National trends in collegiate mathematics - The Charles A ...€¦ · to knock off problems, and solving those problems—to looking outward ... Ben Green and Terence Tao ... National

National trends in collegiate mathematics: The structural forces shaping our future

Spring 2015

Context: The Four Structural Forces Shaping Undergraduate Mathematics Education

I have been asked to talk about the forces that are reshaping American undergraduate mathematics education.1 I want to give you my sense of the direction that reform is taking in response to these tectonic shifts.

Specifically, I think there are four gigantic forces reshaping the everyday life of math departments and of higher education institutional mathematics programs more generally.

The first structural force is coming out of mathematics itself, the second is in higher education, the third is in K–12, and the fourth is tied to fundamental changes in the American economy.

The First Force: A Glorious Time in Mathematics

Let me begin with mathematics. First, this is a glorious, unbelievable time in mathematics.

Just think of the progress the field has made in the last 20 years.

Uri Treisman, professor of mathematics, professor of public affairs, and executive director of the Charles A. Dana Center, an organized research unit in the College of Natural Sciences at The University of Texas at Austin.

Some of the hardest problems of mathematics—problems that people have been working on for more than 100 years—have been resolved.

The Poincaré conjecture—knocked off. The Langlands conjecture—proof of the fundamental lemma—people could not have imagined 25 years ago that we could even make progress on it. Compressed sensing—tools for quantifying uncertainty. And the Green-Tao theorem: for the math audience out there the idea that the primes contain arbitrarily long sequences of arithmetic progressions and polynomials progressions.2

For nonmath people out there, what does all this mean? When you see a Pixar movie, do a Google search, use your credit cards, get medical imaging, or check the weather forecast—all these things have been made possible, or have been revolutionized by—advances in modern mathematics. And it’s not the mathematics of your parents’ generation or the generations before them.

Mathematics is changing in fundamental ways.3 And it’s probably the case when you look in our field that every 30 or 40 years we shift from looking inward—building monster powerful machinery to knock off problems, and solving those problems—to looking outward.

1 For a general overview of the history of the undergraduate program in mathematics, see Tucker (2012). 2 Henri Poincaré’s 1904 conjecture, a topological theorem, was solved in 2002–2003 by Russian Grigori Perelman.

In 1983, Robert Langlands conjectured the fundamental lemma as part of the Langlands program of conjectures; the fundamental lemma was proved by Ngô Bảo Châu in 2008. Compressed sensing, also known as sparse sampling, can be used to reconstruct a signal from a relatively small sampling of that signal. In 2004, Ben Green and Terence Tao proved what is now known as the Green-Tao theorem, a theorem in number theory related to prime numbers. For additional information, see “References cited and resources for further reading” at the end of this paper.

3 National Research Council, 2013. For a list of references cited, see the end of this paper.

National trends in collegiate mathematics

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So the big message is that this is a period where we in the mathematics community are looking outward and collaborating with other fields to use our techniques to solve problems—and also looking outward to new sets of problems that will drive future mathematics research. This is a glorious time in mathematics, a time in which we can make changes based on strengths and achievements.

Editors’ note: This essay is an updated and enhanced version of an hour-long informal talk given by Uri Treisman to an audience of faculty and other higher education leaders.

The talk kicked off a discussion on January 29, 2014, in Round Rock, Texas.This event was hosted and sponsored by the Charles A. Dana Center; the American Mathematical Association of Two-Year Colleges; and the Mathematical Association of America, along with TG.

Professor Treisman was introduced by Donna Boutwell, director, TG Center for Community Colleges, and Amy Getz, strategic implementation lead, higher education, the Charles A. Dana Center.

A link to the video of this talk is available via the Dana Center website.

The Dana Center is pleased to present this revised and edited version covering highlights of the talk. We hope it will continue to spur conversations and inspire change.

The Second Force: High Failure Rates in Higher Education Remedial and Gateway Courses

The second big structural change is within higher education. The most profound change is the shift from enrollment as the primary driver of funding in higher education to a focus on completion—and timely completion at that.

Almost all states have shifted, and some dramatically, the way they fund higher education. And this change in the driver of state funding has caught higher education somewhat by surprise.

We are also seeing a historically rare event—activist legislatures, executive branches, and private foundations that are focused on higher education. Traditionally, higher education associations and other advocates have been particularly effective at preserving core features of higher education.

Now there are groups such as Complete College America and Jobs For the Future that are at least as influential as these advocates in shaping the direction of mathematics in higher education.4

Who would have thought that the Connecticut legislature would get directly involved in determining what kind of courses should be offered and funded in higher education? Or that the Florida legislature would lay out metamajors and talk about programs of study?5

These are deep sea changes that affect our lives in our institutions and, in particular, in our mathematics departments.

Why mathematics departments? Because when you look at the issue of student completion (that is, graduation with a certificate or degree), the courses with highest failure rates are, unfortunately, mathematics courses. I think the top three courses in terms of failure, as Cliff Adelman6 found years ago, were in mathematics. So the spotlight is on us, and it is up to us to really respond in constructive ways.

