laura martignon - Academia.edu (original) (raw)

Drafts by laura martignon

When learners have to make sense of risky situations, they can use mathematical models and repres... more When learners have to make sense of risky situations, they can use mathematical models and representations which facilitate successful risk assessment. Based on theoretical considerations on the benefits of specific models and specific representations in such contexts, we present empirical findings of a study which examined whether students use such models and representations in their risk assessment. We conclude that the availability of adequate models to learners may help them gain transparency when facing risks and thus foster their decision-making.

Papers by laura martignon

Promoting Understanding of Statistics about Society IASE Roundtable Conference

Risks have to be evaluated on the basis of information that media, advertisements and brochures p... more Risks have to be evaluated on the basis of information that media, advertisements and brochures pro- vide. These are often incomplete, reporting, for instance, only relative risks instead of both relative and absolute risks. While it is important for the informed citizen to be trained in the evaluation of scales and diagrams on risk-related topics it is also relevant that she acquires basic competencies for the understanding of risk; this requires, as is the claim of this paper, minimal effort. Results will be presented that demonstrate current deficits in the understanding of risk which are the consequence of misinformation or of bad representation formats and can be eliminated by a good yet elementary training in the understanding of basic risk-related concepts.

AStA Wirtschafts- und Sozialstatistisches Archiv

After a brief description of the four components of risk literacy and the tools for analyzing ris... more After a brief description of the four components of risk literacy and the tools for analyzing risky situations, decision strategies are introduced, These rules, which satisfy tenets of Bounded Rationality, are called fast and frugal trees. Fast and frugal trees serve as efficient heuristics for decision under risk. We describe the construction of fast and frugal trees and compare their robustness for prediction under risk with that of Bayesian networks. In particular, we analyze situations of risky decisions in the medical domain. We show that the performance of fast and frugal trees does not fall too far behind that of the more complex Bayesian networks.

AStA Wirtschafts- und Sozialstatistisches Archiv

Zusammenfassung Demokratie lebt von Argumenten, die auf nachweisbaren Fakten basieren. Lebendige ... more Zusammenfassung Demokratie lebt von Argumenten, die auf nachweisbaren Fakten basieren. Lebendige Demokratien brauchen gut informierte Bürger, die relevante gesellschaftliche Fragen verstehen, diskutieren und sich in öffentliche Entscheidungsprozesse einbringen können. Dieser Aufsatz stellt in Erweiterung von Statistical Literacy eine Teildisziplin vor, die wir Zivilstatistik nennen. Zivilstatistik konzentriert sich auf das Verstehen statistischer Informationen über die Gesellschaft, wie sie von den Medien, Statistikämtern und anderen Statistikanbietern bereitgestellt werden. Die Herausforderung, Menschen zu befähigen, Sinn aus diesen Daten zu erschließen, richtet sich gleichermaßen an Bildungseinrichtungen (Schulen und Hochschulen) wie auch an Medien und Statistikanbieter. Im vorliegenden Aufsatz beschreiben wir die spezifischen Charakteristika von Zivilstatistik und begründen die Notwendigkeit dieser Teildisziplin, die im Schnittfeld von Statistik, Gesellschaftswissenschaften und –...

Avances de Investigación en Educación Matemática

This paper is devoted to examining the validity of a hierarchical competency model of statistical... more This paper is devoted to examining the validity of a hierarchical competency model of statistical literacy by assessing the corresponding competency levels of primary and secondary students from Colombia and Germany. The results replicate prior findings and confirm the hierarchical competency model. The study has two novel components with respect to previous work on competency levels in statistical literacy: it examines elementary school performance and it includes an intercultural comparison. The competency scores reached by the students, however, suggest specific profiles of sub-groups of learners included in the study. The intercultural study is clearly exploratory since the samples both in Colombia and in Germany were not representative. The results point to interesting new questions and motivate further intercultural research.

International Electronic Journal of Mathematics Education

The article reports an empirical study on the introduction of elementary probabilistic concepts i... more The article reports an empirical study on the introduction of elementary probabilistic concepts in school, focusing on tasks related to the psychological tradition of heuristics and biases. The concepts involved were studied using an extensional natural frequencies approach. We describe the school intervention conducted in an interaction across different school levels (5th and 9th grades) with the aim of promoting motivation and cooperation thereby strengthening learning. The different tests were assessed both qualitatively (based on argumentation analyses) and quantitatively. The results provide further evidence on the diversity of obstacles tied to probabilistic notions. More importantly, they exhibit an overall improvement in performance of students at both levels. This work confirms the efficacy of natural frequencies in eliciting the intended interpretation of probabilistic tasks and suggests that an appropriate interaction between different scholastic levels can be implemented as a fruitful learning arrangement.

Physica Scripta

The introduction of operator states and of observables in various fields of quantum physics has r... more The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured that we deal with Hilbert spaces although the mathematical background was not entirely clear, particularly, when dealing with bosonic operators. This in turn caused some doubts about the correct way to combine bosonic and fermionic operators or, in other words, regular and Grassmann variables. In this paper we present a formal answer to the problems on a simple and very general basis. We illustrate the resulting construction by revisiting the Bargmann transform and finding the known connection between L 2 (R) and the Bargmann-Hilbert space. We then use the formalism to give an explicit formulation for Fock spaces involving both fermions and bosons thus solving the problem at the origin of our considerations.

