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The understanding process of primary education students was analyzed when they solve tasks related to the concept of ratio. The study was based on the theoretical framework of Pirie and Kieren (1994). The methodology was qualitative with the case study method. The study was carried out in three stages: planning, development and analysis, using the field observation technique. Data collection was carried out through a task and an interview. The data were analyzed based on theoretical articulation. The results revealed that students lack the prior knowledge necessary to understand the concept of ratio. In conclusion, it can be noted that students do not present logical arguments to formalize the concept, and their understanding process is reduced to memorization or the use of mathematical strategies without understanding the relationship between the task and the mathematical concept. [ABSTRACT FROM AUTHOR]

The research goal is twofold: to articulate neuro-mathematics with the extended theory of mathematical connections that uses onto-semiotic approach tools and to explore the connections established by a teacher and his student when solving a problem about the volume of two boxes, one of toothpaste and the other of tomato. This research was developed in two stages: the theories were articulated assuming concordances and complementarities, highlighting the notion of connection, and a context of reflection was considered carried out in three phases where the participants were selected, participant observation was carried out in the classroom during solving a problem and then analyzing the data with the new tool to explore mathematical and neuromathematical connections. The findings present the mathematical connections established by the teacher and the student of meaning, feature, procedural, different representations (alternate, equivalent, and from a horizontal mathematization view), and part-whole, as well as neuromathematical connections of: recognition of terms and symbols; visual perception, spatial skills and motor coordination; association of mathematical concepts and formulas; intermediate calculations and unit conversion; solve operations step by step and understand the process; verification and conclusion, activated in the brain areas linked to each mathematical practice sequentially. [ABSTRACT FROM AUTHOR]

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Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper shows the mathematical connections that university students make when solving tasks involving first-order Ordinary Differential Equations. We consider mathematical connections as a process by which a person relates one or more ideas, concepts, representations, theorems, or meanings to each other, to those in other disciplines or to real-life situations. For data collection, task-based interviews were used, which were analyzed with the Thematic Analysis method. The results indicate the use of seven types of mathematical connections: different representations, procedural, meaning, characteristic, part-whole, implication and reversibility. However, it was observed that a high academic performance is not an indicator that the connections emerge adequately in the resolution of tasks. [ABSTRACT FROM AUTHOR]

The understanding study of linear algebra concepts is an interesting research topic in mathematics education, mainly because of its abstraction and complexity. A goal concept for teaching linear algebra in a mathematics teaching degree course is that of a diagonalisable linear operator, therefore, based on APOS theory, a cognitive model that considers its construction as an object is given. A questionary was applied to five postgraduate students (25-30 years old) and a semi-structured interview. The results show two ways of construction followed by the students to construct the study concept, which required conjectured mental structures obtained from preliminary genetic decomposition. In addition, it was found that the students prefer to determine whether the matrix representation of the linear operator is similar to a diagonal matrix than to coordinate the ordered basis and eigenvectors processes in the eigenbasis process, with their conception process of similar matrix. [ABSTRACT FROM AUTHOR]

The mathematical connections made by five Pre-Service Mathematics Teachers (PSMTs) when solving problems on the derivative were analyzed. The conceptual framework used was the typology of intra-mathematical connections. For data collection, semi-structured interviews were conducted, and a questionnaire was designed, which included three tasks about of the derivative, which were analyzed through the thematic analysis method. The results showed that PSMTs made mathematical connections: meaning, different representations, procedural, part-whole, implication and feature. We identified that the PSMTs’ difficulties in establishing connections are caused by the meaning they have on the derivative concept, acquired in their received teaching and, if they are not attended, they can be reproduced in their future practice as in-service teachers. [ABSTRACT FROM AUTHOR]