Using WAMAP to Facilitate a Mastery Approach to Developmental Math Mike Jenck, Matt Lewis, Ben Mayo Yakima Valley Community College

Problem Rate of degree/certificate completion for students placement testing into developmental math is extremely low. The sequence of developmental courses is very long. At YVCC a student placing at the lowest math level will progress through one of the following sequences to get to the 100-level: Math 49 – Math 50 – Math 75 – Math 85 – Math 95 Math 49 – Math 50 – Math 75 – Math 84 – Math 91 – Math 94

Problem Students who pass our developmental courses do not necessarily have the skills to be successful in subsequent courses. As an example, consider the following test grades for an arithmetic student: Whole Numbers Exam: 92% Integers Exam: 90% Fractions Exam: 45% Decimal Exam: 85% Final Exam: 74% Grade: C

Addressing the Problem A few department members showed interest in pursuing alternate ways of moving students through our developmental curriculum. There would be two main changes to the traditional model. Students move through the material at their own pace, rather than at the instructor’s. Students must show mastery on a topic before being allowed to move on. Our focus was initially on changing the delivery of Math 49 (Number Sense), Math 50 (Arithmetic), and Math 75 (Pre-algebra).

Advantages of Self-Pacing The highly motivated student has the ability to accelerate. A student may progress through up to three of our developmental classes in one quarter, and only pay for the highest class he or she completes. Example: A student completing Math 49 and Math 50 in one quarter will only pay for Math 50. In the winter 16% of our students who began in Math 49 were able to also pass Math 50 in the same quarter. One student was able to complete the material for Math 49, Math 50, and Math 75 in the same quarter.

Advantages of Self-Pacing Students may quickly show mastery over topics they know, leaving more time for topics they struggle with. Example: Many successful students took only a week to complete their work in whole numbers, and then took up to 5 weeks on fractions. Students who struggle on foundational topics (i.e. whole numbers) are not forced to go to the next topic after they fail a test.

Implementation of Self-Pacing Students meet 5 hours per week in a large computer classroom. The class capacity is 64 with two instructors per class. Student learning is achieved… through the text-book for the class. through videos from the Internet vetted by department members. through one-on-one interaction between the instructors and students. through mini-lectures given to groups of students who are in the same place in the material.

Implementation of Self-Pacing Assessment of student progress is done in three ways: Section Diagnostics A 10-15 question diagnostic quiz must be passed with at least 80% accuracy to complete a section. Subsection Mini-Quizzes Students may try to get 100% on 2-3 question mini-quizzes within subsections to “test out” of a particular problem type. Subsection Practices When a mini-quiz for a subsection is not passed, students complete practice assignments. Students must pass with 100% accuracy but have unlimited attempts on each problem. However, the numbers involved in the problem change with each attempt.

Implementation of Self-Pacing At the end of each chapter students must take a test. The test is completed on the computer, but the students must show all of their work on a designated test form. Students must complete the tests with 75% accuracy to move on. When a student earns a raw score less than 75%, the test is graded for partial credit. When a test is attempted and not passed, an item analysis is conducted to determine which sections of that chapter need to be reset for the student.

Anatomy of Self-Pacing

Why WAMAP? We use WAMAP (Washington Mathematics Assessment and Placement) as the platform for the class. WAMAP allows us to write our own assessment questions or use problems already created by other instructors who use WAMAP. WAMAP is free for the students and for the school. We are able to easily share with others what we have created on WAMAP.

Administrative Logistics We are currently offering two courses, Math 049C and Math 050C. Both of these classes meet at the same time, in the same classroom. Math 049C is for students who place into our Adult Basic Education program in math, but above this level in writing. To pass Math 049C, a student must complete the curriculum on whole numbers and integers, as well as pass four timed skills tests. Math 050C is for students who have passed Math 049C. To pass Math 050C, a student must complete the curriculum on fractions and decimals, as well as pass a final exam over all arithmetic material.

Administrative Logistics At this point, all students who place above adult basic education in math must take our lecture arithmetic course. In the fall, we will be conducting an arithmetic class taught in a self-paced mode to these students so we can compare short-term and long-term success rates as compared with our lecture classes. We do not have immediate plans to implement this modality for our pre-algebra courses, but we allow students who accelerate through the arithmetic material to attempt to pass pre-algebra by working through what we have created for that material on WAMAP.

Lessons Learned Mini-lectures are an essential part of a self-paced class. Students need as much well-defined structure as we can give them in this model. Students are required to complete time-logs to record how much time they are spending working on math outside of class. Students are given benchmark schedules to help keep them at a pace that will lead to success. Strict attendance rules must be put in place to discourage absenteeism.