Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

The concrete-representational-abstract (CRA) approach is an instructional framework for teaching math wherein students move from using concrete materials to solve problems to using visual representations of the materials, and finally abstract concepts. This study provides a literature synthesis and meta-analysis of the effectiveness of the CRA…

The increasing screen time and digital distractions in modern education have underscored the need for innovative approaches to early childhood learning that reconnect children with the natural world. This study investigates the integration of cooperative learning methods in nature within the "Mathematics and Environmental Exploration"…

Digital game-based learning (DGBL) has emerged as an effective strategy to enhance students' learning effectiveness. Concept mapping, recognized as a valuable tool for knowledge construction, has been widely implemented in educational settings. However, research indicates challenges when integrating concept maps into games, particularly when the…

This study reviews the literature on error patterns in mathematics among students with mathematics difficulty. We analyzed and synthesized the findings from 17 studies, focusing on the characteristics of error analysis studies, the mathematics topics examined, and the specific error patterns identified. The results revealed the following: (a) the…

The contribution aims at subject-specific analyses of student solutions of an exercise from an electrical engineering signal theory course. The basis for the analyses is provided by praxeological studies (in the sense of the Anthropological Theory of Didactics) and the identification of two institutional mathematical discourses, one related to…

Quadratic functions are explained in the three equivalent formats: Standard (or Expanded), Vertex and Factorised. However, cubic functions are represented only in the two equivalent formats: Standard (or Expanded) and Factorised. In this article, the author shows how cubic functions can be expressed in three equivalent formats like quadratic…

This study explores how three widely used US kindergarten mathematics textbooks, each written to align with the Common Core State Standards for Mathematics (CCSSM), vary in terms of content coverage, instructional grouping, and use of representational strategies. Results show that all textbooks (i) primarily emphasize math practices related to…

This study examines in-service mathematics teachers' problems on linear relationships that they posed in a semi-structured problem posing situation with a group and their ideas about the factors affecting the quality of the posed problems. Eight groups of 24 teachers participated in the study. Teachers' problems, written group work, and class…

In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…

Since its first notable appearance in the "Second Handbook of Research on Mathematics Teaching and Learning," the phrase productive struggle has garnered support from a few, yet very influential, educational researchers. However, since the phrase was popularized by Hiroko Warshauer in 2011, examinations of the productive struggle have…

"Assumptions" play a fundamental role in disciplinary mathematical practice, especially concerning the relativity of truth. However, much is still unclear about ways to help students recognize key aspects of this role. In this paper, we propose a set of principles for task design to introduce students to the role of assumptions in…

This article draws from Hiroko Kawaguchi Warshauer's conceptualisation of productive struggle, which capitalises on experiences that elicit struggle, that is, those that require students to 'expend intellectual effort' and that are productive, in the sense that they seek to 'advance thinking and deepen' understanding of mathematical concepts and…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

This study aims to analyze and to describe, in terms of information processing theory, the thinking processes of junior high school students as they solved problems involving direct and inverse proportions. This study design is qualitative and exploratory-descriptive in nature. 26 students in the seventh grade of SMP Negeri 1 Kota Ternate were…