The book describes the results of a 3-year longitudinal study of kindergarten through 2nd-year students in both U.S. and Australian schools. Both quantitative and qualitative data were collected to investigate the development of analogical and mathematical reasoning in young children and to look for possible relationships between these two constructs. Lyn English, the editor of the book, characterizes both types of reasoning in an introductory chapter. The findings of the study are then reported in a set of six chapters, written by different members of the research team. Three leading researchers in the field of analogical reasoning, Usha Goswami, Giyoo Hatano, and Tomomi Sakakibara comment on the study in two concluding chapters.
Anne R. Teppo and Ted Hodgson
In their article “What Every High School Graduate Should Know about Statistics,” Scheaffer, Watkins, and Landwehr (1998) contend that one cannot understand statistics without understanding probability. As a consequence, the authors outline several recommendations regarding teaching probability in the secondary school.
Warren W. Esty and Anne R. Teppo
The NCTM's Curriculum and Evaluation Standards for School Mathematics states, “Evaluation is a tool for implementing the Standards and effecting change systematically” (1989, 189). Tests are one facet of evaluation, and we maintain that mathematics classes are strongly affected by the way in which test scores are used to generate final course grades. In the traditional secondary school mathematics class, current grading practices tend to drive instruction by putting constraints on specific course content and its organization. In turn, content and its organization affect testing and therefore grading. The interaction of these factors is an aspect of assessment that is not specifically discussed by the NCTM's evaluation standards. The purpose of this article is to examine the impact of grading on mathematics instruction and on the implementation of the curriculum and evaluations standards.
Linda M. Simonsen and Anne R. Teppo
During their undergraduate program, preservice elementary teachers are expected not only to become generalists across a wide range of school subjects but also to develop pedagogical knowledge of the developmental and social needs of children. We have developed a twosemester freshman-level mathematics-content course that attempts to address multiple needs of preservice teachers. The goals of this course are to help preservice teachers (a) deepen their understanding of mathematical concepts; (b) restructure their attitudes toward, and beliefs about, the nature of mathematics and how it is learned; (c) investigate pedagogical issues; and (d) experience mathematics learning within a reformbased environment. These goals are interrelated and reflect the complexity of the nature of the knowledge and disposition, both mathematical and pedagogical, that preservice teachers are expected to develop.