Autor: somidem

Praxeologies analysis of mathematical modeling in textbooks of primary education

  Por

Samantha Quiroz Rivera y Ruth Rodríguez Gallegos

Abstract:Abstract: The present study aims to analyze the mathematical modeling praxeology of the mathematics textbooks for primary school students in Mexico. Based on a qualitative methodology, a detailed description of the types of mathematical modeling tasks present in the lessons of the books chosen are performed. Based on them, there are put into consideration the techniques, technologies and theories using the theoretical framework of the Anthropological Theory of Didactics. The results contribute a description of the mathematical modeling cycle through its praxeological elements. It is also described, in a diagnostic way, a detailed report about the materials that the Secretary of Education makes to students and the poor agreement of these with the objectives proposed in the actual curriculum.

Keywords: mathematical modeling, Anthropological Theory of Didactics, praxeologies, elementary school, textbooks.

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Methodological proposals that constituted illusions in the teaching of mathematics process

  Por

Bruno D’Amore y Martha Isabel Fandiño Pinilla

Abstract:In this paper we present and critically discuss methodologies and tools that have been proposed in illusory way as positively decisive in the complex process of learning mathematics. We present historical and didactic analysis to show the futility in some cases and in others the harmfulness.

Keywords: tools for the teaching of mathematics, historical evolution of mathematics education, teacher training in mathematics.

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Mathematical objects linked to Regression in High School textbooks

  Por

Carmen Batanero, M. Magdalena Gea,
Danilo Díaz-Levicoy y Gustavo R. Cañadas

Abstract:The aim of this paper is to characterize the presentation of regression in Spanish high-school textbooks. To achieve this aim we analyse the problem-fields, procedures, concepts and properties linked to regression in sixteen high Spanish textbooks, eight in the modalities Humanities and Social Sciences, and another eight directed to Science and Technology. We classify the concepts identified according to their definition (operational, structural or using examples). Results show no much difference between the textbooks directed to the two high school modalities. We found a wide variety of number and type of properties presented. The assessment of the goodness of fit and the building of non linear models is hardly included. These results provide criteria to improve the presentation of regression in high school textbooks.

Keywords: Regression, Textbooks, High school, Concepts and Properties.
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To recognize and refine personal meanings addressing an error: the case of the Point Localization Theorem

  Por

Óscar Molina, Patricia Perry,
Leonor Camargo y Carmen Samper

Abstract:The purpose of this article is to present the meaning that pre-service teachers give to the Point Localization Theorem, a Euclidean plane geometry theorem. We infer the meaning from the students’ use of the theorem when they try to justify a procedure for which it is not adequate. We point out that the error this mistake entails becomes a path used deliberately by the teacher to favor semiosis with respect to the meaning of the theorem; we expose how the teacher recognizes the importance of this incident and therefore opens a space so that the students can explicit their meanings, possible genesis of the inadequate use, as a means to approach the desired shared meaning of the so said theorem. To describe the semiosis and identify the meanings, we use the semiotic perspective inspired in Peirce’s idea of triadic sign.

Key words: Making meaning, Point Localization Theorem, semiosis, Peirce’s idea of triadic sign.download

The role of arithmetic problems analysis in teachers service training

  Por

Cecilia Papini

Abstract:In this article, we interpret the discussions of a primary school teachers group in the context of a formation course related with mathematics teaching. In the first part, we briefly describe the framework and the implementation context of the proposed course. Then we analyze the teachers group production and we propose an interpretation of the dialogues that took place during the formation meeting. Participants teachers, coordinated by a researcher in mathematics education, collaboratively produce knowledge
on teaching mathematics when faced with tasks such as: design, implement, record and analyze teaching situations.

Keywords: teacher training, arithmetic problems analysis, students strategies anticipation,
teacher explanations, mathematics teaching.

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Construction and mental mechanisms for learning matrix theorem associated with a linear transformation

  Por

María Trigueros Gaisman, Isabel Maturana Peña,
Marcela Parraguez González y Miguel Rodríguez Jara

Abstract:Based on apos theory (Actions, Processes, Objects and Schemes) as a theoretical and methodological framework, we investigate the mental constructions and mechanisms required to construct the associated matrix of a Linear Transformation (matl). We design a genetic decomposition
(dg) of the theorem matl to discuss how college students learn it. We report three cases of study. The results show how students construct the concept of coordinates of a vector as an object, but have difficulty using it in the construction of the coordinate matrix associated to the image of vectors. Results also show students’ difficulties to construct matl as an object and the crucial role of considering tl as a function in order to attain a deep comprehension of tmatl.

