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.

scholarly journals Ethnomathematics and indigenous teacher education: Waka migrations

Revemop ◽  
2020 ◽  
Vol 2 ◽  
pp. e202008
Author(s):  
Tony Trinick ◽  
Tamsin Tamsin Meaney
Keyword(s):  
Teacher Education ◽  
Preservice Teacher ◽  
Indigenous Peoples ◽  
Mathematical Knowledge ◽  
Preservice Teacher Education ◽  
Traditional Methods ◽  
Mathematical Practices ◽  
Language And Culture ◽  
Primary Identification

In order to assist Indigenous peoples to revive their language and culture, teachers need strategies to enhance both cultural and mathematical knowledge for students. This paper presents findings from a project in which pre-service teachers investigated ethnomathematical practices using the context of ancestral ocean voyages by canoes. This context was chosen because a primary identification marker for Māori are their ancestral canoes. The results indicated that these pre-service teachers did not generally associate these ancestral voyages with mathematical practices, indicating that more work is needed to increase their understandings of ethnomathematics. Their understandings about the knowledge and practices connected to traditional methods of navigation were disrupted by myths perpetuated by European colonists. Despite this, a renaissance in canoe building and interest in traditional navigation practices provided the pre-service teachers with valuable information.Keywords: Traditional navigation. Ethnomathematics. Preservice teacher education. Cultural symmetry.Etnomatemáticas y formación de professores indígenas: migraciones de canoas WakaPara ayudar a los pueblos indígenas a revivir su idioma y su cultura, los maestros necesitan estrategias para mejorar el conocimiento cultural y matemático de los estudiantes. Este artículo presenta los hallazgos de un proyecto en el cual los maestros de pre-servicio investigaron las prácticas etnomatemáticas utilizando el contexto de viajes oceánicos ancestrales en canoas. Este contexto fue elegido porque un marcador de identificación principal para los Māori son sus canoas ancestrales. Los resultados indicaron que estos maestros de pre-servicio generalmente no asociaron estos viajes ancestrales con las prácticas matemáticas, lo que indica que se necesita más trabajo para aumentar su comprensión de las etnomatemáticas. Su comprensión sobre el conocimiento y las prácticas relacionadas con los métodos tradicionales de navegación fueron interrumpidos por los mitos perpetuados por los colonos europeos. A pesar de esto, un renacimiento en la construcción de canoas y el interés en las prácticas tradicionales de navegación proporcionaron a los maestros de pre-servicio informaciones valiosas.Palabras clave: Navegaciones tradicionales. Etnomatemáticas. Formación de profesores. Simetría cultural.Etnomatemática e formação de professores indígenas: migrações de canoas WakaBuscando auxiliar os povos indígenas a reavivar a sua língua e cultura, os professores precisam utilizar estratégias para aprimorar os conhecimentos culturais e matemáticos dos alunos. Esse trabalho apresenta os resultados de um projeto em que os professores em formação docente investigaram as práticas etnomatemáticas utilizando o contexto de viagens oceânicas ancestrais por canoas. Essa conjuntura foi escolhida porque uma das principais marcas identitárias dos Māori são as suas canoas ancestrais. Os resultados indicaram que, geralmente, esses professores não associaram essas jornadas ancestrais com as práticas matemáticas, sinalizando ser necessário um maior treinamento para aumentar o seu entendimento da etnomatemática. A compreensão sobre os conhecimentos e as práticas ligadas aos métodos tradicionais de navegação foram prejudicados por mitos perpetuados pelos colonizadores europeus. Contudo, um ressurgimento da construção de canoas e do interesse pelas práticas tradicionais de navegação propiciou valiosas informações para os professores em formação docente.Palavras-chave: Navegações tradicionais. Etnomatemática. Formação de professores. Simetria cultural.

scholarly journals Exploring Mathematical Concepts and Philosophical Values in Jember Batik

Abjadia ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 144-159
Author(s):  
Devita Amalia ◽  
Dwi Noviani ◽  
M. Fadil Djamali ◽  
Imam Rofiki
Keyword(s):  
Data Collection ◽  
Mathematical Knowledge ◽  
Geometric Transformation ◽  
Mathematical Concepts ◽  
Design Data ◽  
Mathematical Practices ◽  
Different Cultures

Ethnomathematics are different ways of doing mathematics taking into account the academic mathematical knowledge developed by different sectors of society as well as taking into account the different modes in which different cultures negotiate their mathematical practices (ways of grouping, counting, measuring, designing tools, or playing). Based on this research, this study aims to describe the results of ethnomathematics exploration in Jember batik motifs. The method of analysis used in this research was a qualitative approac with an ethnographic design. Data collection techniques were observation, documentation, and interviews. This research was conducted at Rumah Batik Rolla Jember and Rezti'z Batik Tegalsari Ambulu Jember. The research was conducted for one week. The results of this study indicate that the ethnomathematics in the Jember batik motif has a philosophical value that describes the natural wealth of Jember Regency in each of its motifs, and there are mathematical concepts in the form of geometric transformation concepts (reflection, translation, rotation, and dilation) along with the concept of number patterns.

