Laura Martignon

Laura Martignon
Pädagogische Hochschule Ludwigsburg · Mathematics and Computer Science

Prof. Dr.

About

217
Publications
42,259
Reads
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4,349
Citations
Introduction
Laura Martignon worked until March 31, 2020 at the Institut für Mathematik und Informatik, Pädagogische Hochschule Ludwigsburg. Laura does research in Mathematical Modelling as well as in Reasoning and Mathematics Education. Her current projects include 'Reasoning and deduction: back and forth between classical and defeasible interpretations of logical tasks.'.
Additional affiliations
May 2003 - present
Pädagogische Hochschule Ludwigsburg
Position
  • Professor (Full)
Description
  • I am a mathematical modeler, i.e., I have used Mathematics to model, for instance, synchronization of neurons. I have also modeled decision making. I am a Math Educator and have done many experiments teaching probability in elementary school.
May 2003 - present
Ludwigsburg University of Education
Position
  • Professor
October 2002 - May 2003
Universität Kassel
Position
  • Research Associate
Education
April 1972 - May 1975
University of Tuebingen
Field of study
  • Mathematics
February 1968 - December 1971

Publications

Publications (217)
Article
Full-text available
Cummins (1995) had subjects generate explanations of failures of naive causal conditional inferences, and showed that the heuristic “tallying” of inference defeaters thus generated, inversely predicts other subjects judgments of confidence in those inferences. This is the basis for a probability-free computational model of simple heuristic naive ca...
Article
Full-text available
We present arguments in favor of an interdisciplinary approach in mathematics education. As an instance, we briefly recall how cognitive neuropsychologists promoted intense finger gnosis acquisition, i.e., acquiring the ability to mentally represent one's fingers, at an early age. Mathematics educators definitely recommended the development of fing...
Article
Full-text available
Lernen und Lernstörungen, 4, 91-98 Risikokompetenz in der Schule lernen Dieser Beitrag beschreibt Situationen, bei denen Informationen zu Risiken unentbehrlich sind. Diese Informationen können verständlich ausgedrückt werden oder auch unverständlich, mit schwieri-gen Formeln und undurchsichtigen Graphiken. Hier wird für sehr einfache, transparente...
Article
Full-text available
This paper presents a Bayesian approach to learning the connectivity structure of a group of neurons from data on configuration frequencies. A major objective of the research is to provide statistical tools for detecting changes in firing patterns with changing stimuli. Our framework is not restricted to the well-understood case of pair interaction...
Article
Full-text available
Fast and frugal heuristics are well studied models of bounded rational-ity. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-the-best searches for a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We in...
Chapter
Through our lives we face risks which may appear scary and threatening. Estimating risks is often experienced as difficult. This is important when we make decisions about how to take actions and order our lives. In many cases risks can be measured based on
Article
Full-text available
Conceptual descriptions and measures of information and entropy were established in the twentieth century with the emergence of a science of communication and information. Today these concepts have come to pervade modern science and society, and are increasingly being recommended as topics for science and mathematics education. We introduce a set o...
Article
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Preparing people for dealing with hazards, diseases and disasters requires teaching them statistics, and ideally doing so by means of good representation formats in a dynamic fashion. Translating these dynamics to simple communication is what governments need from scientists.
Conference Paper
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Bounded rationality is a term coined by H. Simon, describing the theory that an individual's decision-making ability is limited by a set of constraints such as lack of information, cognitive biases or lack of time. From this perspective, decision-makers tend to choose "satisficing" solutions rather than optimal ones. In particular in difficult time...
Conference Paper
The paradigm of classical rationality, based on logic and probability theory are briefly described and the drawbacks of these paradigms are illustrated. The principles of adaptive rationality, fast and frugal heursitics and satisficing strategies are discussed and illustrated with examples. Emotions are described as important stopping rules in deci...
Chapter
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Simon's legacies for Mathematics education are briefly explained with examples-.
Article
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It briefly explains the scientific loneliness of Einstein's last years.
Conference Paper
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It is an established opinion that young children have good probabilistic intuitions although their mental framework for reasoning probabilistically may be fragmentary and even contain inconsistencies. We join the camp of mathematics educators who advocate an early training in stochastic thinking. We recognize, however, that such early training can...
Conference Paper
Full-text available
Wason cards were originally designed for an experiment evaluating subjects' reasoning abilities. Our claim is that they may be used as an educational tool in the classroom and their didactical value is enormous. Fourth graders can be trained in logical reasoning by playing not only with four Wason cards, as in the original experiment, but with samp...
