Idioma Inglés

Descripción

We present the results of a research project which deals with a qualitative case study in the field of mathematical modeling. The study investigates the role of "real" life modeling situations of the learner in the construction of mathematical knowledge at school. The study of episodes, interviews, questionnaires and direct observations allowed analysis on how teachers describe their teaching performance when approaching the content of school mathematics. However, the most important aspect was to be able to detect the necessity of a "sense of reality", which is characterized in this paper. The development of this research project shows that it is still necessary to develop a sense of reality as a tool to facilitate interaction between the socio-cultural context and school mathematics, all through modeling.

Lista de autores

Villa-Ochoa, Jhony y Jaramillo, Carlos Mario

Fecha

2009

Autores

Descripción

According to Baki, (2008), in teaching environments equipped with technology, learning becomes easier, and the learning process quickens; deficiencies are eliminated by means of feedback, individual learning increases, active learning, creativity and equality of opportunity are enabled and consequently students reach the information first hand. This research project was focused on enhancing counting skills through solving math problems by using the communicative approach “CLIL” as vehicle to the design of the tasks which were based on adding up and subtracting in one number within problem solving exercises done on a math (APP) called “Have fun learning” which was designed for children of 1st grade who belong to a bilingual and private school. For this school is quite important that its students get ready for the standardized exams as the Cambridge test starters, in which students are assessed according to the Common European Framework since early stages.

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Olaechea, Nasly Katherine

Fecha

2016

Autores

Descripción

In this article we describe analyse and evaluate the implementation of an educational design to develop the prospective mathematics teacher’s didactical analysis and reflection competence. Planning of the experience, its implementation, and evaluation are based on the application of theoretical tools of the onto-semiotic approach. In several studies supported within this theoretical framework, the notion of didactical suitability as a tool of reflection on a study process has been developed and applied. In this sense, the main objective of the learning processes described here is that prospective teachers know and be competent in the application of this tool. The research scenario is a Master course for Secondary education mathematics teachers in which 27 students participated. The information gathered is based on the analysis of: observer-researcher and teacher-researcher’s annotations on the debate in the classroom, audio recordings and the participants’ responses throughout the design cycle. The a priori analysis of the educational situation reveals a high epistemic and ecological suitability; nevertheless, time constraints have conditioned an adequate learning achievement. Finally, the analysis of class episodes, using the tools described in this article, is revealed as an ideal educational strategy, but it should be complemented with situations focused on the development of other didactical competencies.

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Giacomone, Belén, Godino, Juan D. y Beltrán-Pellicer, Pablo

Fecha

2018

Autores

Descripción

This article discusses evidence of 24 fifth graders’ (10-11 year olds’) ability to generalize when solving a problem which involves a linear function. Analyzed in the context of the functional approach of early algebra, the findings show that 3 students generalized both when solving specific instances and when asked to provide the general formula; while 15 students generalized only when asked to define the general formula. The results are described in terms of the functional relationship identified, the types of representation used to express them and the type of questions in which students generalized their answers. Most of the pupils who generalized did so based on the correspondence between pairs of values in the function at issue.

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Pinto, Eder y Cañadas, María C.

Fecha

2018

Autores

Descripción

This research is part of a broader project, based on the proposal of early algebra, the main purpose of which is to explore the algebraic abilities displayed by primary school students in tasks involving a functional relationship. Our goals in this communication are two. First, to describe how third-grade students represent indeterminate quantities when expressing functional relationships. Second, to illustrate how students make use of the letter in such representations when this one is proposed as a representation for the independent variable of the function.

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Ayala-Altamirano, Cristina y Molina, Marta

Fecha

2018

Autores

Descripción

In this paper, the effect of holding a math training workshop using GeoGebra software has been studied on the changes on teachers' knowledge and beliefs. The selected sample is 40 male and female teachers in Iran. Before and after the intervention were administered a pre and post questionnaire with two components: TPACK knowledge and teachers’ beliefs. Fuzzy logic and Fuzzy TOPSIS methods were used to analyze the data. The results of this method showed a significant difference between the results before and after the workshop.

