Opportunities to learn related to the use of quantitative reasoning to solve higher-order real-world applications that reflect the messy nature of the world are scarce and vary across countries. Those experiences are essential to the development of quantitative literacy. This literacy, like that related to language, is critical for all children.…

The current study is part of a comprehensive research on linking visualization, students' construction of geometrical concepts and their definitions, and students' ability to prove. The aim of the current study is to investigate the effect of learners' understanding of definitions of geometrical concepts on their understanding of the essence of…

Constructing mathematical proofs is a fundamental yet challenging skill in secondary school geometry. While technology has been used to scaffold different aspects of the proving process, existing approaches often separate inquiry and conjecturing from formal proof or focus on structural and technical assistance without addressing students' initial…

This study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in…

Proof and argumentation are essential components of learning mathematics, and technology can mediate students' abilities to learn. This systematic literature review synthesizes empirical literature which examines technology as a support for proof and argumentation across all content domains. The themes of this review are revealed through analyzing…

Thinking development processes among high-school students is an important and significant issue that has been widely investigated (Leviathan, 2012; Ball, 1996; De Risi, 2015). A few studies discuss the development of mathematical thinking as this field contains additional difficulties to the traditional factors, teachers, students, and parents,…

This study sets for itself the task of constructing a learning trajectory for the fundamental theorem of calculus (FTC) that takes into account the interaction with an educational digital tool. Students were asked to explain the connections between interactive and multiple-linked representations in an educational digital tool, and to conjecture…

Researching students' responses to tasks at different year levels and in varied curriculum contexts can provide insights that relate their understandings to prior learning experiences and teaching approaches. In this article, we discuss evidence of students from three curriculum contexts (English, Australian, and Israeli) (n = 350) ways of…

The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…

We present the second stage of a study within the context of geometry, whose aim is to investigate relationships between and influence of visualization, the concept images of students concerning geometrical concepts and their definition, and students' ability to prove. We focus on links between the understanding of the definition's role in…

Acquaintance with various ways of inculcating concepts in any studied area of knowledge is one of teachers' duties, particularly mathematics teachers. Studies indicate errors and difficulties when inculcating concepts in mathematics and learning them. Many concepts have different meanings in different contexts. Hence, teachers should deal with the…

This study analyzes six seventh grade Israeli mathematics textbooks, examining (1) the extent to which students are required to justify and explain their mathematical work, and (2) whether students are asked to justify a mathematical claim that is stated by the textbook or a mathematical claim that they themselves generated when solving a problem.…

Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…

Looking for closed forms for an integral depending on one parameter, we obtain integral identities and new integral presentations of Catalan numbers. Wallis formula appears as an important tool.

This study focuses on the knowledge exhibited by 30 elementary school in-service and pre-service teachers in solving non-routine mathematical problems and on their beliefs regarding these kinds of problems. Interviews were used to reveal teachers' knowledge and beliefs. The findings indicated that these teachers had difficulty in solving…