In this study, the effects of personal factors relevant for academic achievement and beliefs abou... more In this study, the effects of personal factors relevant for academic achievement and beliefs about mathematics on performance in modelling tasks are illuminated and empirically validated. Relations between performance in certain steps of the modelling process and reading competence, mathematical competence, general knowledge, word comprehension, fluid intelligence (reasoning ability) and beliefs about mathematics are particularized. Empirical validity of the postulated relations was tested by a structural equation approach with a sample of 959 students (grade six). Model fit and parameter estimates support the postulated relations between these personal factors and performance in mathematical modelling. Thereby, the construct of mathematical modelling was illuminated and conclusions for fostering mathematical modelling could be drawn by accounting for those personal factors affecting academic achievement that are related to mathematical modelling.
This paper presents an intervention study whose aim was to promote teacher beliefs about mathemat... more This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and findings from mathematics education. Teacher beliefs about mathematics, learning and self-efficacy were expected to have a major impact on their classroom practices. We therefore assessed teacher beliefs about the usefulness of mathematics, learning (constructivist and socio-constructivist beliefs) and teacher self-efficacy when teaching modeling (teacher or class level variable). The student level variables assessed were modeling competence and other individual factors, such as basic mathematical skills and cognitive abilities. The effectiveness of the intervention was measured in a pre-post control group design using multilevel structural ...
Die nationalen deutschen Bildungsstandards fur die Grundschule nennen Modellieren als eine von fu... more Die nationalen deutschen Bildungsstandards fur die Grundschule nennen Modellieren als eine von funf allgemeinen Kompetenzen, die die Lernenden in der Grundschule erwerben sollen. Doch was versteht man unter Modellieren und wo liegen die Unterschiede zum Sachrechnen? Konnen die Schulerinnen und Schuler der Grundschule uberhaupt das Modellieren lernen? Wie sieht guter Unterricht zum Modellieren aus? Das sind alles Fragen, die sich in der Praxis stellen. Dieser Artikel versucht, darauf Antworten zu geben und eine Ubersicht uber die Thematik des Modellierens in der Grundschule zu geben.
International Journal of Science and Mathematics Education, 2021
The world is facing severe global challenges such as climate change, food security, rising migrat... more The world is facing severe global challenges such as climate change, food security, rising migration, social justice, or the current corona crisis. In these times, citizenship education seems more important than ever. How can this citizenship education relate to mathematics and science learning? The research project MaSDiV (Supporting mathematics and science teachers in addressing diversity and promoting fundamental values) connected mathematics and science with citizenship education by modeling real-life problems relevant to society. In this paper, we present the foundational design features of the PD course as well the results from the accompanying evaluation of this PD course, which was implemented by partners in six countries to support teachers in connecting mathematics and science education with citizenship education. More specifically, we investigate how participating teachers experienced the PD program; how their self-efficacy beliefs, learning-related beliefs, as well as te...
Mathematisches Modellieren tragt dazu bei, dass die Schulerinnen und Schuler Einblick in die Nutz... more Mathematisches Modellieren tragt dazu bei, dass die Schulerinnen und Schuler Einblick in die Nutzlichkeit von Mathematik bekommen und lernen, Mathematik im Leben anzuwenden. Daruber hinaus kann dieses sinnhafte Lernen von Mathematik die Lernfreude an Mathematik und die motivationale Bereitschaft, sich mit Mathematik auseinanderzusetzen, erhohen. Mathematisches Modellieren erscheint daher gerade fur leistungsschwachere Schulerinnen und Schuler von groster Bedeutung zu sein. Doch die bisher entwickelten Modellierungsaufgaben sind vielfach fur diese Zielgruppe zu komplex. Daher wurde im Projekt STRATUM – basierend auf der aktuellen Diskussion zum Modellieren und zur Motivationspsychologie – ein systematischer Lehrgang entwickelt, der empirische Ergebnisse zu leistungsschwacheren Lernenden zum Ausgang nimmt und sie schrittweise zum selbstandigen Modellieren fuhrt. Der Aufsatz stellt den theoretischen Hintergrund und die Konzeption des Lehrgangs vor und gibt Einblick in die Ergebnisse de...
