The quality of the intra-mathematical connections made by Mexican university students when solving tasks on the derivative was characterized. The typology of mathematical connections and the quality levels of mathematical connections were used. Interviews were conducted based on eight tasks applied to three case studies. The results showed that…

The current paper aims to identify the mathematical connections activated by 10 Mexican high school students while solving mathematical tasks that involve the exponential and logarithmic function. We used the Expanded Mathematical Connections Model (EMCM) and the OntoSemiotic Approach of Cognition and Mathematical Instruction (OSA) as theoretical…

A math walk is a planned walk during which students talk about mathematical concepts embedded in their everyday environments. The walk is based on relatively permanent objects or locations, such as trees, artworks, playground equipment, and building elements, and can be shared with the broader school community in a variety of different ways. In…

This article is part of a wider research project that has the educational goal of supporting students in the production of conjectures, arguments and proofs, as well as promoting a move from the production of arguments expressed in colloquial registers to arguments expressed in literate registers. In this regard, we Giovannina Albano, Umberto…

Textbooks play an important part in teaching and learning mathematics. However, textbook research on spatial ability has so far received little attention. In this study, we investigated whether school mathematics textbooks provide enough opportunities for primary students to learn three-dimensional shapes and help them acquire spatial ability.…

Today, it is important how much individuals acquire knowledge and use this theoretical knowledge in their daily life. A qualified training program is expected to train individuals who can solve problems. The prospective classroom teachers, who are expected to train individuals who can solve problems, should also have knowledge about the…

In this paper we present the results of a survey of research studies on the learning of multivariable calculus in a wide geographic spectrum. The goal of this study is to describe what research results tell us about students' learning of calculus of two-variable functions, and how they inform its teaching. In spite of the diversity of cultures and…

This article aims to investigate the teaching of chance in the context of tactile models (TM) from the perspective of the Theory of Register of Semiotic Representations. In this qualitative research, we sought to identify the different types of semiotic registers and transformations (treatment and conversion), in the solutions of the tasks of the…

Molecular symmetry is a topic that requires mental manipulation of molecules when searching for symmetry elements and their corresponding symmetry operations. Such mental activities are difficult for students in a traditional classroom where only definitions and demonstrations are provided. Therefore, an exploration-based activity was developed to…

The aim of this study is revealing the strategies used by 5th-grade students in comparing fractions. In line with this purpose the study is based on qualitative research. Participants of the study conducted with convenient sampling method are seventy 5th-grade students. The students have been asked six questions which necessitate comparison of…

The purpose of the study was to explore students' consistency in their notions encountering different methods in solving the same task of comparing values of certain infinite series. The participants were 93 male students aged 16-17. Applying cognitive conflict approach and the data were collected through a questionnaire administrated in two…

Using a randomized controlled trial, we examined the effect of a fractions intervention for students experiencing mathematical difficulties in Grade 5. Students who were eligible for the study (n = 205) were randomly assigned to intervention and comparison conditions, blocked by teacher. The intervention used systematic, explicit instruction and…

Cognitive difficulty arises from two types of cognitive processes: treatments; within the same, conversions; between different types of representational registers. Conversions are difficult since they ask for understanding of two representations. Direction and the choice of first register could be a threshold for the student. Wasan geometry is…

The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners' procedural and conceptual knowledge of…

Ethnomathematics can empirically improve the cognitive abilities of students in elementary and secondary schools. However, in undergraduate study, there are still limited studies on integrating ethnomathematics in learning resources. This study aims to apply interpolation in modelling polynomial functions and integral volume on the shape of…