Joachim Engel | PH Ludwigsburg (original) (raw)

Papers by Joachim Engel

Research paper thumbnail of A Transparent, Simple AI Tool for Constructing Efficient and Robust Fast and Frugal Trees for Classification Under Risk

Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics

Artificial Intelligence (AI) has produced extremely efficient and effective classification and de... more Artificial Intelligence (AI) has produced extremely efficient and effective classification and decision “machines” that learn from given data sets and generalize well to unknown data. These are mostly celebrated tools produced by methodologies of machine learning. There is a drawback, though, namely their lack of transparency in construction. Agents often ignore the construction steps and use them as black-box algorithms. We exhibit simple and transparent steps for creating robust and yet simple heuristics for classification based on the AI tool ARBOR. We also claim that these transparent classifiers compete well against powerful machines, especially when training sets are small.

Research paper thumbnail of The COVID-19 Crisis as a Challenge for the Integration of Statistical and Citizenship Education

Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics

The COVID-19 crisis has shown how fundamentally important it is to weigh up risks and probabiliti... more The COVID-19 crisis has shown how fundamentally important it is to weigh up risks and probabilities on the basis of statistical data for shaping social coexistence. A vibrant democracy that wants to prove resilient to expertocratic strategies of rule needs citizens who take part in public deliberations and intervene in political affairs. However, without a basic understanding of statistical concepts, it is difficult to follow media coverage of the pandemic and policy actions taken, let alone intervene in political processes. It is therefore necessary to link statistical and citizenship education. We present our concept of a joint course for mathematics and political science students preparing to be secondary teachers that is currently given at Ludwigsburg University of Education (Germany). Empirical results are forthcoming.

Research paper thumbnail of Data Science for Informed Citizens: On Synergies Between Data Literacy and Civic Statistics

Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics

Data science as a practical science has been conceived to address tangible problems in science, t... more Data science as a practical science has been conceived to address tangible problems in science, technology, and society. These problems require skills and dispositions beyond the technical mastery of algorithms such as interrogating measurability issues, classifying results under uncertainty and risk, and being aware of data ethics and implications for policy and society. These features relate data science education closely to the recently developed field of civic statistics. This conceptual paper looks at the common grounds between these two areas. It investigates how digital literacy and data science can enhance civic statistics and, vice versa, how civic statistics concepts have the potential to enrich the teaching of data science and data literacy. Hence the paper contributes to the development of new curriculum guidelines and, ultimately, courses.

Research paper thumbnail of Competencies and dispositions for exploring micro data with digital tools

Promoting Understanding of Statistics about Society IASE Roundtable Conference

Exploring micro data requires the ability to use digital tools for managing large multivariate da... more Exploring micro data requires the ability to use digital tools for managing large multivariate data. Digital tools allow changing easily between different uni- and multivariate displays and summary statistics for a deeper insight into the data. In this paper we examine the suitability of several digital data analysis tools for exploring a large, multivariate socio-economic dataset, ranging from educational tools (TinkerPlots, Fathom) to professional software (R). Based on German income structure data, we will point out benefits and limitations of TinkerPlots, Fathom and R for comparing groups, investigating subgroups, analyzing relationships between variables and for exploring multivariate phenomena.

Research paper thumbnail of Fast-and-frugal trees for decision-making

Decision Making Based on Data Proceedings IASE 2019 Satellite Conference, 2019

Fast-and-frugal trees for classification/decision are at the intersection of three families of mo... more 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. The heuristic approaches, Naïve Bayes and fast- and-frugal trees, outperform models that are normatively optimal when fitting data. The success of fast-and-frugal trees lies in their ecological rationality: their construction exploits the structure of information in the data sets. The tool ARBOR, a digital learning tool, which is a plug-in to the freely available data-science education software CODAP can be used for constructing and interpreting fast- and-frugal classification and decision trees. This paper is an abridged version of work by Woike, Hoffrage & Martignon on the integration of classification and decision models into a common ...

Research paper thumbnail of Cultura estadística y sociedad: ¿Qué es la estadística cívica?

