We examine how extended engagement in argumentation with peers leads to enhanced metalevel understanding of argumentive discourse. Following such engagement, young adolescents demonstrated enhanced understanding of counterargument and use of evidence as objectives of skilled argumentation, relative to a nonparticipating comparison group. Among the…

Previous research has demonstrated the effectiveness of particular instructional practices that support students' constructions of the partitive unit fraction scheme and measurement concepts for fractions. Another body of research has demonstrated the power of a particular mental operation--the splitting operation--in supporting students'…

Using data collected in 125 seventh-grade and 56 eighth-grade Texas classrooms in the context of the "Scaling Up SimCalc" research project in 2005-07, we examined relationships between teachers' mathematics knowledge, teachers' classroom decision making, and student achievement outcomes on topics of rate, proportionality, and linear…

We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The participants (n = 549) were asked how many (i.e., a finite or infinite number of numbers) and what type of numbers (i.e., decimals, fractions, or any type) lie between two rational numbers. The…

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…