Geometric concepts are fundamental to early geometry education, and developmentally appropriate practices are crucial for teaching them to young children. Robotic coding is an effective tool in many areas of early mathematics and has significant potential in teaching geometric concepts. This study aimed to test the impact of a research-based…

This cross-sectional study investigated the conceptual understanding of linear relationships for 195 students enrolled in a single school in a large, urban district across five mathematics courses: Grade 7 Math (n = 24), Grade 8 Math (n = 52), Geometry (n = 43), Algebra 1 (n = 31), and Algebra 2 (n = 45). The following questions guided this study:…

Mathematical concepts have been a consensus goal for decades, yet there is little consensus on what is meant by the terms "mathematical concept" and "mathematical understanding." This article attempts to discuss these terms in a way that can be of practical use to teachers. Greater clarity on "mathematical concept"…

On the basis of a substantial, robust, and well-replicated cognitive science research literature, interleaving has been recommended across a range of professional pedagogical works as an evidence-based strategy for mathematics teachers. This report first notes the conflation of interleaving and spacing effects underpinning those recommendations…

Numerous studies (Anwar et al., 2016; Carpenter et al., 1980; Huang & Witz, 2013; Outhred & Mitchelmore, 1996; Machaba, 2016; Van de Walle, Karp & Bay-Williams, 2014; Winarti et al., 2012) have shown that students need help understanding the concept of area and perimeter. This study aimed to investigate what students know about finding…

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

"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…

Special tasks for pre-service teachers (PSTs) in university mathematics courses ("interface tasks") are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and…

Technological mediums such as dynamic environments with drag-and-drop features have been considered promising agents in helping students explore and generate conjectures about mathematical concepts. This study investigated the dragging modalities sixth and seventh-grade students use in solving proportional problems in a dynamic geometry…

Mathematical justifications offer an approach to which students deepen and extend their mathematical thinking. This process has the potential to enhance students' conceptual understanding. Mathematical practices and process standards ask students to use critical thinking skills to justify their reasoning, but this is usually seen as proofs in high…

This study explored pre-service teachers' perceptions of a 3D printing integrated science, technology, engineering, and mathematics (STEM) module within a college-level mathematics content course. Data from surveys and reflections collected from nineteen participants were analyzed. Results indicated that the pre-service teachers perceived…

According to the author, the "Australian Curriculum: Mathematics (AC:M) requires primary school students to measure the attributes of angle, time, temperature, length, area, capacity and mass. This article outlines some misconceptions held by primary school students which appear to stem from them not understanding terminology concerning the…

This research aims to investigate the construction of the area of rectangle with GeoGebra and how students can formulate it. It focuses on describing the cognitive process involved in constructing this concept and how technology mediates such a process. The research was conducted in a classroom with 5th grade students in a secondary school and was…

Concept-based teaching is presumably more effective than popular procedure-based instruction in helping students develop conceptual understanding, an important conceptual base for mathematics teaching reforms in many countries. This study examined the extent to which this assumption is true by controlling the influences of student socioeconomic…

In the world where we always meet geometric constructions, it is a necessity to make sense of the objects belonging to these constructions. In this respect, this study aimed to examine the teaching of volume with the blending of the realistic mathematics education (RME) and GeoGebra. The study group consisted of 12 students attending lessons…