When implementing digital technologies into mathematics teaching and learning situations, new representational and communication infrastructures arise that allow for new speech acts and actions. These new speech acts and actions are also referred to as 'representational expressivity'. Such expressivity arises in the intersection of…

The paper addresses concept formation processes of students in the field of geometry. More precisely, the paper deals with the questions of what knowledge do students activate about triangles in different contexts with different (digital) tools and furthermore what content-related meaning do they give to the concept of triangles? Methodologically,…

This study reports on the development, validation, and reliability of a geometry disposition scale (GDS) to measure pre-service teachers' (PSTs') attitudes to geometry learning. PSTs from two Colleges of Education (CoEs) in Ghana volunteered to participate in the study (N = 153). A principal component analysis (PCA) extracted four factors: deep…

In this paper we show how we can utilize human-guided machine learning techniques coupled with a learning science practitioner interface (DataShop) to identify potential improvements to existing educational technology. Specifically, we provide an interface for the classification of underlying Knowledge Components (KCs) to better model student…

These Proceedings are a written record of the research presented at the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Greenville, South Carolina, November 15-18, 2018. The theme of the conference is "Looking Back, Looking Ahead: Celebrating 40…

Research in Educational Data Mining could benefit from greater efforts to ensure that models yield reliable, valid, and interpretable parameter estimates. These efforts have especially been lacking for individualized student-parameter models. We collected two datasets from a sizable student population with excellent "depth" -- that is,…

The aim of this study is to analyse the impact of the shared use of the interactive whiteboard (IWB) on the perceptions, learning processes and performance of learners. It was carried out with lower secondary school students within the context of a class on dynamic geometry. The work is based on a set of indicators and the results were obtained…

The theme of the 39th proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) conference was "Synergy at the Crossroads: Future Directions for Theory, Research, and Practice." The metaphor of crossroads was inspired by the conference venue--the historic Indianapolis Union…

The theme of this year's conference is "Sin Fronteras: Questioning Borders with(in) Mathematics Education." This theme is intended to encourage research presentations, discussion, and reflection on the variety of borders within mathematics education, as well as those that might be probed, challenged, explained, enhanced and/or…

This research investigated the viability of learning by self-managing split-attention worked examples as an alternative to learning by studying instructor-managed integrated worked examples. Secondary school students learning properties of angles on parallel lines were taught to integrate spatially separated text and diagrammatic information by…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

These Proceedings are a written record of the research presented at the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2013) held in Chicago, Illinois, November 14-17, 2013. The theme of the conference is Broadening Perspectives on Mathematics Thinking and Learning.…

The reported exploratory study consisted primarily of classroom visits, videotaped sessions, and post-treatment interviews whereby second graders (n = 12) worked on problems in planar geometry, individually and in triads, using physical and virtual manipulatives. The goal of the study was to: 1) characterize the nature of geometric thinking found…

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

One of the most useful ways to enhance collaboration is to create scenarios where learners are able to interact more effectively. Nevertheless, the design of pedagogically sound and well-thought-out collaborative learning scenarios is a complex issue. This is due to the context of group learning where the synergy among learners' interactions…