Improving Retention By Redesigning Freshman Mathematics With The Dimensions Of Learning Pedagogy, Assessment, And Technology Framework

The retention of engineering students continues to be a major issue affecting engineering schools across the country and unsuccessful experiences in freshmen mathematics is one of the factors attributing to this problem. This paper presents a freshman mathematics course reform aimed at reducing Calculus I preparation time by at least one semester, improving pass rates and ultimately increasing the retention of engineering and computer science students. The Dimensions of Learning pedagogy, the use of technology and performance assessment are the main components of the framework used. A wireless mobile classroom was the key technological feature used in the redesign. The innovative Pre-Calculus course (IPC) redesign was performed by a multidisciplinary team of faculty from the Schools of Engineering, Science and Education. The project design, implementation aspects, assessment techniques and evaluation results are given. The first course offering shows a 14% higher pass rate (‘C’ or better) in the innovative pilot course than that of the sections taught in a traditional format. Moreover, 81% of the new freshmen enrolled in the IPC and who placed in a mathematics course one or two levels below the IPC, via the University’s placement test, received a ‘C’ or better. Assessment results of the frameworks used will be given as well. Preliminary results indicate that this comprehensive approach can be a viable format for optimizing teaching and learning, and thereby improving student retention and academic success. Introduction Many students are not Calculus ready upon entering colleges and universities and they also are unsuccessful at negotiating Calculus I at the first attempt, both which affects time to degree completion and impacts the students desire to remain in engineering, thereby affecting retention. In addition, when students initially take engineering courses, they often have difficulty translating mathematical concepts and knowledge to solve engineering problems. A Calculus Preparatory course has been redesigned by a multidisciplinary team of faculty from the Schools of Engineering, Science and Education in order to increase the retention and academic success of engineering and computer science students. This course is being developed with the intent of engineering and computer science students, with varying mathematics preparation, completing Calculus I by the end of the first year, at a maximum. The objectives of this redesign are to 1) understand the learning process; 2) develop faculty who model best practices in integrating teaching and instructional technology; 3) increase the short and long term retention of electrical P ge 903.1 “Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education” engineering and computer science students; and 4) increase students’ ability to apply mathematics to engineering and scientific problems. The innovative course unit redesign is comprehensive in pedagogy, assessment and resource support, including the integration of technology and learning. The pedagogy that is used is based on the Dimensions of Learning (DOL) framework, a powerful, effective and comprehensive model that uses what researchers and theorists know about learning to define the learning process. It differs from most pedagogical approaches used in higher education, and with this technique the optimum approach to teaching and learning is being sought. Engineering applications are being incorporated to motivate students and enhance their learning. Typically only 25% of new freshmen engineering students at Morgan State University enroll in Calculus I (MATH241), based on the University’s mathematics placement test, leaving 75% who are not “Calculus ready.” The average success rate (‘C’ or better) in Calculus I is 49.5%. Based on these statistics and our awareness of the difficulty students have in negotiating their first math courses, it is clear that mathematics has a profound impact on student success. Although Calculus I is the first math course required of engineering students, since 75% of our new freshmen begin in a math course other than Calculus I, (Basic Algebra, Pre-Calculus I, or Comprehensive Pre-Calculus), based on the University’s mathematics placement test, a much stronger affect on retention could be obtained if the Calculus Preparatory courses were impacted as well as Calculus I. Depending on students’ mathematics course placement, it could take one to four semesters to complete Calculus I. Using an integrated and comprehensive approach with novel pedagogy, assessment, and technology, and other strategies, an innovative Pre-Calculus course (IPC) has been designed and offered for the first time in Fall 2003. Dimensions of Learning (DOL) Pedagogy A major component of the course reform is the pedagogy used which is based on the Dimensions of Learning (DOL) framework. Its premise is that five types of thinking, or five “dimensions of learning,” are essential to successful learning. Robert Marzano of the Midcontinent Research for Education and Learning (McREL) Institute developed the Dimensions of Learning Framework in 1997. The framework grew out of many years of research into how we learn most effectively, and is designed to translate research into a practical classroom application to improve teaching and learning in any content area 1 . It ensures that instruction takes into account all five of the critical components of learning which include 1) Positive Attitudes and Perceptions about Learning; 2) Thinking Involved in Acquiring and Integrating Knowledge; 3) Thinking Involved in Extending and Refining Knowledge; 4) Thinking Involved in Using Knowledge Meaningfully; and 5) Productive Habits of the Mind. Implicit in the Dimensions of Learning model are six basic assumptions: Instruction must reflect the best of what we know about how learning occurs. •Learning involves a complex system of interactive processes that includes five types of thinking—the five dimensions of learning. •What we know about learning indicates that instruction focusing on large, interdisciplinary curricular themes is the most effective way to promote learning. •The curriculum should include explicit teaching of higher-level attitudes and perceptions and mental habits that facilitate learning. •A comprehensive approach to instruction includes at least two distinct types of instruction: one that is more teacher-directed and another that is more studentdirected. P ge 903.2 “Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education” •Assessment should focus on students' use of knowledge and complex reasoning rather than on their recall of low-level information. The Dimensions of Learning (DOL) framework is different from the traditional approach to teaching in that all five dimensions of learning are addressed in unison. Most traditional approaches to teaching tend to focus on one or two of the aforementioned dimensions. The goal is to develop a learner with the knowledge, skills, and dispositions to succeed as a student and as a professional. The framework has been adopted by educators and researchers in several countries including Japan, Germany, South America and Canada. It is popular because it can have an impact on virtually every aspect of education and can be used as a resource for instructional strategies, a framework for planning staff development, a structure for planning curriculum, and performance assessment such as reflection logs, portfolio, performance tasks, and rubrics, features that may not be included in traditional teaching approaches 2 . Attitudes and perceptions affect students’ abilities to learn. DOL 1 indicates that a key element of effective instruction is helping students to establish positive attitudes and perceptions about the classroom and about learning. Helping students acquire and integrate new knowledge is another important aspect of learning. According to DOL 2, when students are learning new information, they must be guided in relating the new knowledge to what they already know, organizing that information, and then making it part of their long-term memory. When students are acquiring new skills and processes, they must learn a model or set of steps, then shape the skill or process to make it efficient and effective for them, and finally, internalize or practice the skill or process so they can perform it easily. Once knowledge is acquired, it can then be extended and refined, according to Dimension of Learning 3 (DOL 3), by applying reasoning processes. Dimension 4 uses knowledge to perform meaningful tasks, which is what engineers do. This is one of the most important parts of planning a unit of instruction. The problem solving, inquiry and system analysis associated with this dimension is well suited for engineering and scientific applications. Dimension 5 indicates that most effective learners have developed powerful habits of mind that enable them to think critically, think creatively, and regulate their behavior. The five dimensions work together to ensure that students acquire conceptual understanding of their subject matter. All of these dimensions are important in the learning process, and by using all of the five dimensions of learning in the course redesign, it illustrates that the optimum approach for teaching and learning is being sought. Table 1 summarizes the advantages of the Dimension of Learning approach over the traditional teaching pedagogy. DOL is comprehensive, integrated and connected while the traditional mode of teaching is separated. Table 1 Traditional versus DOL (Mastery Learning) Traditional Dimensions of Learning (DOL) Lecture Contextual Learning, Reciprocal Teaching & Lecture Technology Technology-mobile, instantaneous feedback Separated Tests Comprehensive,