• August 30, 2015

Make Math a Gateway, Not a Gatekeeper

Make Math a Gateway, Not a Gatekeeper 1

Doug Paulin for The Chronicle

The story is a familiar one: A high-school dropout and single mother works the supermarket late shift. Motivated to earn a four-year degree so she can have a better life for herself and her 4-year-old daughter, she enrolls in a community college after earning a GED. Three years later, she still hasn't completed the sequence of three remedial math courses required before she can take college-level math. Defeated, she says, "I just couldn't do it anymore." For this student and too many others, the dream stops here.

Remedial math has become an insurmountable barrier for many students, ending their aspirations for higher education. To earn a degree, certificate, or license, community-college students usually must complete a college-level math course. However, the relationship between this particular course requirement and the specific quantitative competencies necessary for future success at work is often unclear to students. In addition, some students must take as many as four remedial courses before they are considered "college ready." Recent studies report that between 60 and 70 percent of students placed into remedial math either do not successfully complete the sequence of required courses or avoid taking math altogether and therefore never graduate.

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The relevance question—"Why do I really need this to succeed?"—is often hard to answer. It's time to ask fundamental questions about why people who care about student learning, despite Herculean efforts, are still not able to help these students realize success. It's time to decide what these students really need to know to succeed. For these reasons, we think that it's time to revisit both the structure and goals of remedial math. We want to create a challenging, alternative math pathway that emboldens students to realize their goals and prepares them well for life beyond the math classroom.

Math should be a gateway, not a gatekeeper, to a successful college education. Students must come to see math as an essential aspect of their everyday lives, no matter what their field of study. They need to think, "I can understand this, I can do this, this is important to know." The math pathway for students pursuing majors in the math-oriented disciplines is well established: Students work their way through algebra to calculus. Certainly, students entering science, technology, engineering, and mathematics fields need to be proficient in pre-calculus and the algebra on which it depends.

However, many students in the social sciences, arts, and humanities, and those seeking careers in business, applied technologies, health sciences, and other fields, could be served just as well by another pathway. The skills in those professions can require rigorous preparation in statistics. Statistical reasoning supports decision making under conditions of uncertainty, an inescapable condition of modern life. This is math that will help these students understand the world around them, and it's the math they can use right now.

The current lengthy sequence does little to support student success. The Carnegie Foundation for the Advancement of Teaching is organizing a network of faculty members, researchers, community colleges, and professional groups to develop a statistics pathway that will provide a challenging alternative to the current developmental-mathematics sequence. This sequence will bring students to and through a course in statistics in one year that would count toward both college credit and transfer. This would replace the current sequence that takes multiple years, if—and that's a big if—students persist through the process.

We know that redesigning the mathematical content isn't enough to help these students through. With the dismal pass rates of students in math, it is clear that we must change not only the curriculum itself, but also the academic-support system that should be integrated within it. Students need college knowledge as well as content knowledge. Many community-college students are the first in their extended families to pursue postsecondary degrees; they need to learn how to "do" college in order to be successful in college. And, yes, colleges need to review their policies and practices to make sure they are doing everything possible to help their students realize their hopes. We need to strengthen the connections of students to successful peers, to their institutions, and to pathways to occupations and education.

The development of a statistics pathway is Carnegie's best bet for what might help solve the remedial-math problem for a significant number of community-college students. We have consulted community-college leaders and members of national education and mathematics groups. We are also coordinating closely with such programs as Achieving the Dream and the California community-college system's Basic Skills Initiative. These programs have redesigned mathematics courses and created courses that help students succeed in college, as well as mentoring and tutoring programs. While successful intervention strategies exist at many community colleges, they tend to be costly add-ons and extra courses and therefore can have an impact on only a small number of students. Carnegie will instead weave into developmental courses units and activities that provide students with strategies that support persistence while building skills in mathematics. If we integrate such concepts as goal setting, resilience, time management, and study skills into the classroom, they could gain the serious attention they deserve.

The groundwork begins this summer, when Carnegie will bring community-college teams together to collaborate with other practitioners, designers, and researchers to begin the development of materials and assessments for this pathway. During the next year, Carnegie, through face-to-face and online collaborations, will support a networked community using newly developed materials and ideas, continuously improving them and documenting practices that will guide expansion. If we are initially successful, we aim to expand the network to more than 100 colleges over the following three years. Our ultimate goal is to double the proportion of students who, within one year of continuous community-college enrollment, are mathematically prepared to succeed in further academic study or occupational pursuits.

If we truly want to make math the gateway rather than the gatekeeper to a college education, then remedial math is an obvious place to help students develop the knowledge, skills, and social connections for success beyond the math classroom. We need to create a sense of opportunity, of possibilities for those who otherwise might see a lengthy road ahead. This pathway would make it possible for students to fulfill the mathematics requirement needed for many occupations and learn what it takes to be academically successful.

