In this paper, we discuss the characteristics of microaggressions based on minority language(s) as a form of discriminatory practice against non-dominant students in the mathematics context. Microaggressions are subtle, brief, and commonplace verbal, behavioral, or visual negative slights or insults toward people of color. We extend the concept of…

This paper reports results of a design experiment regarding young children's concepts of mass measurement. The research built on an earlier study in which a framework of "growth points" in early mathematics learning and a related, task-based, one-to-one interview to assess children's understanding of the measurement of mass…

The purpose of this paper is to contribute to development of research tools for observation and analysis of educational practices used by teachers in preschool classrooms. More specifically, we approached the implemented curriculum of mathematics in Greek preschool education. We analysed the recorded data from a week of teaching practices in eight…

In this article I present some results from a 5-year longitudinal investigation with young students about the genesis of embodied, non-symbolic algebraic thinking and its progressive transition to culturally evolved forms of symbolic thinking. The investigation draws on a cultural-historical theory of teaching and learning--the theory of…

Drill-and-practice mathematics software offers teachers a relatively simple way to use technology in the classroom. One of the reasons to use the software may be that it motivates children, working on the computer being more "fun" than doing regular school work. However, students' own perceptions of such software are seldom studied.…

This is the report of an investigation in partnership with a team of junior secondary classroom teachers of the potential of posing more challenging tasks to their students. A range of data sources are used to represent the experience of teachers and students in a unit of work that incorporated a range of challenging tasks. Students learned the…

In this paper, we discuss the process of identifying and validating students' abilities to think proportionally. More specifically, we describe the methodology we used to identify these proportional reasoning attributes, beginning with the selection and review of relevant literature on proportional reasoning. We then continue with the…

The use of formal observation in primary mathematics classrooms is supported in the literature as a viable method of determining effective teaching strategies and appropriate tasks for inclusion in the early years of mathematics learning. The twofold aim of this study was to (a) investigate predictive relationships between primary mathematics…

This study explores, from both constructivist and cognitive perspectives, teacher guidance in student-centered classrooms when addressing a common learning difficulty with equivalent fractions--lines or pieces--based on number line models. Findings from three contrasting cases reveal differences in teachers' facilitating and direct guidance…

Novice secondary mathematics teachers attempting teaching consonant with the National Council of Teachers of Mathematics (1991, 2007) "Professional Standards for Teaching Mathematics" experience many stresses related to their attempts at student-centered instruction; prominent among those were novices' challenges when orchestrating…

Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for…

We analyze a classroom design experiment, conducted in a fourth grade classroom, that served to explore an instructional path in which the introduction of unit fractions and supporting proportional reasoning coincide. Central to this path is the use of means of support in which the objects that unit fractions quantify are not characterized as…

Drawing on evidence from the Longitudinal Investigation of the Effect of Curriculum on Algebra Learning (LieCal) Project, issues related to mathematics curriculum reform and student learning are discussed. The LieCal Project was designed to longitudinally investigate the impact of a reform mathematics curriculum called the Connected Mathematics…

Unlike a child's observable, physical interactions with mathematical tools (e.g., physically touching blocks in order to count them), the subtle manifestations of imagery construction can be considerably more challenging to identify and act upon. Although there have been substantive examinations of mental imagery in a variety of mathematical…

As a consequence of the increased use of data in workplace environments, there is a need to understand the demands that are placed on users to make sense of such data. In education, teachers are being increasingly expected to interpret and apply complex data about student and school performance, and, yet it is not clear that they always have the…