Relearning: a unified conceptualization across cognitive psychology and mathematics education

We propose a unifying conceptualization of “relearning”, a construct that has a long history in the field of cognitive psychology and has recently been reconceptualized in the mathematics education with respect to teacher training. We argue that existing accounts of relearning are versions of the same phenomenon subjected to different motivations for relearning and intended relearning outcomes. Utilizing the existing theoretical rigor behind existing conceptualizations of relearning, we demonstrate the utility of the unified conceptualization in using findings from one section to suggest new avenues for others, and in addressing issues posed by a lack of theoretical framing in the studies of remedial mathematics education and repeated mathematics courses

Generation and characterization of the human iPSC line PBMC1-iPS4F1 from adult peripheral blood mononuclear cells

AbstractHere we describe the generation and characterization of the human induced pluripotent stem cell (iPSC) line PBMC1-iPS4F1 from peripheral blood mononuclear cells from a healthy female with Spanish background. We used heat sensitive, non-integrative Sendai viruses containing the reprogramming factors Oct3/4, Sox2, Klf4 and c-Myc, whose expression was silenced in the established iPSC line. Characterization of the PBMC1-iPS4F1 cell line included analysis of typical pluripotency-associated factors at mRNA and protein level, alkaline phosphatase enzymatic activity, and in vivo and in vitro differentiation studies

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

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

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

“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

Usurpación agravada y la afectación al derecho de la propiedad, y la jurisprudencia de la Corte Suprema de la República en los años 2015 a 2020.

La presente investigación tiene como propósito analizar como la usurpación agravada ha afectado al derecho de la Propiedad, en la Jurisprudencia de la Corte Suprema de la Republica en los años 2015 a 2020. Debido a los altos índices de ocurrencia del delito de usurpación en el Perú, se considera importante conocer las causas que han generado el incremento de esta infracción, a su vez, como el derecho de propiedad se ha visto afectado En tal sentido, la usurpación es un acto por el cual una persona en forma violenta ingresa a una propiedad que no le corresponde, perturbando o generando un malestar a su propietario o poseedor, así como a su entorno social y económico. Aunado a esto, en el campo del derecho lo que defiende la usurpación no es la propiedad, sino la posesión, en este sentido se hace indispensable conocer los estatutos y reglamentos que el ordenamiento jurídico peruano rige para controlar la ocurrencia del hecho. Por ende, estos hechos deben ser puestos inmediatamente al ente competente, con la finalidad que tome las acciones pertinentes y aplique las medidas correctivas ante el evento suscitado, incurrir en actos delictivos como la usurpación de un inmueble es perjudicar el derecho propiedad, y no solo afecta a su dueño sino también a su entorno. Finalmente, la indagación minuciosa sobre la eficacia de los dictámenes en este delito de un juicio específico acarrea el estudio del escenario jurídico, teniendo en cuenta que las sentencias están fundamentadas en una acción de la actividad del individuo que actúa a nombre y en representación del Estado.The purpose of this research is to analyze how the aggravated usurpation has affected the right of Property, in the Jurisprudence of the Supreme Court of the Republic in the years 2015 to 2020. Due to the high rates of occurrence of the crime of usurpation in Peru, it is considered important to know the causes that have generated the increase of this offense, in turn, how the right of property has been affected. In this sense, usurpation is an act by which a person violently enters a property that does not belong to him, disturbing or causing discomfort to its owner or possessor, as well as to his social and economic environment. In addition to this, in the field of law what defends the usurpation is not the property, but the possession, in this sense it is essential to know the statutes and regulations that the Peruvian legal system governs to control the occurrence of the fact. Therefore, these facts must be immediately reported to the competent entity, with the purpose of taking the pertinent actions and applying the corrective measures before the event occurred, incurring in criminal acts such as the usurpation of a property is to damage the property right, and not only affects its owner but also its surroundings. Finally, the thorough investigation on the effectiveness of the judgments in this crime of a specific trial, involves the study of the legal scenario, taking into account that the judgments are based on an action of the activity of the individual acting on behalf and in representation of the State

Quantum Kernel Mixtures for Probabilistic Deep Learning

This paper presents a novel approach to probabilistic deep learning (PDL), quantum kernel mixtures, derived from the mathematical formalism of quantum density matrices, which provides a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random variables. The framework allows for the construction of differentiable models for density estimation, inference, and sampling, enabling integration into end-to-end deep neural models. In doing so, we provide a versatile representation of marginal and joint probability distributions that allows us to develop a differentiable, compositional, and reversible inference procedure that covers a wide range of machine learning tasks, including density estimation, discriminative learning, and generative modeling. We illustrate the broad applicability of the framework with two examples: an image classification model, which can be naturally transformed into a conditional generative model thanks to the reversibility of our inference procedure; and a model for learning with label proportions, which is a weakly supervised classification task, demonstrating the framework's ability to deal with uncertainty in the training samples