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

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.


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

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,


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

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.


Attitudes towards statistics of university students from Colombia

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.


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

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.


Praxeologies analysis of mathematical modeling in textbooks of primary education

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.


Methodological proposals that constituted illusions in the teaching of mathematics process

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.


Mathematical objects linked to Regression in High School textbooks

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.

To recognize and refine personal meanings addressing an error: the case of the Point Localization Theorem

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

The role of arithmetic problems analysis in teachers service training

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.