Dieser Aufsatz skizziert zunachst, warum mathematische Modellierungen in den Unterricht der Sekun... more Dieser Aufsatz skizziert zunachst, warum mathematische Modellierungen in den Unterricht der Sekundarstufe I integriert werden sollten. Anschliesend wird ein Modellierungsbeispiel vorgestellt, das in Klasse 6 oder 7 behandelt werden kann und sich auch fur die Ersteinfuhrung von Modellierungen eignet: Die Berechnung des Lackverbrauchs beim Porsche 911. Ein Beispiel fur eine Klassenarbeit sowie ein Bewertungsschema ermoglichen den Einsatz im „alltaglichen“ Unterricht.
This article is based on the panel on inquiry based mathematics education and the development of ... more This article is based on the panel on inquiry based mathematics education and the development of learning trajectories held at the VARGA 100 Conference. After an introduction presenting the theme and organization of the panel, this article focuses on the diversity of conceptualizations of inquiry based education existing today in mathematics education and their influence on the vision and development of learning trajectories. More precisely, it considers the conceptualizations respectively associated with Realistic Mathematics Education, Genetic Constructivism, Tamás Varga's educational approach and the Anthropological Theory of the Didactic, presented by the panellists, and also shows the efforts undertaken in European projects to reach consensusal visions.
Although well researched in educational studies, inquiry-based learning, a student-centred way of... more Although well researched in educational studies, inquiry-based learning, a student-centred way of teaching, is far away from being implemented in day-to-day science and mathematics teaching on a large scale. It is a challenge for teachers to adopt this new way of teaching in an often not supportive school context. Therefore it is important to provide high-quality professional development (PD) at a large scale. However, there is little empirical evidence about the effects of scaled-up professional development initiatives. Therefore, this paper presents an international research study for which long-term PD courses have been designed. These courses have been implemented across Europe in twelve different countries at scale by using the so-called “Cascade Model”. Here, course leaders are educated, who in turn educate other teachers. The research study aimed at evaluating the overall impact the scaled-up PD had on teachers and at also identifying variables influencing this impact.
This paper reports on a professional development activity (PD) for course leaders, which was desi... more This paper reports on a professional development activity (PD) for course leaders, which was designed within the European project Primas (2010-13, www.primas-project.eu). Primas aimed at the implementation of inquiry-based learning (IBL) in day-to-day teaching on a large scale. The focus is on the education of mathematics course leaders in Germany, who were all teachers. In order to support them in taking up their role and run courses on (IBL), a course leader seminar following design research was developed. The course aimed at course leaders’ learning on two levels: (1) as mathematics teachers about IBL and (2) as course leaders about running PD on IBL. A small scale retrospective interview study gives insights into the needs the participants face when learning about IBL as teachers and when learning as future course leaders. It also illuminates in which way participants took up their role as a course leader. These insights suggest how to optimize the course following design research.
This paper addresses a particular aspect of 21st century skills: the potential of STEM (science, ... more This paper addresses a particular aspect of 21st century skills: the potential of STEM (science, technology, engineering and mathematics) to support students in developing skills for citizenship, life and careers. In this respect, including connections to the world of work in mathematics and science classes seems to be indispensable. Therefore, in this paper we outline the necessity of including such connections in education and the related theoretical background. We then present an international research study of long-term professional development courses involving inquiry-based learning and connections to the world of work. The course was designed on an international level for use in 13 countries and was subsequently implemented in these countries. The results of the pre-post study across all these countries show that such a course can indeed lead to the desired outcomes concerning the teachers and their teaching, but also that these outcomes are associated with teachers’ beliefs as well as their perceptions of policy support, classroom management and time issues.
Mathematical and scientific knowledge are integral to preparing our population to be actively eng... more Mathematical and scientific knowledge are integral to preparing our population to be actively engaged and responsible citizens. Science and mathematics education, however, has mainly focused on concepts and skills detached from societal implications. In this paper we present an interdisciplinary international design research study in which we developed teaching and professional development materials connecting mathematics and science education to citizenship education. We outline the design research process, its theoretical basis as well as the design products. The study shows that it is indeed possible to develop such approaches supporting active citizenship and thereby the development of 21st century skills in mathematics education, thus strengthening the role of mathematics education in the STEM field.
This paper presents an international research study of long-term professional development courses... more This paper presents an international research study of long-term professional development courses on modelling. It addresses the question of scaling-up professional development. So far, there has been much research on small-scale professional development courses, but we know very little about what it means to scale up such a course and to reach out to large numbers of teachers. Therefore, our study researches the impact of a scaled up professional development course on teachers and their teaching, as perceived by the teachers themselves and their students. The course was designed on an international level for use in 12 countries. The results show that such a course can indeed lead to desired outcomes concerning the teachers and their teaching, and the research therefore adds to our understanding of scaling-up.
