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;&p;&;&l0": : ad ;&X a: Teaching and Learning Developmental Mathematics at
Community Colleges
By
Flix Apfaltrer and Marcos Zyman
January 2008
This paper is based on our experience in teaching developmental mathematics at Borough of Manhattan Community College of The City University of New York. The problems and challenges involved in this experience certainly apply to the practice of teaching and learning mathematics at community colleges in general, and their international counterparts, known collectively as Non-University Tertiary Institutions. Our aim is to analyze some of these problems and discuss how we have addressed them at BMCC.
Borough of Manhattan Community College has a policy of open admissions. This policy provides affordable access to quality education for all who seek it. As a consequence, students of all kinds of educational backgrounds are accepted into BMCC and a majority of these enroll in our developmental program. Indeed, over 75% of entering freshmen lack the necessary skills to take a credit-bearing mathematics course and must take at least one of the developmental classes, which encompass two broad areas of basic mathematics: Arithmetic and Algebra. Most entering students are placed in our Elementary Algebra class, MAT 051. In the fall of 2006, the passing rate for this course was 38% and approximately 12% of the students taking the class had taken it twice before. A high percentage of students - about 60% - fail developmental courses at BMCC.
There are several problems pertaining to the teaching and learning of these developmental courses. Some of the most pressing ones are the lack of study habits and motivation, serious gaps in necessary skills to approach any mathematics class, and considerable variations in former mathematical knowledge. These, together with math anxiety, teaching and learning styles, and scheduling conflicts constitute a mere sample of the issues that students and faculty have to cope with. In what follows we concentrate on these problems and discuss some of the ways in which they can be handled.
Study habits. Students often approach our developmental courses with a serious lack of study habits. Many have difficulty concentrating on the material; they struggle to keep up with assignments, and simply fail to understand the value of studying and doing homework on a daily basis. They come to class late, they miss many classes throughout the semester and they suffer from a lack of interest and motivation.
How to deal with this? The answer is not easy. Many students are used to their previous experience of social promotion and expect to simply pass the class without doing much, or simply by showing some effort. When they are faced with the fact that they have to pass two exams, a standardized computer exam (the ACT-COMPASS) and a departmental final, they simply hope that things will go well in the end regardless of their actual work and effort during the semester. Some students realize the inherent problem of this approach when it is already too late.
As instructors of these courses, not only do we constantly stress the value of doing homework and attending the course regularly, but we also make these notions very explicit. In order to insure that students arrive on time, some faculty members give daily quizzes at the beginning of the class period, but reportedly this technique is not as effective as expected. Other professors give students with good class participation and homework incentives like bonus points and even candy and chocolates. These methods are effective with some students, but some of them still remain unmotivated and apathetic. Some instructors remind the students about the passing statistics in the course at the beginning of the semester, in an attempt to make them aware of the risks of not taking the class seriously. They remind them that they are investing in a class that gives them no credit in order to encourage them to study hard and exit remediation as soon as possible. It is hard to quantify the effect of these techniques on learning habits and motivation. However, there seems to be a consensus that students who are offered more individualized attention and help become more motivated and study better. This leads to our next issue:
Previous mathematical knowledge and the need for individualized attention. A typical developmental classroom frequently suffers from large variations in the level preparation of its students. Those placed in Developmental Algebra are supposed to be proficient in Arithmetic, but this is often not the case, as many still exhibit serious deficiencies in this material. At the same time, some students do have a good general knowledge of Arithmetic and at times even an acceptable understanding of some topics in Algebra (such as Linear Equations and Inequalities), but not enough to be exempt from the class. These variations in mathematical proficiency raise a substantial problem for teaching developmental mathematics. In addition, students have to cope with their own math anxiety, low self-esteem, and a negative attitude toward mathematics, by expressing statements such as I hate math or Im not good at math. These attitudes are often derived from their past unsuccessful experience with the subject. Dealing with such variations in mathematical proficiency requires individualized attention that the instructor alone cannot provide during class. For this reason, BMCC runs a large tutoring facility (the Math Lab), which operates on a generous schedule to make it convenient and accessible to busy students. Some instructors require their students to visit the Math Lab regularly, while others simply encourage the students to use it as much as possible. Besides having tutors ready to assist students in their assignments, the center counts with computers, mathematics software, and videos to assist students in the process of learning specific topics. The lab also offers various problem sets and practice tests to help students prepare for exams.
In addition, BMCC has been piloting a Supplemental Instruction program, in which some sections of our Developmental Algebra MAT-051 course have a 'personal' tutor assigned to them. The tutor attends lectures and holds office hours. Students often feel more comfortable approaching the tutor rather than the instructor for questions about the course, and they frequently develop a good rapport with the tutor. This process eliminates some of the natural barriers that occur between the instructor and the student. Instructors who participate in this program encourage students to meet the tutor during office hours, and some faculty members make this compulsory. The program has been successful in improving passing rates in MAT-051 and is currently being expanded.
