We explore the connection between the notion of critical point for a function of one variable and various inequalities for iterated exponentials defined on the positive semiline of real numbers.

Human reasoning about and with uncertainty is often at odds with the principles of classical probability. Order effects, conjunction biases, and sure-thing inclinations suggest that an entirely different set of probability axioms could be developed and indeed may be needed to describe such habits. Recent work in diverse fields, including cognitive…

Students use a variety of resources to make sense of integration, and interpreting the definite integral as a sum of infinitesimal products (rooted in the concept of a Riemann sum) is particularly useful in many physical contexts. This study of beginning and upper-level undergraduate physics students examines some obstacles students encounter when…

Part of the international reflection on the use of history in mathematics teaching consists in a quest of frameworks and models suitable for empirical studies. Following this demand, this paper explores the way Balacheff's cK? model, a model taken from the didactics of mathematics, can be used in the analysis of learning at student level. In the…

Algebra as a study of quantitative relationship is one of four conceptions of school algebra which serves as a foundation for the concept of function. However, there is still a lack of attention to this particular relationship, especially in early algebraic reasoning. This study aims to investigate how the aspect of quantitative relationship in…

This research aimed to determine the effectiveness of the issue, discussion, establishment, and application (IDEA) learning model in embedding mathematical concepts understanding. It is a quantitative study with a quasi-experimental approach. This research was conducted at Malang Islamic University with students majoring Mathematics education…

Problem-solving is considered as an important skill for learning Mathematics. Integration of cloud technology into Model-Eliciting Activities (MEAs) has been considered as an instructional approach to study students' mathematical problem-solving abilities. The purposes of this study were to evaluate the suitability of the MEAs using cloud…

This article explores three attributes of teachers' understanding of fraction magnitude: the accuracy and reasonableness of teachers' estimations in response to fraction arithmetic tasks as well as the alignment of the estimation strategies they used with the concept of fraction magnitude. The data were collected from a national sample of…

This study examined students' views on geometry teaching via three-dimensional dynamic geometry software Cabri 3D. Teaching designed with Cabri 3D for solids volume measurement was implemented for 16 students in the eighth grade from a public secondary school in Turkey. The data obtained from the interviews with the students about the teaching,…

Using robot programming activities for learning in the classroom is one way to drive interest and engagement in the STEM field among students, especially girls. And this is afield that is particularly characterized by an underrepresentation of women. Accordingly, many countries are increasingly integrating activities related to computer science…

The integration of mathematics and science in teaching facilitates student learning, engagement, motivation, problem-solving, critical thinking, and real-life application. Although curriculum integration is theoretically desirable for many educators, what to integrate and how to integrate are often the big questions facing teachers working within…

Language and numerical development are associated in early childhood. In the present study, we focused on the association of the development of children's cardinality understanding of small numbers and their knowledge on unspecific quantifiers (i.e., many, a few). In a longitudinal study, we pursued the research question whether children's…

This longitudinal quantitative study determined the impact of a summer mathematics academy for early learners on their number sense and how their number sense compared to that of their peers who did not attend the academy. The Texas Early Mathematics Inventory -- Progress Monitoring (TEMI-PM) was used to measure students' number sense. Results…

This article presents activities focused on developing some essential Year 1-3 fraction understandings (i.e., joining/composing, decomposing/ partitioning) while aligning these activities to the Australian Curriculum content strands and content descriptions. Additionally, the authors describe the materials/resources needed, the key vocabulary…

A number of previous studies have identified cognitive deficits in developmental dyscalculia (DD). Yet, most of these studies were in alphabetic languages, whereas few of them examined Chinese DD. Here, we conducted a study aiming to determine the cognitive factors associated with DD in Chinese children. Five candidate cognitive factors of…