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Focus On Basics

Volume 6, Issue D ::: February 04

A Conversation with FOB...

Transitions and Math

Even after receiving high school diplomas or certificates of General Educational Development (GED), a large percentage of community college students need remedial - often called developmental - math before they can move into college-level math courses. Why is this, and what, if anything, can be done about it? Focus on Basics invited five math specialists from around the country who work in adult basic education (ABE) or community colleges - Lynda Ginsburg, Myrna Manly, Pam Meader, Linda Murphy, and Mary Jane Schmitt - to talk about the problem. 

FOB: Why are so many community college students in developmental math courses? What's the issue?

LINDA: I find that most students have an issue with transition. Many students coming into developmental math have poor study skills and poor study habits. For example, with attendance: they don't come to every class. They don't ask questions. They need to know that they can interact with their instructors; they also need to make use of the services the college has to offer.

MYRNA: This is especially true with the transition from adult programs, where the structure has been one of open entry and self paced instruction. Students could proceed when it was convenient for them. The structure of most community colleges does not allow that freedom. 

PAM: In Maine, ABE is separate from the community college and developmental system. We [the ABE system] play a big role; this is where students learn how to be students and how to be not fearful to ask a question. I think the biggest gatekeeper to math transitions is phobia. When I have a student, not only do I teach them algebra but to be in touch with their phobias, and how to deal with them.

MYRNA: A general point of view is that GED grads don't quite measure up with high school graduates. I'm not aware of any evidence that shows that. When I was teaching in community college, the high school graduates had just as poor study habits as people who were coming in from adult ed. 

MARY JANE: You seem to be in agreement that most students have an issue with transition. We don't have evidence that the GED grad and the high school grad are different in that.

LINDA: Without any hard statistics in front of me, I can't say. But I work with incoming [community college] students on assessment and placement. I sometimes know, when I'm talking with students, whether they are GED or high school graduates, and I don't find a difference between them. GED [holders] might even have been better prepared for college in their arithmetic skills.

MYRNA: That's really no surprise, because the GED is normed so that four out of every 10 high school students won't pass it.

FOB: I still have trouble understanding why people can complete the GED or high school and still need developmental math before they're ready for college level math. 

PAM: The GED isn't enough, you need at least an algebra course. We suggest that students take an algebra course with us [at the ABE program] before they take a college math course.

ABE teachers often don't have the math content credentials to be able to teach the level of math that is needed for college credit courses. As soon as you try to teach a good solid algebra course, you need math credentials. ABE is a population laden with great people in language and literacy but the math content people are few and far between.

And learners who are preparing for the GED want to do it quickly. So most times, even if a teacher is comfortable teaching math, she won't teach the whole algebra sequence, because the students are in a hurry to pass the GED.

PAM: We teach the whole [algebra] sequence, in two parts, over the course of a year. It's applied [algebra]. 

MYRNA: In typical algebra classes in community colleges, an entire year of high school algebra is condensed into one semester. We had to design a pre-algebra class to make the transition to abstract thinking easier.

LINDA: Why is it that the teachers hired for GED programs aren't prepared to teach algebra? 

The pay in adult ed isn't enough to attract them.

MARY JANE: Maybe in ABE we should start an "Algebra for all movement," similar to the one in K-12, but "all" would mean teachers and administrators as well as students. All adults should be up to snuff in algebra. 

MYRNA: That's what a survey found of adult ed teachers in Pennsylvania found. They wanted staff development to be algebra, algebra, algebra.

PAM: You can be knowledgeable in math and not be a great teacher. On the other hand, you absolutely have to have background in math so you don't pass on math misconceptions.

LYNDA: As to the teaching piece: there's a growing body of knowledge about how to teach math effectively. The professional development has to be from that body of research. There are two pieces: accurate math knowledge, and more of it, and math pedagogy. What are effective ways to help other people to learn math?

MARY JANE: The adult education system has to put 25 percent of its focus on math overall, to even get a jump start. To start some serious research, some serious staff development, so the math doesn't stay a gatekeeper and our students can get a leg up. I don't see that happening because the field is led by literacy and language. 

LYNDA: What would you say about the model that has specialists teaching math, rather than everyone teaching everything. Recognize that it's a different bag of skills that are needed to teach math well, and that programs should be encouraged to have math specialists. We need to acknowledge that it's a different body of knowledge and skills.

MYRNA: That's a good point.

FOB: So, students enter community college with math deficits for a number of reasons. They completed high school weak in math. They didn't get algebra in high school. They were so focused on getting the GED quickly that they didn't want to invest the time in more math skills development. And even if they wanted more math, many GED teachers don't have the math knowledge to teach algebra. 

At the same time, students are often unprepared for the structural academic demands of community college such as fewer class hours, knowing how to study, knowing how to access resources. 

What happens when these students get into community college?

MARY JANE: There are some incredible statistics: 80 percent of people in Massachusetts who go into community college are in developmental, non-credit math courses. Only 50 percent really make it out of there. Those numbers were so striking to me. 

LYNDA: There are lots of instances of people taking developmental math over and over and over. Some have math learning disabilities that are hard to diagnose. Teachers don't recognize the problems that their students are having. You often have adjuncts teaching who aren't necessarily great teachers. They're not using strategies that are most helpful: looking for meaning, hooking it on to people's understanding of what they already know.

The other problem with developmental level courses is that they're college system courses: they meet two or three times a week for 15 weeks, versus more intensity in high school. The pace [in community college courses] is too fast for people who are struggling.