How can we prepare students to understand statistical data and get insights regarding trends and ... more How can we prepare students to understand statistical data and get insights regarding trends and changes on key societal issues such as demographic change, crime, unemployment, pay equity, migration, health, racism, and other areas of concern to society? This paper, summarizing issues of my plenary talk, introduces by extending the notion of statistical literacy a sub-discipline we call civic statistics. Civic statistics focuses on understanding statistical information about society, as provided by the media, statistical offices and other statistics providers. Civic statistics skills are required for participation in democratic societies, but include data that are open, official, multivariate and dynamic, and that are usually neglected in regular statistics education. I present some specific features of civic statistics, provide examples and describe implications for curricula, teacher activities and the future of statistical education. In my presentation, I will give a short online...

Research paper thumbnail of Authors’ response: on the role of data, statistics and decisions in a pandemic

AStA Advances in Statistical Analysis

Research paper thumbnail of A Multilevel Perspective on Factors Influencing Students' Statistical Literacy

Over the last two decades statistics has been recognized as an important part of the school curri... more Over the last two decades statistics has been recognized as an important part of the school curriculum worldwide. As a result, questions related to impact factors on statistical literacy merit focused attention in empirical research. For instance, interdependencies with individual factors such as general cognitive abilities, reading comprehension or specific elements of mathematical content knowledge is still scarce. We report empirical results from two studies on relationships between statistical literacy and potential influencing factors. The findings provide insight into the role of such covariates and support the validity of the competency measure we used to assess a key aspect of statistical literacy. The evidence further suggests that statistical literacy also depends on class variables beyond individual dispositions. Statistical literacy involves abilities of making sense of statistical data for decision-making under uncertainty and active participation in society. Hence, a l...

Research paper thumbnail of Statistical literacy and society: What is civic statistics?

How can we prepare students to understand statistical data and get insights regarding trends and ... more How can we prepare students to understand statistical data and get insights regarding trends and changes on key societal issues such as demographic change, crime, unemployment, pay equity, migration, health, racism, and other areas of concern to society? This paper, summarizing issues of my plenary talk, introduces by extending the notion of statistical literacy a sub-discipline we call civic statistics. Civic statistics focuses on understanding statistical information about society, as provided by the media, statistical offices and other statistics providers. Civic statistics skills are required for participation in democratic societies, but include data that are open, official, multivariate and dynamic, and that are usually neglected in regular statistics education. I present some specific features of civic statistics, provide examples and describe implications for curricula, teacher activities and the future of statistical education. In my presentation, I will give a short online...

Research paper thumbnail of Exploring civic statistics with CODAP

Data are abundant, quantitative information about the state of society and the wider world is aro... more Data are abundant, quantitative information about the state of society and the wider world is around us more than ever. In order to root the public debate based on facts instead of emotions and to promote evidence-based policy decisions we as statistics educators are challenged to promote understanding of statistics about society. This report summarizes a hand-on workshop in which participants explored the potential of the freely available web-based data platform CODAP (http://codap.concord.org) and its usefulness for investigating civic statistics data. Materials of the workshop were developed as part of the EU-funded ProCivicStat Project and are freely available (www.procivicstat.org)

Research paper thumbnail of Implementing Civic Statistics in Mathematics Teacher Education

Research paper thumbnail of Data and Statistics as basis for political decisions: lessons to be learnt from the COVID-19 pandemic

Proceedings of the IASE 2021 Satellite Conference, 2022

The Covid-19 crisis has impressively raised the general awareness that our social coexistence and... more The Covid-19 crisis has impressively raised the general awareness that our social coexistence and political decisions are essentially based on data, the weighing of risks and thus on probability estimates. This places high demands on the ability of health authorities, policy makers and the media to communicate statistical information as well as on the ability of citizens to understand these messages. In this paper we reflect on the role of scientific evidence in democratic societies and analyze selected illustrative examples of communicating evidence via visualizations and simulation, media reports, and expert’s statements. We identify venues and formats of communicating statistical information about the pandemics to the public that seems to be effective contrasting less helpful formats. We conclude by presenting recommendations for stakeholders in politics, media and statistics agencies on how to communicate empirical evidence to the public efficiently, released by the Deutsche Arb...