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 An Ethnomathematical Perspective of STEM Education in a Glocalized World

2021 ◽  
Vol 35 (70) ◽  
pp. 840-876
Author(s):  
Milton Rosa ◽  
Daniel Clark Orey
Keyword(s):  
Stem Education ◽  
Mathematical Knowledge ◽  
Transformative Pedagogy ◽  
Mathematical Practices ◽  
Making Sense ◽  
Pedagogical Action ◽  
Science Technology ◽  
Modelling Problem ◽  
And Mathematics ◽  
School Curricula

Abstract An Ethnomathematics-based curriculum helps students demonstrate consistent mathematical processes as they reason, solve problems, communicate ideas, and choose appropriate representations through the development of daily mathematical practices. As well, it recognizes connections with Science, Technology, Engineering, and Mathematics (STEM) disciplines. Our pedagogical work, in relation to STEM Education, is based on the Trivium Curriculum for mathematics and ethnomodelling, which provides communicative, analytical, material, and technological tools to the development of emic, etic, and dialogic approaches that are necessary for the elaboration of the school curricula. STEM Education facilitates pedagogical action that connects ethnomathematics; mathematical modelling, problem-solving, critical judgment, and making sense of mathematical and non-mathematical environments, which involves distinct ways of thinking, reasoning, and developing mathematical knowledge in distinct sociocultural contexts. The ethnomathematical perspective for STEM Education proposed here provides a transformative pedagogy that exposes its power to transform students into critical and reflective citizens in order to enable them to transform society in a glocalized world.

On Knowledge and Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Cognitive Abilities ◽  
Historical Development ◽  
Mathematical Knowledge ◽  
General Scheme ◽  
Philosophy Of Mathematics ◽  
Scientific Practices ◽  
Advanced Mathematics ◽  
Mathematical Practices ◽  
Everyday Practices ◽  
Different Levels

This book proposes a novel analysis of mathematical knowledge from a practice-oriented standpoint and within the context of the philosophy of mathematics. The approach it is advocating is a cognitive, pragmatist, historical one. It emphasizes a view of mathematics as knowledge produced by human agents, on the basis of their biological and cognitive abilities, the latter being mediated by culture. It also gives importance to the practical roots of mathematics—that is, its roots in everyday practices, technical practices, mathematical practices themselves, and scientific practices. Finally, the approach stresses the importance of analyzing mathematics' historical development, and of accepting the presence of hypothetical elements in advanced mathematics. The book's main thesis is that several different levels of knowledge and practice are coexistent, and that their links and interplay are crucial to mathematical knowledge. This chapter offers some remarks that may help readers locate the book's arguments within a general scheme.

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 The Wittgensteinian Perspective and Ethnomathematics: An Analysis of Language Games and the Rules Governing their Uses in Certain Work Activities

2019 ◽  
Vol 21 (5) ◽  
pp. 28-43
Author(s):  
Luis Tiago Osterberg ◽  
Isabel Cristina Machado de Lara
Keyword(s):  
Mathematical Knowledge ◽  
Research Method ◽  
School Mathematics ◽  
Language Games ◽  
Mathematical Concepts ◽  
Mathematical Practices ◽  
Work Activities

This work, adopting a Wittgensteinian perspective, aims to analyze the language games that involve mathematical concepts present in certain work activities, as well as the rules of use of such concepts, comparing them with the existing rules in School Mathematics. The studies analyzed used Ethnomathematics as a research method to understand the generation, organization and dissemination of mathematical knowledge in certain professions, in particular carpenters, fishermen, farmers and artisans. In considering the language games present in the mathematical practices existing in these professions, it is possible to show that in some games rules are presented that have strong family similarities to the games that make up the School Mathematics when they need a written mathematics, however, the expression of language games orally assume different meanings for terms present in both grammars. In addition, it presents examples of the use of mathematical knowledge without the formalism and rigor present in the language games of School Mathematics. It is a way of doing mathematics generated by another grammar that uses other rules, in this case estimation and rounding, a type of rationality distinct from that which constitutes School Mathematics, but which is effective in that form of use.

Situating race: the case for examining Black children’s informal mathematics learning outside of schools

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jahneille Cunningham ◽  
Kimberley Gomez
Keyword(s):  
Mathematics Education ◽  
Learning Theory ◽  
Situated Learning ◽  
Students Of Color ◽  
Mathematical Knowledge ◽  
Black Children ◽  
Community Based ◽  
Mathematical Practices ◽  
Content Type ◽  
Mathematics Classrooms

Purpose The purpose of this paper is to highlight the ways racialization in K-12 mathematics classrooms has narrowed the understanding of mathematical learning for Black children. Design/methodology/approach Drawing on situated learning theory and funds of knowledge, the authors argue that the social learning context of mathematics classrooms has limited the understanding of what Black children are capable of mathematically. The authors suggest that as a community of practice, mathematics classrooms may be marginalizing Black children, as well as other students of color, by devaluing their community-based knowledge and ways of knowing. Findings The extant literature portrays Black children as struggling in mathematics; however, this research is overwhelmingly conducted based on school performance measures. Yet, if one looks beyond the classroom to Black children's homes and communities, a plethora of mathematical knowledge tied to cultural and community practices may be found. As such, Black children who struggle in mathematics classroom may be experiencing misalignment across contexts, rather than a lack of mathematical knowledge altogether. Practical implications This paper has implications for classroom practice, particularly teacher ideologies pertaining to community-based knowledge. The authors urge mathematics education researchers and practitioners to look beyond the classroom, as community-based mathematical practices may provide more insight into students’ mathematical capabilities. These implications are particularly important for educating students of color, who often experience a subpar classroom education. Originality/value In this paper, the authors provide a critical lens to situated learning theory, pushing mathematics education research to examine the underexplored topic of Black children's out-of-school mathematical practices.

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