The Nature of Arguments Provided by College Geometry Students With Access to Technology While Solving Problems
Karen F. Hollebrands, AnnaMarie Conner, and Ryan C. Smith
Prior research on students’ uses of technology in the context of Euclidean geometry has suggested that it can be used to support students’ development of formal justifications and proofs. This study examined the ways in which students used a dynamic geometry tool, NonEuclid, as they constructed arguments about geometric objects and relationships in hyperbolic geometry.
Enacting Proof-Related Tasks in Middle School Mathematics: Challenges and Opportunities
Kristen N. Bieda
Discussions about school mathematics often address the importance of reasoning and proving for building students’ understanding of mathematics. However, there is little research examining how teachers enact tasks designed to engage students in justifying and proving in the classroom. This article presents results of a study investigating the processes and outcomes of implementing proof-related tasks in the classroom. The findings suggest that students’ experiences with such tasks are insufficient for developing an understanding of what constitutes valid mathematical justification.
One Hundred Years of Elementary School Mathematics in the United States: A Content Analysis and Cognitive Assessment of Textbooks From 1900 to 2000
David Baker, Hilary Knipe, John Collins, Juan Leon, Eric Cummings, Clancy Blair and David Gamson
A content analysis of over 28,000 pages from 141 elementary school mathematics textbooks published between 1900 and 2000 shows that widely used mathematics textbooks have changed substantially. Textbooks from the early part of the century were typically narrow in content but presented substantial amounts of advanced arithmetic and also asked students simultaneously to engage with material in effortful and conceptual ways. Implications of these findings are discussed in terms of the historical study of mathematics and curriculum in U.S. schools.