4 In December 2012, the Dana Center, Complete College America, the Education Commission of the States, and

Jobs for the Future released a joint statement, Core principles for transforming remedial education, available at www.utdanacenter.org/downloads/spotlights/STATEMENT_Core_Principles_(final).pdf

5 See Inside Higher Ed (2012 May 7), and Fain, P. (2013 June 5). 6 See, for example, Table 6.4.: Undergraduate Courses with Highest Rates of Failure / Penalty Grades: High, page

203 in Adelman (1995, 1999), in http://files.eric.ed.gov/fulltext/ED434647.pdf


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And then there are the functions that have historically been seen as the direct responsibility of the faculty, such as shaping the requirements of majors and determining what students must learn to earn a degree in a given field. Now private foundations and other organizations with tax-privileged (e.g., nonprofit) dollars are launching organizations that are helping shape the fundamental inner workings of higher education.

Where are these politics around higher education coming from? While it’s not 100 percent clear, my sense is that the U. S. population at large understands that postsecondary education is now necessary for achieving—or maintaining—a middle class life.

We are a wonderful country, but we do have some small faults here and there. As much as I love this country, one of those faults is that when we think something is necessary, we can quickly perceive it as a right. There is very little tolerance in the public for obstacles blocking what they think they need to preserve their economic well-being.

When people believe they need higher education to attain or maintain a middle class life, they are not going to tolerate obstacles that block them from getting certificates, licenses, or degrees. That concern is part of what’s fueling political interest in higher education.

I think another issue is massive student debt. As of 2013, U.S. students were carrying more than a trillion dollars of student loan debt.7

And given the recession and the fiscal stresses facing families, people are asking whether higher education is still as good an investment as it was in the past.

But now people are also asking hard questions about the return on investment of higher education.

That question has interested the White House, that held the January 2014 summit on college opportunity,8 in which some 150 institutions, including the Dana Center, were invited to make commitments to support student success initiatives at their institutions.9

I wonder when we’ll have an administration that has the courage to ask 150 institutions to rescind previous commitments? Wouldn’t that be interesting? I think it will be a while before that’s politically viable. It’s easy to make new commitments. It’s much harder to rescind last year’s commitments when they do not pan out.

I say this because the reality is that institutions of higher education are doing too much—e.g., taking on MOOCs,10 emporiums, flipped classrooms—in order to be legitimate to other institutions.11

Giving up the addiction to having one of every innovative program is harder than giving up chocolate and cigarettes. The real issue is how can we best support the many people aspiring to higher education without eliminating existing benefits to talented students. I will say the White House summit was an important event, and it shows federal interest as well as state and local interest in higher education transformation.

7 Touryalai, 2014 8 The College Opportunity Summit at the White House, January 16, 2014. See the remarks from the President and

First Lady at www.whitehouse.gov/the-press-office/2014/01/16/remarks-president-and-first-lady-college-opportunity-summit

9 Slack, 2014, and www.whitehouse.gov/sites/default/files/docs/college_opportunity_ commitments_report.pdf

10 Massive Open Online Courses 11 See, for example, Dimaggio and Powell, 1983.


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As a consequence of these political and financial forces, what changes are we seeing in higher education? What is the first focus? Remediation.

Keep in mind that roughly half of all math enrollment in four-year higher education is at the precalculus level (e.g., college algebra and below).

More than half of all four-year enrollment and more than 90 percent of all two-year enrollment is in courses that cover the content typically addressed in middle and high school–level mathematics courses.

Very few people even knew that data until it was published by the Conference Board of the Mathematical Sciences,12 a sort of Bible of data on the state of mathematics in the U.S.

Higher Education Mathematics Course Enrollment

Adapted from the CBMS 2010 Census Report, Table S.2

When people focus on mathematics remediation, they are actually focusing on the majority of mathematics offerings in higher education. What is the public sense of the state of remediation, and what do the data actually show?

While there are certainly islands of wonderfulness in remediation, the data largely show that the remediation (or developmental) enterprise, while it has helped individual students in particular places, has on the whole failed to help large numbers of students complete a college degree.13 At the macro level, remediation has been a failure. Large numbers of students in remedial mathematics courses are more likely to end up with debt than they are to end up with a certificate, license, or degree with labor market value.

I think the data also suggest that the failure of mathematics remediation courses is more than an administrative and political problem; it is essentially a moral and ethical problem for the mathematicians whose departments depend on enrollment in these remedial courses that are the classic bridge to nowhere. This is a real challenge.

This concern about student success and completion is now spreading from remediation and developmental education to gateway mathematics courses. People are asking, “Why are these students failing?”

We noticed first the high failure rates in remediation. Now we are noticing in state data sets that failure rates in freshman mathematics courses typically are 30 to 35 percent, and in spring semesters they are often as high as 45 percent.14

12 Blair, Kirkman, & Maxwell. (2013). 13 For one of many recent analyses of this issue, see Complete College America (2012 April). 14 For example, a policy brief from the National Center for Public Policy and Higher Education notes “high failure

rates in freshman courses—15 percent at research universities, 30 to 40 percent at comprehensive universities, and 50 to 60 percent at community colleges—are costly to both institutions and students” (Twigg, 2005, page 2). A July 2014 post by John Gardner notes that 35 percent of students at 10 colleges participating in a Gardner Institute initiative failed to complete college-level mathematics (by earning a D or F, withdrawing, or taking an incomplete). See Gardner, 2014.


