The subject of geometry in the curriculum continues to be an area of concern among mathematics educators. The gap between standards expectations and actual textbook content continues to reflect the need for substantial change. In this study, the geometry language introduced in K‐6 textbooks was carefully examined and compared to the language used in the Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, 1989), Principles and Standards for School Mathematics (NCTM, 1999), and New Standards Elementary School Mathematics Performance Standards (National Center for Education and the Economy, 1997). The. logic followed was that the language in textbooks reflects the content presented in the textbook, and the language in the standards reflects what should be presented. The results of the study clearly indicate that there is a substantial misalignment between the geometry presented in the textbooks, the. geometry expected to be taught by groups such as NCTM, and the geometry being assessed in student performance measures as suggested by NCEE. Specific areas of misalignment are identified, along with implications, and some areas in which the curriculum should be revised are identified.

In 1973, Bruner maintained that teachers need clear and correct mathematical words to describe problem situations, to question students' unreasoned statements in mathematics, and to encourage students' further research and reading in mathematics. Bruner insisted that “good mathematical language challenges—relights the flame of curiosity” and further said that people use words to resolve puzzling situations. He suggested, however, that using words correctly in solving problems is not easy. To encourage students to speculate, teachers need to help them to understand the use of the words.

Because an increasing number OF school districts requires the successful completion of an algebra course to graduate from high school, many middle school teachers are beginning to focus more attention on introducing algebraic thinking to their students (NCTM 2003). Consequently, it becomes important to consider ways to ensure that these experiences are meaningful and connected to arithmetical experiences from the earlier grades. We believe that presenting middle school students with activities that involve exploring computational algorithms—how and why they work—can contribute to the development and promotion of algebraic thinking.