Research paper thumbnail of Standardmodelle und Naturgesetz: Was uns der Kontext und unser Vorwissen verraten kann

Wie kommt man von Daten, die aus den Beobachtungen von zwei Variablen gewonnenwurden, zu einer Fu... more Wie kommt man von Daten, die aus den Beobachtungen von zwei Variablen gewonnenwurden, zu einer Funktion, die die Abhangigkeit zwischen den beiden Variablenbeschreibt? Wie lasst sich ein funktionaler Zusammenhang zwischen zwei Variablenspezifizieren und die Herleitung eines Graphen oder einer Funktionsgleichung begrunden? Hierzu gibt es eine Vielzahl von Ansatzen, wie mit mathematischen Methodenein Sachzusammenhang modelliert werden kann.

Research paper thumbnail of 3. Lösungen algebraischer Gleichungen

Research paper thumbnail of Funktionen, Daten und Modelle: Vernetzende Zugänge zu zentralen Themen der (Schul-)Mathematik

Journal für Mathematik-Didaktik, 2016

Zusammenfassung Wie lassen sich Zusammenhänge zwischen zwei Größen mit Hilfe des mathematischen F... more Zusammenfassung Wie lassen sich Zusammenhänge zwischen zwei Größen mit Hilfe des mathematischen Funktionsbegriffs modellieren? Das zentrale Anliegen dieses Aufsatzes besteht darin, ein bis in die Schulmathematik der unteren und mittleren Klassen reichendes Thema der modernen Mathematik konsistent zu rekonstruieren. Es wird dabei aufgezeigt, wie mit zunehmender mathematischer Kompetenz verfeinerte Methoden eingesetzt werden können, um auf zunehmend anspruchsvolle Weise ein und dasselbe Ziel zu verfolgen: Abhängigkeiten zwischen zwei metrisch skalierten Größen zu modellieren. Zugleich wird gezeigt, wie grundlegende Ideen zum Modellieren funktionaler Abhängigkeiten lebendig und wirklichkeitsnah gestaltet werden können. Dieser Zugang vernetzt zentrale Themen der Schulmathematik, insbesondere Funktionenlehre, Analysis, Stochastik, Lineare Algebra und Numerik. Die einzelnen Ansätze verwenden nicht nur unterschiedliche mathematische Methoden, sondern basieren auch auf unterschiedlichen konzeptionellen Vorstellungen und Modellierungsannahmen. Schlüsselwörter Funktionaler Zusammenhang • Modellieren • Daten und Zufall • Analysis • Stochastik MESC Codes D30 • I10 • K40 • M10 Functions, data and models: connecting central topics of the mathematics curriculum Abstract How to model dependencies between two variables using the mathematical concept of a function? The central concern of this paper is to reconstruct a modern

Research paper thumbnail of Statistics for Empowerment and Social Engagement

Statistics for Empowerment and Social Engagement

The first three chapters of this book have identified societal demands for understanding Civic St... more The first three chapters of this book have identified societal demands for understanding Civic Statistics (Chap. 1), described specific features of the statistical and mathematical information citizens receive about civic issues (Chap. 2), and mapped out the facets and tools (skills, knowledge, mental and motivational tools) needed to critically understand such statistical and mathematical information about society (Chap. 3). The present chapter examines issues that are essential for promoting necessary changes in the teaching and learning of Civic Statistics, which are needed for empowering citizens to engage with and analyze data sources and data-informed reasoning about burning issues in society, and critically interpret messages related to Civic Statistics encountered in the news media, social networks and related digital sources. The chapter first provides further illustrations of activities or tasks pertaining to Civic Statistics and shows how to analyse task demands in terms ...

Research paper thumbnail of Civic Statistics in the training of pre-service mathematics teachers

In an increasingly complex world, the involvement of informed and committed citizens is a critica... more In an increasingly complex world, the involvement of informed and committed citizens is a critical resource in public decision-making at international, national and local levels. The project ProCivicStat, a strategic partnership of six universities funded through the Erasmus+ program of the European Union (funding period September 2015 to August 2018), explores a subfield we call Civic Statistics which focuses on understanding quantitative and statistical information about society as provided by the media, statistics offices and other statistics providers (Engel et al. 2016). Understanding Civic Statistics is required for participation in democratic societies, but involves data that often are open, official, multivariate in nature, and/or dynamic, that is not normally taught in regular mathematics and statistics education, let alone in civics or social study classes. Few high school teachers in mathematics receive any training on how to teach statistics, not to speak of social science teachers who may have no training in statistics at all. As a result, teachers stay within their comfort zone and overemphasize a narrow range of statistical techniques and computations (mathematics) or fail to engage with statistical ideas at all (social science). They pay too little attention to working with and understanding multivariate data that describe social trends, and to the analysis, interpretation and communication about the meaning of such data. But capacity building for informed and committed citizens has to start in school education. While focusing on curricula at the secondary and tertiary level, the ultimate goal of ProCivicStat is to strengthen civil society, empowering informed citizens for evidence-based decision-making and civil society engagement. The challenge is multi-facetted. Data literacy for civic engagement involves, among many other aspects, specific statistical knowledge, ICT skills, knowledge about computing and data structures, critical thinking, and much more.

