Autor: somidem

Treatment of finite limit in spanish textbooks of middle school: 1933–2005

  Por

Javier Claros Mellado
Mª Teresa Sánchez Compaña
Moisés Coriat Benarroch

Abstract:We describe a study of Spanish mathematics text books (secondary level) that allowed us to develop, in part, the field work in two doctoral theses. It’s an experimental study in which an intentional sample, with a total of 40 textbooks, was used to search for, separately, the development made by the respective authors in regard to the finite limit of a sequence (Claros, 2010, doctoral
thesis) and the finite limit of a function at a point (Sánchez, 2012, doctoral thesis). From our theoretical framework (phenomenology of limit), we describe the phenomena that we looked for in the textbooks sample. This has been done following a systematic method to analyze each book, we also include a description of such a method. We summarize the results obtained, by integrating them into useful time ranges for the literature in Spanish, and indicate some pathways for the future of our research.

Key words: textbooks, limits, phenomena, function, sequence.

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Breaking the didactic contract in solving a geometry problem with high school students

  Por

Apolo Castañeda
Juan Arturo Hernández-Morales
Rosa Isela González-Polo

Abstract: This study reports the results of the implementation of an experimental design in a high school mathematics classroom (students 12-14 years old) aimed at the construction of triangles, given three segments. Within the experimental design, there is a problem of calculation of area and perimeter where the ruptura and establishment of didactical contract is analysed. For the design of the sequence, theoretical reflections on the concept of didactical contract of Brousseau were considered, as well as the problem solving model of (Lester, 2013: 258), this allowed the design of activities regarding triangles construction using paper strips. These activities served as a prelude to address a problem of calculation of area and perimeter of a triangle with wrong measures. The results show that students get into contradictions, because despite finding certain conditions for the measure of the segments of a triangle and working previously with unsolvable problems, they cannot recognize a triangle with wrong measures and even claim that it is possible to obtain the perimeter of three segments of a figure which is not closed.

Key words: Didactical Contract, problem solving, geometry, high school students.

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Mathematics teaching beyond classrooms. Analysis of urban and rural activities

  Por

Diana V. Solares Pineda
Armando Solares
Erika Padilla

Abstract:In this paper we analyze a variety of ways of teaching from work activities that involved mathematical knowledge. These activities are given in the rural environment of Sonora state as well as in the surroundings of the Mexico City conurbation. We present the results of two independent research projects that, in the quest for mathematical knowledge from work activities, concur in reporting evidence of such knowledge in the communication process, between experts and apprentices, of certain work techniques. The theoretical grounds that guide this inquiries are supported on didactical and not-didactical theoretical approaches: the Anthropological theory of Didactics, the Theory of Didactical Situations and the Cognition in Practice, respectively. The methodological design consisted in observations of the work activities and in situ interviews. Mathematical problems designed considering the contexts of the activities were also posed. The obtained results show the presence of a variety of ways of teaching, which reveal not only mathematical knowledge, but also contribute to the shaping of it.

Keywords: mathematical knowledge from work activities, situated learning, teaching practices, mathematical techniques and tasks, technological discourse.

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Different interpretations of mathematics learning difficulties

  Por

Gustavo Barallobres

Summary: This article, based on the discussion of some examples, proposes a reflexion on the way cognitive sciences and mathematics didactics addresses the issues related to learning difficulties in mathematics, trying to highlight the theoretical conceptions underlying the analysis as well as certain reasons why these conceptions are considered fundamental for it.

Keywords: Learning Difficulties, Mathematics, Cognitive Psychology, Interactionism,
Mathematics Didactics
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Multiplicative structure problems: Evolution of students’ levels of success and strategies from 6 to 12 years

  Por

Pere Ivars
Ceneida Fernández

Abstract: The aim of this study is to characterize the evolution of the levels of success and strategies used by primary school students (6-12 years old) when solving multiplicative structure problems. Results show that students between 6-8 years old used mostly modelling and counting strategies, but after the third course, the majority of students used the algorithm. However, the use of the algorithm did not imply a decrease of the use of incorrect strategies and encouraged the appearance of a new incorrect strategy, the use of the inverse algorithm. These data suggest that the introduction of the algorithm to solve multiplicative structure problems is linked to a decrease in the use of other correct strategies that involved a proper understanding of the situation, but it does not entail an
improvement in students’ understanding of these situations.

Keywords: Multiplicative structure problems, strategies, Primary Education, evolution,
algorithm.

