Strategies to help developmental math students

Nationally about 70% of incoming community college students are placed into developmental (a.k.a. “remedial” or “foundational”) math classes that earn no college degree credit. But only 10% of these students successfully move past developmental math to earn their degrees.

Four broad areas are being addressed to increase student success through developmental mathematics (1) Placement, (2) Pedagogy, (3) Curriculum, and (4) Student attitudes.

Improving Placement

Failing a class is not the only barrier to completion--the length of the developmental math path defeats many students. More developmental math students drop out of college without ever failing a math class than flunk out of math. One strategy to reduce the number of “exit points” is to help students place into as high a math level as reasonable.

For example, Cañada College uses its Math Jam both as an intensive preparation for the math placement exam and also as a recruitment tool to get more students into STEM fields.

The placement instrument itself, typically a machine-graded standardized test, can be augmented or replaced.  High school GPA, recency of the previous math course, weekly work hours, and total course load could be part of “multiple measures.” Some schools have abandoned placement into developmental math courses, typically offering supplementary resources for students in credit-bearing classes.

Modifying Pedagogy

James Stigler lists three key types of learning opportunities that students need to experience to become flexible learners: productive struggle, explicit connections, and deliberate practice.

Modularized courses can allow students to spend time only on topics they need to study. The Emporium Model relies on software to do the pretest, primary instruction, and mastery testing, with human interaction largely limited to one-on-one tutoring in the computer lab (where students work lessons and take assessments). The University of Illinois uses software for placement and remediation, and California State University Northridge uses software as part of its hybrid lab remediation for students considered “at risk.”

Technology also plays a key role in both MOOCs (Massive Open Online Courses) and the “flipped” classroom. However, the “MO” aspects of MOOCs appear not to improve student success compared with the online developmental math courses that have existed for decades.

Another way to address the attrition between courses in a sequence is to offer “compressed” courses. The students take two courses during one term, but each course meets the standard number of hours per term--students are essentially immersed in math, which comprises most or all of their studies for that term.

Adjusting the Curriculum

The American Mathematical Association of Two-Year Colleges (AMATYC) has a 2014 position paper that states, “Prerequisite courses other than intermediate algebra can adequately prepare students for courses of study that do not lead to calculus.”

There are numerous “pathways” that have been created to allow developmental math students to pass a transferable math course--typically statistics or a quantitative reasoning course--that do not require many topics typically associated with intermediate algebra. The pathways normally reduce the number of developmental math courses required before earning transferable math units.

• Path2Stats is part of the California Acceleration Project, based on a program developed by Myra Snell at Los Medanos College.
• Statway and Quantway are projects of the Carnegie Foundation for the Advancement of Teaching.
• The Dana Center’s Math Pathways include pathways for both STEM and non-STEM students.
• Mathematical Literacy for College Students (MLCS) and Algebraic Literacy grew out of an AMATYC project. They can serve as alternatives to beginning and intermediate algebra classes for STEM majors, or the MLCS  can serve as prerequisite for a transferable non-STEM math course.

Addressing student attitudes

The “affective domain” includes attitudes, values, beliefs, interests, and motivation.

Carol Dweck’s research indicated that students (from grade school through graduate school) with “growth mindsets” persist and succeed better than peers with “fixed mindsets”. And importantly, students can learn to move from a fixed mindset to a growth mindset.

David Yeager’s research suggests that the performance gap in math--specifically developmental math--suffered by women and other underrepresented groups can be eliminated by specific brief interventions.

City University of New York's Accelerated Study in Associate Programs (ASAP) is an initiative that does not attempt to modify what occurs in the classroom. ASAP stipulates full-time enrollment and provides participants with academic advisement, career services, tutoring, financial supports, specially blocked or linked courses.

Alternative Pathways and transferability in California

California is home to the Carnegie Foundation for the Advancement of Teaching, the current force behind two pathway projects:  Statway and Quantway. 

An underlying assumption behind alternative pathways is that mathematics requirements for degrees and/or certificates should vary according to discipline. California's Student Success Task Force report contends, "Improved student support structures and better alignment of curriculum with student needs [Emphasis added] will increase success rates in transfer, basic skills, and career technical/workforce programs." The National Center on Education and the Economy 2013 report, "What Does It Really Mean to Be College and Work Ready?" states, "But our research...shows that students do not need to be proficient in most of the topics typically associated with Algebra II and much of Geometry to be successful in most programs offered by the community colleges."

The Carnegie Foundation, The Charles A. Dana Center at U.T. Austin, and the California Community College Success Network (3CSN) all promote alternative pathways to allow students in non-STEM disciplines an option of completing a university-transferable mathematics course without requiring the students to demonstrate completion of an intermediate algebra course.

The two California university systems, the University of California (UC) and the California State University (CSU) have been cautious in embracing the idea of alternative pathways in California Community Colleges (CCCs).

One pathway strategy is to provide students with an alternative  prerequisite to an existing transferable statistics class.  The alternative prerequisite does not have all traditional intermediate algebra topics and does not have elementary algebra as prerequisite. And in response to this strategy, Nancy Purcille of the UC Office of the President sent a March 7, 2013 email to CCC articulation officers:

"The prerequisite for UC-transferable math courses continues to be intermediate algebra or equivalent.  No attempt at this time will be made by UC to define specific content/courses that may be deemed “valid” alternate prerequisites.  When submitting a course for TCA review, if CCC faculty propose a prerequisite that they judge to be the equivalent of intermediate algebra, then UCOP articulation analysts will treat the prerequisite as such and evaluate the course outline as usual.  UC will not be evaluating the prerequisites listed – unless it is jointly requested by the CCC and UC faculty."

