The historical roots of the limit notion: Cognitive development and the development of representation registers

Bagni, Giorgio T.

doi:10.1080/14926150509556675

Cited by 14 publications

(6 citation statements)

References 27 publications

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“…In the same vein, Kidron and Tall (2015) argued for more consideration, in teaching Calculus, of the distinction between potential and actual infinity of the limit process. Assuming that these parallels should not be stated uncritically, Bagni (2005b) went further, asking for the investigation of the historical development of representation registers. For students, limit is often seen in terms of the potential infinity of the on-going process rather than the fixed limit that can be calculated to any desired accuracy.…”

Section: Potential And/or Actual Infinity: Beyond the Status Quomentioning

confidence: 99%

Teaching and Learning of Calculus

Bressoud

Ghedamsi²,

Martínez-Luaces

et al. 2016

ICME-13 Topical Surveys

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Section: Potential And/or Actual Infinity: Beyond the Status Quomentioning

confidence: 99%

Teaching and Learning of Calculus

Bressoud

Ghedamsi²,

Martínez-Luaces

et al. 2016

ICME-13 Topical Surveys

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“…Apart from this, research outputs on overcoming such obstacles were very scant, if any, and were only theoretical considerations driven mainly by cognitive constructivism. For instance, Cottrill et al [7] utilized "APOS theory" coupled with genetic decomposition (a seven step model) to investigate the conception of limit; Bagni [18] explored the notion of limit using "Register semiotic representations"; and Juter [19] explained students' concept growth using "Three worlds of mathematics" coupled with "Concept image and concept definition". Nevertheless, endeavors to understand epsilon-delta form of defining and proving the limit concept did not make a significant contribution to alleviating the perennial problems in mathematics education, and students are still struggling to learn abstract mathematical concepts.…”

Section: Introductionmentioning

confidence: 99%

Implementing GeoGebra integrated with multi-teaching approaches guided by the APOS theory to enhance students’ conceptual understanding of limit in Ethiopian Universities

Baye

Ayele

Wondimuneh

2021

Heliyon

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The notion of limit is one of the fundamental concepts which underpins advanced calculus of one or more variables in the field of analysis. However, understanding the concept of limit has been an impenetrable problem for many students in Ethiopian Universities. Only very few literatures were documented focusing on overcoming the difficulty of learning the concept of limit. For this reason, the overarching aim of the present study is to enhance students' conceptual understanding of limit by empowering their visualization skills using GeoGebra integrated with multi-teaching approaches. The study employed mixed methods experimental (intervention) design within an APOS paradigm. Both qualitative and quantitative data were collected. Qualitative data was collected using students' reflections and interviews, whereas quantitative data was collected through pretest and posttest using diagnostic tests. The results of the qualitative data analysis revealed that the learning milieu created a positive impact on students' understanding of the concept of limit. Additionally, students provided coherent and viable reasons while making mental constructions and their coordination in the learning process based on the genetic decomposition grounded in APOS theory. Furthermore, the results of the quantitative (posttest) data analysis proved that students' mean scores on conceptual understanding of limit in the experimental group was significantly better than those in the control group. Thus, it could be possible to conclude that students' conceptual understanding of limit is improved using GeoGebra integrated with multi-teaching approaches within an APOS paradigm. The findings open a great opportunity to suggest technology integrated mathematics curriculums for the teaching and learning of mathematics.

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“…Las tendencias actuales en Educación Matemática atribuyen importancia y dedican especial atención a la perspectiva histórica-epistemológica (Anacona, 2003;Godino, 2003Godino, , 2010 como un medio de comprensión de los distintos procesos que gestaron el nacimiento y desarrollo de diferentes nociones y objetos matemáticos, ya que la matemática es una producción humana situada en épocas y contextos determinados e influenciada por las respectivas culturas. Algunas obras que se refieren al desarrollo histórico-epistemológico del cálculo (Bagni, 2005;Ferrante, 2009;Molfino y Buendía, 2010), exponen que hubo mezcla de ideas estáticas y dinámicas para conceptualizar algunos objetos matemáticos.…”

Section: Introductionunclassified

Manifestaciones Emergentes del Pensamiento Variacional en Estudiantes de Cálculo Inicial

Cabezas

Mendoza

2016

Form. Univ.

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En este trabajo se presentan los resultados obtenidos mediante el análisis didáctico de producciones estudiantiles, relativas al pensamiento variacional, usando el enfoque onto-semiótico del conocimiento y la instrucción matemática. La investigación persiguió como objetivos la caracterización y categorización de las producciones identificando particularidades de las mismas, y que dieran cuenta de las diversas formas de manifestación del pensamiento variacional. La investigación se realizó en un curso regular de cálculo inicial de ingeniería en la Universidad Católica del Maule, en Chile. Se analizaron las producciones escritas de los estudiantes en una prueba inicial. Esto se hizo generando categorías de manifestaciones de pensamiento variacional, de acuerdo a un primer nivel de análisis provisto por el enfoque onto-semiótico. Los resultados de esta investigación evidenciaron que gran parte de los estudiantes hace uso de ciertos aspectos del pensamiento variacional.

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The historical roots of the limit notion: Cognitive development and the development of representation registers

Cited by 14 publications

References 27 publications

Teaching and Learning of Calculus

Teaching and Learning of Calculus

Implementing GeoGebra integrated with multi-teaching approaches guided by the APOS theory to enhance students’ conceptual understanding of limit in Ethiopian Universities

Manifestaciones Emergentes del Pensamiento Variacional en Estudiantes de Cálculo Inicial

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