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Alizadeh-Jamal, Mohammad, Shahvarani, Ahmad, Iranmanesh, Ali y Tehranian, Abolfazl

Fecha

2018

Autores

Descripción

This paper focuses on functional thinking as an approximation to algebraic thinking in third-year primary-school students. It describes a study with a class group of 24 Spanish pupils displaying functional thinking to solve a contextualised problem, identifying the type of functional relationships distinguished by these students and the ability to generalise observed in some of them. It contains an analysis of the information collected in one questionnaire, which is part of a teaching experiment. The students distinguished two types of functional relationships, correspondence and covariation, predominantly the former. Three students generalised as well

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Pinto, Eder y Cañadas, María C.

Fecha

2017

Autores

Descripción

Against the backdrop of functional thinking to early algebra, this paper discusses an initial study of how 24 fifth year elementary school students (10 to 11 years old) perceived the inverse function. This notion has been scarcely tackled in the context of early algebra and, particularly, within the functional thinking approach. Based on structure and generalisation notions, we analysed the responses of a group of 24 students when solving a problem, which contains questions involving the direct and inverse forms of a problem involving a linear function. Ten of the 24 students were observed to establish structures involving inverse function and five to generalise that form of the function.

Lista de autores

Pinto, Eder y Cañadas, María C.

Fecha

2018

Autores

Descripción

One of the challenges in mathematics education research is to provide a comprehensive description of mathematical activity carried out by university students. Taking this challenge as an objective, this paper analyses the answers of 30 prospective teachers of primary education to a typical mathematics problem on fractions using area and tree diagrams. Theoretical and methodological tools from the onto-semiotic approach to mathematical knowledge and instruction support the cognitive analysis; hence, the underlying complexity of applying the area diagram to express a multiplicative reasoning should be highlighted. However, the structure of the system of practices that have to be carried out to solve the problem in the tree diagram are better aligned with this kind of reasoning. Furthermore, the use of the natural language in order to communicate the answer has been observed as a necessary register. This result lead to a deeper comprehension of the role played by these two types of diagrams and of the mathematical objects that emerge from such representations. As a conclusion, the type of analysis presented here is revealed as a strategic tool for instructors of primary education students to emphasize the importance of meanings negotiation.

Lista de autores

Giacomone, Belén, Beltrán-Pellicer, Pablo y Godino, Juan D.

Fecha

2019

Autores

Descripción

In this study we analyze the generalization levels shown by eight 4th grade Spanish students while working, during an interview, on a task based on the functional relationship x+2. The task had an inductive structure and asked about the relation between the hours of stay of a car in a parking lot and the money to be paid. At the same time we study how the stimuli made by the interviewer (e.g. suggest, summarize information, redirect, etc.) influence the manifestation of generalizations.

Lista de autores

Ureña, Jason, Molina, Marta y Ramírez, Rafael

Fecha

2018

Autores

Descripción

In this paper we present an analysis of the inductive reasoning of twelve secondary students in a mathematical problem-solving context. Students were proposed to justify what is the result of adding two even numbers. Starting from the theoretical framework, which is based on Pólya’s stages of inductive reasoning, and our empirical work, we created a category system that allowed us to make a qualitative data analysis. We show in this paper some of the results obtained in a previous study.

Lista de autores

Cañadas, María C. y Castro, Encarnación

Fecha

2005

Autores

Descripción

In this paper we present different ways used by Secondary students to generalize when they try to solve problems involving sequences. 359 Spanish students solved generalization problems in a written test. These problems were posed through particular terms expressed in different representations. We present examples that illustrate different ways of achieving various types of generalization and how students express generalization. We identify graphical representation of generalization as a useful tool of getting other ways of expressing generalization, and we analyze its connection with other ways of expressing it.

Lista de autores

Cañadas, María C., Castro, Encarnación y Castro, Enrique

Fecha

2011

Autores