Conference Paper
Fast-and-frugal trees for classification/decision are at the intersection of three families of models: lexicographic, linear and tree-based. We briefly examine the classification performance of simple models when making inferences out of sample, in 11 medical data sets in terms of Receiver Operating Characteristics diagrams and predictive accuracy....
Article
Full-text available
The article describes materials and activities which can be used with great success to foster first robust intuitions about Stochastics in general.
Chapter
The chapter analyzes the predictive accuracy of different decision making strategies and comes to the conclusion, that fast and frugal heuristics do not have to trade off simplicity for accuracy.
Article
Full-text available
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...
Conference Paper
Fast-and-frugal trees for classification/decision are at the intersection of three families of models: lexicographic, linear and tree-based. We briefly examine the classification performance of simple models when making inferences out of sample, in 11 medical data sets in terms of Receiver Operating Characteristics diagrams and predictive accuracy....
Conference Paper
In times of big data tree-based algorithms are an important method of machine learning which supports decision making, e.g., in medicine, finance, public policy and many more. Trees are a versatile method to represent decision processes that mirror human decision-making more closely than sophisticated traditional statistical methods like multivaria...
Chapter
Full-text available
The chapter describes simple heursitics for bthe estimation of numerical values of criteria which take advantage of skewness of certain environments.
Conference Paper
A list of fast and frugal trees successfully used in different fields of application are described, presented and illustrated. Fast-and-frugal trees can be used as decision-making tools which operate as lexicographic classifiers, and, if required, associate an action (decision) to each class or category. They were introduced and conceptualized in 2...
Article
Full-text available
Erratum to: AStA Wirtsch Sozialstat Arch 2019 10.1007/s11943-019-00260-w The original version of this article was revised: The article “Zivilstatistik: Konzept einer neuen Perspektive auf Data Literacy und Statistical Literacy”, written by Joachim Engel, Rolf Biehler, Daniel …
Article
Full-text available
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 f...
Article
Full-text available
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...
Conference Paper
Full-text available
In this research project, a novel app-based version of the code breaking game Mastermind, Entropy Mastermind, was introduced and evaluated as a learning medium in undergraduate cognitive psychology and in primary mathematics education. In a quasi-experimental pre-and posttest design we investigated a) the role of individual differences in game play...
Conference Paper
Full-text available
Através de metodos didácticos interactivos con el uso de una website dinámica se desarrolla un cursillo de alfabetización al riesgo.
Book
The book treats Risk Literacy as composed by 4 levels: 1. Detecting and identifying uncertainty 2. Analyzing and modeling 3. Comparing and pondering 4. Deciding and acting Each level is described, discussed and enriched by examples stemming from school interventions. It also contains a QR-Code to a dynamic webpage that illustrates typical situati...
Article
Full-text available
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 dif...
Article
Wie groß ist die Wahrscheinlichkeit, denjenigen Partner in der großen Menge an Menschen zu finden, der perfekt zu einem passt? Diese anspruchsvolle Problemstellung aus dem Song „80 Millionen“ von Max Giesinger bietet, wie wir in unserem Beitrag zeigen werden, vielfältige Lernanlässe für den Mathematikunterricht der Sekundarstufe. Indem die Schüleri...
Article
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Gute Fragen zu stellen, ist eine grundlegende Kompetenz für das Lösen alltäglicher Aufgaben. Der vorliegende Beitrag skizziert eine spielerische Möglichkeit, anhand von gut überlegten Fragen zu verschiedenen Merkmalen und Fabelwesen erste Kentnisse über Information, sowie einfache Strategien (Heuristiken) der Informationssuche Schüler/inne/n zu ver...
Conference Paper
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La evidencia experimental acumulada en las últimas décadas en la literatura psicológica muestra que la interpretación y uso de los conectivos lógicos en distintos contextos están lejos de ser obvios. Estos resultados son a menudo interpretados sólo como una falta respecto a una única lógica tomada como normativa. Esto mismo ocurre muy frecuentement...
Article
Full-text available
This article relates natural frequency representations of cue-criterion relationships to fast-and-frugal heuristics for inferences based on multiple cues. In the conceptual part of this work, three approaches to classification are compared to one another: The first uses a natural Bayesian classification scheme, based on profile memorization and nat...
Conference Paper
Full-text available
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...
Article
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 mat...
Poster
Full-text available
In der Gegenwärtigen Gesellschaft stehen Kindern und Jugendliche mit Fernsehapperaten, Radios, Telefone und Computern eine Menge an Geräten zur Verfügung, die Informationen speichern und verarbeiten. Diese Informationen müssen, um von den Lernenden adäquat im (Unterrichts) Alltag eingesetzt werden zu können, nach bestimmten Kriterien gefiltert werd...
