The present study seeks to explore the mathematical connections that 13-14-year-old secondary school students establish when solving area tasks. Emphasis is placed on different mathematical objects, and the connections between them, that allow students to successfully solve the tasks. The study follows a mixed methodology using qualitative and…

The area concept may appear in a wide range of problem situations. The representations used (geometrical, numerical and algebraic) in such situations entail particular practices that condition the partial area meanings. Thus, this study aims to characterize the partial area meanings mobilized in the resolution of area tasks. Each of the area…

Interference of irrelevant salient variables may cause difficulties for students. This study focused on eye tracking during the comparison of perimeters task, in which area is the interfering irrelevant salient variable. There were three trial types: congruent (larger area-larger perimeter), incongruent inverse (larger area-smaller perimeter), and…

This article presents the analysis and discussion of solving geometry tasks by Portuguese Basic Education students, using material from the Poly-UNiverse in Teacher Training Education (PUNTE) project. The teaching experience developed was aimed at testing and disseminating new resources, and innovative and transdisciplinary methodologies in the…

We present the analysis of an episode of mathematical problem solving in a group, where data came from multiple advanced recorders, including multiple video cameras, Smartpen recorders, and mobile eye tracking glasses. Analysis focused on a particular group that was ineffective in their problem-solving process. Relying on the commognitive theory…

This paper presents research activity in the solution of geometric tasks by mathematics teachers and by mathematics teacher trainees at a College of Education as part of an advanced courses. This activity tested the level of knowledge and ability to apply it in the solution of problems that can be solved in a number of ways: by using various tools…

Mobile eye-tracking research has provided evidence both on teachers' visual attention in relation to their intentions and on teachers' student-centred gaze patterns. However, the importance of a teacher's eye-movements when giving instructions is unexplored. In this study we used mobile eye-tracking to investigate six teachers' gaze patterns when…

Students' issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students' outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by…

Nowadays, digital technologies are crucial in supporting students in geometry in secondary mathematics classrooms. However, in some cases, the role of visual function in technology was only utilized for seeing and conjecturing, not for experimenting, while to develop a relational understanding of geometry concepts, students should actively…

In this research study, I investigated the relationships between preferences for solution methods, task difficulty, gender, and high school students' geometry performance. Data were collected from 161 geometry students at six high schools at a county located in the southeastern region of the USA at the time of the 2013-2014 school year. The result…

To fulfill the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA Center & CCSSO], 2010), it is important for teachers to empower students to critique, revise, and expand their ideas as they solve problems. However, students often face challenges such…

We live in the challenging times of the 21st-century with the increased need for humans to possess specific skills that will help them to be successful in this era. This means that education should in learners, develop these skills effectively. Different global countries have begun to recognize the significance of multiple solutions tasks in the…

A digital wall is a tool for students to structure and register their online work on mathematical problem-solving activities that involve the coordinated use of digital technologies. How could students use such digital wall to understand mathematical concepts and to develop problem-solving competencies? The aim of this study is to analyze and…