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So, again, mathematics is an impediment to completion and certainly timely completion. We are in the spotlight, which gives us an opportunity to play a constructive role in higher education transformation.

Keep in mind that a relatively small percentage of higher education math enrollment—less than 10 percent—is at the upper division level.15 Most math enrollment is in “service courses” (the mathematics courses that serve to prepare students for other disciplines).

And these service courses are now being discussed and questioned. They’re getting such attention not only because of the high failure rates but because other disciplines—such as engineering, business, nursing, and the medical professions—are changing their expectations for what mathematics students really need to be able to progress in these professions.

In many places, the math community hasn’t really been connected to this discussion. How big are these changes? For the first time we see, in the Mathematical Association of America’s Calculus Study data16 that more calculus students are headed to biology and the medical sciences than to engineering.

And it’s only a few lead institutions that offer multiple (in at least one instance, seven!) versions of calculus, each version tailored to particular majors. As I like to think of it, seven different flavors, but one gray taste. So we’re just seeing the beginnings of the profession responding to the felt needs of its client disciplines, and this response feeds the potential for transformation.

So in higher education, we are experiencing big structural changes and increasing attention to what are extremely high failure rates. This situation calls on us to account for these rates and to be a force in changing higher education for the better.

The Third Force: The Bifurcation of Access and Opportunity in K–12 Education

We are also seeing a massive shift from the understanding that holding a high school diploma means that you have completed a set of classic high school courses to the expectation that a high school diploma certifies you are ready for college and the workplace.

By any standard, we have not yet gotten “college readiness” and “workplace readiness” right. This college-readiness movement is relatively new, so there is a lot of work to be done.

The early phase of this movement focused on readiness for higher education in general—it did not really take into account the enormous and healthy diversity within higher education institutions and the varying readiness needs for each education sector (e.g., flagship universities, liberal arts colleges, community colleges, high schools) and each career path.

Nonetheless, state after state is defining the high school diploma as meaning its recipients are ready for college. This emphasis on college readiness means the connection and articulation between K–12 and higher education is becoming much more important.

Historically, people have treated “college readiness” symbolically.

15 Blair, Kirkman, & Maxwell, 2013. 16 See Bressoud, D. (2013 August 1), one of many posts and articles on the MAA calculus study, “The

Characteristics of Successful Programs in College Calculus.” For a list of resources about and generated from this study, see www.maa.org/programs/faculty-and-departments/curriculum-development-resources/characteristics-of-successful-programs-in-college-calculus


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I hope this assessment isn’t too harsh. I have been on many state K–12 or PK–16 steering committees in which it looked like each education sector had hired somebody to meet with the other sectors (e.g., a representative for the community college sector, another for the liberal arts colleges). And so you’d see in these meetings too many individuals who had little or no authority in their own sector.

We are not seeing that dynamic now because high schools need to ensure that their students are college ready, and people are starting to work at mechanisms for shared accountability for students’ successful transition from high school to higher education.

As the meaning of the high school diploma has changed, it has increased the importance of real relationships across sectors and levels of education.17 For example, the Washington State Board for Community and Technical Colleges is now a leader in creating human connections between high school and community college faculty.

We’re seeing changes in state and local governance in which high school districts and baccalaureate institutions are sharing responsibility for students making the transition from high school to higher ed. Just last year, the University System of Georgia Mathematics Task Force recommended systems policies and college practices for mathematics instruction “requiring fundamental changes in the ways in which higher education supports its students in completing key gateway course sequences.”18

What we are seeing is a bifurcation in K–12 access and opportunity. I remember when in 1962 or 1963, I took the Advanced Placement calculus exam. I had the feeling then that I knew all the other students in the country who were taking it because I was involved in national math competitions. I think there were 7,000 students who took it, and I think when I took it we used roman numerals in our calculations.

In 2013, more than half a million students (about 550,000) took an AP mathematics exam—either AB or BC calculus or statistics.19 Also in 2013, about a third of all high school students in the United States who went directly into higher education took calculus in high school. Twenty-two percent of all the students who took calculus in either two or four-year institutions in the U.S. had attained a 3 or better on an AP math exam while they were in high school.

These are data we have because of the wonderful MAA calculus study20 led by David Bressoud, one of my heroes (the data man), Marilyn Carlson (one of my first doctoral students) at Arizona State University, Vilma Mesa at University of Michigan, and Chris Rasmussen at San Diego State University.

We actually have large-scale data for the first time on calculus enrollments. That 22 percent of students in calculus who got a 3 or better on the AP exam (which means that presumably you can

17 For example, see Chapter 3, “Recommendations: Mathematics for Teachers; Roles for Mathematicians,” pages

17–21 in Conference Board of the Mathematical Sciences (CBMS). (2012). The mathematical education of teachers II. Providence RI and Washington DC: American Mathematical Society and Mathematical Association of America. Retrieved January 6, 2015, from www.cbmsweb.org/MET2/index.htm

18 University System of Georgia Mathematics Task Force, 2013. 19 In 2014, AP mathematics exams were taken by some 561,802 students, per the College Board Program Summary

Report, http://research.collegeboard.org/programs/ap/data/participation/ap-2014 20 www.macalester.edu/~bressoud/talks/2011/portland-apcalc.pdf


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“credit out” of a course)—is also the percentage of students in all calculus courses who got As.21

We do not know that it was the same 22 percent, but there is a high likelihood that it was.

