Questions for Practice: Reflecting on Developmental Mathematics Using 19th-Century Voices

Many authors of 19th-century arithmetic and algebra textbooks have made profound statements that have remarkable relevance for mathematics instruction today. Listening to their voices has made me question much of what is currently done in the teaching of developmental mathematics. In this article I review the writings of some historic authors, as found in their book introductions, as a way to reflect on current philosophies and methodologies.Just as a mirror helps one to see their own physical reflection, educational statements from the distant past can be used to help instructors better see their own educational practice. Concerning the concept of reflection in education, Rogers (2001) analyzed a number of theoretical approaches and determined, with regard to antecedents to reflection, that "most authors agreed that an event or situation beyond the individuals typical experience must occur if the reflective process is to be triggered" (p. 42). I propose that the voices of 19th-century textbook authors can provide that reflective trigger by speaking from a different time and a different context, but with an air of familiarity.In this article I provide a number of quotes from the introductions of textbooks from the 1800S pertaining to various issues that are relevant today. In one respect, relevance is understandable because, after all, math is math and certainly the basics of algebra have not changed much over the years. In fact, at least once a semester I have students work problems directly from these antiquarian books. I want them to make a connection with history and realize that a basic understanding of mathematics is something that, for years, has been considered to be important to what an educated person should know. The contexts of the word problems are sometimes humorous to modern readers, but the problems are remarkably similar to those that students do today. For example, instead of solving for how many hours it will take for two planes to meet, students in the 1800s calculated the number of days it would take for two people walking to meet or the number of hours for a pirate ship to overtake a schooner. But, essentially, the problems are the same.Areas of Special InterestIn reviewing the philosophical statements from the introductions of several textbooks, I have found five areas of special interest for today's developmental mathematics educators: motivation, relevance, depth, pedagogy, and textbooks. These are important educational concepts in any academic discipline but they have special significance to developmental math instruction. Motivation and relevance are closely related and must be strongly addressed by the developmental instructor, especially in teaching students who are potentially at risk. Pedagogical approaches and selection of textbooks are typically more complicated in developmental math. Classrooms often have a mix of traditional and nontraditional students who all have had some level of math instruction earlier in their educational experience. Many students have developed attitudes and emotions towards math that can inhibit self-confidence and learning. Also important to developmental math instruction is the depth of the students' learning. Going beyond rote memorization of math concepts and skills is important especially because developmental math is preparation for at least one more college-level math course. In addition, the importance of effective instruction is critical, especially given that developmental math courses are must-pass courses for students who may have had previous negative experiences in learning math and are seeking a higher education degree. This is contrasted with the fact that developmental math courses often top the list of "graveyard" courses at many institutions. So, can these voices from the dust trigger reflection on important aspects of practice? I explore each area of interest and discuss questions and implications for practice today.MotivationQuestions. …