The Abacus: Teachers' Preparation and Beliefs about Their Abacus Preservice Preparation

In the 1960s, Tim Cranmer based his abacus designed for individuals who are blind on the Japanese soroban. Today the Cranmer abacus (referred to in the remainder of this article as the abacus) is manufactured by the American Printing House for the Blind (APH) and can be used by people with visual impairments (that is, those who are blind or have low vision) to compute addition, subtraction, multiplication, division, and more advanced mathematical functions. There are several computation methods for the abacus that are used in the field of visual impairment. The logic-partner method focuses on understanding the "what" and "why" of the steps in solving a problem on the abacus. It requires that a student know the "partners" or complements of the numbers up to 10 (5 = 2 + 3 and 5 = 1 + 4). This method uses synthesis when abacus beads cannot be set directly. Verbalizing the steps and the reasons for each movement made on an abacus is an important feature of this approach (Livingston, 1997). The secrets method focuses on the process of moving the abacus beads in a particular sequence, following a specific set of rules for different numbers and operations. It does not emphasize the understanding of that process, rather the rote memory of the bead movements (Davidow, 1988). In the counting method, the student counts each bead as it is added or subtracted, moving from the unit beads to the 5 beads (but counting only 1 for all beads). There are also specific rules regarding certain numbers and operations, but fewer than the full set of secrets (Millaway, 2001). The paper-compatible method has the user complete problems in the same way an individual completes them using paper and pencil. The standard mathematical facts are used, not the secrets or a series of questions (Willoughby & Duffy, 1989). Finally, the Hadley School for the Blind method uses the indirect method to teach the abacus. The indirect method combines both the logic-partner method and the secrets method. Complements are explained, and students are expected to use that understanding to follow a specific set of rules for adding and subtracting. In the first two decades following its inception, studies were conducted to examine the use of the abacus in residential schools for students with visual impairments (Steinbrenner, Becker, & Kalina, 1980) and the way in which university preparation programs were preparing future teachers of students with visual impairments to teach computation with an abacus (Steinbrenner & Becker, 1982). More than 30 years ago, Steinbrenner and Becker (1982) reported that universities were ineffective in their preparation of teachers of students with visual impairments to teach abacus computation to students who are blind. During the 1990s, no studies on the use of the abacus were published. However, recommendations in the literature during that period continually stated that university personnel preparation programs should teach computation using an abacus to future teachers of students with visual impairments and help practicing teachers update their skills (Rapp & Rapp, 1992). Sakamoto (1999) noted that little attention had been paid to the potential of the abacus in the past several decades. More than a decade has passed since Sakamoto's study, and the abacus continues to be relegated to a few words in articles that discuss mathematics instruction for students who are blind or in articles about the expanded core curriculum. For example, Smith and Kelly (2007) reported that teacher preparation programs teach computation with an abacus at different technology-awareness levels; 27% teach at the "awareness" level, 33% teach at the "proficient" level, and 40% teach at the "advanced" level. Rosenblum and Smith (2012) reported that of 26 university programs, 10 programs instructed students in using an abacus as a primary focus of a course, 13 programs provided instruction in using an abacus as an embedded skill in a course, and 3 programs had students complete their instruction through a correspondence course. …