Research paper thumbnail of The importance of statistical literacy for democracy : civic-education through statistics

Civic Education has had the same objective (“Mündigkeit”) for the last 50 years, but the conditio... more Civic Education has had the same objective (“Mündigkeit”) for the last 50 years, but the conditions to achieve it have changed. Mündigkeit is a prerequisite for citizen’s participation, to strengthen and stabilize democratic structures. In the information age, Mündigkeit regarding statistics means having an orientation in the confusion of the modern information jungle and the deluge of quantitative information and statistics. The requirements for understanding and evaluating information about societal developments have changed: Statistical skills are becoming increasingly important for an evidence-based judgment in today's society. They entail understanding data-related arguments and representations, questioning possible conclusions as well as uncovering opinions and already made decisions

Research paper thumbnail of Editorial: Research on Data Science Education

STATISTICS EDUCATION RESEARCH JOURNAL

A very warm welcome to this Special Issue of the Statistics Education Research Journal (SERJ) on ... more A very warm welcome to this Special Issue of the Statistics Education Research Journal (SERJ) on data science education. Our hope is to give an overview of selected theoretical thoughts and empirical studies on data science education from a statistics education research perspective. Data science education is rapidly developing but research into data science education is still in its infancy. The current issue presents a snapshot of this developing field.

Research paper thumbnail of Topic Study Group No. 14: Teaching Learning of Probability

Proceedings of the 13th International Congress on Mathematical Education, 2017

Research paper thumbnail of A Transparent, Simple AI Tool for Constructing Efficient and Robust Fast and Frugal Trees for Classification Under Risk

Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics

Artificial Intelligence (AI) has produced extremely efficient and effective classification and de... more Artificial Intelligence (AI) has produced extremely efficient and effective classification and decision “machines” that learn from given data sets and generalize well to unknown data. These are mostly celebrated tools produced by methodologies of machine learning. There is a drawback, though, namely their lack of transparency in construction. Agents often ignore the construction steps and use them as black-box algorithms. We exhibit simple and transparent steps for creating robust and yet simple heuristics for classification based on the AI tool ARBOR. We also claim that these transparent classifiers compete well against powerful machines, especially when training sets are small.

Research paper thumbnail of The COVID-19 Crisis as a Challenge for the Integration of Statistical and Citizenship Education

Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics

The COVID-19 crisis has shown how fundamentally important it is to weigh up risks and probabiliti... more The COVID-19 crisis has shown how fundamentally important it is to weigh up risks and probabilities on the basis of statistical data for shaping social coexistence. A vibrant democracy that wants to prove resilient to expertocratic strategies of rule needs citizens who take part in public deliberations and intervene in political affairs. However, without a basic understanding of statistical concepts, it is difficult to follow media coverage of the pandemic and policy actions taken, let alone intervene in political processes. It is therefore necessary to link statistical and citizenship education. We present our concept of a joint course for mathematics and political science students preparing to be secondary teachers that is currently given at Ludwigsburg University of Education (Germany). Empirical results are forthcoming.

Research paper thumbnail of Data Science for Informed Citizens: On Synergies Between Data Literacy and Civic Statistics

Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics

Data science as a practical science has been conceived to address tangible problems in science, t... more Data science as a practical science has been conceived to address tangible problems in science, technology, and society. These problems require skills and dispositions beyond the technical mastery of algorithms such as interrogating measurability issues, classifying results under uncertainty and risk, and being aware of data ethics and implications for policy and society. These features relate data science education closely to the recently developed field of civic statistics. This conceptual paper looks at the common grounds between these two areas. It investigates how digital literacy and data science can enhance civic statistics and, vice versa, how civic statistics concepts have the potential to enrich the teaching of data science and data literacy. Hence the paper contributes to the development of new curriculum guidelines and, ultimately, courses.