We want to help community colleges build new pathways worthy of mathematics, worthy of their students, and worthy of their institutional missions.

Anthony S. Bryk is president of the Carnegie Foundation for the Advancement of Teaching. Uri Treisman is a senior partner with Carnegie and founder and executive director of the Charles A. Dana Center at the University of Texas at Austin.


1. painter33 - April 19, 2010 at 02:51 pm

The age-old "I'll never use this" is completely false but difficult to overcome - overcome to the point where students realize how much they indeed will use computational skills. I'll be watching for the outcomes in solving this on-going dilemma.

2. mathmaven - April 19, 2010 at 03:36 pm

The problem I see is that the topics in remedial math (arithmetic; fractions, decimals, and percents; basic algebraic manipulation) are just as necessary for success in a college-level statistics as they are in college-level algebra, precalculus, and calculus. I don't care what kind of supports you put in place-- a student who has been unable to get past these basic topics in multiple tries over multiple semesters is not going to pass a college-level stats class in a year no matter what you do.

I don't recall being exempted from the humanities because, as a science major, I didn't see when I was ever going to need to quote Beowulf or write in iambic pentameter later in life. Math gets singled out as the "bad" subject because it's the one people struggle with most often. Since when do we elimiate a degree requirement just because it's hard?

3. marvchron - April 20, 2010 at 11:30 am

It is true that the concepts mentioned in comment 2 are as essential in statistics as in the classical mathematics track. What is not essential is that these concepts be taught in the same tired way, that is in a way that values manual computations over calculator computations. Students need to be taught to use calculators properly. They should not blindly accept the first result they get from the calculator, but need to learn ways to estimate and round using the calculator, so that there is a check on the veracity of their results. The electronic calculator should not be treated as an obstructive outsider, but needs to be come a full partner in the developmental mathematics curriculum.

4. kathymizereck - April 20, 2010 at 11:59 am

Curriculum in general needs a radical, radical overhaul. The old adherence to discipline specific standards, long lists of terms and authors and formulae and factoids needs to be replaced with a set of SKILLS in finding, analyzing, critically appraising and using information. From that will come, in time, a knowledge base. Curriculum design is backwards, and has been for years. It is becoming more and more obsolete and uninteresting as the "factoids" become available at our fingertips, and thus do not need to be memorized . . . but the skill in evaluating and using what we find is sadly lacking.

5. rotmanj - April 20, 2010 at 12:39 pm

For those involved in the mathematical education community college students ... the work that Bryk and Treisman describe is very valuable, and they should be commended for undertaking this project.

In addition, a user-network is forming based on a core faculty group from AMATYC, NADE and MAA ... our work complements the 'statway' project. We maintain a web site (a wiki) for this collaboration; see http://dm-live.wikispaces.com/ for information. Our project is called 'New Life for Developmental Mathematics", and we seek a better mathematics pathway for ALL students.

Jack Rotman
Lansing Community College, Chair of AMATYC's Developmental Mathematics Committee, and leader of the "New Life" project

6. cmcclain - April 21, 2010 at 12:36 pm

At this moment, there are nurses in hospitals across the country giving ten times the proper dosage of medication to a patient because they screw up decimal points. It happened in my town just a few weeks ago. So please do not tell me that the remedial math is not needed.

Furthermore, if you provide a detour around algebra, you provide an exemption from abstract thinking. When the students graduate from this statway approach, will they be able to solve the following problem: if you pay $50.40 for an item at a 10% off sale, how much did you save? Remedial students who use a calculator but not algebra get this wrong every time. Do we really want someone who can't answer this question to actually get a college degree.

The goal is to make students successful, but what do we mean by success? My definition of a successful college graduate necessarily includes a basic understanding of algebra and geometry (in addition to science, history, culture, language, arts, etc).

7. cmcclain - April 21, 2010 at 12:39 pm

By the way, I know I missed a question mark in my above post.

And the answer to the math problem is $5.60, just in case you though it was $5.04 and didn't get my point.

8. cmcclain - April 21, 2010 at 12:48 pm

Last post... there is something I agree with in this article:

"Students must come to see math as an essential aspect of their everyday lives, no matter what their field of study."

Yes, they must. So let's not give them an opportunity to avoid doing so by continuing to lower standards or create "alternate pathways". Instead, let's make "Innumeracy" by John Allen Paulos required reading.

9. wrwood - April 22, 2010 at 11:27 am

Doctors Bryk and Treisman are to be congratulated. Sounds like an extremely useful and necessary project. Aside from the need for many students to develop good learning habits, the challenge is to promote conceptualization as well as mechanics (procedures) in math and stat. My broad based fear is that we are pushing college on everyone to the complete disregard for "trade school." Oh, that label may be the problem. My experience after many years of teaching in both community college and university is that some folks simply do not belong in an institution that I think should be aimed at developing abstract thinking and conceptualization. Don't take me wrong, I am all for helping youth of all capabilities to reach for the stars. I just have come to believe we must preserve the highest stars for those (perhaps with encouragement) who show thenmselves willing to reach up.

