Given the important role played by students' spatial reasoning skills, in this paper we analyse how students use these skills to solve problems involving 2D representations of 3D geometrical shapes. Using data from in total 1357 grades 4 to 9 students, we examine how they visualise shapes in the given diagrams and make use of properties of shapes…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

This article explores the benefits of using digital technology to support and enhance students' understanding during mathematical inquiry. The use of digital technologies enabled students to focus on the problem-solving aspects of the task such as how to compare and represent the data effectively.

We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative…

In this work we examined the content of approximately 950 mathematics questions used in measuring achievement among 4th, 5th and 6th graders in the US in an attempt to determine how the current standardized examinations, which were developed to reflect new national curricular mandates, compared to the old measures used for the same purpose. Using…

The use of high-stakes assessment to measure students' mathematical performance has become commonplace in schools all over the world. Such assessment instruments provide national or international comparisons of student (and potentially teacher performance). Each form of assessment is specialised in nature and is characteristic of the culture and…

Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering the role that context plays in developing ISI calls into question the need to be more explicit about the reasoning that underpins ISI. This paper uses educational literature on informal statistical inference and philosophical…

In this chapter, we describe several intelligent tutoring systems (ITSs) designed to support student literacy through reading comprehension and writing instruction and practice. Although adaptive instruction can be a powerful tool in the literacy domain, developing these technologies poses significant challenges. For example, evaluating the…

There is little discussion in the Design-Based Research (DBR) literature on how to design an intervention that has the potential to be highly effective. The act of designing is usually viewed as engineering something from theory or research on best practices. This paper challenges that universal belief and presents successful design as an…

This study examines patterns in middle-grade boys' and girls' written problem solving strategies for a mathematical task involving proportional reasoning. The students participating in this study attend a coeducational charter middle school with single-sex classrooms. One hundred nineteen sixth-grade students' responses are analyzed by gender…

Children's conceptions of career choice and attainment were evaluated in two studies to test whether reasoning levels varied by grade level (Studies 1 and 2) and perspective-taking complexity (Study 2). Results indicated that younger children (Grade K) were more likely to use reasoning strategies associated with fantasy and magical thinking and…

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students'…

Mixed-aged (MA) classes are a common phenomenon around the world. In Sweden, these types of classes increased rapidly during the 1980s and 1990s, despite the fact that existing empirical support for MA classes is weak. In this paper, the effect of attending an MA class during grades 4-6 on students' cognitive skills is estimated. Using a unique…

This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity in elementary school classrooms. Collective learning takes place when mathematical ideas and actions, initially stemming from an individual, are built upon and reworked,…

This article illustrates how test specifications based solely on academic content standards, without attention to other cognitive skills and item response demands, can fall short of their targeted constructs. First, the authors inductively describe the science achievement construct represented by a statewide sixth-grade science proficiency test.…