Volume 106 (3), March 2006

Alfinio Flores
Arizona State University

This article presents ways in which students ascertain that what they have learned in mathematics is true. Students in the middle school (and a few from other grades) were interviewed by prospective and in-service teachers. Students were asked what they had learned recently in mathematics and how they knew it was true. The answers were grouped by the author according to the justification schemes used by the students in their explanations. Students interviewed used three kinds of justification schemes: externally based, empirical, and analytic. For each kind, examples are provided of students’ justifications. Additional insights are included from the reflections of the interviewers. Some suggestions are offered regarding how teachers can help increase their students’ ability to give convincing arguments in mathematics.
 

Frances Lawrenz, Amy Gravely, and Ann Ooms
University of Minnesota

Use of technology in science and mathematics classes has been increasing, but there are differences in the amount of use of and students’ perceptions of its helpfulness across grade levels and subject areas. Technology was reported as used only occasionally. Technology was used most often to understand or explore in more depth concepts taught in class. The second most frequent use was as a tool of investigation or assessment. The lowest reported use of technology was as tool of communication. Students in middle school classes perceived technology as less helpful than did students in elementary or high school classes. Students in mathematics classes perceived technology as more helpful than did students in science classes. Girls perceived technology as more helpful than did boys. Additionally, teacher and student perceptions of amount of use varied with teachers reporting more use than students.
 

Stephanie Z. Smith, Georgia State University
Marvin E. Smith, Georgia Southern University

This article summarizes the basic concepts of multiplication and provides some evidence that the traditional third-grade curriculum and instruction emphasizing memorization of multiplication facts produces much less understanding of the basic concepts of multiplication than a standards-based curriculum and instruction emphasizing construction of number sense and meaning for operations. This study also describes a collection of assessment tasks that provided meaningful evidence of children’s understandings of basic multiplication concepts, including understandings of the relationships between multiplication and addition.

 

Dr. Carla C. Johnson
University of Toledo

This study focused on two middle schools in the central US who participated in collaborative, sustained, whole-school professional development in implementing inquiry as part of National Science Education Standards, or standards-based instructional practices. Participants were involved in their second year of the professional development experience. The research question explored was, “What barriers do science teachers encounter when implementing standards-based instruction while participating in effective professional development experiences?” Qualitative data collected in the form of teacher interviews and classroom observations were utilized and were analyzed using a barrier to reform rubric. Findings indicate that even with effective professional development, science teachers still encounter technical, political, and cultural barriers to implementation. More support is required for professional development efforts to be successful, such as resources and time, as well as administrative buy-in and support. Findings also revealed that even the best intended professional development efforts do not reveal and address existing beliefs for all teachers. Implications for future science education reform stakeholders are discussed.