Inquiry-based learning (IBL) is a more student-centered approach to mathematics teaching that is ... more Inquiry-based learning (IBL) is a more student-centered approach to mathematics teaching that is recommended by many policy and curriculum documents across Europe. However, it is not easy for teachers to change from a more teacher-centered way of teaching to inquiry-based teaching as this involves a change of their role in class. Professional development courses are one way to help teachers with this endeavor. Within the discussion of effective professional development, beliefs are often named as an important influencing factor. In this respect, much research has been carried out on how beliefs on mathematics teaching impact the outcomes of the course. However, there has been much less research on what beliefs mathematics teachers develop on inquiry-based learning and how this might impact their (perceived) classroom teaching. Therefore, this paper presents an international research study carried out within the European Project Primas, in which professional development courses on in...
In the following, I will comment on the chapter by Haines on “Drivers for Mathematical Modelling:... more In the following, I will comment on the chapter by Haines on “Drivers for Mathematical Modelling: Pragmatism in Practice” in this volume. The examples described by Haines exemplify in an expressive way that modelling can be quite challenging and many reality-related problems can be only dealt with at tertiary level. Subsequently, it may be questioned if modelling is possible in lower secondary school and even in primary school. When it comes to lower secondary level, this has been widely accepted (see e.g. Blum and Leiß 2007). Additionally, modelling is also possible at primary level, when appropriate tasks for children are chosen (see, e.g. Biembengut 2007).
Abstract Modelling and application are regarded as an important topic for maths lessons. But so f... more Abstract Modelling and application are regarded as an important topic for maths lessons. But so far the concept 'modelling competencies” has not been described in a comprehensive manner. The aim of this paper is to supplement former descriptions of modelling competencies based on empirical data. An empirical study was carried out which aimed at showing the effects of the integration of modelling tasks into day-to-day maths classes. Central questions of this study were - among others: How far do math lessons with focus on modelling enable students to carry out modelling processes on their own? What are modelling competencies? The paper describes the theoretical and the methodological approach, the classroom settings, and the results of the study.
In this study, the effects of personal factors relevant for academic achievement and beliefs abou... more In this study, the effects of personal factors relevant for academic achievement and beliefs about mathematics on performance in modelling tasks are illuminated and empirically validated. Relations between performance in certain steps of the modelling process and reading competence, mathematical competence, general knowledge, word comprehension, fluid intelligence (reasoning ability) and beliefs about mathematics are particularized. Empirical validity of the postulated relations was tested by a structural equation approach with a sample of 959 students (grade six). Model fit and parameter estimates support the postulated relations between these personal factors and performance in mathematical modelling. Thereby, the construct of mathematical modelling was illuminated and conclusions for fostering mathematical modelling could be drawn by accounting for those personal factors affecting academic achievement that are related to mathematical modelling.
This paper presents an intervention study whose aim was to promote teacher beliefs about mathemat... more This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and findings from mathematics education. Teacher beliefs about mathematics, learning and self-efficacy were expected to have a major impact on their classroom practices. We therefore assessed teacher beliefs about the usefulness of mathematics, learning (constructivist and socio-constructivist beliefs) and teacher self-efficacy when teaching modeling (teacher or class level variable). The student level variables assessed were modeling competence and other individual factors, such as basic mathematical skills and cognitive abilities. The effectiveness of the intervention was measured in a pre-post control group design using multilevel structural ...
Die nationalen deutschen Bildungsstandards fur die Grundschule nennen Modellieren als eine von fu... more Die nationalen deutschen Bildungsstandards fur die Grundschule nennen Modellieren als eine von funf allgemeinen Kompetenzen, die die Lernenden in der Grundschule erwerben sollen. Doch was versteht man unter Modellieren und wo liegen die Unterschiede zum Sachrechnen? Konnen die Schulerinnen und Schuler der Grundschule uberhaupt das Modellieren lernen? Wie sieht guter Unterricht zum Modellieren aus? Das sind alles Fragen, die sich in der Praxis stellen. Dieser Artikel versucht, darauf Antworten zu geben und eine Ubersicht uber die Thematik des Modellierens in der Grundschule zu geben.
