Studies that consider the displays that students create to organize data are not common in the literature. This article compares fifth through eighth graders' difficulties with the creation of bar graphs using either raw data (Study 1, n = 155) or a provided table (Study 2, n = 152). Data in Study 1 showed statistical differences for the type…

Explanations are considered to be key aids to understanding the study of mathematics, science, and other complex disciplines. This paper discusses the role of students' explanations in making sense of data and learning to reason informally about statistical inference. We closely follow students' explanations in which they utilize their experiences…

This theoretical paper relates recent interest in informal statistical inference (ISI) to the semantic theory termed inferentialism, a significant development in contemporary philosophy, which places inference at the heart of human knowing. This theory assists epistemological reflection on challenges in statistics education encountered when…

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…

Upper primary school children often routinely apply proportional methods to missing-value problems, even when it is inappropriate. We tested whether this tendency could be weakened if children were not required to produce computational answers to such problems. A total of 75 sixth graders were asked to classify 9 word problems of three types (3…

For nine-week periods during two consecutive years, sixth-grade students at the same school were taught identical mathematics content using two different instructional approaches. Year 1 involved low achievers, whereas Year 2 was mixed ability students. The experimental treatment was a problem-centered approach (PCL) where potentially meaningful…

Despite widespread agreement that the activity of "reasoning-and-proving" should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that…

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an…

This article aims to identify the mathematical reasoning strategies expressed through gestures and speech used by two groups of sixth-grade pupils when solving a task related to the transition between two semiotic representations: figure and Cartesian diagram. The article also identifies the difficulties the pupils meet in the solution process.…

The expectation that students be introduced to algebraic ideas at earlier grade levels places an increased burden on the classroom teacher to help students construct and justify generalizations. This study provides insight into the reasoning of 25 sixth-grade students as they approached patterning tasks in which they were required to develop and…

In this study, children were encouraged to abstract mathematical principles by making connections between procedures. Children from 2 sixth-grade classes (N = 58) were asked to solve and explain subtraction examples in 3 different number domains (whole numbers, fractions, and decimals), solve subtraction word problems, compare the procedures, and…

This article highlights the similarities between sixth-grade students' developing notions of angle and mathematicians' struggles to define this complex concept. Students learning from a reformed curriculum had the opportunity to voice their ideas concerning the definition of angle. These conversations were compared with past discussions and…