The present study aims to examine the preservice middle school mathematics teachers' ability to perform the process of mathematizing and to identify their competencies within this context. For this purpose, the study was conducted with 43 preservice teachers attending a state university. The research method used is descriptive research. As the…

The present research focuses on analyzing how fourth-grade elementary school students (ages 9 to 10) solve and interpret the result of non-routine problems, precisely division measurement and division-partition with remainder. The methodology is qualitative, with a descriptive and interpretative approach. The information was collected using a…

In this case study, we investigate one teacher's implementation of DNR-based combinatorics curriculum in their high school discrete mathematics class. By examining the teacher's practices in whole-class discussions of two counting problems, we study how they advanced a variety of ways of thinking to support the development of a set-oriented way of…

The present study aimed to determine the effectiveness of the concrete-representational-abstract instruction strategies employed in the direct instruction of fractions to students with learning disabilities. Furthermore, the generalization of the instruction to different settings and tools, the follow-up data for one and three weeks after the…

Completion of a first-semester chemistry (Chem I) course lays the foundation for understanding second-semester chemistry (Chem II) topics. The purpose of this study is to evaluate the influence of basic arithmetic skills on students' Chem II success in understanding mathematics-grounded concepts (e.g., solutions and aqueous reactions, kinetics,…

Proof is central to mathematics and has drawn substantial attention from the mathematics education community. Yet, valid and reliable measures of proof comprehension remain rare. In this article, we present a study investigating proof comprehension via students' summaries of a given proof. These summaries were evaluated by expert judges making…

This study utilizes the Cartesian Connection and the action, process, object, and schema (APOS) theory to investigate how preservice mathematics teachers constructed and justified graphs of two-variable inequalities. The analysis shows that most teachers were not equipped with the skills and knowledge that were prerequisites for action, process,…

The ability to choose the larger between two numbers reflects a mature understanding of the magnitude associated with numerical symbols. The present study explores how the knowledge of the number sequence and memory capacity (verbal and visuospatial) relate to number comparison skills while controlling for cardinal knowledge. Preschool children's…

The use of written or graphic representations is essential in mathematics. Graphic representations are mainly used and researched as instruments for problem solving. There is a gap in research for interventions that use learner-generated graphic representations as documents for reflection processes for promoting the development of children's…

This paper introduces a new mode of variational and covariational reasoning, which we call scaling-continuous reasoning. Scaling-continuous reasoning entails (a) imagining a variable taking on all values on the continuum at any scale, (b) understanding that there is no scale at which the continuum becomes discrete, and (c) re-scaling to any…

The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration. In an effort to better understand students' reasoning about the MP, we had two undergraduate students reinvent a statement of the MP in a teaching experiment. In this paper, we adopt an actor-oriented perspective (Lobato, "Educational Researcher,"…

In this paper we report on findings from a study of 5-to-6-year-old children's ways of structuring part-part-whole relations using finger patterns. We focused our analysis on data from interviews with 28 children who during their last year of preschool learned to enact a structural approach. We used this data set to analyze their different ways of…

Promoting mathematical creativity is an important aim of mathematics education, which may be promoted by engaging students with open-ended tasks. Most studies of students' creativity have investigated the creativity of students working individually. This study concerns the mathematical creativity of students working as individuals as compared with…

The relationship between spatial and mathematical ability is controversial. Thus, the current study conducted a meta-analysis of 73 studies, with 263 effect sizes to explore the relationship between spatial and mathematical ability. Furthermore, we explored potential factors that moderate this relationship. Results showed that the relationship…

Although the roles of symbolic numerical magnitude processing (SNMP) and working memory (WM) in mathematics performance are well acknowledged, studies examining their joint effects are few. Here, we investigated the profiles of SNMP (1- and 2-digit comparison) and WM (verbal, visual and central executive) among Norwegian first graders (N = 256),…