Optimization is introduced to teaching in secondary school, focussing on functions of one variable with the first derivative criterion for critical points and monotonicity of functions. The second derivative criterion is also used to determine the nature of the critical points. Similarly, in university-level teaching, algebraic work using criteria…

Using teaching representations is one of the common means for preparing pre-service mathematics teachers (PSTs) to learn how to teach mathematics meaningfully. However, turning PSTs' attention to the mathematical objects that students engage with during the lesson is a challenging pursuit. This paper suggests using the Realization Tree Mediator…

Research studies support caregivers' involvement in children's mathematical journeys, as foundational to their cognitive development and academic success as mathematical learners. The purpose of this intrinsic case study was to understand how a caregiver initiated and/or continually engaged their child in spontaneous mathematical moments during a…

The aim of this study was to examine how pre-service teachers performed in tasks related to three specific aspects of curricular noticing. The participants completed a two-part written task in which they solved three pattern generalization problems and sequenced them for teaching purposes. Inductive content analysis was used to analyze the…

An important approach for developing children's algebraic thinking involves introducing them to generalized arithmetic at the time they are learning arithmetic. Our aim in this study was to investigate children's attention to and expression of generality with the subtraction-compensation property, as evidence of a type of algebraic thinking known…

The aim of this study is to examine the concept images of mathematics educators and pre-service elementary mathematics teachers regarding the relationships between the concepts of slope, rate of change and derivative. Four mathematics educators working in different state universities and responsible for Analysis courses, three pre-service…

Ratios and proportions are new topics in the primary curriculum. Previous research shows that Year Five pupils have difficulty in learning ratio and proportion. This study aims to identify the conceptions of ratio and proportion of seven year five pupils. It is based on radical constructivism using qualitative case study. Data was collected…

The aim of this research was to explore the mathematical connections that pre-university students make when they sketch the graph of a derivative function and an antiderivative function. Also, we tried to explain the origin of the mathematical connections identified. We assume mathematical connections as a cognitive process through which a person…

In the world where we always meet geometric constructions, it is a necessity to make sense of the objects belonging to these constructions. In this respect, this study aimed to examine the teaching of volume with the blending of the realistic mathematics education (RME) and GeoGebra. The study group consisted of 12 students attending lessons…

This study investigated how 155 pre-service teachers solved three pattern generalization problems in a two-part written test and sequenced them for teaching purposes to demonstrate their curricular noticing. Participants' solutions were analyzed using inductive content analysis, which showed that only 8.4% of PSTs produced correct answers to all…

In this research, a new test for understanding simple fractions has been developed for students at the beginning of lower secondary education. In many countries, mathematics education in Grade 5 builds on elementary students' developing concepts of fractions. Understanding fractions causes many difficulties for students, and research on mental…

In this paper the authors described the influence of the computer-based environment on students' learning achievement of the multidimensional calculus, in particular double integrals. The research was conducted with the second year students at the University of Kragujevac, Serbia, with two groups of students: the experimental and the control one.…

Reasoning is handled as a basic process skill in mathematics teaching. When the literature was examined, it was seen that many types of reasoning related to mathematics education were mentioned. In the present study, it was focused on visual reasoning, which is one of the types of reasoning and also used in different research areas. The purpose of…

Teachers whose mathematical meanings support understanding across different contexts are likely to convey them in productive ways for coherent student learning. This exploratory study sought to elicit 67 secondary mathematics pre-service teachers' (PSTs) meanings for quadratics with growing pattern creation and multiple translation tasks. A…

In this research we investigate how mathematics teachers, as graduate students, estimate the value of [pi] by exploring the problem of "squaring the circle" using digital technology. Initially, we mention some aspects of teaching and learning of calculus in the literature, emphasizing studies that use the notion of humans-with-media to…