The Journal of Machine Learning Research, 2006

Fast and frugal heuristics are well studied models of bounded rationality. Psychological research... more Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Takethe-best searches for a sufficiently good ordering of cues (or features) in a task where objects are to be compared lexicographically. We investigate the computational complexity of finding optimal cue permutations for lexicographic strategies and prove that the problem is NP-complete. It follows that no efficient (that is, polynomial-time) algorithm computes optimal solutions, unless P = NP. We further analyze the complexity of approximating optimal cue permutations for lexicographic strategies. We show that there is no efficient algorithm that approximates the optimum to within any constant factor, unless P = NP. The results have implications for the complexity of learning lexicographic strategies from examples. They show that learning them in polynomial time within the model of agnostic probably approximately correct (PAC) learning is impossible, unless RP = NP. We further consider greedy approaches for building lexicographic strategies and determine upper and lower bounds for the performance ratio of simple algorithms. Moreover, we present a greedy algorithm that performs provably better than take-thebest. Tight bounds on the sample complexity for learning lexicographic strategies are also given in this article.

Unterrichtswissenschaft, 2004

Gewährt wird ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf N... more Gewährt wird ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen, nicht-kommerziellen Gebrauch bestimmt. Die Nutzung stellt keine Übertragung des Eigentumsrechts an diesem Dokument dar und gilt vorbehaltlich der folgenden Einschränkungen: Auf sämtlichen Kopien dieses Dokuments müssen alle Urheberrechtshinweise und sonstigen Hinweise auf gesetzlichen Schutz beibehalten werden. Sie dürfen dieses Dokument nicht in irgendeiner Weise abändern, noch dürfen Sie dieses Dokument für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, aufführen, vertreiben oder anderweitig nutzen. We grant a non-exclusive, non-transferable, individual and limited right to using this document. This document is solely intended for your personal, non-commercial use. Use of this document does not include any transfer of property rights and it is conditional to the following limitations: All of the copies of this documents must retain all copyright information and other information regarding legal protection. You are not allowed to alter this document in any way, to copy it for public or commercial purposes, to exhibit the document in public, to perform, distribute or otherwise use the document in public. Mit der Verwendung dieses Dokuments erkennen Sie die Nutzungsbedingungen an. By using this particular document, you accept the above-stated conditions of use.

Sonderforschungsbereich 504 Publications, Feb 14, 1999

... class. Lewis and Keren's num-bers do not relate to one reference class. Observe ... 9900... more ... class. Lewis and Keren's num-bers do not relate to one reference class. Observe ... 9900 Page 196. 178 S. KrauS, L. Martignon, and U. Hoffrage Multiplying this with the likelihood ratio for the mammography, 3 we u• 80 obtain. 950 ...

Nips, 2005

Neural Information Processing Systems, 1996

This paper develops arguments for a family of temporal log-linear models to represent spatio-temp... more This paper develops arguments for a family of temporal log-linear models to represent spatio-temporal correlations among the spiking events in a group of neurons. The models can represent not just pairwise correlations but also correlations of higher order. Methods are discussed for inferring the existence or absence of correlations and estimating their strength. A frequentist and a Bayesian approach to correlation detection are compared. The frequentist method is based on G 2 statistic with estimates obtained via the Max-Ent principle. In the Bayesian approach a Markov Chain Monte Carlo Model Composition (MC3) algorithm is applied to search over connectivity structures and Laplace's method is used to approximate their posterior probability. Performance of the methods was tested on synthetic data. The methods were applied to experimental data obtained by the fourth author by means of measurements carried out on behaving Rhesus monkeys at the Hadassah Medical School of the Hebrew University. As conjectured, neural connectivity structures need not be neither hierarchical nor decomposable.

Our comparative studies investigate the influence of different representations (i.e. formulas or ... more Our comparative studies investigate the influence of different representations (i.e. formulas or graphical models and numeric formats) on the understanding of "big ideas" in stochastics (e.g. characteristics of probability, conditional probability, distribution, significance). We know from previous work (e.g. Sedlmeier & Gigerenzer, 2001) that special tree-representations combined with frequency-formats increase the performance in understanding dramatically. Another aspect of the experiments is the utility of different presenting-modes (e.g. static vs. dynamic, imitation vs. learning by doing). The pupils of age 15-19 receive a computer-based training with different representations resp. modes on basic probability tasks. The effects of the training are measured by subsequent tests. Thus we obtain insight, if they succeed easily in using the learned representations and if they benefit from it. The first results support the assumption that groups of pupils trained with frequency-representations have a better understanding of key-problems in stochastics.

New ICMI Study Series, 2011

ABSTRACT This chapter describes some relevant features of the training in statistics and probabil... more ABSTRACT This chapter describes some relevant features of the training in statistics and probability future mathematics teachers receive in Germany. It also discusses aspects of the stochastic courses taught in school as well as some of the relevant textbooks on the subject.

Promoting Understanding of Statistics about Society IASE Roundtable Conference

AStA Wirtschafts- und Sozialstatistisches Archiv

Avances de Investigación en Educación Matemática

International Electronic Journal of Mathematics Education

Physica Scripta

The Journal of Machine Learning Research, 2006

Unterrichtswissenschaft, 2004

Sonderforschungsbereich 504 Publications, Feb 14, 1999

Nips, 2005

Neural Information Processing Systems, 1996

New ICMI Study Series, 2011

Journal of experimental child psychology, Jan 16, 2016

Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one&... more Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one's own fingers) is associated reliably with basic numerical competencies. In this study, we aimed at examining whether finger gnosis is also a unique predictor for initial arithmetic competencies at the beginning of first grade-and thus before formal math instruction starts. Therefore, we controlled for influences of domain-specific numerical precursor competencies, domain-general cognitive ability, and natural variables such as gender and age. Results from 321 German first-graders revealed that finger gnosis indeed predicted a unique and relevant but nevertheless only small part of the variance in initial arithmetic performance (∼1%-2%) as compared with influences of general cognitive ability and numerical precursor competencies. Taken together, these results substantiated the notion of a unique association between finger gnosis and arithmetic and further corroborate the theoretical ...