Research paper thumbnail of Competencies and dispositions for exploring micro data with digital tools

Promoting Understanding of Statistics about Society IASE Roundtable Conference

Exploring micro data requires the ability to use digital tools for managing large multivariate da... more Exploring micro data requires the ability to use digital tools for managing large multivariate data. Digital tools allow changing easily between different uni- and multivariate displays and summary statistics for a deeper insight into the data. In this paper we examine the suitability of several digital data analysis tools for exploring a large, multivariate socio-economic dataset, ranging from educational tools (TinkerPlots, Fathom) to professional software (R). Based on German income structure data, we will point out benefits and limitations of TinkerPlots, Fathom and R for comparing groups, investigating subgroups, analyzing relationships between variables and for exploring multivariate phenomena.

Research paper thumbnail of Fast-and-frugal trees for decision-making

Decision Making Based on Data Proceedings IASE 2019 Satellite Conference, 2019

Fast-and-frugal trees for classification/decision are at the intersection of three families of mo... more 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. The heuristic approaches, Naïve Bayes and fast- and-frugal trees, outperform models that are normatively optimal when fitting data. The success of fast-and-frugal trees lies in their ecological rationality: their construction exploits the structure of information in the data sets. The tool ARBOR, a digital learning tool, which is a plug-in to the freely available data-science education software CODAP can be used for constructing and interpreting fast- and-frugal classification and decision trees. This paper is an abridged version of work by Woike, Hoffrage & Martignon on the integration of classification and decision models into a common ...

Research paper thumbnail of Cultura estadística y sociedad: ¿Qué es la estadística cívica?

How can we prepare students to understand statistical data and get insights regarding trends and ... more How can we prepare students to understand statistical data and get insights regarding trends and changes on key societal issues such as demographic change, crime, unemployment, pay equity, migration, health, racism, and other areas of concern to society? This paper, summarizing issues of my plenary talk, introduces by extending the notion of statistical literacy a sub-discipline we call civic statistics. Civic statistics focuses on understanding statistical information about society, as provided by the media, statistical offices and other statistics providers. Civic statistics skills are required for participation in democratic societies, but include data that are open, official, multivariate and dynamic, and that are usually neglected in regular statistics education. I present some specific features of civic statistics, provide examples and describe implications for curricula, teacher activities and the future of statistical education. In my presentation, I will give a short online...

Research paper thumbnail of Authors’ response: on the role of data, statistics and decisions in a pandemic

AStA Advances in Statistical Analysis

Research paper thumbnail of A Multilevel Perspective on Factors Influencing Students' Statistical Literacy

Over the last two decades statistics has been recognized as an important part of the school curri... more Over the last two decades statistics has been recognized as an important part of the school curriculum worldwide. As a result, questions related to impact factors on statistical literacy merit focused attention in empirical research. For instance, interdependencies with individual factors such as general cognitive abilities, reading comprehension or specific elements of mathematical content knowledge is still scarce. We report empirical results from two studies on relationships between statistical literacy and potential influencing factors. The findings provide insight into the role of such covariates and support the validity of the competency measure we used to assess a key aspect of statistical literacy. The evidence further suggests that statistical literacy also depends on class variables beyond individual dispositions. Statistical literacy involves abilities of making sense of statistical data for decision-making under uncertainty and active participation in society. Hence, a l...

Research paper thumbnail of Statistical literacy and society: What is civic statistics?

How can we prepare students to understand statistical data and get insights regarding trends and ... more How can we prepare students to understand statistical data and get insights regarding trends and changes on key societal issues such as demographic change, crime, unemployment, pay equity, migration, health, racism, and other areas of concern to society? This paper, summarizing issues of my plenary talk, introduces by extending the notion of statistical literacy a sub-discipline we call civic statistics. Civic statistics focuses on understanding statistical information about society, as provided by the media, statistical offices and other statistics providers. Civic statistics skills are required for participation in democratic societies, but include data that are open, official, multivariate and dynamic, and that are usually neglected in regular statistics education. I present some specific features of civic statistics, provide examples and describe implications for curricula, teacher activities and the future of statistical education. In my presentation, I will give a short online...

