Teaching and Learning Authentic Mathematics: The Case of Proving

Stylianides, Andreas J.; Komatsu, Kotaro; Weber, Keith; Stylianides, Gabriel J.

doi:10.1007/978-3-030-44982-7_9-1

Cited by 7 publications

(10 citation statements)

References 64 publications

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“…Pese a que el concepto de demostración es imprescindible para la disciplina matemática y para el aprendizaje por parte de los estudiantes, es considerado un concepto difícil de enseñar y de aprender en los diferentes niveles educativos (Montoro, 2007;Selden y Selden, 2008; G. J. Stylianides y Stylianides, 2017; A. J. Stylianides et al, 2022). En nuestra investigación partimos de un problema recurrente vinculado a las dificultades que manifiestan estudiantes que ingresan a la universidad en relación con la posibilidad de validar proposiciones matemáticas y, en particular, de comprender y desarrollar demostraciones (Milanesio et al, 2023;Peparelli et al, 2011).…”

Section: La Complejidad Ontosemiótica De Demostraciones Matemáticas Q...unclassified

“…Sería de gran interés poder extender este estudio a otras universidades para realizar un análisis más exhaustivo sobre el tipo de prácticas de validación que se llevan a cabo en distintos contextos. Continuamos nuestra línea de investigación en la búsqueda continua de mejoras para los procesos de enseñanza y aprendizaje de la demostración a partir de la construcción de propuestas que lo posibiliten (Lew y Mejía Ramos, 2019;A. J. Stylianides et al, 2022).…”

Section: Conclusiones De Los Análisisunclassified

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La complejidad ontosemiótica de demostraciones matemáticas que se proponen en la entrada a la universidad

Milanesio,

Markiewicz

2024

Rev. Educ. Mat.

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En este trabajo se abordan aspectos vinculados a la validación de proposiciones matemáticas en la entrada a la universidad. A partir de las dificultades que muestran estudiantes ingresantes para validar deductivamente, realizamos una selección de las primeras prácticas de validación que se presentan en los materiales de trabajo de asignaturas del primer año de la carrera de grado Profesorado en Matemática. Escogimos tres demostraciones, representativas del tipo de prácticas de validación que se promueve en dichos materiales, y las analizamos utilizando herramientas del Enfoque ontosemiótico del conocimiento y la instrucción matemáticos. Esto nos permitió develar la complejidad ontosemiótica de las demostraciones pretendidas y prever conflictos semióticos potenciales que pueden explicar las dificultades de los estudiantes en la comprensión y la realización de las mismas.

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Section: La Complejidad Ontosemiótica De Demostraciones Matemáticas Q...unclassified

Section: Conclusiones De Los Análisisunclassified

La complejidad ontosemiótica de demostraciones matemáticas que se proponen en la entrada a la universidad

Milanesio,

Markiewicz

2024

Rev. Educ. Mat.

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“…The literature about mathematical proof has devoted attention to several topics, some of them focusing on the students and some others focusing on the teachers. In what concerns teachers, the research has focused on ways of addressing proof in the classroom and on the teachers' knowledge and professional development (Stylianides et al, 2016(Stylianides et al, , 2017. Nevertheless, and besides all the interest in different topics related to proof and its teaching and learning, not much attention has been given to proof in a context of technology integration.…”

Section: Mathematical Proofmentioning

confidence: 99%

The impact of teachers' knowledge on the connection between technology supported exploration and mathematical proof

Rocha

2023

EUR J SCI MATH ED

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Technology is recognized for its potential to implement exploration tasks. The ease and speed with which it becomes possible to observe many cases of a situation, allows the development of conjectures and brings conviction about their veracity. Mathematical proof, assumed as the essence of Mathematics, tends to appear to the students as something dispensable. Based on KTMT – Knowledge for Teaching Mathematics with Technology model, this study intends to understand the impact of the teachers’ knowledge on mathematical proof in a context of technology integration. The study adopts a qualitative and interpretative methodology, based on case study, analyzing the practice of one teacher. The conclusions emphasize the relevance of the teacher’s MTK – Mathematics and Technology Knowledge, and TLTK – Teaching and Learning and Technology Knowledge. The teacher's MTK guides her decisions, leading her to focus on helping students understand the meaning of conjecture and proof, valuing, at the same time, the relevance of algebraic manipulations. However, the teacher’s TLTK guides her practice, where the knowledge about the students is determinant. The study provides evidence about the difficulty of articulating proof and technology, but it also clarifies the relevance of this articulation and of how the teacher’s KTMT can impact the teacher’s decisions.

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“…The concept of proof is at the core of every undergraduate mathematics curriculum, but it continues to be a difficult concept for university students to understand and for university instructors to teach. Prior studies at various levels of education have contributed useful research knowledge about the nature and sources of students' difficulties with proof, but on the whole less attention has been paid to the development of effective teaching practices to enhance students' learning of proof (for a review, see Stylianides, Stylianides, & Weber, 2017). This is especially problematic at the undergraduate level where there are relatively fewer studies than at the school level that documented promising or potentially effective teaching practices.…”

Section: Introductionmentioning

confidence: 99%

Demystifying Proofs Through Structured Interaction: A Case Study of One Instructor’s Teaching in an Undergraduate Analysis Course

Narain¹,

Stylianides²

2020

JERM

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The concept of proof is central to every undergraduate mathematics curriculum, but it is also a difficult concept for university students to understand and for university instructors to teach. Prior studies have contributed useful research knowledge about the nature and sources of undergraduate students' difficulties with proof, but they have paid less attention to the development of effective instructional practices to enhance student learning of proof. As a step towards this direction, this paper makes a contribution to the limited body of case studies of promising or potentially effective teaching practices in undergraduate mathematics by reporting a case study of an instructor's teaching, locally characterized as "effective," in an undergraduate analysis course at a leading Indian university. The instructor did not deviate from the so called "Definition-Theorem-Proof" (DTP) format that is followed in most prooforiented university mathematics courses, but her teaching presented a set of features that, collectively, form a rather innovative teaching practice at the undergraduate level. Specifically, our case study shows that, even in the context of a rather crowded university classroom, proof can be demystified for students through structured interaction between the instructor and the students, that is, an interactive, conversational style of proof instruction invoking the participation of students. This is based on a solid foundation in symbolic logic at the very outset and on a significant time investment in definitions being explained in depth using informal language, visual aids, and real-life analogies. In addition to contributing to existing images of potentially effective teaching practices in undergraduate mathematics, this paper draws attention to the Indian educational context that has had little representation in international forums of mathematics education research thus far. ' This is obviously equivalent to |𝑎 " -a|< ! '* and |𝑏 " -b| < ! '+ Now as <𝑎 " > → 𝑎, so corr. to ! '* > 0, ∃ 𝑛 & 𝜖𝑵 such that |𝑎 " -a|< ! '* ∀ 𝑛 ≥ 𝑛 & Also as < 𝑏 " > → b, so corr. to ! '+ >0, ∃ 𝑛 ' 𝜖𝑵 such that |𝑏 " − 𝑏| < ! '+ ∀ 𝑛 ≥ 𝑛 '

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Teaching and Learning Authentic Mathematics: The Case of Proving

Cited by 7 publications

References 64 publications

La complejidad ontosemiótica de demostraciones matemáticas que se proponen en la entrada a la universidad

La complejidad ontosemiótica de demostraciones matemáticas que se proponen en la entrada a la universidad

The impact of teachers' knowledge on the connection between technology supported exploration and mathematical proof

Demystifying Proofs Through Structured Interaction: A Case Study of One Instructor’s Teaching in an Undergraduate Analysis Course

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