scholarly journals Algebraization Levels in the Study of Probability

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 91
Author(s):  
María Burgos ◽  
Carmen Batanero ◽  
Juan D. Godino
Keyword(s):  
Mathematical Activity ◽  
Mathematical Practices ◽  
Educational Levels ◽  
Semiotic Approach ◽  
Mathematical Formalization ◽  
Selection Of

The paper aims to analyze how the different degrees of mathematical formalization can be worked in the study of probability at non-university educational levels. The model of algebraization levels for mathematical practices based on the onto-semiotic approach is applied to identify the different objects and processes involved in the resolution of a selection of probabilistic problems. As a result, we describe the possible progression from arithmetic and proto-algebraic levels of mathematical activity to higher levels of algebraization and formalization in the study of probability. The method of analysis developed can help to establish connections between intuitive/informal and progressively more formal approaches in the study of mathematics.

scholarly journals Index Kultural pada Penerjemahan Novel Eclipse: Sebuah Pendekata Semiotik

2019 ◽  
Vol 25 (2) ◽  
pp. 323-342
Author(s):  
Tri Pujiati
Keyword(s):  
Qualitative Method ◽  
The Other ◽  
Target Language ◽  
Source Language ◽  
Semiotic Approach ◽  
The Right ◽  
The Impact ◽  
Bahasa Indonesia ◽  
Selection Of ◽  
Stephenie Meyer

Budaya merupakan salah satu tantangan utama yang ditemukan dalam menerjemahkan bahasa Inggris ke dalam bahasa Indonesia. Penelitian ini bertujuan untuk mengetahui dampak indeks budaya terhadap terjemahan Novel Eclipse karya Stephenie Meyer. Penelitian ini menggunakan metode kualitatif dan pendekatan semiotik dalam penerjemahan. Terdapat 30 data yang diambil dari novel Eclipse dan terjemahannya dalam bahasa Indonesia dengan teknik. Hasil penelitian ini menunjukkan bahwa (1) indeks budaya yang digunakan oleh penerjemah sebagai cara untuk mempertahankan budaya sumber itu sendiri memiliki dampak besar pada bahasa target. Ada beberapa terjemahan yang tidak dapat diterima dalam bahasa target karena maknanya tidak tersedia dalam bahasa Indonesia, indeks budaya lainnya diterima dalam bahasa target karena ada persamaan arti yang sesuai dengan bahasa sumber; (2) sebagai cara untuk menyelesaikan masalah dalam menerjemahkan budaya, penerjemah menggunakan prosedur transferensi dan naturalisasi. Terdapat 87% menggunakan prosedur transferensi dan 13% menggunakan naturalisasi. Simpulan umum dari penelitian ini menunjukkan bahwa beberapa strategi penerjemahan tersebut tidak akurat di dalam bahasa sasaran sehingga penerjemah perlu mempertimbangkan pemilihan prosedur yang tepat sehingga terjemahan yang dihasilkan dapat diterima dalam bahasa sasaran. Culture is one of the main important challenges found in translating English into Indonesian language. This research aims to know the impact of cultural index on translation of Eclipse Novel by Stephenie Meyer. This research uses qualitative method and semiotic approach in translation. There are 30 data taken from Eclipse novel and its translation in Indonesian language. The results of this study show that (1) cultural index which used by translator as a way to defend the source culture and source language (henceforth SL) itself has a great impact on target language (henceforth TL). There are some translations which cannot be accepted in target language because the meaning is not available in Indonesian language, the other cultural index are accepted in TL as there are equivalence meaning that correspondence the SL; (2) as a way to solve the problem in translating culture, the translator uses transference and naturalization procedure. There are about 87% used transference procedure and 13% used naturalization. The general conclusion of this study shows that some of these strategies are not accurate in the target language so translators need to consider the selection of the right procedure so that the resulting translation can be accepted in the target language.

scholarly journals Norms That Regulate the Theorem Construction Process in an Inquiry Classroom of 3D Geometry: Teacher’s Management to Promote Them

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2296
Author(s):  
Oscar Molina ◽  
Vicenç Font ◽  
Luis Pino-Fan
Keyword(s):  
Mathematics Teacher ◽  
Three Dimensional ◽  
Construction Process ◽  
Mathematical Practices ◽  
3D Geometry ◽  
Semiotic Approach ◽  
Different Types ◽  
Whole Class ◽  
Toulmin’S Model