Research paper thumbnail of Exploring civic statistics with CODAP

Data are abundant, quantitative information about the state of society and the wider world is aro... more Data are abundant, quantitative information about the state of society and the wider world is around us more than ever. In order to root the public debate based on facts instead of emotions and to promote evidence-based policy decisions we as statistics educators are challenged to promote understanding of statistics about society. This report summarizes a hand-on workshop in which participants explored the potential of the freely available web-based data platform CODAP (http://codap.concord.org) and its usefulness for investigating civic statistics data. Materials of the workshop were developed as part of the EU-funded ProCivicStat Project and are freely available (www.procivicstat.org)

Research paper thumbnail of Implementing Civic Statistics in Mathematics Teacher Education

Research paper thumbnail of Data and Statistics as basis for political decisions: lessons to be learnt from the COVID-19 pandemic

Proceedings of the IASE 2021 Satellite Conference, 2022

The Covid-19 crisis has impressively raised the general awareness that our social coexistence and... more The Covid-19 crisis has impressively raised the general awareness that our social coexistence and political decisions are essentially based on data, the weighing of risks and thus on probability estimates. This places high demands on the ability of health authorities, policy makers and the media to communicate statistical information as well as on the ability of citizens to understand these messages. In this paper we reflect on the role of scientific evidence in democratic societies and analyze selected illustrative examples of communicating evidence via visualizations and simulation, media reports, and expert’s statements. We identify venues and formats of communicating statistical information about the pandemics to the public that seems to be effective contrasting less helpful formats. We conclude by presenting recommendations for stakeholders in politics, media and statistics agencies on how to communicate empirical evidence to the public efficiently, released by the Deutsche Arb...

Research paper thumbnail of Standardmodelle und Naturgesetz: Was uns der Kontext und unser Vorwissen verraten kann

Wie kommt man von Daten, die aus den Beobachtungen von zwei Variablen gewonnenwurden, zu einer Fu... more Wie kommt man von Daten, die aus den Beobachtungen von zwei Variablen gewonnenwurden, zu einer Funktion, die die Abhangigkeit zwischen den beiden Variablenbeschreibt? Wie lasst sich ein funktionaler Zusammenhang zwischen zwei Variablenspezifizieren und die Herleitung eines Graphen oder einer Funktionsgleichung begrunden? Hierzu gibt es eine Vielzahl von Ansatzen, wie mit mathematischen Methodenein Sachzusammenhang modelliert werden kann.

Research paper thumbnail of 3. Lösungen algebraischer Gleichungen

Research paper thumbnail of Funktionen, Daten und Modelle: Vernetzende Zugänge zu zentralen Themen der (Schul-)Mathematik

Journal für Mathematik-Didaktik, 2016

Zusammenfassung Wie lassen sich Zusammenhänge zwischen zwei Größen mit Hilfe des mathematischen F... more Zusammenfassung Wie lassen sich Zusammenhänge zwischen zwei Größen mit Hilfe des mathematischen Funktionsbegriffs modellieren? Das zentrale Anliegen dieses Aufsatzes besteht darin, ein bis in die Schulmathematik der unteren und mittleren Klassen reichendes Thema der modernen Mathematik konsistent zu rekonstruieren. Es wird dabei aufgezeigt, wie mit zunehmender mathematischer Kompetenz verfeinerte Methoden eingesetzt werden können, um auf zunehmend anspruchsvolle Weise ein und dasselbe Ziel zu verfolgen: Abhängigkeiten zwischen zwei metrisch skalierten Größen zu modellieren. Zugleich wird gezeigt, wie grundlegende Ideen zum Modellieren funktionaler Abhängigkeiten lebendig und wirklichkeitsnah gestaltet werden können. Dieser Zugang vernetzt zentrale Themen der Schulmathematik, insbesondere Funktionenlehre, Analysis, Stochastik, Lineare Algebra und Numerik. Die einzelnen Ansätze verwenden nicht nur unterschiedliche mathematische Methoden, sondern basieren auch auf unterschiedlichen konzeptionellen Vorstellungen und Modellierungsannahmen. Schlüsselwörter Funktionaler Zusammenhang • Modellieren • Daten und Zufall • Analysis • Stochastik MESC Codes D30 • I10 • K40 • M10 Functions, data and models: connecting central topics of the mathematics curriculum Abstract How to model dependencies between two variables using the mathematical concept of a function? The central concern of this paper is to reconstruct a modern