Key words: Matrix associate, Linear Transformation, apos Theory, Linear Algebra.

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Rule of signs of the multiplication: a proposal didactic

  Por

José Benjamín Chan Domínguez y Genny Rocío Uicab Ballote

Abstract:This project describes the design and implementation of a methodological approach to introduce the rules of multiplications signs through the geometric representation of the
product like the area of a rectangle. The proposal considers two sequences of activities organized, both on a worksheet as well as the software Cabri II Plus. This proposal is designed in the focus of Brousseau’s theory of didactic situations, and it has the student as the principal actor, which is in charge of an experimentation and explanation process during the resolution of learning activities, for building of the signs rules. This proposal is designed for middle school students.

Key words: Rules of the signs, learning environment, school treatment, theory of the didactic
situations, didactic engineering.

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Analysis of the coupling process between the epistemic and cognitive facets of mathematical knowledge in the context of an exploratory-investigative task about patterns

  Por

Luis R. Pino-Fan, Adriana Assis y Juan D. Godino

Abstract: In this paper, we explore the coupling between the intended and implemented meanings by the teachers and the meanings achieved by the students in the context of an exploratory- investigative task on patterns, implemented in a class of the 7th grade of the basic education in Brazil. For this, we use the theoretical model known as Onto-Semiotic Approach (osa) of mathematical knowledge and instruction, which allowed us to describe and interpret the interaction processes in the classroom and establish relations between the facets that, according to this model, compose the process of teaching and learning. As a result, we emphasize the complexity of the teacher’s work, which should be able to recognize and negotiate the
meanings produced by the students –not always contemplated in her initial planning– making decisions about the type of performance that should be adopted, moment-to-moment, throughout the process of study to ensure the optimization of learning.

Key words: Instructional process analysis. Patterns. Classroom interaction. Onto-semiotic
approach.

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An overview of the mathematical beliefs system of pre-service teachers

  Por

Santiago Hidalgo Alonso, Ana Maroto Sáez y Andrés Palacios Picos

Abstract:The study of affective factors has responded to uncertainties present in some processes of teaching and learning mathematics. In this paper we propose to study one of the components of the affective domain: mathematical beliefs; in particular, we are interested in making a categorization system of mathematical beliefs of future teachers and knowing the verbal associations engaged on mathematics. In a sample of more than a thousand students of the Degree of Master of Primary Education of ten public universities in Spain, we applied a Likert scale of mathematical beliefs. Statistical analysis indicates that the associations that future teachers do about maths are at the cognitive and metacognitive (knowledge strategies). However, regarding their experiences with mathematics, the students show a strong, mostly negative, with respect to the self-concept, the tasting to mathematics, the affective component and the causal attributions and the positive
assessment of their social connection: usefulness and necessity.

Keywords: pre-service teachers, affective domain, mathematical beliefs system, academic performance, statistic analysis.

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A mathematical modelling as a means to detection student’s obstacles and difficulties related to the function concept: extension of a spring under a weight

  Por

Jose Benito Búa Ares, Teresa Fernández Blanco y Mª Jesús Salinas Portugal

Abstract:In this article we present a research about a mathematical modelling for the secondary school. Students start with a data table, it obtained experimentally by themselves, on the behavior of a spring subjected to a weight. From the data table and using the GeoGebra program, students obtain an analytical expression that relates the two variables (mass and length of the spring). After they obtained the model, students have to answer questions related to the mathematical model and the original extramathematical situation. The main objectives of the research are to show how students use their unserstanding about functions during the process to obtain the model and if students interpret the mathematical result in the context of the original extramathematical situation. The investigation results show it is possible obtain a mathematical model without the use of implicit mathematical knowledge and without the interpretation of the mathematical result in the original extramathematical situation.

Keywords: Modelling, functions, GeoGebra, lower secondary education, upper secondary education

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