Volume 97 (5), May 1997

Table of Contents

Abstracts

Table of Contents

Abstracts

 
• Mathematics for All: Perspectives and Promising Practices

ChristiR. Hirsch, Western Michigan University
Arthur F. Coxford, University of Michigan


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        The Core-Plus Mathematics Project (CPMP, 1995) is one of four comprehensive curriculum development projects that, in 1992, were awarded 5-year grants by the National Science Foundation to design, avaluate, and disseminate innovative high school curricula that interpret and implement the recommendations of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) and Professional Standards for Teaching Mathematics (NCTM, 1991). This article describes CPMP perspectives on a new curriculum organization for high school mathematics, identifies implications of these perspectives for promoting access and equity for all students, and reports some of the supporting oral data from an ongoing formative evaluation of the curriculum.

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• The Beliefs of Georgia Teachers and Principals Regarding the NCTM Standards: A Representative View Using the Standards' Belief Instrument (SBI)

Lynn Deal Futch, Stilson Elementary School
James C. Stephens, Jr., Georgia Southern University


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        The comparative beliefs of Georgia middle school mathematics teachers and administrators regarding the NCTM Standards are examined using the Standards' Belief Instrument (SBI). Responses from 172 administrators and 1264 teachers of Grades 6, 7, and 8 were analyzed using descriptive measures of central tendency for within-group agreement and Manova for between-group differences. Strong within-and Between-group agreement among all respondent classes characterizes the findings. Slightly more than two thirds (69%) of the beliefs underlying the SBI statements are validated by all respondent groups, and nearly one third (31%) are rejected at some level by all groups. No significant differences were found between teachers' and principals' beliefs for the collection of items (F _{(16, 138)} = 1.53, p = .080) or among the teachers grouped by grade(s) taught (F _{(32, 2224)} = .97, p = .487). Group membership accounts for 2.7 and 3.88%, respectively, of the variance. More philosophical and general standards are validated, but standards representing changes in traditional practice and processes are rejected this group teachers and administrators. Implications for reform are discussed.

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• What Children Bring to the Classroom: Learning Science From Experience

Stephen J. Farenga, Dowling College
Beverly A. Joyce, Dowling College


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        Extracurricular science-related experiences of young students were examined. The sample consisted of 539 elementary school students between the ages of 9 and 13. Students completed the Science Experiences Survey (SES) to identify the number of common scientific materials and activities they experienced outside of the classroom. The factor analysis isolated three underlying factors of extracurricular science-related experiences: life science-related experiences, physical science-related experiences, and general learning attributes related to science. Further analysis identified differences in reported experiences by gender. The data indicate that young girls tend to participate in nurturing life science-related activities, and young boys favor hands-on, action-oriented physical science-related experiences. The research suggests that the gender disparity in science follows a continuum that begins with the experiences of elementary school students.

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• Collaborative Curriculum Investigation as a Vehicle for Teacher Enhancement and Mathematics Curriculum Reform

Barbara J. Reys, Robert E. Reys, David Barnes, John Beem , Ira Papick
University of Missouri


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        The Missouri Middle Mathematics (M³ ) Project is an NSF-funded 3-year professional development project involving teacher/administrator teams from districts statewide. Project activities focus on collaborative investigation of emerging reform-based middle school mathematics curricula to support individual and systemic reform. Collaborative review and field-testing of material facilitates awareness and exploration of alternative instructional and assessment strategies and informed decision making. Early indicators of the model's success are reflected in participants' enthusiasm and professional growth. Project activities stimulate discussions of critical topics including questioning appropriateness of various teaching practices, research about teaching and learning, tracking policies, appropriate assessment models for gauging student learning and the importance of calculators and manipulatives as teaching and learning tools. these discussions transcend curriculum materials being reviewed and serve as a powerful vehicle for professional growth and development for individual teachers and districts.

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• Looking Back in Mathematical Modeling: Classroom Observations and Instructional Strategies

Ted Hodgson, Indiana University
David Harpster, Montana State University


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        Theorists often characterize modeling as a cyclic problem-solving process. One builds the model, assesses its validity with regard to the underlying problem situation, and revises accordingly. The process halts when, in the opinion of the modeler, the model generates a valid solution to the underlying problem. Recent research suggests that students, like experts, employ cyclic modeling processes. Extensive observations of university and high school students' modeling efforts, however, suggest the use of linear rather than cyclic modeling strategies. That is, novice modelers often fail to look back or revise their initial models. This paper offers empirical evidence on behalf of the linear modeling theory and identifies five factors that promote the use of linear modeling strategies: students' conceptions of models and the modeling process, the perceived objectives of the modeling activity, constraints on time and resources, statistical misconceptions, and an overall lack of interest. The paper concludes with several promising instructional strategies (strategies that address students' difficulties and promote reflective modeling behavior), as well as suggestions for future research.

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