This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class excerpts in which students address tasks that require formulating conjectures, that emerge as a solution to a problem and proving such conjectures, and the teacher leads whole-class activities where students’ productions are exposed. For this, we used elements of the didactical analysis proposed by the onto-semiotic approach and Toulmin’s model for argumentation. The teacher’s professional actions that promoted reiterative actions in students’ mathematical practices were identified; we illustrate how these professional actions impelled students’ actions to become norms concerning issues about the legitimacy of different types of arguments (e.g., analogical and abductive) in the theorem construction process.

scholarly journals Epistemic Criteria for Designing Limit Tasks on a Real Variable Function

2021 ◽  
Vol 35 (69) ◽  
pp. 179-205
Author(s):  
Daniela Araya Bastias ◽  
Luis R. Pino-Fan ◽  
Iván G. Medrano ◽  
Walter F. Castro
Keyword(s):  
Mathematical Knowledge ◽  
Real Variable ◽  
Regulatory Elements ◽  
Theoretical Framework ◽  
Mathematical Practices ◽  
Variable Function ◽  
Semiotic Approach ◽  
Epistemic Criteria

Abstract This article aims at presenting the results of a historical-epistemological study conducted to identify criteria for designing tasks that promote the understanding of the limit notion on a real variable function. As a theoretical framework, we used the Onto-Semiotic Approach (OSA) to mathematical knowledge and instruction, to identify the regulatory elements of mathematical practices developed throughout history, and that gave way to the emergence, evolution, and formalization of limit. As a result, we present a proposal of criteria that summarizes fundamental epistemic aspects, which could be considered when designing tasks that allow the promotion of each of the six meanings identified for the limit notion. The criteria presented allow us to highlight not only the mathematical complexity underlying the study of limit on a real variable function but also the richness of meanings that could be developed to help understand this notion.

The Web of Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Current Trend ◽  
Mathematical Practice ◽  
Mathematical Activity ◽  
Scientific Practices ◽  
General Introduction ◽  
Philosophical Work ◽  
Mathematical Practices ◽  
David Hilbert ◽  
Different Levels ◽  
The Web

This chapter is a general introduction to the current trend of studies of mathematical practice, with particular emphasis on historical and philosophical work. It offers a preliminary explanation of the notion of mathematical practice, first by considering the work of historians and philosophers on mathematical practices, from Archimedes and David Hilbert to Jens Høyrup, Penelope Maddy, Marcus Giaquinto, and Philip S. Kitcher. The chapter then characterizes the notion of mathematical practice by successively proposing several constraints. It argues that several different levels of practice and knowledge are coexistent and that their interrelationships are crucial to mathematical knowledge. It shows how the scheme of a web of interrelated practices—counting practices, measuring practices, technical practices, scientific practices—with their systematic links acting as constraint and guide, can be applied in the analysis of very different levels of mathematical activity.

Putting Technology in Its Place

2020 ◽  
Vol 113 (2) ◽  
pp. 140-146
Author(s):  
Jason Knight Belnap ◽  
Amy Parrott
Keyword(s):  
Mathematical Tasks ◽  
Mathematical Activity ◽  
Mathematical Practices

Technology is used effectively when it enables students to engage in authentic mathematical activity. Using four mathematical tasks, we discuss how technology, carefully designed tasks, and orchestrated discussions can both reveal our students' mathematical practices and provide opportunities to shape those practices.

scholarly journals Connecting expectations of Te Whāriki and The New Zealand Curriculum: Examples of mathematical practices

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Jane McChesney ◽  
Margaret Carr
Keyword(s):  
Early Childhood ◽  
New Zealand ◽  
Mathematics Curriculum ◽  
First Year ◽  
Mathematical Activity ◽  
Early Childhood Mathematics ◽  
Conceptual Tool ◽  
Mathematical Practices ◽  
Childhood Education ◽  
Te Whāriki

