What math do students need to know?

Students get extra help in math at Tarrant County College in Texas. (Photo: TCC)

Community colleges across the country are implementing a series of reforms to eliminate one of the chief barriers to completion: the failure to pass math, particularly developmental courses.

Among the reforms are math pathways with different strands for non-STEM majors, co-requisite courses for students who aren’t ready for college-level courses, more placement options and more of a focus on engaging students in active learning rather than lecture-based instruction.

There is growing acknowledgement in the field that many community college students required to take developmental math could have done well in a traditional credit-bearing course, says Susan Bickerstaff, a senior research associate at the Community College Research Center (CCRC) at Columbia University’s Teachers College. Multiple studies show that students do better in the aggregate when they are placed in higher level courses more quickly, she says.

Too often, the problem stems from the use of placement tests that pigeonhole students in the “abyss of developmental math,” when they are capable of passing college-level math with a little extra help, adds Linda Braddy, vice president for academic affairs at Tarrant County College’s (TCC) Northeast Campus in Texas and former deputy director of the Mathematical Association of America.

As a result, more colleges are turning to multiple measures of placement. In California, a state law that took effect January 2018 that requires community colleges to use multiple measures, including  high school coursework, grades and GPA to place students in math and English courses, rather than relying solely on a single assessment.

TCC is in the process of switching from the Accuplacer test to determine whether students are ready for college-level math to the ALEKS (Assessment and Learning in Knowledge Spaces) system, produced by McGraw Hill. ALEKS uses artificial intelligence and adaptive questioning that gives students problems about math concepts based on what they already know and what “they’re ready to learn,” Braddy says. A student who gets a wrong answer gets immediate feedback, and “that is hugely valuable.”

The co-requisite approach

For students who still need remediation in math, a growing number of colleges are adopting the co-requisite model. The goal is to minimize the amount of time students spend taking developmental education courses by having them simultaneously enroll in remedial and college-level math courses during their first semester. They also have access to tutoring and other support.

“When you require development education, you lose a lot of students,” Braddy says. There’s a stigma to being required to take developmental education, and when students don’t get credit toward a degree for those courses, they are more likely to drop out of college, she says.

Several studies – include a 2015 CCRC study of community colleges in Tennessee – found students who participated in a co-requisite approach had higher pass rates in college-level courses.

As part of a nationwide shift away from traditional developmental education, Texas passed a law in 2017 calling for colleges to cut back on such programs. This year, colleges there are required to have at least 25 percent of students who are unprepared for college-level math to be placed in a co-requisite course or given a “non-course-based option” (NCBO) as an alternative. That percentage rises to 50 percent of students next year and 75 percent in 2021-22.

TCC is in the process of adopting co-requisites in developmental math education, Braddy says, along with an NCBO allowing students who need extra help to visit a lab for one-on-one instruction.

The right path

“Nationally, there is really strong data supporting robust outcomes in Mathways,” the pathways approach developed by the Charles A. Dana Center at the University of Texas at Austin, Braddy says. The pathways model, such as those promoted by the Dana Center and the Carnegie Foundation for the Advancement of Teaching, are based on the idea that not all students need to take algebra. Students in the social sciences would do better taking math courses geared toward statistics, for example, while those in the humanities should focus on quantitative mathematics.

At a recent conference of the American Mathematical Association of Two-Year Colleges, “there was a degree of skepticism about the non-algebraic pathways; that they are less rigorous, somehow,” Braddy says. “One of the goals of the math community in higher education is to change the culture so people understand all three pathways are rigorous.”

The pathways are continually evolving, as colleges find what curriculum works best for different careers. There’s now some interest in developing a new math pathway for people going into healthcare careers, Braddy says. As an example, it would cover the type of math nurses need to know in determining medication doses.

TCC has adopted the Mathways concept relatively recently, so it doesn’t have longitudinal data yet to gauge its success, Braddy says.

At TCC, concerns have been raised about math pathways pigeonholing students in a way that could limit them when they transfer to a four-year institution. As a result of that concern, she says, there’s a tendency among advisors to encourage all students to get into an algebra pathway if they aren’t sure what they want to do or might transfer into a STEM field later.

“That happens less frequently than we fear,” she says. And if students do decide to become STEM majors, they can always take algebra later.

“In reality, algebra is not the best course for all students,” Braddy says. “It’s only good for students planning to take calculus. For students in the social sciences, statistics is much better.”

New ways of teaching

Even with the reforms in placement and developmental education, math faculty are still finding there are students with significant learning challenges, Bickerstaff says, noting there are several programs under way to improve learning through conceptually oriented methods.

She cites the CUNY Start program for developmental math education – which is used in seven community colleges in the City University of New York system – as particularly effective. It upends the approach used in a typical classroom, where students are taught an algorithm for something like how to multiply fractions. Instead, students carry out a series of problems, then try solving a problem they might encounter in real life.

With CUNY Start, the teacher would begin with “intuitive number relationships” then move into questioning, discovery and open-ended activities, Bickerstaff says. “Students develop an understanding first, then the algorithm would emerge from that.”

While students in traditional developmental math understand math as being all about memorizing a set of procedures, CUNY Start focuses on a deeper conceptual understanding of number relationships, she says. A 2018 evaluation found students in CUNY Start are much more likely to enroll in and pass gateway courses in their first year.

A collaborative approach

At the classroom level, one reform that’s being tested is the “Lesson Study” model, which aims to make classrooms more student-centered by using evidence-based instructional practices, Bickerstaff says. Lesson Study is a structured, collaborative professional development intervention that has shown evidence of improving math instruction among K-12 teachers but has rarely been used in higher education.

Instead of having faculty do most of the talking – the “chalk and talk” approach – students provide a justification for math learning, Bickerstaff says. The faculty who have used this method are “extremely enthusiastic,” but it’s too early to gauge its effectiveness.

Three community colleges in Oregon – Portland, Clackamas and Lane – are participating in a pilot to adapt the Lesson Study approach to teaching developmental math. The pilot is being conducted by Education Northwest, a federally funded education research laboratory, in collaboration with CCRC.

The developmental course is part of Oregon’s quantitative math pathway, which looks to help students seeking liberal arts degrees and thus do not need a heavy emphasis on algebra or statistics, said Nicole Edgecombe, a senior research scholar at CCRC. Students in this pathway wouldn’t need to learn how to factor a polynomial, for example, but would need to understand ratios, pre-algebra concepts and proportionality, she says. The math instruction ties to real-world applications and problem-solving, such as how to understand a political poll.

Lesson Study is a collaborative process, not a curriculum, Edgecombe says. “It’s a process that allows faculty to reflect deeply on how they present a lesson,” she says. It’s not even tied to a specific discipline, although it is primarily used in math.

A faculty team at each college – comprising full- and part-time instructors – teach the same lesson to their classes, set goals around the lesson and observe one another’s classrooms. As they see the extent to which students understand the material or have problems with certain concepts, they work together to strengthen the curriculum and the delivery of instruction.

Lesson Study “makes student learning transparent,” Edgecombe says. “It’s all about collaborative learning among faculty grounded in high levels of practice.”

About the Author

Ellie Ashford
is associate editor of Community College Daily.