 

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Probability in the way of an ant: a proposal for teaching use of metaphors

  Por

Gamaliel Cerda-Morales

Abstract: Based on the theory of Lakoff and Núnez (2000) on “Where mathematics comes from?”, this work shows some reflections on the phenomena related to the use of metaphors in the learning of mathematics. In particular, we propose a concrete example of mathematical modelling to explain how the construction of the term “probability” may be supported by the use of metaphors that exist in the teacher’s speech.

Keywords: education, mathematics, metaphors, cognitive sciences, modelling.

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The construction of tangent circumference. Theoretical study from a heuristic perspective

  Por

Liliana Siñeriz y Trinidad Quijano

Abstract:This paper describes a theoretical study of the process of solving an open situation, in the framework of a research focused on geometric constructions. On one hand, we intend to show the multiplicity of aspects inherent to posing and solving problems from it. On the other hand, our aim is to provide some guidelines or suggestions to organize how to teach, in order to rescue methods and heuristics that underlie when it is solved, and to promote the generation of new problems arising from processes to develop and test conjectures by means of exploration.

Keywords: constructions, problem solving, problem posing, heuristics methods,
phases.

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Trends teaching math teachers and their conceptions of the role of educational media in the classroom

  Por

José Francisco Leguizamón Romero, Olga Yanneth Patiño Porras
y Publio Suárez Sotomonte

Abstract:This article informs of a study where we identified the didactic tendencies of some teachers and their conceptions about the role of educational resources in the processes of teaching and learning of mathematics. The trends classification was assumed from the Porlan’s proposal (1995). The research was developed under a qualitative paradigm, through a case study. The participants were teachers from both public and private schools. Data were gathered through a questionnaire as well as class observations. Conclusions showed that teachers have technological tendencies with traditional features; they conceived the educational resources as aids of study (Godino, 2003), elements that allow motivation, support the memorization of concepts, and support the exposition of the thematic by the teacher.

Keywords: conceptions, didactic trends, educational resources, mediation, mathematics education.

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Attitudes towards statistics of university students from Colombia

  Por

Luis Eduardo Pérez Laverde, Ana Sofía Aparicio Pereda,
Jorge Luis Bazán Guzmán y Oscar Jõao Abdounur

Abstract:We analyze the attitudes towards Statistics of Colombian students of a private university in Bogotá, who begin in a discipline of Statistics. To measure the attitudes three scales are considered: Estrada (2002) (ase), Cazorla et al. (1999) (asc) and a conjoint scale based in both. The final sample consisted of 545 students between 17 and 25 years, 64.2% male, of nine careers of the professional schools of Exact Sciences and Engineering, Economics and of the International School of Management and Marketing. The analysis for quality assessment of the scales used, shows high reliability of the final version of the scales with 23, 20 and 43 questions respectively to the ase, asc and Global scales. The analysis of the specific attitudes show that students recognize the importance of statistics both in academia and in everyday life; however, have distrust in relation to use, ability required and taste for the discipline that they take. Also, wer found significant differences (p < 0.05) of the attitudes measured by the three scales by school and careers evaluated, but not in relation to the gender of the students. Through the use of these scales, future investigations are suggested as complement to the didactic approach of actions to be considered in the teaching of this discipline.

Keywords: scale, attitudes toward statistics, item analysis, reliability, Colombian students, teaching of statistics.

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Previous ideas about multiplication and division with decimals: its evolution from an experience with the Laberinto de decimales

  Por

Evelyn Valencia y Alicia Ávila

Abstract:For several decades, students’ learning processes of decimal numbers have been investigated. Difficulties and obstacles have been identified, some of which can be attributed to the instructional approaches that are used. One of those obstacles is related to the intuitive models of the meaning of multiplication and division, which students develop as they engage with these operations in the context of natural numbers. In this paper, results are analyzed of the 82 Educación Matemática, vol. 27, núm. 3, diciembre de 2015 Ideas previas sobre la multiplicación y división con decimales implementation of a didactical situation, named “The maze of decimals”, aimed at overcoming those models. The analysis centers on the evolution of students’ reasoning while engaging in the situation. It is noticeable how students struggle to abandon the conceptions of “multiplication makes bigger, division shrinks.” This process is mediated by diverse ideas that lead to the construction of new rules about the meaning of multiplication and division.

Keywords: multiplication and division with decimals, intuitive models, learning decimals, didactic situations, knowledge building.

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