This article analyzes how three mathematics preservice teachers (PSTs) reasoned quantitatively and covariationally while making sense of the Earth's energy budget (EB)--a model of energy circulation within the Earth's climate system--and discusses how their quantitative and covariational reasonings influenced their understanding of climate change.…

This study builds on two lines of research that have so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution methods. We gave a test containing missing-value…

Using the perspective of instructional conversation, we investigated how one teacher regulated student participation and conceptual reasoning in the middle-school mathematics classroom. We examined the elicitations--questions and provocative statements--made by the teacher over a four-day algebra lesson. Analyses showed how the teacher…

Learning science includes learning to argue with "inscriptions": images used to symbolize information persuasively. This study examined sixth-graders learning to invest inscriptions with representational status, in a geographic information system (GIS)-based science investigation. Learning to reason with inscriptions was studied in emergent…

This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns,…

Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…