In numerous studies, intelligent tutoring systems (ITSs) have proven effective in helping students learn mathematics. Prior work posits that their effectiveness derives from efficiently providing eventually-correct practice opportunities. Yet, there is little empirical evidence on how learning processes with ITSs compare to other forms of…

This work deals with the role of social practice in the construction of models related to advanced mathematical knowledge; specifically, with the way an individual uses the notion of "variation" in different phenomena while predictive thinking is the underlying principle in the mathematical process. The mathematical modelling of…

K-12 students are expected to acquire competence in data display as part of developing statistical literacy. To support research, assessment design, and instruction, we developed a hypothesized learning progression (LP) using existing empirical literature in the fields of mathematics and statistics education. The data display LP posits a…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

The concept of variability is central to statistics. In this research report, we review mathematics education research on variability and, based on that review and on feedback from an expert panel, propose a learning progression (LP) for variability. The structure of the proposed LP consists of 5 levels of sophistication in understanding…

The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory…

With regard to transfer, is it better to provide pupils with ready-made representations or is it more effective to scaffold pupils' thinking in the process of generating their own representations with the help of peers and under the guidance of a teacher in a process of guided co-construction? The sample comprises 10 classes and 239 Grade 5…

This study investigates relationships between differences in students' achievement and differences obtained by a technique held to yield a reasonably valid representation of students' memory structures of a particular subject matter. Also investigated was the nature of the flow of information between curriculum materials, teachers, and students.…

Several studies have shown the difficulties students encounter in making sense of situations involving rate of change. This study concerns how students discover errors and refine their knowledge when working with rate of change. The part of the study reported here concerns the responses of four precalculus students to a task which asked them to…

Statistical data can be represented in a number of qualitatively different ways, the choice depending on the following three conditions: the concepts to be investigated; the nature of the data; and the purpose for which they were collected. This paper begins by setting out frameworks that describe the nature of statistical thinking in schools, and…

Reports on the graphing work of children, aged eight and nine years, who have access to portable computers across the curriculum. Describes two learning sequences: in one, the children collected data and then explored the computer graphing facilities; and in the other, graphing is used iteratively as an integral part of the ongoing task.…

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…

This guide presents math-focused learning projects and accompanying inquiry activities to help students pass the math portion of the GED 2002. It is Volume 2 of a proposed four-volume series; Volume 1 describing the concept of the GED as project is also available. Section 1 relates GED as project to the math portion of the GED and explains how…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…