Technology as a medium for elementary preteachers' problem-posing experience in mathematics.

This article attempts to extend current research and development activities related to the use of technology in problem posing, to early grades mathematics. It is motivated by the authors' work with elementary preservice teachers toward this goal, both at the graduate and undergraduate levels. New York State Learning Standards for K-4 mathematics serve as a background for technology-enabled learning. Spreadsheet-based environments designed by the authors (using Microsoft Excel 2004) are introduced from a tool kit perspective, enabling a meaningful combination of manipulative and computing activities by elementary preteachers and their students alike.

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One of the central tenets of the current reform movement in mathematics education holds that appropriate use of tools of technology is integral to the teaching and learning of mathematics at all grade levels. In the context of preparing teachers for the 21st century classrooms, the word "appropriate" may include the notion of teacher as a technologically minded curriculum developer, capable of exploring--and helping his/her students to explore--new avenues in mathematical content; in particular, being skillful in the use of technology for posing and solving problems. This puts mathematics educators involved in the preparation of teachers for elementary schools in a unique position because such technology-enabled changes in pedagogy must be feasible from the very outset in the chain of children's educational experiences.

It has been more than a decade since the National Council of Teachers of Mathematics (1991) suggested that technology has the potential "to enhance and extend mathematics learning and teaching" and that "the most promising are in the areas of problem posing and problem solving in activities that permit students to design their own explorations and create their own mathematics" (p. 134). Nonetheless, as an extensive search of the literature indicates, the few existing papers that describe the use of technology as a medium for problem posing are mostly concerned with the secondary mathematics education (Abramovich & Brouwer, 2003; Abramovich & Norton, 2006; Hoyles & Sutherland, 1986; Laborde, 1995; Noss, 1986; Yerushalmy, Chazan, & Gordon, 1993).

This article attempts to extend current research and development activities related to the use of technology in problem posing, to mathematics education in early grades. It has been motivated by the authors' work with elementary preservice teachers (referred to as teachers) toward this goal, both at the graduate and undergraduate levels, using a resource guide (New York State Education Department, 1998) that provides guidance to districts and schools in New York for structuring local curricula and instruction. This curriculum document focuses on using open-ended problems with young children, something that requires special skills by the teachers. These skills may include the ability to use computers as cognitive amplifiers in exploring the open-ended nature of appropriate mathematical situations. In an open-ended environment of a technology-enhanced classroom, one can expect young children to ask unforeseen questions about familiar concepts. This, in turn, has a potential for learning to become a reciprocal process (Confrey, 1995; Steffe, 1991). Apparently, the implementation of such a dynamic perspective on the learning of mathematics begins with the preparation of teachers.

It should be noted that to make technology integration into a quality teacher education program a success, one has to make right decisions regarding the choice of software involved. One type of software, which for more than two decades has gained widespread recognition as an exploratory tool, is a spreadsheet (Baker & Sugden, 2003). Designed originally for non-educational purposes, a spreadsheet may be conceptualized in educational terms as a combination of an electronic blackboard and electronic chalk (Power, 2000). Thus, it came as no surprise that the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000) recommended that spreadsheets be used with children as early as in grades 3-5. In support of such a recommendation, several authors reported successful uses of spreadsheets with young children, as well as with their future teachers in various grade-appropriate contexts (Abramovich, 2003; Abramovich, Stanton, & Baer, 2002; Ainley, 1995; Drier, 1999, 2001). This article introduces spreadsheet-based environments to be used both with the teachers and their students in the context of situated addition and subtraction as a medium for both problem posing and ...