do we want to make these decisions ahead of time for all students?
The American education system differs from many of the nations that are touted as high performers. In most of those countries, students are channeled into various tracks early on. This nation does not regiment its schoolchildren, because we believe that all children have potential and that they can make choices once they are old enough to know what is out there.
And the American education system is still one of the best in the world. I know the international test scores and rankings, but I also know to read the fine print. Therein you learn that once you restrict to schools where less than 50 percent of the class is in the free lunch program, the performance of students is in par with those high-performing nations. The schools that are “failing” are the ones that have 75 percent or more of their students in free lunch programs. So our schools are not failing our students; it is our society that is failing them. As most education researchers (and teachers in classrooms across the nation) will agree, the problem of public education in the United States is one of poverty. And that problem is not going to get solved by dropping the mathematics requirement in the K-12 curriculum.
In fact mathematics can help. Here is where Plato’s virtue and St. Augustine’s moral compass come back into school mathematics. Brazilian mathematician Ubiratan D’Ambrosio has been telling us for years that it is mathematics that will help our children solve the varied problems of today and tomorrow -- if we can teach them to see the inherent mathematics involved. Mathematics, historian Judith Grabiner points out, has evolved precisely to describe social, environmental and political, as well as industrial and scientific, problems that a society happens to confront. And it remains, to this day, our most successful method to seek out creative and productive solutions for them. (Readers perplexed by my inclusion of social, environmental and political problems above might like to google “mathematics for social justice” or “mathematics of sustainability.”)
I write this with the hope that some good may come out of Hacker’s simplistic recommendations. Students reciting their multiplication tables as fast as a bullet train are not the desired outcome of mathematics education. We want students to understand the power and limitations of the mathematics they are learning. We want students to move flexibly from one specific model of a situation to another. We want students to be able to find unexpected and novel solutions to problems that are ever-growing in their complexity.
Mathematics is where we can train young minds to do all these things. Mathematics is where we can teach that critical ability to reason analytically. Mathematics is also where we can encourage creative exploration of the multitude of options a problem solver invariably has. As college and university educators, these are points we must not forget when the next cycle of general education debates begins to shake things up on our campuses.
Gizem Karaali is an associate professor of mathematics at Pomona College, editor of the Journal of Humanistic Mathematics, associate editor of Mathematical Intelligencer and associate editor of Numeracy. Follow her on Twitter @GizemKaraali_.
Online master's program in computer science -- a much-watched attempt to apply the MOOC model to for-credit programs -- may not be the big revenue generator the institute projected it would be, but administrators deem it a success and plan to expand it.
A friend who teaches classics at a fine liberal arts college told me that she had met the president of the institution walking across campus. He greeted her, and they chatted for a few seconds. Then the president asked, “How can we justify putting resources into Ancient Greek 101 where the enrollment is eight, while the enrollment in Economics 101 is 189?” My friend reported she had become flustered because she was unprepared for that question. She told me she believed that we needed to be doing a better job of making the case for the classics, the humanities and liberal education in general.
Wait a minute, I thought. That’s his job, or ought to be. Her job is to advance and transmit knowledge in a core humanistic discipline. What’s his game? Intimidation? Making himself look good because, in fact, he was not about to let the teaching of ancient Greek end on his watch after more than two centuries on that campus? Or was he genuinely asking for help?
Still, I thought, she is right: we do need to improve the understanding of why studying the humanities is important for today’s students (and administrators). Maybe, I thought, I should pitch in by writing an op-ed piece for Inside Higher Ed making the case for these fields.
But the phrase “making the case” stuck in my craw. It sounded so courtroom, so defense attorney, or rather so much like the message behind a now-terminated presidential candidacy: “Trust me, we know best.” It is surely self-serving.
