Conceptions of Proof – In Research and Teaching

Cabassut, Richard; Conner, AnnaMarie; İşçimen, Filyet Aslı; Furinghetti, Fulvia; Jahnke, Hans Niels; Morselli, Francesca

doi:10.1007/978-94-007-2129-6_7

Cited by 12 publications

(18 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…El conocimiento sobre la naturaleza de la demostración matemática: es el conocimiento sobre lo que constituye una demostración matemática, y considera los siguientes subcomponentes: (a) el concepto de demostración matemática, es decir, el conocimiento sobre qué es una demostración matemática y qué significa demostrar algo en las matemáticas (Flores-Medrano, 2015), (b) la validez lógica, que se refiere al conocimiento sobre cómo proceder en la demostración de afirmaciones matemáticas involucrando de forma implícita o explícita las conectivas lógicas (y, o, si-entonces, no, entre otras) y los cuantificadores existencial y universal, además del uso de las reglas de inferencia, de las equivalencias lógicas y de los métodos de demostración matemática (Durand-Guerrier et al, 2012b), y (c) la validez matemática, que se refiere al conocimiento del rigor en la demostración matemática lo que supone el uso correcto de axiomas, hipótesis y definiciones empleadas en las demostraciones (Cabassut, Conner, İşçimen, Furinghetti, Jahnke, y Morselli, 2011).…”

Section: La Demostración En Relación Con El Conocimiento Del Profesor De Matemáticasunclassified

Conocimiento especializado de profesores de matemática en formación inicial sobre aspectos lógicos y sintácticos de la demostración

Carvajal

Martínez

Soto

2020

pna

View full text Add to dashboard Cite

El artículo presenta los resultados de un estudio cualitativo dirigido a caracterizar el conocimiento de futuros profesores de matemáticas en la Universidad Nacional de Costa Rica sobre los aspectos lógicos y sintácticos de la demostración. Se proponen indicadores para caracterizar el conocimiento relacionado con la práctica matemática de la demostración, destacando aspectos lógicos y sintácticos. Se apreció que la mayoría de los sujetos mostraron conocimiento de los aspectos lógicos de la demostración y que los indicadores de análisis propuestos permitieron clasificar la mayor parte de sus respuestas.The specialized knowledge of the prospective teachers of mathematics on the logical and syntactic aspects of the mathematical proofThe article presents the results of a qualitative study that aims to characterize the knowledge of future mathematics professors at the National University of Costa Rica (UNA) on the logical and syntactic aspects of the mathematical proof. Knowledge indicators are proposed to characterize that related to the mathematical proof practice, focusing on the logical and syntactic aspects. It was appreciated that most of the subjects showed knowledge of the logical aspects of the proof and that the proposed analysis indicators allowed to classify most of their responses.doi: 10.30827/pna.v14i2.9363

show abstract

Section: La Demostración En Relación Con El Conocimiento Del Profesor De Matemáticasunclassified

Conocimiento especializado de profesores de matemática en formación inicial sobre aspectos lógicos y sintácticos de la demostración

Carvajal

Martínez

Soto

2020

pna

View full text Add to dashboard Cite

show abstract

“…In mathematics, the discovery and prove of new theorems is at the highest level of research, yet there is no generalized definition accepted within the mathematical community. In general, there are two main conceptualizations, one approaching the realm of logic that considers proofs as a sequence of mathematical propositions and the other close to the practice of mathematicians, where semantic and informal aspects have more relevance, thereby considereing proofs more as arguments to convince experts of the validity of a theorem by emphasizing on the explanation of veracity (Cabassut et al, 2012;Hanna and De Villiers, 2012;Tall et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments

Alfaro-Carvajal¹,

Flores

Valverde-Soto

2022

Uniciencia

View full text Add to dashboard Cite

The objective of this study is to characterize the knowledge of mathematics teachers in initial training (MTITs) at the Universidad Nacional (Costa Rica) on the logic-syntactic and mathematical aspects involved in proving, when evaluating mathematical arguments. The research is positioned in the interpretive paradigm and has a qualitative approach. It consists of two empirical phases: in the first, a questionnaire regarding logic-syntactic aspects was applied to 25 subjects, during the months of September and October 2018 and; in the second phase, a second questionnaire covering mathematical aspects was applied to 19 subjects, during the months of May and June 2019. For the analysis of the information, knowledge indicators were proposed. Knowledge indicators are understood as phrases to determine evidence of knowledge in the responses of the subjects. It was appreciated that the vast majority of future mathematics teachers show knowledge to discriminate when a mathematical argument corresponds or not to a proof by virtue of the logic and syntactic aspects, and of mathematical elements associated with propositions with the structure of universal implication. In general, subjects displayed greater evidence of knowledge on the logic-syntactic aspects than on the mathematical aspects. Specifically, they evidenced that consideration of a particular case or the proof of the reciprocal proposition does not prove the result; likewise, subjects evidenced knowledge about the direct and indirect proof of the universal implication. In the case of the mathematical aspects considered as hypotheses, axioms, definitions and theorems, it was appreciated that subjects could have different levels of difficulties to understand a proof.

show abstract

“…Although mathematicians are accustomed to think of "proof" as an unambiguous term (Epstein & Levy, 1995), it has a multiplicity of meanings to the extent that its meaning is still unclear in school mathematics (Stylianides, 2007). Along this line, Cabassut, Conner, Ersoz, Furinghetti, Jahnke, and Morselli (2012) point out that whereas mathematicians are convinced that, in practice, they know precisely what a proof is, there exist no easy explanations of what proof is that teachers can provide to their learners. The multiple definitions of proof contribute to the difficulty that learners experience in their learning of the concept.…”

Section: Introductionmentioning

confidence: 99%

Learners’ Functional Understandings of Proof (LFUP) in Mathematics: A Qualitative Approach

Shongwe

2020

IJISME

View full text Add to dashboard Cite

The purpose of this study was to present a revision and validation of the Learners’ Functional Understandings of Proof (LFUP) scale in mathematics using data collected from Grade 11 learners (n = 87) in a high school in South Africa. The LFUP scale was linked to the five-factor model (verification, explanation, communication, discovery, and systematisation) whose items were derived from existing literature on proof functions. Unlike the previous version of the scale, the new scale being validated here blends Likert-scale and constructed-response items to evaluate learners’ conceptions of the essence of the functions of an aspect central to mathematical knowledge development: proof. It is my contention that the LFUP instrument can be used as either a summative or a formative assessment tool, given the argument that learners often require motivation as to why they are required to write proofs. In short, this study provided an instrument to introduce learners to the concept of mathematical proof. Multiple regression analysis revealed that all five LFUP tenets correlated significantly with the total sum of all the functions of proof taken together. In the qualitative analysis, a substantial number of learners (52%) were found to hold hybrid beliefs about the functions of proof in mathematics.

show abstract

Conceptions of Proof – In Research and Teaching

Cited by 12 publications

References 30 publications

Conocimiento especializado de profesores de matemática en formación inicial sobre aspectos lógicos y sintácticos de la demostración

Conocimiento especializado de profesores de matemática en formación inicial sobre aspectos lógicos y sintácticos de la demostración

Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments

Learners’ Functional Understandings of Proof (LFUP) in Mathematics: A Qualitative Approach

Contact Info

Product

Resources

About