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The aim of this article is to understand the learning of five primary teachers participating in a class study that focused on learning multiplication by 2nd year students with regard to the student's knowledge and learning processes and knowledge of teaching practice. It is a qualitative and interpretative investigation. Data collection was undertook by participant observation through the preparation of a research journal, audio and video recording of the sessions and conducting a semi-structured collective interview. The results confirm the potential of the LS by contributing to teachers to deepen their knowledge about the student's thinking and their strategies and difficulties in learning concepts. They also valued the detailed preparation of their action taking into account the previous knowledge of the students, as well as about exploratory learning. [ABSTRACT FROM AUTHOR]

This article aims to identify, characterize and compare the cognitive flexibility profile in mental calculation of brazilian students, based on the analysis of cognitive elements, namely problem characteristics and solution procedures, used during the resolution of arithmetic calculations. The sample of this study included 42 2nd graders (7 to 8 years old) and 42 4th graders (9 to 11 years old), from 4 public schools in Porto Alegre. Each child was encouraged to classify 12 arithmetic calculations, thus demonstrating their numerical knowledge by explaining the thought process involved in solving the calculations through a specific cognitive flexibility assessment instrument. In general, the results revealed that the different proportions of numerical knowledge used made it possible to distinguish the flexibility profiles - flexible, mixed or rigid. [ABSTRACT FROM AUTHOR]

This research aims to identifying children's evolution in classification and seriation criteria using Dienes' logic blocks. Besides, it intends to investigate the construction preferences of children during the development of free play. It is a descriptive study carried out using a previously-constructed observation code. The results showed that color and size are the characteristics most quickly identified by children and most familiar to them. Form is a bit below the previous ones. Thickness is the least observed feature. In week seven, children start to do two-criterion simultaneous seriations, with the majority of them completing it at the end of week nine. Regarding construction preferences, children prefer to recreate the fantasy world of their stories than their daily life objects. [ABSTRACT FROM AUTHOR]

This article presents the results of a qualitative investigation, in which the objective was to investigate what knowledge is produced by future mathematics teachers, in mathematical, methodological, technological aspects and about the approach of socially relevant themes, through design, posing and resolution of open problems and the planning and implementation of pedagogical practices, in which such problems are proposed. To achieve this, three students, in a group, carried out the activities of an extension course, which allowed them to acquire experiences, which contributed to the production of teaching knowledge, related to the design of open problems and which address topics of social relevance with the use of digital technologies and about the planning and implementation of pedagogical practices, in which the posing and resolution of these problems are evidenced. [ABSTRACT FROM AUTHOR]

The purpose of this study was to determine the effects on the cognitive level of two groups of students of Early Childhood Education (49 subjects of 5 and 6 years old), after applying in the classroom of the Experimental Group different musical activities related to mathematics for two months, while the Control Group continued being taught solely with traditional mathematical activities. The used instrument was a questionnaire that the teachers completed before and after the implementation of the activities, after collecting the mathematical learning acquired by students through daily field notes. For data analysis, descriptive and inferential statistics were used. Significant and positive effects on the performance of the Experimental Group were found in all items. It can be concluded that the use of music represents an excellent alternative in Early Childhood Education because it has a positive impact on learning. [ABSTRACT FROM AUTHOR]

This paper presents the results of a research study aimed to explore the main beliefs and conceptions that have teachers who teach mathematics at the secondary level in Honduras (students 13 to 18 years), in relation to the teaching /learning and assessment of mathematics. The results show, among other elements, that for Honduran teachers the learning of mathematics is achieved by the active participation of the students. This belief is highlighted by teachers with a bachelor in Mathematics; and that the evaluation is a process that improves teaching and learning, providing useful results but, they must be taken with special scrutiny due to mistakes and inaccuracies that always exist. As conclusions highlight the need to improve initial training and continuous training of teachers so that use resources that promotes active student participation and improve the evaluation processes. [ABSTRACT FROM AUTHOR]

The goal of this article is to present the role of the technology during the transit between the different stages of the mathematical modeling cycle. Since 2008 at Tecnológico de Monterrey, it was began the development of a course that involves a mathematical modeling perspective as the principal mean for learning Differential Equations. It is presented the design of a specific situation related with Circuits Electric Context with activities based on the use of diverse technology. Based on a praxeological study we describes the types of tasks related to the mathematical modeling cycle when technology is applied, and also how the former ones might propose a better transit between the diverse domains of the modeling cycle. We conclude with the concluding remarks and future lines ofresearch. [ABSTRACT FROM AUTHOR]

This article explores issues related to the relationship between everyday mathematics and academic mathematics within adult education, through a series of workshops with parents. Participants were encouraged to reflect on their perspective on learning and teaching mathematics through different activities in the workshops. All sessions were videotaped. Our analysis of multiple episodes revealed three topics: contextualization, transferring the mathematical knowledge, and sense making. We use three vignettes to illustrate these topics. Our study implications for adult education focus on mathematics as a situated practice produced as a consequence of interaction among learners in egalitarian spaces. [ABSTRACT FROM AUTHOR]

Prospective mathematics teachers often have learned mathematics through situations quite different from current curriculum recommendations. Such is the case of Fábio, who, at the beginning of his practicum, proposes mostly exercises and uses work at the blackboard. Assuming that didactic knowledge is reformulated from practice, this article analyzes the influence of a teacher education setting based on ICT (e-mail and forum) in developing aspects of such knowledge -- tasks proposed and ways of using technological materials. The qualitative and interpretative case study of this prospective teacher is based in interviews and in the analysis of the documentation generated in the teacher education setting. The results show that ICT enabled sharing and discussing classroom experiences and joint work with other prospective teachers, supervisor and mentor. Besides exercises, this prospective teacher begun proposing students tasks more open and challenging as well as the exploration of technological materials. His reflections regarding the tasks and the ways to use the technological materials in his classes contributed to enlarge his didactic knowledge and to regard his own practice as learning setting. [ABSTRACT FROM AUTHOR]

In this Article, we discuss the problem of the relationship between brain, mathematics, and cognition. In the first part, we present some elements concerning the anatomy of the brain and its growth. Against this background and drawing on current neuroscience research, we offer a summary of the cerebral parts usually associated with arithmetic thinking and the transition from perceptual arithmetic (common to several species) to symbolic arithmetic (specific to the human species only). Our discussion then turns around brain research and algebra. The literature review offers a general panorama that points out the multimodal nature of cognition in general and mathematical cognition in particular. This multimodal nature of cognition is compatible at different levels with the ontogenetic development of the brain --a development that turns out to be strongly related to the cultural context. In the conclusions we suggest some problems and questions that may be useful contact points for a research program between educators and neuroscientists. [ABSTRACT FROM AUTHOR]

In this work the main results of the doctoral thesis of the author are exposed. A methodology to design the evaluation system in mathematics is offered, considering to the evaluation as a function of the direction system of the teaching-learning process; besides, the principles and regularities for develop the evaluation in mathematics are defined. The proposed methodology was applied to the Integral Calculus course for electrical engineering of the University of Camagüey, Cuba, having carried out an experimentation that covered two school courses. It was shown that with this methodology it is possible to growth up the dedication of the students to the study, the academic performance and its quality. To determine which indicators permit to test the dedication of the students to the study, it was performed a validation by means of the criterion of experts. [ABSTRACT FROM AUTHOR]