The great majority of students who succeed in calculus in higher education, then, appear to have already had the course in high school. So we’re seeing a bifurcation.

We see one big population of students who go to remediation in higher ed and another big population who have already taken calculus; the latter population consists of extremely well-prepared students going into calculus in higher ed. In 2013, about 8,000 African Americans succeeded in Advanced Placement calculus and more than 7,000 of these were fairly well-to-do students.

We are seeing a clear bifurcation in trajectories into higher education mathematics. One group of students, largely higher income, mostly white and Asian, benefits from Advanced Placement coursework, placing out of lower level college mathematics and moving more quickly into the coursework they want and choose for their program of study.

Another group of students, largely lower income and including many African American and Latino students, has less access to AP courses and advanced mathematics courses in high school generally, and, consequently, less success at avoiding remediation and placing out of gateway courses. This increasing need for advanced coursework in high school to advance successfully to college STEM majors is a big, big structural change in what constitutes adequate preparation for college.

And yet despite the advanced mathematics coursework in high school that students on a calculus path need to be college ready, there has been relatively little increase in the number of STEM majors. We used to think this flat growth in STEM majors was actually terrible, but one of the wonderful things about data: data give you humility.

One thing that we just learned by looking at large data sets is that 28 percent of students choose a STEM major in four-year institutions, and then half of them leave within 2 years.22 But actually it’s about the same attrition rate as that of history majors and English majors and so on. So we mathematicians are not doing worse. The problem is we need to do a lot better, especially given the recent changes in the economy.

So we have come to the economy as the last structural force, and then let me talk about some of the responses to these forces that I think are positive and important.

21 See Bressoud (2013 August 1), one of many posts and articles on the MAA calculus study, “The Characteristics

of Successful Programs in College Calculus.” For a list of resources about and generated from this study, see www.maa.org/programs/faculty-and-departments/curriculum-development-resources/characteristics-of-successful-programs-in-college-calculus

22 Chen & Soldner (2013 November).


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The Fourth Force: The Positive Role of Mathematics in Upward Social and Economic Mobility

What has happened in the economy? A lot of it hasn’t been very good to be sure. But even before the Great Recession of 2008, structural changes were under way. Before the year 2000, most people who succeeded in attaining middle class lives or better did so by staying in the same industry and moving up within it. In about 2000, we started seeing a big shift to mobility across industries.23

Why is that mobility important for mathematics? Because it means that as people move across different fields, they very often find that the new field requires new or better mathematical skills than in the field they left (e.g., moving from news reporter to website developer, or from graphic designer to programmer). Thus, mathematics is increasingly important to the social and upward mobility of people who are moving across different fields.24

Part of that increasing importance is due to the image of mathematics. People take mathematics as a proxy for general problem-solving ability and innovation. And we’re glad of that and we think there’s a lot of truth in that association.

But it is the core mathematics skills—such as number sense, modeling, attending to precision, proportional reasoning, symbolic reasoning—that are common across industries, and the problem-solving ability that you get in mathematics majors and math-intensive programs, that are recognized by employers as a mark of potential suitability for their positions.

When you look at income, researchers have noted that careers at the highest income level—the top half of 1 percent—very few of them are in mathematics or STEM fields. But when you look more closely, almost all of them were in mathematics-intensive fields at one point.

One wag has said that this means there’s no limit to how far you can go once you leave mathematics. So it’s pretty clear that math capability and math achievement are key determinants of income and of access to middle class lives.

The fact again that math is important to upward mobility is one of the underlying pressures in the public demand for mathematics accountability and access to math courses that lead to student success. Even when people aren’t aware of it explicitly, there is a sort of tacit understanding that mathematics is really important.

Given the importance that people assign to it, they are not going to tolerate programs with very high failure rates. That political sea change means that the pressure on us as a community to perform and rethink our work is going to be enormous.

23 See page 111 in Carnevale, Smith, and Strohl. (2010 June): “The emphasis on postsecondary preparation for new

hires means that workers will tend to be attached more to the occupations they will be filling than to the specialized industries in which they work. … Starting out, straight from high school, on the loading dock or in the mail room and climbing to the CEO’s corner office is no longer an option. People do not go work in industries any more. They get educated or trained, go to work in occupations, and progress in an occupational hierarchy.”

24 E.g., as described in Carnevale and Desrochers (2003).


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How Are We Responding? How Should We Respond?

Leading Mathematicians and Mathematics Professional Associations Are Providing a Broad-Based Response

How are these major shifts playing out and what are the current responses to them? Let’s start with mathematics. Any of you who were at the 2014 Joint Mathematics Meetings in Baltimore, Maryland,25 a few weeks ago probably sensed the beginnings of a fundamental shift.

Eric Friedlander, one of the great figures of American mathematics and the recent past president of the American Mathematical Society, gave an address as retiring president that moved people to tears and stunned them.26

He’s long been seen, I think unfairly, as a conservative and traditional force. I think he is one of the most wonderful people in the world of mathematics. He gave a talk about this being the time for change, and there is very little time for us to make these changes. His talk alarmed (and inspired) many of the leading figures in mathematics with a sense of urgency and knowledge of the political forces changing our field.