After all, like most people who write such pieces, I have made my living on the humanities. Of course, I want them to flourish, but who will pay attention to an obviously self-interested spokesperson? Preaching to the choir may win praise from like-minded colleagues but will never be seen by the people who most need to rethink the assumptions that shape contemporary higher education: that college is a commodity sold to student-consumers, it’s all about “workforce readiness,” its goal is “return on investment” and only the STEM disciplines can guarantee success after graduation. These unexamined premises pose the most insidious threat, not just to humanists, but to all students over their lifetimes.
So it’s worth brainstorming about alternative strategies. Here are a half dozen possibilities. A brief brainstorming session with friends and colleagues can, I am sure, produce other, perhaps better ones. However, these are, as we say nowadays, cost-efficient -- that is, they do not take a lot of time away from teaching and scholarship. The effort is focused on helping people outside academe do the heavy lifting. Alumni, civic and business leaders, parents, and undergraduates themselves have more credibility than professional humanists, and they can surprise you by their articulate enthusiasm. And, yes, they can have more impact than another op-ed piece “making the case.”
That’s even more likely to be the case with shorter pieces. Here’s one example: Hunter Rawlings, the president of the Association of American Universities, published a powerful op-ed piece, “College Is Not a Commodity,” in The Washington Post not long ago, attacking one of the clichés that are so prevalent these days. The essay is an evergreen that merits a second wave of circulation on social media. In fact, it should be handed to any college administrator who seems to talk commodity talk when they should be thinking hard about how best to educate today’s students.
Second: Check the departmental website. Does it really address the questions that parents and students are likely to have about majoring in the field? Ask some students to grade the content. They’ll probably want to see if claims about the desirability of such a major are backed up by strong evidence and clear argumentation.
Douglas MacLean, a professor in the philosophy department at University of North Carolina at Chapel Hill, got thinking about that after Marco Rubio made his famous pronouncement, “Welders make more money than philosophers. We need more welders and less (sic) philosophers.” Answering that claim led to collecting data, as MacLean explained in a Time magazine article, some of which was posted on the department’s webpage. MacLean notes, “Studies have shown philosophy majors have outperformed nearly every other major on the law school aptitude test, the GREs and the GMAT, the admission test for business schools. (They also outearn welders.)”
Third: Ask former students to reflect on their educational experience in the humanities and then disseminate their observations. One way to get the discussion started is to provide the link to comments by students on other campuses, such as the remarks in Frank Bruni’s New York Times piece “College, Poetry and Purpose.” Ask if the experiences cited there match their own. Then put students’ own stories on the departmental website and out on social media. Ask, don’t tell. It doesn’t all have to be glory hallelujah! Find out what graduates working outside the academic humanities have found valuable in their education, then help their message be heard. And keep the email addresses for the following strategy.
Fourth: Put the alumni office to work. Vanessa Ryan, associate dean of the graduate school at Brown University, describes a plan that worked well there: “In 2012, I organized a TEDx [talk] on life, learning and liberal education, bringing back eight alumni from different career paths, including a doctor, an engineer, a film producer and a person in finance. It also features two current Brown faculty members and a current Brown undergraduate, selected through a student challenge event. Each speaker reflected in short talks on the value of liberal education. You can find the videos here and our website here.” Alumni Relations officers love events of this sort and can help organize (and pay for) them.
Fifth: Set clear responsibilities in institutional leaders’ jobs. When selecting a senior administrator -- a dean, provost, chancellor or president -- ask if the job description includes the ability to articulate the value of a broad liberal education. If not, why not? The same questions apply to incentive packages that are increasingly part of senior-level compensation. Making this criterion explicit early on gives leverage once the person is in place -- and especially when performance reviews are conducted.
Finally: Hijack Parents’ Day. Parents are understandably worried about the hollowing out of the economy and the horror stories they hear of students with huge debt loads who can’t find a decent job. Again, both data and descriptions of the actual lives of recent graduates can help allay their fears.
