The level of arithmetic knowledge of a high school student was explored when solving additive word problems considering the semantic structure and syntactic component. The methodology was qualitative and developed in four stages: the first is the selection of the participant, the second is the design of a questionnaire with twenty additive…

Classroom dialogue is widely used in mathematics teaching and learning, and if managed strategically, it will have productive benefits for mathematics achievement. However, dialogic participants often lack awareness of how dialogue could be constructed, and few studies show the characteristics of dialogic patterns in different stages of education.…

This study sought to investigate whether there were performance differences between the children who engaged with the Ignite by Hatch™ educational gaming system using the English- or Spanish-language versions of the games. Differential item functioning methods (DIF) were employed to investigate these differences. Specifically, DIF analyses can…

Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…

A vast majority of elementary students struggle with the core, pre-algebraic concept of mathematical equivalence. The Improving Children's Understanding of Equivalence (ICUE) intervention integrates four research-based strategies to improve outcomes for second grade students: (1) introducing the equal sign before arithmetic, (2) non-traditional…

In this article the authors overview how the recently revised (version 9) Australian Curriculum (Australian Curriculum Assessment and Reporting Authority, 2022) and student difficulties with fractions relate to five developmental Fraction Schemes developed from multiple research projects in the literature. The article shares research findings from…

Background: Students commonly struggle with mathematics and mathematical problem-solving. Therefore, it is necessary to design and implement interventions aimed at improving these essential components of learning. Furthermore, the outcomes of these interventions can vary significantly and appear to be a function of a student's initial competencies…

Powell, Berry, et al. (in press) conducted a randomized control trial assessing the effects of two variants of word-problem intervention with third graders (n = 304) experiencing mathematics difficulty. Students were assigned to a business-as-usual condition (BaU) or one of two variants of word-problem intervention. One variant included a…

The purpose of this study was to analyze the perceptions of academic rigor by teachers and administrators of secondary mathematics classrooms in Maryland, during a crisis. The identified problem is, during COVID-19 pandemic, school district leadership may not have effectively communicated with employees about rigor application expectations. The…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

Aiming to enhance understanding of visual obstacles inherent in two-dimensional (2-D) sketches used in high school spatial geometry instruction, we propose a measure of visual difficulty based on two attributes of the sketches: potentially misleading geometrical information (PMI) and potentially helpful geometrical information (PHI). The…

Students in the elementary grades often experience difficulty setting up and solving word problems. Using an equation to represent the structure of the problem serves as an effective tool for solving word problems, but students may require specific pre-algebraic reasoning instruction about the equal sign as a relational symbol to set up and solve…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

Personalizing the use of educational mathematics applets to fit learners' characteristics poses a great challenge. The present study adopted a unique approach by comparing personalization processes implemented by a machine to those implemented by a human teacher. Given the different affordances--the machine's access to historical log file data,…

Geometry subject that prosecute students to comprehend abstracts things is one of the causes of students' difficulties in mathematics learning. This study aims to determine the effect of Problem Posing and Problem Solving learning models with the Scientific Approach to students' adaptive reasoning on plane figure materials. It was conducted at the…