One of the major responses of the mathematics community has been the creation of Transforming Post-Secondary Education in Mathematics (TPSE Math).27

Funded by the Carnegie Corporation of New York and the Alfred P. Sloan Foundation, TPSE Math is led by six figures in contemporary mathematics and mathematics education, five of whom are senior-most and one of whom is junior-most (that would be me). At my age and level of experience, it is fun being the junior-most member of a national initiative.

TPSE Math is chaired by Phillip Griffiths, who long helmed the Institute for Advanced Study at Princeton and who remains one of the seminal figures in American mathematics, and includes in its leadership team Eric Friedlander, who, as I mentioned, is a past president of the American Mathematical Society; Jim Gates, one of the senior-most physicists in the United States and a member of the President’s Council of Advisors on Science and Technology28; Mark Green, who cofounded the Institute for Pure and Applied Mathematics at the University of California, Los Angeles; Tara Holm at Cornell University, chair of the American Mathematical Society Committee on Education . . . and me.

At the 2014 Joint Mathematics Meetings, attended by leading figures in American mathematics, science, and policy, we heard calls for transforming and modernizing undergraduate mathematics into a discipline that looks outward and works with our client disciplines and, in fact, with all the disciplines that depend on mathematics.

We heard the call to extend and expand the reach and productivity of math departments in this time of fiscal stress and the call to look at the gateway courses in mathematics and ensure that math is

25The 2014 Joint Mathematics Meetings: Largest Mathematics Meeting in the World. Hosted by the American

Mathematical Society and the Mathematical Association of America. Retrieved from http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program.html

26 Friedlander, E. M., (2014, January 16). 27 For more on Transforming Post-Secondary Education in Mathematics, see its website, www.tpsemath.org 28 For President’s Council of Advisors on Science and Technology (also known as PCAST) member biographies,

see www.whitehouse.gov/administration/eop/ostp/pcast/about/members


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not a barrier to our citizens’ upward social and economic mobility. With few exceptions, these are not scholars who have historically been involved in public policy or education.

But when you have people of the professional stature of Phillip Griffiths, Eric Friedlander, Jim Gates, Mark Green, and Tara Holm publicly discussing the need to modernize the American undergraduate mathematics curriculum, it is clear that change is afoot.

It’s important to note that these new voices for change are not coming from the perennial advocates for reform—e.g., those who always think that the future will be better than the past and are always up for change. These voices, rather, are coming from the core of the profession, responding directly to the need to respond to these disciplinary changes and economic changes by calling for reform.

Similarly, take a look at the National Science Foundation–funded INGenIOuS (Investing in the Next Generation through Innovative and Outstanding Strategies)29 project, led by the Mathematical Association of America and the American Statistical Association, in cooperation with the American Mathematical Society and the Society for Industrial and Applied Mathematics (SIAM). In summer 2013, INGenIOuS issued a report.30 What does it call for? A shift to outward-looking mathematics; a shift into new partnerships with our client disciplines.

For a long time, departments in engineering, science, economics, and so on, have looked to us in mathematics with ideas and suggestions for things we could do better. But now we are looking back at them, and what are we are seeing? An unnatural suppression of mathematics requirements in fields in which mathematics has become a central driver.

More of these disciplines can now be classified as grounded in applied mathematics. We must rethink how we interact with these disciplines and how we contribute to majors in these disciplines so that these students graduate with the mathematical skills they need to succeed—and that the economy needs to move forward.

What are our partner disciplines calling for? New gateway mathematics course pathways that are aligned to the programs of study in these disciplines. That call—that need— means it’s time to stop making college algebra a general education requirement. We need to stop teaching 16th- and 17th- century mathematics to journalists who actually need to understand how to analyze data or quantify uncertainty. This shift will be very hard for us, but there is near unanimity that we must make it.

We’re seeing professional organizations individually—such as the American Mathematical Association of Two-Year Colleges (AMATYC) that are working on what I think are revolutionary statements about the proper role of intermediate algebra and college algebra in the undergraduate curriculum.31 We are seeing a call for change. The question is, “How do we best organize to achieve this change?” All of us understand that meeting this challenge will not be easy. Why won’t it be easy? For economic reasons.

29 For more on INGenIOuS, see www.maa.org/programs/faculty-and-departments/ingenious 30 Zorn, P., Bailer, J., Braddy, L., Carpenter, J., Jaco, W., & Turner, P. (2014). The INGenIOuS Project

Mathematics, Statistics, and Preparing the 21st Century Workforce. Washington, DC: Mathematical Association of America. Retrieved from www.maa.org/sites/default/files/pdf/ingenious/INGenIOuS-report.pdf

31 “Position Statement of The American Mathematical Association of Two-Year Colleges: The Appropriate Use Of Intermediate Algebra As A Prerequisite Course.” A final hearing was held at the 2014 AMATYC conference in Nashville; as of January 2015, the position statement is listed as “Under Consideration” on the AMATYC Guidelines and Position Statements page, www.amatyc.org/?GuidelinesPositions. A draft is also available here: https://sites.google.com/site/amatycdmc/position-statements


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Needed Reforms Must Overcome Economic and Policy Barriers

All things being equal, math departments are relatively cheap to run. Historically, the economics of math departments has been that we are a revenue center that supports higher cost majors. So there is going to be an enormous reluctance of central administration in the time of fiscal stress to invest in us or to limit our historical enrollments for fear that such actions will affect the high-yield majors.

