La fuerza de la aserción y el poder persuasivo en la argumentación en matemáticas

El análisis de la construcción y evaluación de argumentos en matemáticas se ha convertido en una parte importante de la investigación en Educación Matemática a nivel universitario. En este artículo notamos que hasta el momento este análisis se ha hecho desde una perspectiva restringida que se concentra en argumentos construidos para eliminar toda duda en torno a una conjetura. Discutimos una perspectiva más amplia de la argumentación en matemáticas, que toma en consideración las distintas maneras por medio de las cuales tanto estudiantes como matemáticos califican sus conclusiones y se sienten persuadidos por argumentos en matemáticas. Esta perspectiva esta basada en el esquema de argumentación propuesto por Toulmin (1958) y permite analizar argumentos construidos par areducir el nivel de incertidumbre asociado a una conjetura, al mismo tiempo que permite el análisis de distintos tipos de persuasión en la evaluación de argumentos en matemáticas

KSU Symphony Orchestra, Stars: In our galaxy and in one far, far away...

This performance of the KSU Symphony Orchestra conducted by Nathaniel F. Parker features Matthew Hodgetts, clarinet, and Huijeong Lee, violin, winners of the KSU Concerto Competition. Also featured is the world premiere performance of Cascading, composed by Eric Louis Ramos, winner of the KSU Composition Competition.https://digitalcommons.kennesaw.edu/musicprograms/2058/thumbnail.jp

The effect of authority on the persuasiveness of mathematical arguments

Three experiments are reported which investigate the extent to which an authority figure influences the level of persuasion undergraduate students and research-active mathematicians invest in mathematical arguments. We demonstrate that, in some situations, both students and researchers rate arguments as being more persuasive when they are associated with an expert mathematician than when the author is anonymous. We develop a model which accounts for these data by suggesting that, for both students and researchers, an authority figure only plays a role when there is already some uncertainty about the argument’s mathematical status. Implications for pedagogy, and for future research, are discussed

How persuaded are you? A typology of responses

Several recent studies have suggested that there are two different ways in which a person can proceed when assessing the persuasiveness of a mathematical argument: by evaluating whether it is personally convincing, or by evaluating whether it is publicly acceptable. In this paper, using Toulmin’s (1958) argumentation scheme, we produce a more detailed theoretical classification of the ways in which participants can interpret a request to assess the persuasiveness of an argument. We suggest that there are (at least) five ways in which such a question can be interpreted. The classification is illustrated with data from a study that asked undergraduate students and research-active mathematicians to rate how persuasive they found a given argument. We conclude by arguing that researchers interested in mathematical conviction and proof validation need to be aware of the different ways in which participants can interpret questions about the persuasiveness of arguments, and that they must carefully control for these variations during their studies

Functional explanation in mathematics

Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s (2014, Synthese, 191, 3367-3391) suggestion that explanations are those sorts of things that (in the right circumstances, and in the right manner) generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all derivable consequences of Wilkenfeld’s ‘functional explanation’ proposal. We therefore argue that the explanatory criteria offered by earlier accounts can all be thought of as features that make it more likely that a mathematical proof will generate understanding. On the functional account, features such as characterising properties, unification, and salience correlate with explanatoriness, but they do not define explanatoriness

Exploring New Frontiers in Children\u27s Literature

Panel Chair: Sean Ferrier-Watson, Collin College Our panel will explore various issued related to children’s literature, but will specifically focus on the way old and new children’s literature are being adapted into cinematic and digital productions. We will also explore the way fairy tales are used to incorporate a wide array of social issues into child culture. The panelists have each prepared papers that explore the issues touching on new frontiers in children’s literature, ranging from classic fairy tales to contemporary comic books

Semantic contamination and mathematical proof: can a non-proof prove?

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Hereweargue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to argument evaluation tasks suggest that students may hold two different and contradictory conceptions of proof: one related to conviction, and one to validity. We demonstrate that these two conceptions can be preferentially elicited by making apparently irrelevant linguistic changes to task instructions. After analyzing the occurrence of “proof” and “prove” in natural language, we report two experiments that suggest that the noun form privileges evaluations related to validity, and that the verb form privileges evaluations related to conviction. In short, we show that (what is judged to be) a non-proof can sometimes (be judged to) prove

“Explanatory” talk in mathematics research papers

In this paper we explore the ways in which mathematicians talk about explanation in their research papers. We analyze the use of the words explain/explanation (and various related words) in a large corpus of text containing research papers in both mathematics and physical sciences. We found that mathematicians do not frequently use this family of words and that their use is considerably more prevalent in physics papers than in mathematics papers. In particular, we found that physicists talk about explaining why disproportionately more often than mathematicians. We discuss some possible accounts for these differences