Most important, however, is a carefully structured dialogue among parents themselves. Make sure they have before them the 2014 Purdue-Gallup Index report, a study of more than 30,000 college graduates, showing what aspects of education make a positive difference in the workplace and the community. That report should move the conversation from nervous chatter about debt loads and return on investment to an exploration of what parents really want for their kids and what can best build satisfaction over the long run.
Once you introduce the idea of satisfaction in life, it should be possible to problematize (as we humanists like to say) assumptions about success and rewards. Such discussions play out on the humanities’ home turf: many humanists have thought long and hard about discourses and how they change over time. Here’s a chance to move from theory to practice. That’s what is most needed right now: not making the case but developing richer and more meaningful ways of thinking about what a college education should be.
W. Robert Connor has served as director of the National Humanities Center and president of the Teagle Foundation. He blogs at www.wrbertconnor.com.
We need only two things to convince our communities, public officials, local employers and parents of students and prospective students about the value of a degree in the humanities: stories and data.
In the humanities, we have always used stories well. We can assemble lots of anecdotes about our graduates and how, now that they’re gainfully employed, they use what they learned in our classes. Anecdotes are clearly not enough, however. We’re definitely not winning the public relations contest about what aspects of public higher education are worth investing in. So how can we supplement our good stories with good data, while keeping the discussion firmly rooted in the humanities?
In an effort to share strategies and to get better at making the case for the value of humanities education, a group of about 40 humanities faculty members and administrators, local employers, and public humanities representatives in southern New England got together recently. We talked about what student success in the humanities looks like, how we could measure what it gives students and how we would know when we’ve helped students to achieve it.
The question of student success is on everyone’s radar these days, and the discussion usually refers to retention and graduation rates. Our discussion in New England pointed a different way, however. We wanted to bring employers into the conversation to help them to understand what our students are learning and to help us to learn what they value in new employees. That is especially important for those of us who take issues of racial and economic diversity seriously. As Karen Cardozo, assistant professor of interdisciplinary studies at Massachusetts College of Liberal Arts, pointed out at the meeting, if we can show that humanities degrees have value in the workplace, we can assure working-class students, first-generation students and students of color that following a passion for history, philosophy, literature or music can lead to a good job, too.
Here’s how our meeting went:
First, we assembled by tables, trying to making sure an employer and a public humanities representative were at each table. (Public humanities representatives include those who work at museums, state National Endowment for the Humanities affiliates, cultural councils and the like.) Employers from publishing, local government and local small businesses also participated. (We hope to involve some larger employers next time we meet.) We also mixed in representatives of two- and four-year colleges, as well as public and private institutions.
Each table considered one question at a time, and we then discussed our answers in the group as a whole. Here are the questions:
What can a humanities graduate do?
What (else) should a humanities graduate be able to do?
How can we make sure students graduate with this knowledge or these skills?
How can we measure or assess whether they can do what we say they can do?
It was great to have employers at each table, and we moved them around between groups for each question so the tables could get different perspectives. Some of the employers were already savvy about what a humanities education delivers; others weren’t sure what exactly constitutes the humanities.
Together, we compiled a list of the skills that we think graduates have cultivated in their humanities education:
Writing skills, with style
Cultural competencies, intercultural sensitivity and an understanding of cultural and historical context, including on global topics
As part of our list, we also agreed that graduates should have the ability to:
Construct complex arguments
Provide attention to detail and nuance (close reading)
Ask the big questions about meaning, purpose, the human condition
Communicate in more than one language
Understand differences in genre (mode of communication)
Identify and communicate appropriate to each audience
Be comfortable dealing with gray areas
Think abstractly beyond an immediate case
Appreciate differences and conflicting perspectives
Identify problems as well as solving them
Read between the lines
Receive and respond to feedback
Then we asked what we think our graduates should be able to do but perhaps can’t -- or not as a result of anything we’ve taught them, anyway. The employers were especially valuable here, highlighting the ability to:
Use new media, technologies and social media
Work with the aesthetics of communication, such as design
Perform a visual presentation and analysis
Identify, translate and apply skills from course work
Perform data analysis and quantitative research
Be comfortable with numbers
Work well in groups, as leader and as collaborator
Identify processes and structures
Write and speak from a variety of rhetorical positions or voices
Support an argument
Identify an audience, research it and know how to address it
Know how to locate one’s own values in relation to a task one has been asked to perform
They also mentioned a need for better technological, project-management and conversational and interview skills.