A very significant part of undergraduate mathematics instruction occurs in access institutions—that is, in the two-year colleges. And 52 percent of courses that are at the high school level and the vast majority (70 to 90 percent of community college mathematics courses) overall are taught by adjuncts making between $1,800 and $2,500 per course per semester.32

These are individuals who love to teach. Research suggests that they are just as good at teaching particular courses as their full-time counterparts. But they are not paid (or, often, even encouraged) to participate in institutional improvement.

So reliance on low-cost adjuncts actually exerts an enormous force to maintain the status quo in the field. The challenge for policymakers for investing in education is that the costs are now so low to offer mathematics courses at that level that any increase (e.g., for salaried professors) will look like a large proportionate increase. So making such a change requires courage on the part of policymakers.

Policymakers are under pressure to find revenue-neutral solutions to large-scale problems. And the massive defunding in mathematics, and the lowering of investment—especially in the students who come in with the least preparation—is going to make addressing this problem very challenging. But it needs to happen and it’s going to force us to be creative.

We Now Have the Data to Make Informed Changes

Another big force in the math community has been ongoing introspection and collection of data on our performance. Again I want to commend the Mathematical Association of America and David Bressoud for their leadership in this area. Twenty years ago, if you would have come from outer space and looked at the American higher education enterprise and investigated what questions you could answer with available data, the only conclusion you would have come away with is that people really didn’t want to know.

The joke was that higher ed studied everything but itself. No longer!

Through David Bressoud’s work and that of others, we have a robust set of data on calculus enrollment and on remediation. Having such a dataset is the beginning of real transformation because it’s hard to institute change if you can’t answer basic questions about your performance. This data collection has not been driven by external forces but by seat-of-your-pants, rank-and-file department chairs looking to improve the discipline.

I will say that though the profession has been thought of by some as stodgy in working with chairs and state task forces and steering committees, I am so impressed by the creativity of math departments and the amount of innovation going on in this data collection and analysis.

The challenge then becomes that the reform initiatives often start out local and idiosyncratic. The task for higher ed is to organize and implement effective innovations fundamentally at scale.

32 See Center for Community College Student Engagement, 2014, and Berl (2014 April 24).


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Effective Policy Changes Must Involve the Math Community

What are we seeing at the higher ed level that is promising? In states such as Ohio, Georgia, and Washington, you have higher education boards of governance who understand that these are times of fundamental change in curriculum matters—and these boards have the humility and wisdom to reach out to the senior math people in the state and build structures for formal communication.33

My colleague Jenna Cullinane and I have been privileged to serve as consultants to some of these state governance groups.

It is the first time in my career that I’ve seen legislators and governance personnel sitting down with math department chairs and other department leaders and talking about what kind of changes have to take place on the ground. Rather than seeking deficiencies with an eye toward punitive measures, these policy leaders are looking at the strengths and assets of the math community.

It’s very hard to effect change unless you understand the strengths of the community and how best to build on those strengths. And we are seeing more and more states move in that direction, and such movements should be a beacon to states that are not currently doing that—a beacon to build structures for communicating with the math and technical leadership of their state.

When we do that, we can truly capitalize on the findings in the President’s Council of Advisors on Science and Technology’s (PCAST) reports, in which they pointed out that math is too important to be left to mathematicians alone.34 When we do these convenings of policy and mathematics leaders, it should not be just an insider group.

We need to think of all the stakeholders in mathematics and mathematics education. Because mathematics knowledge and know-how is now the core driver of the economy and the key determinant of most people’s economic futures.

College Readiness: K–12 Must Choose the Path of Quality Mathematics

What’s happening on the K–12 level? In the first wave of interactions, some really bad stuff. The standard canonical strategy appears to be panic.

That said, there is the Common Core State Standards35 movement. About 40 states at this point have adopted the Common Core without changing the intent of the standards in fundamental ways. There is legislation such as Texas House Bill 5,36 which I think is a courageous effort to modernize mathematics and make it more relevant to students and their future college or career choices.

Now that high schools have to produce students who are “college ready,” we are recognizing that 60 to 70 percent of graduating students nationally are actually not ready for college. The ACT data and the College Board data are showing this lack of readiness.37

33 See, for example, Ohio Mathematics Initiative (2014, March) and University System of Georgia Mathematics

Task Force (2013). 34 See President’s Council of Advisors on Science and Technology (PCAST), 2012 February and 2010 September. 35 The Common Core State Standards for Mathematics are available here: http://www.corestandards.org/Math. 36 House Bill 5 (HB5) passed in the 83rd Texas Legislature, Regular Session, 2013. Information on HB5 is

available on numerous Texas government websites, including the Region 13 Education Service Center site, http://www4.esc13.net/cc/house-bill-5

37 ACT, 2013; The College Board, 2013.


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But now there is pressure to ensure that students graduate college ready. The most common solution is to try offering 11th and 12th graders outmoded remedial courses from community colleges. I want to commend people such as those school district superintendents who meet with higher ed people to work on solutions.