The first year of primary school aims to be closely connected with early childhood education, yet this is often invisible in the curriculum of specific subjects. This paper sets out an approach that uses mathematical practices as a curriculum tool that reconceptualises school mathematics. Using the early childhood mathematics framework of Te Kākano, the strands of mathematical practices are important descriptors of mathematical activity for children. We describe examples of mathematical learning from both early childhood and the first year of school, and make a case for using mathematical practices as a conceptual tool for designing a mathematics curriculum in the first years of school.

scholarly journals Cognitive Analysis on Prospective Mathematics Teachers’ Reasoning Using Area and Tree Diagrams

2019 ◽  
Vol 27 (2) ◽  
Author(s):  
Belén Giacomone ◽  
Pablo Beltrán-Pellicer ◽  
Juan D. Godino
Keyword(s):  
Primary Education ◽  
Prospective Teachers ◽  
Mathematical Knowledge ◽  
Mathematical Activity ◽  
Education Students ◽  
Cognitive Analysis ◽  
Comprehensive Description ◽  
Semiotic Approach ◽  
Tree Diagram ◽  
Mathematics Problem

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.

Les pratiques info-documentaires des élèves sur Internet au croisement de trois espaces : la classe, le C.D.I. et la maison

2013 ◽  
Author(s):  
Béatrice Micheau
Keyword(s):  
Information Literacy ◽  
School Library ◽  
The Internet ◽  
Semiotic Approach ◽  
Selection Of

Grâce à une approche ethno-sémiotique, nous observons les pratiques info-documentaires des élèves lors de sélection de l’information sur Internet. Ces pratiques sont établies au croisement de trois espaces : la classe, le centre de documentation et d’information (C.D.I.) et la maison. Ces trois espaces sont des espaces d’apprentissage multidimensionnels, souvent tacites et parfois conflictuels, de la maîtrise de l’information.With an ethno-semiotic approach, we observed the pupil’s practices of selection of information on the Internet. These practices are built at the crossing of three places: the classroom, the school library and the home. Because these spaces are places of a multidimensional learning, often tacit and sometimes conflicting, of information literacy.

scholarly journals Meanings that engineering students confer to the antiderivative

2019 ◽  
Vol 13 (2) ◽  
pp. 331-336
Author(s):  
Wilson Gordillo-Thiriat ◽  
Luis Roberto Pino-Fan ◽  
Víctor Larios-Osorio
Keyword(s):  
College Students ◽  
Theoretical Model ◽  
Engineering Students ◽  
Civil Engineering ◽  
Mathematical Activity ◽  
Semiotic Approach ◽  
Mathematics Cognition

In this article, are presented the results of a questionnaire designed to evaluate college students’ understanding of the antiderivative. Specifically, by civil engineering students when answering the questionnaire tasks, in order to identify and characterize the meanings on the antiderivative that are developed by them. In order to analyse the answers given, were used some theoretical and methodological notions provided by the theoretical model known as the Onto-Semiotic Approach (OSA) of mathematics cognition and instruction. The results show the knowledge of antiderivative by the Civil Engineering students. Furthermore, the comparison between the mathematical activity of students provides information that allows concluding that the meanings that they mobilized might be shared among their communities

scholarly journals Intellectual humility in mathematics

Synthese ◽  
2021 ◽  
Author(s):  
Colin Jakob Rittberg
Keyword(s):  
Case Studies ◽  
Virtue Theory ◽  
Philosophical Analysis ◽  
Mathematical Activity ◽  
Intellectual Virtues ◽  
Intellectual Humility ◽  
Mathematical Practices ◽  
The Individual ◽  
Individual Accounts

AbstractIn this paper I explore how intellectual humility manifests in mathematical practices. To do this I employ accounts of this virtue as developed by virtue epistemologists in three case studies of mathematical activity. As a contribution to a Topical Collection on virtue theory of mathematical practices this paper explores in how far existing virtue-theoretic frameworks can be applied to a philosophical analysis of mathematical practices. I argue that the individual accounts of intellectual humility are successful at tracking some manifestations of this virtue in mathematical practices and fail to track others. There are two upshots to this. First, the accounts of the intellectual virtues provided by virtue epistemologists are insightful for the development of a virtue theory of mathematical practices but require adjustments in some cases. Second, the case studies reveal dimensions of intellectual humility virtue epistemologists have thus far overlooked in their theoretical reflections.

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