Article
Full-text available
Representing statistical information in terms of natural frequencies rather than probabilities improves performance in Bayesian inference tasks. This beneficial effect of natural frequencies has been demonstrated in a variety of applied domains such as medicine, law, and education. Yet all the research and applications so far have been limited to s...
Article
Full-text available
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, whe...
Article
Full-text available
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 suc...
Article
Full-text available
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 suc...
Chapter
Full-text available
Article
Full-text available
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 t...
Chapter
Information theory is the mathematical treatment of the concepts, parameters, and rules governing the transmission of messages through communication systems. It was founded by Claude Shannon toward the middle of the twentieth century and has evolved into a vigorous branch at the interface between mathematics and communication theory, fostering the...
Chapter
Information theory is the mathematical treatment of the concepts, parameters, and rules governing the transmission of messages through communication systems. It was founded by Claude Shannon toward the middle of the twentieth century and has evolved into a vigorous branch at the interface between mathematics and communication theory, fostering the...
Article
Full-text available
Dieser Beitrag beschreibt Situationen, bei denen Informationen zu Risiken unentbehrlich sind. Diese Informationen konnen verstandlich ausgedruckt werden oder auch unverstandlich, mit schwierigen Formeln und undurchsichtigen Graphiken. Hier wird fur sehr einfache, transparente Reprasentationen pladiert, die das Verstandnis fordern. Nach einigen Beis...
Article
Der Umgang mit Wahrscheinlichkeiten ist mit vielen Fehlvorstellungen versehen. Jungere Forschungen weisen auf die Bedeutung der Formate hin, in denen Informationen zu Wahrscheinlichkeiten und Statistik reprasentiert werden. Zum Beispiel sind Reprasentationen mit naturlichen Haufigkeiten fur die Weiterverarbeitung viel weniger fehleranfallig als Dar...
Chapter
The ABC of probabilistic literacy for good decision-making should be conveyed to children at an early stage, or more precisely, before they reach their 11th year of age. This conviction is based on the view of experts who maintain that the mathematical competencies of adults who are not especially trained in mathematical subjects are those they dev...
Article
Full-text available
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, whe...
Article
Full-text available
We investigated 4th-grade children's search strategies on sequential search tasks in which the goal is to identify an unknown target object by asking yes-no questions about its features. We used exhaustive search to identify the most efficient question strategies and evaluated the usefulness of children's questions accordingly. Results show that ch...
Article
Full-text available
Bank customers are not financial experts, and yet they make high-stakes decisions that can substantively affect personal wealth. Sooner or later, every individual has to take relevant investment decisions. Using data collected from financial advisors, bank customers and university students in Italy, this paper aims to reveal new insights about the...
Chapter
Nach einer kurzen Beschreibung der zwei Hauptströmungen in der aktuellen feministischen Diskussion werden die Positionen zu Geschlechtsunterschieden in Mathematik thematisiert und kurz skizziert. Erklärungsansätze zu den kulturell bedingten Geschlechtsunterschieden in der mathematischen Leistung werden kurz aufgezählt. Schließlich wird die Rolle de...
Article
Full-text available
Wason cards were originally designed for an experiment evaluating subjects' reasoning abilities. Our claim is that they may be used as an educational tool in the classroom and their didactical value is enormous. Fourth graders can be trained in logical reasoning by playing not only with four Wason cards, as in the original experiment, but with samp...
Article
Full-text available
This paper aims to uncover the decision processes used by average investors, including their investment goals, the information sets they consider, and the number of factors that influence high-stakes financial decisions. We present new experimental and survey data collected from bank customers at several Italian banks. Most subjects use a strict su...
Article
Full-text available
Zusammenfassung: Wir schlagen eine Lehr-Lernum-gebung vor, die erste Kompetenzen für den Umgang mit Risiko von Viertklässlern fördern kann. Es geht dabei primär um erste Konzepte für einen Diskurs über Risiko, die anhand von einfachen Aufgaben und die Diskussion, die sie entfachen können, von Kin-dern aufgenommen werden. Diese Lehr-Lernumgebung ist...
Article
Full-text available
Children typically learn basic numerical and arithmetic principles using finger-based representations. However, whether or not reliance on finger-based representations is beneficial or detrimental is the subject of an ongoing debate between researchers in neurocognition and mathematics education. From the neurocognitive perspective, finger counting...
Article
Full-text available
Gender differences in mathematics can be assessed by means of different, alternative measurement models. In the Standard Model of empirical education research it is usually assumed that performance in solving mathematical tasks depends only upon a mathematical competency. By contrast the Nested-Factor Model, based on theoretical tenets of intellige...