Using e-Learning Platforms for Mastery Learning in Developmental Mathematics Courses

Mathematics and Computer Education, Spring 2004 by Boggs, Stacey, Shore, Mark, Shore, JoAnna

Introduction

Many colleges and universities have adopted e-learning platforms to utilize computers as an instructional tool in developmental (i.e., beginning and intermediate algebra) mathematics courses. An e-learning platform is a computer program used to enhance course instruction via computers and the Internet. Allegany College of Maryland is currently using the e-learning platform Blackboard to teach developmental mathematics in a Mastery Learning format. Mastery Learning is a teaching technique in which students do not advance in the curriculum until a specified level of subject mastery is attained. Mastery Learning is defined by the Department of Mathematics at Allegany College of Maryland as passing a test or other assignment with a score of seventy percent or greater.

Although there are other e-learning platforms available, such as Web-CT and AngleSoft, this paper addresses (but does not endorse) using Blackboard as a viable method of instruction enhancement for Mastery Learning in developmental mathematics courses.

Nationwide estimates are: between sixty to seventy-five percent of entering community college freshman require remediation in mathematics in order to succeed in a college environment (Cox, 1993). Unfortunately, the failure rate in such courses is alarming and unacceptable. Of students enrolled in developmental mathematics courses, "... fewer than one-half are able to pass the course on their first attempt" (Hackett, 1985). Therefore, it is not difficult to understand why it is not unusual for more than forty percent of mathematics courses offered at two-year community colleges to be developmental (Chang, 1993). For example, at Allegany College of Maryland, eighty percent of 18 to 24 year old students are enrolled in the developmental mathematics courses. Of those students, only thirty-four percent successfully complete the coursework required to continue with a college level mathematics course.

A major problem facing developmental mathematics instruction that inflicts such an alarming failure rate is that mathematics concepts build upon one another. When students fail to understand concepts in the first chapter, they are still required to move on to the next chapter. Mastery Learning is desirous in developmental mathematics courses; however, teachers often have an extremely difficult, if not impossible, task of teaching multiple groups of students who are working in different chapters simultaneously. Moreover, the duties of the instructor are compounded by difficulties in managing the grading and testing needed to give students several attempts on each chapter with different chapter tests.

For successful Mastery Learning to occur in developmental mathematics courses, several obstacles must first be overcome. The obstacles discussed in this paper are those which most hindered developmental mathematics faculty at Allegany College of Maryland. These four obstacles have, so far, kept Mastery Learning from becoming a standard method of instruction. They include: 1) creating multiple versions of each test, 2) grading multiple versions of tests for students at varying stages of the course, 3) scheduling time for students to take several versions of tests, if needed, to attain a certain level of mastery, and 4) teaching students who are at different learning objectives.

1. Creating multiple versions of each test

Mastery Learning requires instructors to test students at varying points in the curriculum. Creating multiple versions of tests to be given to students at different places in the course can be a daunting task for any teacher. The developmental mathematics faculty at Allegany College of Maryland has found that multiple versions of tests can be handled successfully using Blackboard Cartridges and Blackboard Random Blocks.

Blackboard Cartridges are electronic test banks written by the author of the book. They accompany a growing number of mathematics textbooks with many ready to use versions of tests. The cartridges are simply downloaded from password protected instructor resource sites to Blackboard sites. Teachers may use the tests as packaged in the cartridge or write questions of their own. All questions written by the instructor and questions that come with the Blackboard Cartridge can be used to create test pools to make as many versions of tests as needed.

A way of creating a number of tests sufficient for any course is to use an option within Blackboard called Random Blocks. This option pulls questions from question pools and allows the user to set up blocks of questions from which Blackboard randomly selects questions from each question pool. All the questions within a random block must be worth the same point value, but each block of questions can be worth different point values. For example, if a teacher wants to have a test that includes five questions on signed numbers, four questions on fractions, three questions on evaluating expressions, and two questions from the Metric system, the teacher would place all the questions from both the cartridge and those written by the teacher on signed numbers in one question pool, all the questions from fractions in another question pool, all the questions from evaluating expressions in another question pool, and all the questions from the Metric system in another question pool. The instructor would then set up Random Blocks to randomly pick five questions from the first question pool, four questions from the second question pool, three questions from the third question pool, and two questions from the last question pool. Each student then receives a randomly generated test.