We also discussed creating tables that would link the knowledge, skills and aptitudes of the first two questions to the kinds of work students might do after graduation, task by task. We’ve assigned that work to the participating employers.
To make sure that our students can graduate with the knowledge and skills we want to see, we know we would have to make some changes to the way our degrees are structured. Some of the changes we talked about at the meeting were:
Providing more faculty development to help professors be more explicit and intentional in language about the skills being taught
Creating a one-credit course on the relation of humanities to work and the professions
Using required courses (general education) and events (orientation) to introduce the need to connect courses and skills
Being intentional about double majoring, adding minors that enable students to pair professional training with humanities
Using successful alumni in programming
Integrating student employment with academics, through course work or portfolio reflection
Infusing reflective writing into courses
Encouraging community engagement with the curriculum
Providing avenues for student creativity to demonstrate higher-order skills
Taking on the idea of maker space—what are the humanities making?
Giving students self-assessment skills
Developing portfolios that include both work and reflection linking course work to other kinds of engagement, such as employment and student activities
Structured work shadowing opportunities
Creating local employer/faculty advisory groups to determine workforce needs and establish a common language
Building reflection, work, community engagement and shadowing into the credit structure
Capitalizing in four-year colleges and universities on work already being done at two-year institutions
The final task at our meeting was to come up with ways to measure whether we are doing what we say we are doing now, as well as if we pursue the changes we want to make. We developed the following list:
Alumni surveys, to determine short- and long-term impact of humanities education
Student surveys, at entry and exit, about how their ways of thinking have changed
Internship supervisor surveys
Determining whether local employers hire our graduates, why or why not, and whether those graduates have the needed knowledge and skills
Using capstone courses to assess ways students have been asked to combine humanities and work
Gathering information that can contribute to big data. Who else is collecting what we seek, and how can we combine their data with ours?
That was the most difficult assignment, and it’s the shortest list that our group developed. That, of course, was not surprising. Assessment has always been challenging, as any regional accreditation team can tell you.
But we had started the afternoon asserting that we want the general public to support humanities education and to understand the value of what we do, and so we knew we must to find good ways to collect evidence. That’ll be a topic in our next meeting.
We agreed that the next step, when we reconvene in May, will be for all of us to have made some progress on our own campuses toward both adding education in the new skills we think humanities students need and finding ways of measuring our success.
If you’re working on humanities student success initiatives, what tactics are you trying? With whom are you working? Are you getting any traction in your institution or region?
Making the case for the humanities can start on the campus, but it ultimately has to convince funders, parents and employers, too. We’re hoping to make southern New England the first Humanities Success Zone in the country -- where an employer with some job openings asks, “What kind of person would add some real value to our company beyond the specific skills we need for this job?” We want the answer that springs to mind to be: a humanities graduate.
Paula M. Krebs is dean of the College of Humanities and Social Sciences at Bridgewater State University, in Massachusetts. On Twitter, she is @PaulaKrebs.
An assistant professor of outdoor studies at the University of Alaska Southeast was mauled by a bear during a mountaineering class on Monday, the Associated Press reported. The professor, Forest Wagner, was with a group of students on Mount Emmerich when he was attacked by a sow with two cubs. A student hiked down the mountain to notify authorities, since there was no cell phone service at the site of the attack. Students were safely removed from the mountain but the professor remained in the hospital in serious condition on Tuesday.