A sentential logic test consisting of 30 items\vas administered to advanced7th grade, 8th grade, and 12th grade students and preservice secondary mathematics teachers in 1986 and 1992. The resulting data were comparedwith data obtained in a similar study conducted in 1976. An examination of the changes in scores by age level according to item type and semantic form was made over the three data collection periods. The results indicate that the impact of maturation and/or education has decreased in its effect on the development of logic skills. Concern is raised over preservice teachers' level of understanding of sentential logic.
The Curriculum and Evaluation Standards forSchool Mathematics (Commission on Standards for School Mathematics, 1989) provide a guideline for improving mathematics instruction and serve as an excellent resource for mathematics educators formaking curricular decisions and evaluating current needs. One ofthese standards recommends for "grades 9-12, the mathematics curriculum should include numerous and varied experiences that reinforce and extend logical reasoning skills so that all students can... follow logical arguments; judge the validity of arguments; construct simple valid arguments;..." (p. 143).Mathematics educators now have the responsibility ofseeking ways to implement the recommendations set forth in the Standards. However, before they can be implemented, there needs to be an understanding of the current level of content and pedagogical knowledge of mathematics teachers. Such understanding would assist educators in planning efficient and beneficial inservice and teacher education programs.How important is the teacher's level ofknowledge of mathematics? Porter and Brophy (1988) noted that good teachers are knowledgeable about their content area and appropriate strategies for teaching. Stein, Baxter and Leinhardt (1990) found that teachers with "more explicit and better organized knowledge" (p. 641) about their content area were more likely to present lessons leading to conceptual understandings rather than simply a collection of facts. These researchers also suggested that teachers with a weak content knowledge base were more likely to overemphasize procedural rules. After reviewing the literature on effective teaching. Anne Reynolds (1992) concluded that among other skills, beginning teachers should enter the first year of teaching with a strong knowledge base of the subject matter they will teach. As Brophy and Good (1986) noted, this knowledge affects how the teacher presents the material, paces the curriculum and turns unexpected questions or events into meaningful instruction. So if teachers are expected to emulate and teach logical reasoning skills, they need to possess at least a basic understanding of mathematical logic and how it can be applied.Easterday and Henry (1978) examined the relationship between maturation or education and understanding of sentential logic by comparing scores on a test ofsentential logic (Eisenberg &McGinty, 1974) of junior high and high schoo...
