This report details a set of three tasks used in an exploratory study of pre-service teachers' (PSTs) experiences of task design for the mathematics classroom. The three tasks, which I call the "Orange Dot Tasks," were constructed in Desmos, a dynamic geometry environment (DGE), and participants engaged each task through manipulating…

This paper describes the design, implementation, and results of a training action with prospective primary education teachers, focusing on the creation of problems involving proportional and algebraic reasoning. Prospective teachers must solve a proportionality problem using both arithmetic and algebraic procedures, and then vary it to motivate…

There is growing evidence that the ability to perceive structure is essential for students' mathematical development. Looking at students' structure sense in basic numerical and patterning tasks seems promising for understanding how these tasks set the foundation for the development of later mathematical skills. Previous studies have shown how…

The challenge posed by algebra story problems creates a significant hurdle for many students, transcending both the mathematical content of the problem and the specific instructional background received. This study offers a distinctive contribution to the existing literature by focusing on the cognitive conditions essential for comprehension in…

This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…

At the beginning of the 21st century, "number sense" was listed as one of the core words in the mathematics curriculum of compulsory education in China, and it has now become one of the core competencies of primary school mathematics. It is necessary to determine the development of number sense of first-grade primary school students (6-7…

Productive struggle is an effective mathematics teaching practice that provides students opportunities to grapple with challenging mathematical concepts, connect prior knowledge, discover new ideas, and develop their critical thinking skills. Research has documented the benefits of secondary mathematics students engaging in productive struggle.…

The authors wondered if there was a way to support their reluctant Grades 4, 5, and 6 students in contributing their starting points and strategies and advancing their collective knowledge. They wanted to ensure that the students had the space to develop and take ownership of the strategies they produced through a visual representation of ideas…

Successful adoption of proven effective practice strategies such as distributed practice may contribute to much-needed improvement in mathematics performance. However, it is not yet fully understood if distributed practice is beneficial for long-term retention of complex procedural knowledge and, if so, for which initial practice performance level…

The authors developed an instructional nudges as part of a larger research project. These instructional nudges are designed to be small but powerful changes to teachers' existing practices. Some instructional nudges focus on modifying tasks used in classrooms. In this article, the authors share Rate and Review. The goal of Rate and Review is to…

The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla,…

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…

This research explores the impact of ethno-RME on students' thinking processes in solving decimal number operations in Tugu Yogyakarta, Indonesia. The study involved 32 grade 4 students and used three data collection techniques: task provision, cognitive interviews, and documentation. The qualitative data was analyzed using cross-sectional data…

Mathematization is a critical competency in the modelling process. This study aims to elicit prospective mathematics teachers' mathematizing through the analysis of their solution approaches to a modelling problem related to the bales of straw. This study was conducted with 75 fourth-year prospective mathematics teachers (PMTs) enrolled in a…

Increasingly, mathematics educators see the importance of representation of diversity in pedagogical texts. The number of identity markers often considered has increased over the previous half century, and now includes, for instance, gender, class, ethnicity, religion, functionality, and sexual orientation. We investigate representation of…