Research paper thumbnail of Statistics for Empowerment and Social Engagement

Statistics for Empowerment and Social Engagement

The first three chapters of this book have identified societal demands for understanding Civic St... more The first three chapters of this book have identified societal demands for understanding Civic Statistics (Chap. 1), described specific features of the statistical and mathematical information citizens receive about civic issues (Chap. 2), and mapped out the facets and tools (skills, knowledge, mental and motivational tools) needed to critically understand such statistical and mathematical information about society (Chap. 3). The present chapter examines issues that are essential for promoting necessary changes in the teaching and learning of Civic Statistics, which are needed for empowering citizens to engage with and analyze data sources and data-informed reasoning about burning issues in society, and critically interpret messages related to Civic Statistics encountered in the news media, social networks and related digital sources. The chapter first provides further illustrations of activities or tasks pertaining to Civic Statistics and shows how to analyse task demands in terms ...

Research paper thumbnail of Civic Statistics in the training of pre-service mathematics teachers

In an increasingly complex world, the involvement of informed and committed citizens is a critica... more In an increasingly complex world, the involvement of informed and committed citizens is a critical resource in public decision-making at international, national and local levels. The project ProCivicStat, a strategic partnership of six universities funded through the Erasmus+ program of the European Union (funding period September 2015 to August 2018), explores a subfield we call Civic Statistics which focuses on understanding quantitative and statistical information about society as provided by the media, statistics offices and other statistics providers (Engel et al. 2016). Understanding Civic Statistics is required for participation in democratic societies, but involves data that often are open, official, multivariate in nature, and/or dynamic, that is not normally taught in regular mathematics and statistics education, let alone in civics or social study classes. Few high school teachers in mathematics receive any training on how to teach statistics, not to speak of social science teachers who may have no training in statistics at all. As a result, teachers stay within their comfort zone and overemphasize a narrow range of statistical techniques and computations (mathematics) or fail to engage with statistical ideas at all (social science). They pay too little attention to working with and understanding multivariate data that describe social trends, and to the analysis, interpretation and communication about the meaning of such data. But capacity building for informed and committed citizens has to start in school education. While focusing on curricula at the secondary and tertiary level, the ultimate goal of ProCivicStat is to strengthen civil society, empowering informed citizens for evidence-based decision-making and civil society engagement. The challenge is multi-facetted. Data literacy for civic engagement involves, among many other aspects, specific statistical knowledge, ICT skills, knowledge about computing and data structures, critical thinking, and much more.

Research paper thumbnail of The importance of statistical literacy for democracy : civic-education through statistics

Civic Education has had the same objective (“Mündigkeit”) for the last 50 years, but the conditio... more Civic Education has had the same objective (“Mündigkeit”) for the last 50 years, but the conditions to achieve it have changed. Mündigkeit is a prerequisite for citizen’s participation, to strengthen and stabilize democratic structures. In the information age, Mündigkeit regarding statistics means having an orientation in the confusion of the modern information jungle and the deluge of quantitative information and statistics. The requirements for understanding and evaluating information about societal developments have changed: Statistical skills are becoming increasingly important for an evidence-based judgment in today's society. They entail understanding data-related arguments and representations, questioning possible conclusions as well as uncovering opinions and already made decisions

Research paper thumbnail of Editorial: Research on Data Science Education

STATISTICS EDUCATION RESEARCH JOURNAL

A very warm welcome to this Special Issue of the Statistics Education Research Journal (SERJ) on ... more A very warm welcome to this Special Issue of the Statistics Education Research Journal (SERJ) on data science education. Our hope is to give an overview of selected theoretical thoughts and empirical studies on data science education from a statistics education research perspective. Data science education is rapidly developing but research into data science education is still in its infancy. The current issue presents a snapshot of this developing field.

Research paper thumbnail of Topic Study Group No. 14: Teaching Learning of Probability

Proceedings of the 13th International Congress on Mathematical Education, 2017