Monthly Archives: October 2014

Review-Pretest-Retest in Math

Saturday, October 11, 2014

Successful Developmental Math: “Review-Pretest-Retest” Model Helps Students Move Forward

from the New England Journal of Higher Education

by Richard Bisk, Mary Fowler and Eileen B. Perez
April 23, 2013


Much has been written about the failure of “developmental education” in mathematics. Failure has not been our experience at Worcester State University. In response to concerns about both the placement rate into developmental math courses and the failure rate in those courses, we made substantial changes in our placement program and in our course delivery. We have decreased by 50% the number of students placed into developmental math courses. The success rate in these courses has increased from around 30% to around 80%.

Our program is based on several key principles:

  • Students can be successful in mathematics with the correct entry point. Mathematics is a cumulative subject. Because students who take courses they are not prepared for are seldom successful, we rigorously maintain the prerequisite standards for our classes. However, we do not want to place students in developmental classes when all they need is a brief review. We work to ensure that students take placement seriously and are prepared to do as well as possible when they take the placement tests.
  • We provide clear, consistent standards for all students. It doesn’t help students by pretending they have competencies that they don’t. In particular, different sections of developmental math must use equivalent grading techniques. All students must pass the same final exam to pass the class.
  • We provide a nurturing and supportive environment for students who have often had negative experiences in mathematics. Students need to know that their instructors are there to help them when they struggle. However, the most supportive thing we do is placing students appropriately.
  • We encourage all students to enroll in required math classes as soon as possible. Math proficiency atrophies over time. This means we have to offer sufficient seats for first-year students in both developmental and introductory credit-bearing classes. We work with our advising center to place students in these courses.

Reducing need for remediation

The Commonwealth of Massachusetts Department of Higher Education mandates that all incoming students in the state’s public higher education system attain a “passing” score on the College Board’s Elementary Algebra Accuplacer exam or pass an appropriate developmental math class before enrolling in a college credit-bearing math courses. In fall 2004, 54% of our first-year students received a “failing” score.

For the class entering in fall 2005, we required students to take a mock Accuplacer exam before they could register for orientation, where the actual exam was given. This mock exam was taken at home on the student’s own computer. It was not proctored. We saw this as a consciousness-raising activity—a way to give students a sense of what to expect as well as to let them know about the importance of the exam. With this change, our “failure” rate dropped from 54% to 36%.

The following year, we made additional changes. Before a student could register for orientation, he had to achieve a “passing” score on the mock Accuplacer exam. If he didn’t get a “passing score” after two opportunities, he had to come to campus for a two-hour math review session. With this additional change, the “failure” rate dropped to 24%. Since then it has been consistently around 25%

The placement process

The initial Department of Higher Education mandate for developmental math in 1998 set a single passing score of 82 on Elementary Algebra Accuplacer for determining whether a student was ready for college-level math classes. In 2001, the department added a second cut score of 72 for courses that used minimal amounts of algebra, such as a math for liberal arts courses.

At Worcester State’s Mathematics Department, we decided we needed more detail to appropriately place students. Many students needed developmental work in arithmetic as well as algebra. And while a score of 82 on the Elementary Algebra Accuplacer might indicate readiness for a college algebra class, it told us nothing about whether a student was prepared for calculus. We want each student to begin mathematics coursework at the best entry point. As a result, all first-year students begin by taking two Accuplacer exams: Arithmetic and Elementary Algebra.

  • If they need developmental math work, we use a combination of the two scores to determine whether they need to take an arithmetic course before taking a developmental algebra course.
  • If they score 82 or higher on the elementary algebra Accuplacer, they then take the college-level math Accuplacer. This score is used to determine the possible starting points for the student’s college-level math classes.

Logistically, each student is assigned a placement code of 1 through 7 based upon their scores on the two or three Accuplacer exams. Mathematicians call this a function of three variables where the range is: {1,2,3,4,5,6,7}. For example, a code of 1 means a student begins with our developmental arithmetic class. A code of 7 means a student may begin with calculus. During the registration process, placement codes are examined as part of the process of checking prerequisites. A student who wishes to take calculus needs either a code of 7 or successful completion of precalculus with a grade of at least C-. (Our experience has been that a student with a D seldom passes the subsequent course.)

The Developmental Math Program: philosophy

The WSU Developmental Math Program is designed to meet the academic needs of students who scored below 82 out of 120 on the Elementary Algebra Accuplacer exam. Many of these students have negative emotions and thought patterns around mathematics that needed to shift before they would be able to learn the subject matter. Some are so used to failing math that they don’t believe that they have the ability to succeed. They would rather walk away than face the challenge, despite the fact that this would severely limit their ability to earn a bachelor’s degree. For students who had already incurred significant student loans, failure to complete their degree would leave them with increased debt and decreased income potential. This heightens the anxiety associated with learning math.