But let me point out that only offering remediation is Old Testament bad . . . rivers of blood, frogs, locusts.

Let’s not take courses that are being replaced in higher ed as inadequate or too slow and route to them those high school students who most need quality mathematics instruction.

Going for remediation is a natural thing. You can understand it. We have a problem we have to solve now. What has higher ed been doing for remediation? Offering archaic algebra courses that focus on isolated, decontextualized techniques.

So what do you do? You offer these courses to high school students.

The problem is, these courses didn’t work for college students, and they aren’t going to work for high school students who are having trouble. So we need to pay attention to this pattern.

What’s crucial is to understand that solutions can only come about with faculty across sectors—that is, across K–12 education and higher education—actually sitting down and talking with each other.

If that conversation doesn’t happen, then solutions will be imposed from outside by policymakers.

And the further you are away from instruction, the less likely your solutions are to be effective for students.

So this is a time in which leadership has to rise up from within the fields and connections have to be forged.

What’s Next: A Big Tent—Associations, Foundations, Policymakers, Administrators—and, Especially, Faculty—Working Together for Mathematics Reform

Even though there are a lot of challenges, I think this is a period of enormous optimism in the field. People are rolling up their sleeves and getting ready to work together.

If you are a faculty member, what does this opportunity—this convergence of forces—mean? It means it’s time to connect to your professional associations and what is happening in the field as a whole. This is not the time to hunker down, teach your courses, and let the change occur without you. If you’re not a member of AMATYC, MAA, AMS, SIAM, or ASA,38 get your act together and join your professional associations, because they are going to be driving the changes that shape your classes and affect you and your students’ lives. The math professional associations have to be extremely strong.

We want them, rather than state legislatures and governors, to lead the reform and modernization. For that to happen, we need a big tent and broad participation—we need not just the usual activists but the rank-and-file core of math departments involved in these decisions.

38 AMATYC (the American Mathematical Association of Two-Year Colleges): http://www.amatyc.org; MAA (the

Mathematical Association of America): http://www.maa.org; AMS (the American Mathematical Society): http://www.ams.org; SIAM (Society for Industrial and Applied Mathematics): http://www.siam.org; or ASA (the American Statistical Association): http://www.amstat.org.


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If you are a math department chair or an administrator, this is a time to advocate for mathematics and to connect with other chairs and rethink your relations to client disciplines. Meeting this challenge is not going to be easy. It’s going to take a few years of work, and that work should be driven by data, which are now available.39

Let the data guide us. Remember the Lee Shulman comment, “The plural of anecdote is not data.”40

If you are a policymaker, this is the time to create space for the needed reforms. What you do not want to do is look backwards.

You do not want to resurrect placement structures that feed students to courses (e.g., remedial algebra) that are disappearing. In state after state, we have placement strategies based on college algebra, when everybody knows that journalists, emergency medical technicians, and nurses need statistics; HVAC people need to know about precision and proportionality.

When we see bad policymaking, it is when policymakers are looking for uniformity and are looking backward because the instruments and the industry are there. The data on the effectiveness of popular math placement tests to place students correctly into courses are atrocious. Given that legislators and policy makers are activists, let’s—as a discipline, as a nation—create the space that enables improvement.

If we are going to see improvement, it is going to take coordinated efforts at many different levels of the education system.

In the eloquent language of my colleague Jenna Cullinane, we need “cycles of mutual permission giving”41 between all the individuals and programs and institutions and policymakers. Such permission giving and collaboration is going to require the development of leaders within the math community who have the capacity to work with presidents, governance boards, and legislators to put in place new core placement and articulation structures that can become normative.

We have learned that the problem is not a lack of innovation. Part of the problem is, in my opinion, that private foundations and other philanthropists have supported quirky, boutique efforts that suck up the creative energy of faculty on initiatives that have not—and never will—scale.

So this is a time for foundations to invest in the core enterprise of systemic transformation over the latest innovative idea. Basic structural change must take place.

Unless policymakers, foundations, and most importantly math leaders are involved in this transformation—unless we see big tent, broad, diverse thinking—we will see myriads of students trapped in college algebra courses, siting in front of computers, pressing buttons and learning skills that are irrelevant to their intended careers and their futures. And math departments will continue to be a revenue center, and our students will not be the prime beneficiaries of that revenue.

39 E.g., ACT, 2013; Blair, Kirkman, and Maxwell, 2013; Bressoud, 2013; Center for Community College Student

Engagement, 2014; The College Board, 2013, 2014. 40 Actually, a bit of after-the-fact sleuthing reveals that the statement was likely originally made by Raymond

Wolfinger, then a political scientist at UC Berkeley, who is reported to have said “'The plural of anecdote is data” in the late 1960s or early 1970s. This anecdote was recounted in a blog post by David Smith (2011 April 6) of Revolution Analytics. The phrasing is confirmed on page 202 (entry: “The plural of anecdote is data (evidence)”) in The Dictionary of Modern Proverbs (2012), edited by Charles Clay Doyle, Wolfgang Mieder, and Fred R. Shapiro.

