Supporting students in becoming effective problem solvers is a critical component of K-12 mathematics instruction. Unfortunately, little is known about the factors that are related to problem solving proficiency in middle school students. We report the results of a study that employed a hierarchical linear regression analysis to examine the…

In this study, we investigated how sixth and seventh grade students used CODAP to make sense of roller coaster data while engaged in Exploratory Data Analysis (EDA). Using instrumentation theory, we examined students' instrumentation approaches, as well as the types of instrumental orchestration utilized by teachers as they interacted with student…

Attending to students' thinking and using it to inform instruction has been shown to be an effective teaching practice. Although research on teacher noticing has explored how teachers attend to and interpret thinking in the moment and through video, less is known about the ways in which teachers notice students' thinking in written work, as well…

Teachers' beliefs, knowledge, and decisions can affect the way teachers teach, and, consequently, what students learn. Self-efficacy beliefs may also interact with beliefs about the most appropriate and effective teaching and the selection of instructional practices to implement. We examined the relationships among teachers' mathematics…

The frequentist and classical models of probability provide students with different lenses through which they can view probability. Prior research showed that students may bridge these two lenses through instructional designs that begin with a clear connection between the two, such as coin tossing. Considering that this connection is not always…

Despite significant research exploring students' quantitative reasoning, few studies have explored the semiotic processes that mediate its development. In this report, we present a case study to show how one student constructed a semiotic chain for a quantity as he worked with a mathematical task. Importantly, we connect frameworks for…

In this study, we explored teachers' attention to and flexibility with referent units as well as how teachers' understanding of referent units is related to their performance on other fraction concepts and their professional background. By using data collected from 246 U.S. mathematics teachers in Grades 3-7 where fractions are taught, we found…

This research focuses on the retention of students' algebraic understandings one year following a Grades 3-5 early algebra intervention. Participants included 1455 Grade 6 students who had participated in a cluster randomized trial. Approximately half of these students received an early algebra intervention as part of their regular instruction in…

One of the most intransigent problems in mathematics education is the culturally-influenced divide between classroom practice and educational research. This paper describes our explicit attempt to bridge that divide by translating research on instructional practices linked to improving students' mathematics achievement into a brief guide outlining…

This exemplary case study describes the learning process of two sixth-graders that learn from an animated worked-out example and an accompanying self-explanation prompt in the domain of fractions. It is based on a corresponding field study. The analysis focuses on the interaction with the computer, the communication between the students, the…

The data used for the qualitative analysis reported here were generated as part of a larger study to understand and characterize teacher practice related to engaging students in algorithmic thinking associated with the fraction operations of addition, subtraction, multiplication and division. This paper presents ways in which teachers used…

This paper contributes to the discourse in stochastic education of how young students deal with learning settings that allow a data-based approach to probability. By using the micro-structure of arguments by Toulmin (1958), it explores which arguments students use and which role they play in the learning process. The data stems from design…

Results of the last thirty years in mathematics education have shown the importance of an operational concept development. One of the geometrical concepts that has been researched for years already, however, not with the particular focus on its systematic teaching in school mathematics, is the concept of angle. In this paper we focus on children's…