Walt Wood
Adjunct, American University and Montgomery College

10. 11274135 - April 23, 2010 at 04:21 pm

In some ways, I have been stunned by the extremes to which some students will go to avoid a modest college math requirement--something like a college algebra course. Math is, indeed, more difficult than other things for many people, largely because of the level of abstraction involved. And that is the source of the "I'll never have to use it" argument. I was very good in math in grade school and high school, but I quit taking it as soon as I could because I didn't like it. I didn't like it because, the way it was taught once I got into algebra, I had no idea what it was good for. Given a set of textbook problems, I could solve them in no time, but I could not for the life of me figure out how to apply what I could do to any concrete problem. I could handle the mathmatical abstractions but not their connection to concrete particulars. I couldnot recognize a practical problem where math would help me. (Students have the reverse problem with reading poetry. They get mired in the particulars and cannot make the leap to the abstract ideas the writer is getting at. Reading philosophy is more like doing math.) I hope that Treisman and his colleagues can help students understand math by understanding its applications to something other than the next math course.

11. sophox - April 27, 2010 at 10:20 am

"Students must come to see math as an essential aspect of their everyday lives, no matter what their field of study."

I would love to read a thorough, detailed, and cogent demonstration of this idea. And I don't want a cherry-picked handful of occupations and situations thrown at me. I want clear evidence that 80% of college grads really, really, really need more than simple calculations or familiarity with statistical charts.

Or make some kind of humanist argument that math makes you a better person (whatever that is) or a better citizen.

Otherwise, this "conventional wisdom" has all the earmarks of a lie.

Then again, the same is true of a lot of what we call higher education.

12. mathgeek314159 - April 30, 2010 at 04:38 pm

A car purchaser has narrowed their choices between a hybrid vehicle which gets an estimated 52MPG and a conventional model which gets an estimated 38 MPG. The hybrid costs $8000 more than the conventional model, and the purchaser wants to determine if the hybrid model will pay for itself over the life of the vehicle. What additional information is needed, and how does the purchaser determine which choice is more cost effective for their needs?

13. suevanhattum - May 09, 2010 at 11:31 am

cmcclain wrote, comment #6: At this moment, there are nurses in hospitals across the country giving ten times the proper dosage of medication to a patient because they screw up decimal points. It happened in my town just a few weeks ago. So please do not tell me that the remedial math is not needed.

Evidence of more than one? Even the one is scary, but remedial math is not the answer; a course that actually addresses mathematical reasoning might be.

Here's a fascinating study of nurses: http://tinyurl.com/26khelw

Basically, even those who made lots of errors in the classroom never made errors on the floor. Using math is different for many people than learning it in a classroom. A number of jobs that use math have been looked at - many of the people doing those jobs don't think of themselves as soing any math.

I'm not sure I like the ideas of another 'track', but I do think we need to change what we're doing. There are plenty of people who reason well, until they get into a math classroom.

14. suevanhattum - May 09, 2010 at 11:34 am

Here's my problem with a track that puts statistics front and center. You can't really understand statistics (in all its details) without some calculus. What is taught in an introductory statistics class is not really math - it promostes exactly what gets students in trouble in math class - memorizing.

15. mariadroujkova - May 09, 2010 at 12:00 pm

I am copying a comment I sent to the Natural Math Google Group:
I have mixed feelings about this. I respect that leaders of this program do recognize a key problem, and formulate it clearly. I can understand why Dan Meyer wants to tattoo a beautiful quote from the article on his lower back: http://twitter.com/ddmeyer/status/13661464598 However, the network they are building, consisting of "faculty members, researchers, community colleges, and professional groups" is missing something important: it either does not seem to include voices of anyone from their target audience directly, or these voices are not immediately apparent in the descriptions. I would understand it if their target audience were toddlers, but that's not the case.

How about asking the mother described in the first paragraph, and people like her, to take an active role in the planning? How about involving wide masses of these people through the social media? The foundation's Twitter stream has almost six thousand followers and is following two accounts: http://twitter.com/carnegiefdn I found no means for public discussion on the foundation's site http://www.carnegiefoundation.org/

Maybe the "networked community" described toward the end of the paper will include, well, the community it targets, directly. Will it?

16. gclyburn - May 12, 2010 at 12:32 pm

You're ahead of us, in some respects. We are indeed involving students in our planning. We've already conducted focus groups and will have community college students on our Steering Committee and involved in other ways. We're serious about involving all stakeholders and about being student-centric. As for the way others can join our conversation, or as Uri Triesman calls it, the "joyful conspiracy," we're building a collaborative space that should be accessible through our website. We're not there yet though.

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