Our program strives to create a classroom environment where students believe they can succeed and know they will have the support of the instructor. In each new class, the instructor’s initial goal is to build a relationship of mutual trust and respect. When these students enter the developmental math class, many things are different from how they were in their previous math classes. Since they are in a class with students at similar skill levels, most are no longer at the bottom of their class. Furthermore, the students are older and more mature than the last time they took a math class. With a positive environment, they are more likely to persevere and succeed. We find that as student anxiety begins to subside, they relax and start learning. All these benefits are only possible because the students are placed in a class that is being taught at their current proficiency level.

Underlying the program development, we have had a commitment to maintaining consistency of standards for all students and all course sections. Lowering standards for some students is not supportive and nurturing, but propagates student beliefs that they cannot succeed at mathematics. These beliefs reinforce societal perceptions of mathematical reasoning and skills as optional and only obtainable by a select few. Sadly, many higher education administrators and policymakers encourage these negative viewpoints

Implementation and design

Our current program was developed over the past 10 years and evolved through a series of iterations from a computer-based algebra review to one where students are placed according to their arithmetic and algebra skills into one of two developmental math courses that address topics required for success in WSU’s college-level math courses.

The developmental courses meet three hours per week, carry three institutional credits and are taught in a more traditional face-to-face format. (Institutional credit counts toward maintaining full-time status so students are eligible to receive financial aid and live in the residence halls, but not toward graduation.) We have used feedback from assessment data as we sought effective ways to teach and support our students. As we have developed these classes, the success rates of our courses have increased from 31% in 2003 to about 80%.

To maintain consistent standards across students and sections, we use the Arithmetic or Elementary Algebra Accuplacer as the final exam for each class. Students must pass this final exam to pass the course. Since the instructors no longer decide whether a student passes, they become more like coaches, working with the student to increase skills and achieve a common goal. Instructors meet with individual student, assign extra problem sets and arrange for tutoring. While success is ultimately the student’s responsibility, we want to provide as much support as we can.

We believe our students need structure and a series of smaller goals before the final exam. Therefore, we require that all students have a 70% average in the course in order to qualify to take the final exam, the Accuplacer. This requirement is made clear on the syllabus and the instructors discuss this throughout the semester. In the last three weeks of the semester, students with averages below 70% are invited to work with tutors to address topics on which they are struggling. They are given an additional quiz that provides the opportunity to raise their average and qualify for the final. Of course, our real goal is to get them to review the material so they pass the final. It’s a learning activity. The underlying principal is that we want to promote success without lowering standards and expectations.

If students qualify to take the final exam, but do not pass it, we discuss a re-test opportunity with them. The instructor offers these students a set of review problems and gives them a limited amount of time to complete it. This is another learning activity. Once the students complete the review material, they are given a pretest to determine if they have improved their skills. Students who perform favorable on the pretest may retake the final exam. This “review–pretest–retest” process helps most of the students pass and move forward with their mathematics program.

Changing minds

Most of our students who score into the developmental math program are in majors that require only one college-level math course. Many students enter the developmental math program intending to complete their developmental math and a single college level math class; but after experiencing success, they reevaluate their options. This was the situation for Jeremy Hart, a 30-year-old military veteran who entered the developmental arithmetic class as a history major. He had many doubts about his ability to succeed at mathematics and had chosen a major with a minimal math requirement. He planned on finishing his mathematics requirement as quickly as possible by taking our most basic college-level course, called “Survey of Math.” When the arithmetic class began with fractions, Hart found the class a safe place to openly express his confusion and frustration. He became so comfortable with his ability to learn mathematics that he changed his major from history to business administration. He successfully completed many courses that required mathematical and quantitative reasoning including statistics, college algebra, mathematical economics, microeconomics and three accounting classes. He is currently employed in a managerial job that brings together the skills he developed at Worcester State and in the military. He manages a multimillion-dollar budget and performs cost and statistical analyses as he contributes to his organization’s success.

Our program works, but we are constantly looking for ways to minimize the need for remediation. We work with Massachusetts high schools through the state GEAR UP (Gaining Early Awareness and Readiness for Undergraduate Programs) so students can take our placement tests while still in high school. And we are currently studying how students who successfully complete our developmental courses perform in the first college-level math class.

Developmental math education does not have to be a failure, as long as we are all willing to meet the challenge.

Richard Bisk is a professor of mathematics at Worcester State University and was math department chair from 2004-2012Mary Fowler is an associate professor and current chair of the math department at Worcester State. Eileen B. Perez is Developmental Math Program coordinator and lead instructor at Worcester State.


Related Posts:

Improving Math Success in Higher Education Institutions

Developing Story: A Forum on Improving Remedial Education