41 Cullinane. (2013).


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So this is tricky! This is the time to look at statewide reform.

The risks to reform at a higher level are very low. We see reform initiatives in Virginia’s community colleges,42 North Carolina,43 and Texas (the New Mathways Project,44 of which I, and the Center I direct, am a part).

We’re seeing the Carnegie Foundation for the Advancement of Teaching’s StatwayTM and QuantwayTM work changing fundamental course patterns. We now know that Carnegie has tripled the number of students who complete a college credit course from remediation in one year. That’s an unbelievable level of progress. I think our work in the NMP will benefit from Carnegie’s research. We are having comparable results in the early parts of our data-gathering on this project.

In general, success rates in math courses below calculus are still very low, but there are pathways forward that come from mathematicians and math departments themselves that show promise. So foundations, get over boutique, quirky, beautiful. Think of grass roots, blue-collar instruction engineering, systems reform.

Let me just end by saying that I’ve been at this now for a good while. I have been teaching for more than 50 years—in fact, I’ve taught calculus, in one form or another, for 55 years. I’ve seen periods of reform come and go. I’ve seen Calculus Reform. I’ve seen Algebra For All. Those were movements that had a much narrower base of supporters—and of potential beneficiaries—than the movement I am seeing at this particular moment in time.

In the last month, I’ve seen the traditional leadership of the mathematics research profession call for change.

I was privileged to see the President of the United States and members of his cabinet and economic advisors call for change.

I’ve seen department chairs getting together for the first time and talking about the health of their disciplines.

The tectonic forces are moving. Let’s do what we can as mathematicians to direct these forces for the benefit of our discipline and our students.

And let’s make sure that other people don’t determine the content and character of our courses.

42 http://www.vccs.edu/statewide-innovations/developmental-education 43 http://www.successnc.org/initiatives/developmental-education-initiative 44 http://www.utdanacenter.org/mathways


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Resources

Mathematical wonders described early in this talk Poincaré conjecture

http://en.wikipedia.org/wiki/Poincaré_conjecture www.claymath.org/millenium-problems/poincaré-conjecture http://phys.org/news197209671.html

Langlands conjecture—the fundamental lemma http://en.wikipedia.org/wiki/Fundamental_lemma_(Langlands_program) http://en.wikipedia.org/wiki/Langlands_program http://content.time.com/time/specials/packages/article/0,28804,1945379_1944416_1944435,00.html

Compressed sensing: http://en.wikipedia.org/wiki/Compressed_sensing

The Green-Tao theorem: http://en.wikipedia.org/wiki/Green–Tao_theorem Green, B. & Tao, T. (2008). The primes contain arbitrarily long arithmetic progressions. Annals of

Mathematics, 167(2), 481–547. Retrieved January 22, 2015, from annals.math.princeton.edu/2008/167-2/p03

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About this resource

Acknowledgments

We wish to extend our thanks to Dr. Rebecca Hartzler, a professor of Astronomy, Mathematics, and Physics at Seattle Central Community College who worked in collaboration with Professor Treisman and his staff to revise the transcript of Professor Treisman’s talk and augment it with citations, updates, and other enhancements from subsequent conversations with him.

Author Uri Treisman, executive director, the Charles A.

Dana Center at The University of Texas at Austin

Collaborating editor Rebecca Hartzler, Seattle Central Community

College, Seattle, Washington

Project leads Amy Getz, course program specialist,

mathematics, higher education, the Charles A. Dana Center at The University of Texas at Austin

Francisco J. Savina, course program specialist, mathematics, higher education, the Charles A. Dana Center at The University of Texas at Austin

Editing and production Steve Engler, senior writer/editor, resource

development, the Charles A. Dana Center at The University of Texas at Austin

Rachel Jenkins, team lead, publishing and production, the Charles A. Dana Center at The University of Texas at Austin

Francesca Fraga Leahy, project coordinator, the Charles A. Dana Center at The University of Texas at Austin

About the development of this document

This essay is an updated and enhanced version of an informal talk presented by Uri Treisman, professor of mathematics, professor of public affairs, and executive director, Charles A. Dana Center at the University of Texas at Austin, on January 29, 2014, in Round Rock, Texas. The event was hosted and sponsored by the Charles A. Dana Center, the American Mathematical Association of Two-Year Colleges, and the Mathematical Association of America, along with TG (www.tg.org).

Professor Treisman was introduced by Donna Boutwell, director, TG Center for Community Colleges, and Amy Getz of the Dana Center.

A link to the video of this talk is available via the Dana Center website and this webpage: www.tgslc.org/newsroom/videos.cfm#training. The Dana Center is pleased to present this revised and edited print version of the talk, with the hope that it will continue to spur conversations and inspire change.

About the Dana Center The Dana Center develops and scales math and science education innovations to support educators, administrators, and policymakers in creating seamless transitions throughout the K–14 system for all students, especially those who have historically been underserved.

We focus in particular on strategies for improving student engagement, motivation, persistence, and achievement.

The Center was founded in 1991 at The University of Texas at Austin. Our staff members have expertise in leadership, literacy, research, program evaluation, mathematics and science education, policy and systemic reform, and services to high-need populations.

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