Lecture-based instruction. A traditional course, where the instructor only lectures on the material and presents many examples throughout the entire lesson does not work well in developmental mathematics courses. Since there is such a large variation in students mathematical proficiency, a lecture-based format of instruction is an inefficient choice for teaching these courses, because it leaves students behind, bored, or both. A better approach is to teach a course based on practice, and indeed, it is the students who need the practice! Teaching a course in this way entails structuring each session in such a way that the lesson is taught as a mini-lecture, followed by some worked examples and culminating with extensive practice on the spot, preferably in small groups, together with feedback from the instructor. The most obvious practical advantage to this is that students enrolled in a developmental class are often busy people with jobs and family responsibilities. The hands-on approach gives them the opportunity to practice immediately after they see the material, and many report that this way they can approach their homework with confidence. Students benefit greatly if they do some of the homework in class in a monitored environment.
In sections with an assigned tutor, both the instructor and the tutor go through the groups and help the students individually in solving the problems, which allows for the personalized attention that some students need. Several faculty members also reserve computer rooms where the students work individually on computer-based problems similar to those appearing on the standardized computer final exam (ACT-COMPASS). While students are working through the assignment, the instructor (and the tutor, if available) offers individualized supervision. While this method may seem inefficient, students actually welcome this kind of personal attention. A workshop for instructors teaching these courses is offered at the beginning of each semester, in which alternatives to lecture-based instruction are discussed, mentioning and analyzing their advantages.
Professor Apfaltrer implemented several of these techniques in his MAT 051-154 Basic Algebra class, during the spring of 2007. With the help of an assigned tutor, he structured his classes as mini-lectures followed by review exercise sessions. His class met once a week in a computer room, so he was also able to aid students in their preparation for the computerized ACT-COMPASS exam through the review of online materials. Compared to his previous MAT 051 class (section 083), taught in the spring of 2006, his students passing rate in the ACT-COMPASS improved considerably: from 56% to 80%. It is important to mention that for these two semesters, the requirements for passing the ACT-COMPASS were exactly the same. This seems to indicate that the techniques mentioned above had a positive effect on the passing rates.
Conclusion:
Teaching and learning developmental mathematics at a community college such as BMCC is a challenging endeavor indeed, both for students and faculty. Students often approach a developmental class with many deficiencies and disadvantages; several of them work full-time and have family responsibilities. Many students stumble in the process and do not complete the course. As we mentioned before, this is in part due to lack of study habits and motivation, math anxiety, and poor attendance. Other students, much less in number and after a great deal of effort on their part, learn the material, go on to more advanced courses, and eventually earn a college degree that ultimately leads them to a better future.
Teaching these courses has proven to be an immensely challenging task for faculty, albeit potentially quite a rewarding one. Our personal experience indicates that instructors need to be particularly caring and nurturing in these courses to give the students the individualized attention they so desperately need. The instructor needs to be understanding of the special circumstances that these students have to deal with. The personal stories of many of these students are quite distinct from those of college student at more selective campuses. Many of our developmental students have to cope with economic hardship, broken families (or raising a family), working full-time; and they still have to find the time and energy to further their education. Instructors are confronted with these issues while teaching a developmental course.
While instructors would like all their students to pass the course and continue on, it is very difficult to have a passing rate for these courses above 50%. As we mentioned before, some of the chief strategies to attain this goal is to allow students more in-class practice in small groups. Being caring and understanding motivates some to make an extra effort and possibly loose their fear/hate of mathematics. Having a personalized tutor in the classroom furthers this goal, by giving many students the confidence to ask the tutor questions in a more intimate setting.
It is our hope that implementing these strategies in developmental mathematics courses will contribute to the improvement of passing rates. It must be frustrating for any instructor to find that only eight of her students pass in a developmental class of twenty students. If the efforts of the instructor in using small groups, personalized help, and a more nurturing learning environment result in a passing rate of more than half, the outcome can be considered a great success. For the failing students, there is always a second chance. In any case, we believe that an instructor who adopts and practices these techniques can have a major positive impact in the students future.
Further reading:
1. Arenson, Karen W: Class Notes, New York Times article, April 30, 1997.
2. Bain, Ken: What the Best College Teachers Do, Harvard University Press, 2004 (especially pp. 98-134).
3. Miller, Nancy C: Motivational Theories for Developmental Mathematics, available online: HYPERLINK "http://www.austincc.edu/nmiller/AMATYC.html" http://www.austincc.edu/nmiller/AMATYC.html (includes many references).
Based on internal grade analysis from the BMCC registrars office, dated June 25, 2007.
Based on conversations with faculty members utilizing these techniques to improve attendance and timeliness.
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