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Asiala, Mark; Kleiman, Jennifer; Brown, A. H. F.; Mathews, David

doi:10.1023/a:1009738109343

Cited by 10 publications

(2 citation statements)

References 16 publications

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“…La teoría apoe proporciona una base teórica para analizar la forma en la que se construyen los conceptos matemáticos para estudiar cómo evolucionan las construcciones de los alumnos y, al mismo tiempo, permite diseñar estrategias didácticas para ayudar a los alumnos a hacer las construcciones necesarias para que esta evolución tenga lugar y se logre un aprendizaje de los conceptos matemáticos más significativos (Asiala et al, 1998;Dubinsky y McDonald, 2001). Los componentes esenciales de la teoría apoe son: acciones, procesos, objetos y esquemas, además de la abstracción reflexiva que se considera como mecanismo de construcción; este mecanismo da lugar a los procesos de construcción de conocimiento, como son la interiorización, la generalización, la coordinación, la encapsulación y la reversión.…”

Section: Marco Teóricounclassified

Conteo: una propuesta didáctica y su análisis

Salgado,

Trigueros

2009

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conteo: una propuesta didáctica y su análisis Hilda salgado y María trigueros Resumen: En el aprendizaje de las matemáticas se suelen observar problemas debido a que los conceptos involucrados resultan a menudo complejos por su alto nivel de abstracción. Se han detectado problemas en el aprendizaje de los conceptos asociados al tema de conteo. Dos conceptos básicos de conteo son la ordenación y la combinación.En este trabajo se diseña y analiza una propuesta didáctica para el aprendizaje de las ordenaciones y combinaciones apoyada en la teoría apoe. Se presenta dicho análisis y los resultados obtenidos a partir del trabajo de los estudiantes con la propuesta realizada.Palabras clave: combinatoria, teoría apoe, experimento en aula, ordenaciones, combinaciones, álgebra.counting: analysis of a didactic approach abstract: Learning mathematics often causes problems to students. Given the complexity of the concepts involved and their high level of abstraction, their learning becomes a difficult task. Problems arise in the learning of the concepts of counting and in the acquisition of the techniques of counting. Two basic concepts in counting are permutations and combinations.This work considers a didactical approach for the learning of permutations and combinations based in apos Theory. The analysis and the results from the work done by the students are presented and discussed.

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Section: Marco Teóricounclassified

Conteo: una propuesta didáctica y su análisis

Salgado,

Trigueros

2009

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“…Dubinsky et al presented example students who never wrote out all of the elements of cosets and worked entirely with their representatives. Dubinsky and his colleagues also provided this type of genetic breakdown for binary operation (Brown, DeVries, Dubinsky, & Thomas, 1997), normality (Asiala, Dubinsky, Matthews, Morics, & Oktac, 1997), coset multiplication (Asiala et al, 1997), permutations (Asiala, Kleiman, Brown, & Matthews, 1998), and symmetries (Asiala et al, 1998). The researchers worked to validate the framework through analyzing student work on exams and interviewing students.…”

Section: Dubinsky Et Al Summarizementioning

confidence: 99%

The Design and Validation of a Group Theory Concept Inventory

Melhuish¹

2000

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Within undergraduate mathematics education, there are few validated instruments designed for large-scale usage. The Group Concept Inventory (GCI) was created as an instrument to evaluate student conceptions related to introductory group theory topics. The inventory was created in three phases: domain analysis, question creation, and field-testing. The domain analysis phase included using an expert protocol to arrive at the topics to be assessed, analyzing curriculum, and reviewing literature. From this analysis, items were created, evaluated, and field-tested. First, 383 students answered open-ended versions of the question set. The questions were converted to multiple-choice format from these responses and disseminated to an additional 476 students over two rounds.Through follow-up interviews intended for validation, and test analysis processes, the questions were refined to best target conceptions and strengthen validity measures. The GCI consists of seventeen questions, each targeting a different concept in introductory group theory. The results from this study are broken into three papers. The first paper reports on the methodology for creating the GCI with the goal of providing a model for building valid concept inventories. The second paper provides replication results and critiques of previous studies by leveraging three GCI questions (on cyclic groups, subgroups, and isomorphism) that have been adapted from prior studies. The final paper introduces the GCI for use by instructors and mathematics departments with emphasis on how it can be leveraged to investigate their students' understanding of group theory concepts.Through careful creation and extensive field-testing, the GCI has been shown to ii be a meaningful instrument with powerful ability to explore student understanding around group theory concepts at the large-scale.iii Dedication To my parents for teaching me to have a strong work ethic, to live life with kindness, and to pursue a career that truly fulfills you.iv Acknowledgements

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