This position appears to respect the tenet that the community college should be able to decide the appropriate developmental math required to prepare its students for the articulated transfer-level math course.

The CSU provided a different position to accommodate alternative pathways.   Ken O'Donnell of the CSU Office of the Chancellor sent a November 2, 2012 email to CCC articulation officers that appeared to be discouraging alternative pathways:

"Please take this email as a reminder that only courses with a full prerequisite of intermediate algebra, as traditionally understood, will continue to qualify for CSU Area B4 [math/quantitative reasoning requirement to transfer].

"The CSU has made a recent exception for the Statway curriculum, under controlled and very limited circumstances, so we can evaluate whether other approaches will satisfactorily develop student proficiency in quantitative reasoning.  In the meantime, we count on the articulation community to uphold the current standard."

But Ken O'Donnell sent an April 2013 email acknowledging without objection the strategy of keeping the intermediate algebra the official prerequisite for the transfer math course but facilitating CCC student challenges to that prerequisite.

The CSU Chancellor’s General Education Advisory Committee has looked into this use of the prerequisite challenge process, and determined that it has no grounds to comment.  How community colleges meet curricular requirements that are below baccalaureate level is up to the colleges, and not up to the receiving transfer institutions.  In other words, community colleges may participate in initiatives like Acceleration in Context and the California Acceleration Project without jeopardizing articulation, because the transferable B4 course is unchanged; only the intermediate algebra prerequisite is challenged. 

Thus both the UC and the CSU are tacitly giving CCCs the go-ahead to develop alternative pathways.

Contradictory mandates to community colleges

A goal of the Common Core State Standards (CCSS) is to prepare students to be college and career ready.  That goal is also part of the mission of community colleges.  There has been considerable discussion regarding how  the CCSS might affect students' chances for getting into college, but scant discussion about how community colleges fit into the implementation of the CCSS.

Community Colleges might be assumed to have a distorted view of what it means to be college or career ready.  After all, they typically use the word "college" when naming themselves, yet eligibility to become a community college student does not require any minimum GPA nor any minimum score or ranking in any test.  It is sometimes said that the University of California serves the top 12.5% of California high school graduates, the California State University system the top 33.3%, and the California Community Colleges serve the top 100%.  But this is too limiting--a high school diploma is not a requirement for enrollment at any California Community College.

So at community colleges, we may worry less about "college ready" but rather focus on "transfer ready".  UCLA and CSUN are my school's two nearest public universities, and both report that our transfer students perform slightly better than their native students.  So there is evidence that community colleges are not grossly underestimating what is needed to be transfer ready.

California Community Colleges are presented with two conflicting mandates .   Community colleges  are encouraged 1) to align with K-12 standards for college and career readiness (according to the California Community College  Student Success Task Force  http://bit.ly/xOC5aK), and 2)  to provide alternative pathways to transfer (according to the Carnegie Foundation for the Advancement of Teaching  http://bit.ly/y1EZhX, the Charles A. Dana Center  http://www.utdanacenter.org/mathways/, etc.).

Explicitly, a consortium of the Charles A. Dana Center, Complete College America, Inc., Education Commission of the States, and Jobs for the Future, asks community colleges to provide a  "fundamentally new approach for ensuring that all students are ready for and can successfully complete college-level work that leads to a postsecondary credential of value.

"...The content in required gateway courses should align with a student’s academic program of study — particularly in math... Institutions need to focus on getting students into the right math and the right English." (from "Core Principles for Transforming Remedial Education: A Joint Statement" : http://bit.ly/TPqqCp)

The researcher at my institution estimated that 75% of our students interested in transfer are in disciplines that require no mathematics beyond an introductory statistics class to earn a baccalaureate degree at CSUN.  Evidently there are many students who can earn baccalaureate degrees without taking  single course from the mathematics department of any 4-year school.

The California Community College Success Network (3CSN.org), the Carnegie Foundation, the Dana Center, and the Student Success Task Force all recommend removing  curricular requirements  that act as barriers rather than aids to program completion.  The SSTF report contends, "Improved student support structures and better alignment of curriculum with student needs will increase success rates in transfer, basic skills, and career technical/workforce programs." [emphasis added]

The existing and proposed curricula of alternative pathways for non-STEM students omit many topics of intermediate algebra.

On the other hand, neither the University of California nor the California State University accepts a math or statistics course to meet  math transfer requirements unless that course has intermediate algebra as a prerequisite. 

If aligning with the CCSS implies that "intermediate algebra" should mean CCSS Algebra 2 (which includes circular trig and some inferential statistics), then the math requirements for transfer math courses will increase significantly.

And because intermediate algebra is the California Community College minimum math requirement for an associate's degree, the requirement for an AA degree will also increase simultaneously.

It is impossible for community colleges to remove unnecessary but currently required topics (for transfer to non-STEM disciplines) while simultaneously not merely maintaining but augmenting that list of required topics for all students.