Developmental Math at the CROSSroads
February 2013, Volume 16, Number 2
By John Squires
As course redesign sweeps across the nation’s math classrooms and developmental math programs, it’s time to take a second look at a landmark work on developmental education, Accent on Learning, by K. Patricia Cross (1976). From mastery learning to software-guided instruction and self-paced modules, the principles put forth in Accent on Learning are now being implemented at colleges throughout the nation, often with greater success than the traditional lecture system that, until recently, has been the primary mode of instruction in developmental math programs. These principles, what makes their successful implementation possible thirty-seven years later, how they relate to the principles of course redesign, and how they have been adopted in many developmental math programs around the nation are discussed in this paper.
In Accent on Learning, Cross highlights technology as the key to being able to provide individualized instruction and remediation. Similarly, course redesign uses technology to provide ongoing assessment and prompt feedback (National Center for Academic Transformation, 2005). Utilizing technology can result in teachers spending more of their time providing individualized assistance. When Cross wrote Accent on Learning in 1976, the Internet as we know it did not exist and the personal computer was not readily available or affordable. The technology at that time was not where it needed to be in order to transform the nation’s classrooms and the educational experiences of college students. Clearly, that is no longer the case, and as society becomes infused and even saturated with technology, the ability to provide anywhere, anytime, on–demand assistance is limited only by an institution’s and instructor’s imagination. The exponential growth in the accessibility, bandwidth, and capabilities of technology is the main reason computers can now be used to improve student learning and success, as Cross suggested.
Mastery learning is the proposition that students need to master all of the basic skills in a subject, giving them a solid foundation for success in college. At its core, mastery learning removes the limitations of time, allowing the student to spend as much time as needed to actually learn the concepts. Introduced by Bloom in the 1960s, mastery learning has been tried in various settings and programs. Now, mastery learning is serving as the foundation for reform efforts in developmental math. Several states, including the Tennessee and North Carolina, have adopted mastery learning as a core principle in their developmental math programs. The rationale for mastery learning is straightforward: If the developmental math program is based on competencies that students truly need in order to succeed in college, then it makes sense that students should be required to master those concepts.
Cross suggests that content should be modularized, a suggestion that often leads to questions regarding the meaning of modularization. First and foremost, modularization means dividing up the competencies and content in a way that allows for individualization of student learning plans. In addition, Cross recommends the concept of small learning units. At Cleveland State Community College, the developmental math program was based upon the concept of the mini-module, which consists of a weekly homework assignment and quiz (NCAT, 2009). The concept of the mini-module fits nicely with Cross’s recommendation that the course material be divided into small learning units, or modules (Cross, 1976). Establishing weekly expectations helps keep students on track and engaged in their learning, while avoiding the night-before-the-test syndrome that infects many college students.
In the section on individualized instruction, Cross lays out much of the foundation for the National Center for Academic Transformation’s (NCAT) concept of course redesign. She advocates active learning, regular feedback and evaluation, and the need to recognize individual differences in learners, which necessitates individual assistance. Each of these can be found in the principles of course redesign, and rightfully so (NCAT, 2005). Increasing student engagement is directly linked to increasing student learning. Students who don’t do anything, don’t learn anything, and this is far too often the case in college math classrooms. Regular feedback and evaluation also help increase student engagement, as students who receive feedback have a better idea of where they stand in their quest to conquer the material and learn the concepts. This feedback and evaluation can be provided by teachers in classrooms and learning labs, and it can also be provided by the instructional software when the student is working at home and the teacher may not be available. Cross notes the diverse needs of students in developmental studies courses, such as level of preparation and educational background (Cross, 1976). Individualized instruction is critical in order to address the gaps in students’ learning, especially in light of the range of needs in the developmental math classroom.
Traditional Lectures in Developmental Education
Students in developmental education often come from diverse backgrounds and the gaps in their knowledge vary greatly, even within a single classroom. Students who enter developmental math classes directly from high school have often been exposed only to the traditional math classroom, and yet they are lacking the most basic math skills. Clearly, the traditional classroom did not work for these students, and there is little reason to expect a different result by putting them in yet another traditional classroom. On the other hand, some developmental math students need only a tune-up, a refresher to prepare for college, while other students have major gaps in their knowledge and need extensive individualized assistance if they are to succeed in their program of study. Treating these very diverse situations with one solution does not make sense. Students who could exit the developmental studies program quickly in a self-paced program may become frustrated in a more traditional program, while underprepared students lacking basic skills may be set up for failure, as these students tend not to ask many questions in a traditional classroom setting.
Cross (1976) makes a distinction between remedial and developmental education based on the purpose of the program, stating that if the program is designed to overcome academic deficiencies, then it is remedial, and if the program is designed to develop the diverse talents of students, then it is developmental. In designing its new developmental studies program in 2010, the Tennessee Board of Regents took a cue from Cross and shifted the philosophy of the program from “remediating high school competencies and content” to “identifying the skills needed for success in college and their chosen field of study” (Berryman, 2011). This shift is more than semantics, as most students do not need a significant dose of High School Algebra II content to have a successful career. As Betty Frost (2011) of Jackson State Community College correctly states, “nursing students do not need to know how to solve rational equations in order to be a good nurse.” In fact, most students require basic math skills, numeracy, and knowledge of statistics for their chosen careers. STEM students, however, need a solid foundation in algebra skills, which they will use in both pre-calculus and calculus courses. Given these differences, providing different content to students based on their career paths makes sense, as does the shift from remedial to developmental education.
In 1976, Patricia Cross put forth a vision for developmental education. In Accent on Learning, she establishes the rationale for using technology to enhance classroom instruction. She also stresses mastery learning as the key to the education of the underprepared student, while providing individualized assistance for struggling students. Her outline is a blueprint for increasing both student learning and success in developmental math programs. Thirty-seven years later, it appears that many of the nation’s colleges are finally listening.
Berryman, T. (2011). Unpublished personal communication.
Cross, K.P. (1976). Accent on Learning. San Francisco: Jossey-Bass.
Frost, B. (2011). Unpublished personal communication.
National Center for Academic Transformation. (2005). Five principles of successful course redesign. Retrieved from www.thencat.org/PlanRes/R2R_PrinCR.htm
National Center for Academic Transformation (NCAT). (2009, January). Increasing success in developmental math: Following the NCAT playbook. The Learning Marketspace. Retrieved from www.thencat.org/Newsletters/Jan09.htm#1
John Squires is the head of the Math Department at Chattanooga State Community College. He was the recipient of The Cross Papers Fellowship in 2010 and wrote The Cross Papers, Number 13, Changing the Educational Landscape: The Total Impact of Course Redesign.
Opinions expressed in Learning Abstracts are those of the author and do not necessarily reflect those of the League for Innovation in the Community College.