Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

The purpose of this paper is to follow the reasoning of high school students when asked to explain the standard trigonometric limit lim/[theta][right arrow] sin[theta]/[theta]. An observational study was conducted in four different phases in order to investigate if visualization, by means of an interactive technology environment (Geogebra), can…

An inequality concept has an important role; even in advanced mathematics, inequality assists in analysis and proof. However, students' understanding of inequality is not satisfying. The fact shows that students experience difficulties and errors in solving inequality problems. These difficulties and errors are not intentional or do not result…

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,…

Off You Go is a PK-12 mathematical routine that leverages children's home resources and assets to help students take a concept with which they have initial or informal understanding and explore and test its boundaries to support defining or estimating with precision. The authors provide a guide for how to adapt this routine to engage students at…

This paper discusses the significance of model-based teaching on the topic of ionic and metallic bonding in Year 12 Chemistry in a New Zealand secondary school. Based on the conceptualization of the sub-macro level understanding of the bonding structure and properties of ionic and metallic compounds, models and drawings were used as an effective…

The present study investigates the understanding of the equals sign among middle school students. The study data were gathered from a total of 433 middle school students (111 in the fifth grade, 106 in the sixth grade, 95 in the seventh grade and 121 in the eighth grade) using a ten-item equals sign test developed by the researcher. The study…

The present study is motivated by a significant body of research documenting teachers' perennial difficulties with a critical swath of topics related to multiplication. In response, we track how Nina, a future middle grades mathematics teacher, made progress constructing explanations across topics by reasoning with measurement-based definitions of…

This study aims to investigate how primary school students' three-dimensional geometric thinking changes across grades. The survey model was used, and the study group was comprising of 520 primary school students in a large city of Turkey. In the study, the Three-Dimensional Geometric Thinking Test, which is a paper and pencil test, was used to…

This article presents how Problem- and Project-Based Learning (PBL) in engineering education can exploit the theoretical framework of the Space-Time (ST)-Continuum, according to which educational contexts can be classified in terms of the tightness vs. looseness of the relevant conceptual space S and available time T. By crossing these two…

This pilot study examined the promise of a Tier 2 sixth grade intervention program for students at-risk for difficulties in mathematics. The study utilized a quasi-experimental design. The final sample included 112 students in treatment (Promoting Algebra Readiness) and 86 students in control (standard district practice) conditions. The Promoting…

This pilot study examined the promise of a Tier 2 Grade 6 intervention program for students at risk for difficulties in mathematics. The study utilized a quasi-experimental design. The final sample included 112 students in treatment (Promoting Algebra Readiness) and 86 students in control (standard district practice) conditions. The Promoting…

Active learning is widely recognized as superior to traditional passive, lecture-based techniques for fostering learning in STEM courses. Interactive, hands-on learning where students interact with their peers and physical systems is an effective type of active learning. As the need for scientists and engineers continues to grow, understanding and…

The imagination effect occurs when students learn better from imagining concepts and procedures rather than from studying them. Cognitive load theory explains the effect by better use of available working memory resources and increased productive, intrinsic cognitive load. The effect has been found in numerous empirical studies. However, in the…

The purpose of this study was to describe how experienced emergent writing teachers supported 4-year-olds in writing their own messages during the learning centers period of the preschool day. Data were drawn from two, year-long qualitative studies of early writing instruction. Adult participants were three researcher-teachers who worked in…