SSM Table of Contents & Abstracts

Volume 102 (8), December 2002

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Abstracts

Understandings of Solutions to Differential Equations Through Contexts, Web-Based Simulations, and Student Discussion

 

David Slavit, Washington State University Vancouver

Tom LoFaro, Gustavus Adolphus College

Kevin Cooper, Washington State University

 

As in the case of elementary mathematics, the instruction of high-level mathematical concepts can often be sacrificed at the expense of a focus on algorithmic procedures. Computer-based simulations can expand an undergraduate mathematics instructorâs opportunity to explore high-level mathematical concepts in an applied environment. This study describes one instructorâs approach to incorporating simulations and classroom discussions in a differential equations course and the subsequent effects on student learning attitudes and outcomes. Students made modest gains in the area of conceptualizing and applying ideas regarding solutions to differential equations in this learning environment. Implications of the study include the identification of specific gains relative to computer-mediated learning environments and recommendations for using simulations to support conceptual development.

 

 

A Collaborative Effort to Improve University Engineering Instruction

 

Valarie L. Akerson, Indiana University        

Victor F. Medina and Nina Wang, Washington State University

 

This study focused on the instructional development of an assistant professor of environmental engineering in collaboration with science education and higher education faculty members. One semester of data was collected in the assistant professorâs environmental engineering laboratory class as he endeavored to address his teaching goals. Data collection included pre and post interviews with the assistant professor, students, and program coordinator, and collection of course documents, such as the course syllabus and assignments. In addition, all of the classroom sessions were observed and videotaped, and a midsemester video stimulated-recall interview was conducted. Results show the assistant professor made growth in the areas of questioning strategies, ãthink timeä for students, increased class participation, and the implementation of a student-designed field research project. Implications include that new professors can benefit from peer faculty support, and they and their students can benefit when the new professors recognize the complementary nature of research and teaching.

 

 

Intended Treatments of Arithmetic Average in U.S. and Asian School Mathematics Textbooks

 

Jinfa Cai, University of Delaware         

Jane Jane Lo, Western Michigan University 

Tad Watanabe, Penn State University

 

This study examined how selected U.S. and Asian mathematics curricula are designed to facilitate studentsâ understanding of the arithmetic average. There is a consistency regarding the learning goals among these curriculum series, but the focuses are different between the Asian series and the U.S. reform series. The Asian series and the U.S. commercial series focus the arithmetic average more on conceptual and procedural understanding of the concept as a computational algorithm than on understanding the concept as a representative of a data set; however, the two U.S. reform series focus the concept more on the latter. Because of the different focuses, the Asian and the U.S. curriculum series treat the concept differently. In the Asian series, the concept is first introduced in the context of ãequal-sharingä or ãper-unit-quantity,ä and the averaging formula is formally introduced at a very early stage. In the U.S. reform series, the concept is discussed as a measure of central tendency, and after students have some intuitive ideas of the statistical aspect of the concept, the averaging algorithm is briefly introduced.

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