We report on a study focused on identifying how undergraduate students make use of the Internet as a source of help to solve their mathematical queries. In particular, with the help of monitoring software, we observe how a group of engineering students use the Internet to solve a mathematical task related to the concept of definite integral, and…

Students who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of…

Motivation: This research investigates the transformative impact of integrating AI into mathematics education, aiming to enhance students' conceptual understanding and self-efficacy. It addresses the crucial need for innovative teaching methods in response to contemporary challenges in education and aims to fill gaps in understanding the potential…

Supporting young students in developing meanings for the set-theoretic function definition is emphasized in 6th-12th grade curricula around the world. In prior work, we have highlighted how covariational reasoning supports college students in constructing relationships that afford considering mathematical properties important for a set-theoretic…

Ariadne is a touch-based program for the learning of homotopies of paths, without the use of formalism, by building mental models. Using Ariadne, the user can construct points, paths by dragging points and homotopies by dragging paths as well as compute winding numbers of paths, all on a variety of surfaces, through touch gestures. Ariadne…

We present a synthesis of the Onto-semiotic Approach (OSA) theoretical system to mathematical knowledge and instruction, while highlighting the problems, principles and research methods that are addressed in this approach and considering the didactics of mathematics as a scientific and technological discipline. We suggest that Didactics should…

The act of explaining can help students to develop new understandings of mathematical ideas, construct rules for solving problems, become aware of misunderstandings or a lack of understanding and develop their mathematical communication. Their explanations can also offer opportunities for a teacher to understand more fully what the students are…

This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied…

To improve students' mathematics achievement, their errors should be treated as an opportunity to stimulate conceptual and procedural understanding. Using a teaching scenario, this study investigated 40 high school teachers' analyses of and responses to a student error(s) in solving a quadratic equation by using the factoring method. The teachers'…

We present a case of one teacher's engagement in project-based learning for algebra I students. This teacher was a member of a cohort of mathematics teachers and career technical educators who participated in a two-week intensive summer institute investigating autonomous vehicles. During the academic year, the follow up support for these educators…

This study explored students' mathematics-related beliefs and the relationship between the beliefs and their strategies for solving non-routine mathematical problems. The study was guided by Daskalogianni and Simpson's 2001 belief systems categories and strategies for non-routine mathematical problems. The participants were 625 grade 11 students…

There exist many studies on modeling competencies and their promotion; however, there is a need to investigate what modeling competencies are and how they vary in lower and higher-achieving groups of students in mathematics within the current modeling literature domain. This study examined how mathematical modeling competencies were displayed in…

Practical problem solving is not common in many mathematical classes in Malaysian upper secondary schools. Usually, students receive the mathematical concepts through abstract materials (students cannot see some of them in their daily life). Thus some students believe that 'mathematics is not necessary for human life'. In this article, the…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

An inequality concept has an important role; even in advanced mathematics, inequality assists in analysis and proof. However, students' understanding of inequality is not satisfying. The fact shows that students experience difficulties and errors in solving inequality problems. These difficulties and errors are not intentional or do not result…