This paper describes the importance of developing students' reasoning about samples and sampling variability as a foundation for statistical thinking. Research on expert-novice thinking as well as statistical thinking is reviewed and compared. A case is made that statistical thinking is a type of expert thinking, and as such, research…

This research investigates what students' use of statistical language can tell us about their conceptions of distribution and sampling in relation to informal inference. Prior research documents students' challenges in understanding ideas of distribution and sampling as tools for making informal statistical inferences. We know that these…

The expanding use of data in modern society for prediction and decision-making makes it a priority for mathematics instruction to help students build sound foundations of inferential reasoning at a young age. This study contributes to the emerging research literature on the early development of informal inferential reasoning through the conduct of…

This paper is in the form of a reflective discussion of the collection of papers in this Special Issue on "Statistical reasoning: learning to reason from samples" drawing on deliberations arising at the Seventh International Collaboration for Research on Statistical Reasoning, Thinking, and Literacy (SRTL7). It is an important part of…

The goal of this article is to introduce the topic of "learning to reason from samples," which is the focus of this special issue of "Educational Studies in Mathematics" on "statistical reasoning." Samples are data sets, taken from some wider universe (e.g., a population or a process) using a particular procedure…

Finnish students' success on all three content domains of each of the four cycles of the OECD's Programme for International Student Assessment (PISA) has created much international interest. It has also prompted Finnish academics to offer systemic explanations typically linked to the structural qualities of Finnish schooling and teacher…

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged…

This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of…

The data reported in this article come from a large project whose goal was to explore how Latin American students in Catalonia, Spain use their two languages--Spanish and Catalan--to support their learning of mathematics in small groups with other students who are Spanish- or Catalan-dominant. For 5 years, lessons from bilingual mathematics…

Through examining a representative Chinese textbook series' presentation of the distributive property, this study explores how mathematics curriculum may structure representations in ways that facilitate the transition from concrete to abstract so as to support students' learning of mathematical principles. A total of 319 instances of…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving…

Emma Castelnuovo (1913-2014) was an Italian mathematics teacher of grades 6 to 8 in secondary school. During the crucial period of the 1950s and 1960s, when important reforms were proposed, she was involved in significant events such as the first CIEAEM meetings and the Royaumont Seminar. She was an active contributor to the development of…

This paper aims to discuss the emergence, form and likely effects of international surveys of adults' skills by locating them in the global context of policies on education and Life Long Learning (LLL). It focuses on adults' numeracy and discusses its conceptualisation and assessment in the Project for the International Assessment of…

The practices of mathematics education can be investigated at a wide variety of levels: from the actions of individual students or teachers through classroom interactions, school structures, curriculum specifications and materials, teacher development programmes and local, national or international systems of instruction and assessment. These…

Within mathematics education research, the responses to the Programme for International Student Assessment's (PISA's) international testing regime tend to accept its framework and results as necessary points of reference, even when offering a critical reinterpretation or challenging national policy discourses based on PISA. In this…