LINDA: Here at Northern Essex Community College, we have several options. If students are in danger of failing, they can opt into an individualized course, which extends their time and lets them move at their own pace. But most of our students stay in the regular classroom. We have a very good group of adjuncts that has been here for a long time. We have about 1,000 developmental math students per semester across all three levels of math. I don't think that our failure rate is as high as the one that's reported across the country. 

MYRNA: We've been mostly talking about algebra, but there's the course before algebra. To me, that introductory arithmetic course shouldn't be taught in a purely symbolic way. Students who have been through arithmetic over and over and still do not "get it" won't benefit from doing it the same way once again. The pre-algebra content needs to be functional, helping students understand when to use certain math procedures and why they work in the situation.

LYNDA: There is k-12 research on that. Teachers expected that kids would think word problems - the applications - were harder than doing operations, but kids find word problems easier, and symbols [arithmetic operations] harder. 

FOB: That's teaching quality again.

MARY JANE: In ABE in Massachusetts, we have an incredible staff development system, but in the community college system there isn't the same strong support. Community college teachers could really use some time for staff development. 

FOB: Testing often drives curriculum. What about the community college placement tests, such as the ACCUPLACER (which provides information used to place students in the proper levels in different courses)? What role do they play in this?

PAM: You're not allowed to use a calculator on the ACCUPLACER. It's heavy on arithmetic. My fear was the students wouldn't show that they have some algebra.

LINDA: We use it for placement in Massachusetts. It seems to be placing the students properly. Our state has mandated a cut-off score for placement into a college level math course, but cut-off scores for within developmental classes are determined by each community college.

MYRNA: I decided the test was not a huge problem in our college after taking the ACCUPLACER a number of times as if I was a student: I simulated various student profiles. For example, when I answered the questions as a student who knew how to estimate with fractions but had forgotten the procedures to carry out the operations, I could choose the correct answers and was placed at the proper class level. I found that someone who has been taught math using a more progressive, meaning-based approach can use those skills and test well on problems that look like they depend on more traditional, operations- focused skills.

MARY JANE: It [the ACCUPLACER] gives a bad message. It looks like a symbol manipulation test. If teachers in ABE decide to analyze the test, looking at typical items and thinking about what students need, it appears so much like a symbol manipulation test that I fear that teachers will teach in that way. Tests give a message about what's important. I would like to see it revised.

Besides, the people in advanced technical education say that even community college courses that are for credit aren't necessarily preparing students well mathematically for technical tracks. The math in community college is very [focused on] symbol manipulation rather than modeling or taking a functional approach to algebra. In the symbolic approach to algebra, the emphasis is on transformations, such as knowing how to transform x (x + 5) to x2 + 5x. Solving equations, simplifying expressions, and factoring are the central actions. A modeling approach focuses more on what the math is about. Mathematical modeling requires you to examine a situation, search for relationships, and represent those relationships with math structures. So you might start with a situation such as carpeting a room, and describe the relationship between the cost and the dimensions of the room.

The community college placement tests look at algebra as a manipulation of symbols. Some people believe that algebra should be taught using more of a functional or modeling perspective. Some books are being written that way. 

I believe a more functioning approach to algebra is more motivating for people, but the test and basic courses would have to change. So that's the dilemma.

MYRNA: I would add that a student who goes on to most traditional pre-calculus and calculus courses needs skill in symbol manipulation to succeed. While I advocate for the functional approach, I see value in ensuring that students can perform some manipulation techniques on demand. As a teacher of a course that is a preparation for others, you can't fight that.

PAM: It might be dependent upon the field that the student wants to pursue. Here in Maine there are three areas: if a student is going into a field with high math expectations, they need symbol manipulation. If they're not, I'd have them know how to use math in their lives. I have students who say, "How come no one ever told me about this?"

MARY JANE: I'd at least advocate for a balanced approach: learn some symbol manipulation with meaning as well. Most people don't just teach algorithms anymore, they build conceptual knowledge.

FOB: So even if the tests don't change, there's a need for instructional reform so all ABE students get a stronger math education, no matter what their goals.

About the Participants
Lynda Ginsburg, a Senior Researcher at the National Center on Adult Literacy at the University of Pennsylvania, has a doctorate in cognitive psychology and mathematics education and has taught mathematics at the high school, community college and ABE/GED levels. She is a founding member of the Adult Numeracy Network.

Myrna Manly has taught mathematics in junior high, high school, workplace, community college, and college. She  was the mathematics editor of the 1988 version of the GED test. She presents workshops and seminars for adult education teachers, is revising her book, The GED Math Problem Solver, and consults for the GED Testing Service. 

Pam Meader is a former high school math teacher who became an ABE teacher more than 16 years ago. She currently teaches four math classes, including algebra, at Portland Adult Education, Portland, ME, and is involved in a Nellie Mae grant for College Transitions.

Linda Murphy has been in developmental math education for about 22 years at Northern Essex Community College, Lawrence, MA, both as an instructor and as the math center coordinator. She is the grant manager for a three-year FIPSE Grant called 100% Math, a statewide effort to improve retention of the developmental math student.

Mary Jane Schmitt has taught, developed programs in Massachusetts and nationally, and is part of a team creating a numeracy curriculum for adults and out-of-school youth. She co-directs the National Science Foundation-funded Extending Mathematical Power Project (EMPower) at TERC in Cambridge, MA. She helped develop the numeracy portion of the forthcoming international Adult Literacy and Life Skills Survey.

Updated 7/27/07 :: Copyright © 2005 NCSALL