International Journal of Science and Mathematics Education, 2021
The world is facing severe global challenges such as climate change, food security, rising migrat... more The world is facing severe global challenges such as climate change, food security, rising migration, social justice, or the current corona crisis. In these times, citizenship education seems more important than ever. How can this citizenship education relate to mathematics and science learning? The research project MaSDiV (Supporting mathematics and science teachers in addressing diversity and promoting fundamental values) connected mathematics and science with citizenship education by modeling real-life problems relevant to society. In this paper, we present the foundational design features of the PD course as well the results from the accompanying evaluation of this PD course, which was implemented by partners in six countries to support teachers in connecting mathematics and science education with citizenship education. More specifically, we investigate how participating teachers experienced the PD program; how their self-efficacy beliefs, learning-related beliefs, as well as te...
Mathematisches Modellieren tragt dazu bei, dass die Schulerinnen und Schuler Einblick in die Nutz... more Mathematisches Modellieren tragt dazu bei, dass die Schulerinnen und Schuler Einblick in die Nutzlichkeit von Mathematik bekommen und lernen, Mathematik im Leben anzuwenden. Daruber hinaus kann dieses sinnhafte Lernen von Mathematik die Lernfreude an Mathematik und die motivationale Bereitschaft, sich mit Mathematik auseinanderzusetzen, erhohen. Mathematisches Modellieren erscheint daher gerade fur leistungsschwachere Schulerinnen und Schuler von groster Bedeutung zu sein. Doch die bisher entwickelten Modellierungsaufgaben sind vielfach fur diese Zielgruppe zu komplex. Daher wurde im Projekt STRATUM – basierend auf der aktuellen Diskussion zum Modellieren und zur Motivationspsychologie – ein systematischer Lehrgang entwickelt, der empirische Ergebnisse zu leistungsschwacheren Lernenden zum Ausgang nimmt und sie schrittweise zum selbstandigen Modellieren fuhrt. Der Aufsatz stellt den theoretischen Hintergrund und die Konzeption des Lehrgangs vor und gibt Einblick in die Ergebnisse de...
Dieser Aufsatz skizziert zunachst, warum mathematische Modellierungen in den Unterricht der Sekun... more Dieser Aufsatz skizziert zunachst, warum mathematische Modellierungen in den Unterricht der Sekundarstufe I integriert werden sollten. Anschliesend wird ein Modellierungsbeispiel vorgestellt, das in Klasse 6 oder 7 behandelt werden kann und sich auch fur die Ersteinfuhrung von Modellierungen eignet: Die Berechnung des Lackverbrauchs beim Porsche 911. Ein Beispiel fur eine Klassenarbeit sowie ein Bewertungsschema ermoglichen den Einsatz im „alltaglichen“ Unterricht.
This article is based on the panel on inquiry based mathematics education and the development of ... more This article is based on the panel on inquiry based mathematics education and the development of learning trajectories held at the VARGA 100 Conference. After an introduction presenting the theme and organization of the panel, this article focuses on the diversity of conceptualizations of inquiry based education existing today in mathematics education and their influence on the vision and development of learning trajectories. More precisely, it considers the conceptualizations respectively associated with Realistic Mathematics Education, Genetic Constructivism, Tamás Varga's educational approach and the Anthropological Theory of the Didactic, presented by the panellists, and also shows the efforts undertaken in European projects to reach consensusal visions.
Although well researched in educational studies, inquiry-based learning, a student-centred way of... more Although well researched in educational studies, inquiry-based learning, a student-centred way of teaching, is far away from being implemented in day-to-day science and mathematics teaching on a large scale. It is a challenge for teachers to adopt this new way of teaching in an often not supportive school context. Therefore it is important to provide high-quality professional development (PD) at a large scale. However, there is little empirical evidence about the effects of scaled-up professional development initiatives. Therefore, this paper presents an international research study for which long-term PD courses have been designed. These courses have been implemented across Europe in twelve different countries at scale by using the so-called “Cascade Model”. Here, course leaders are educated, who in turn educate other teachers. The research study aimed at evaluating the overall impact the scaled-up PD had on teachers and at also identifying variables influencing this impact.
This paper reports on a professional development activity (PD) for course leaders, which was desi... more This paper reports on a professional development activity (PD) for course leaders, which was designed within the European project Primas (2010-13, www.primas-project.eu). Primas aimed at the implementation of inquiry-based learning (IBL) in day-to-day teaching on a large scale. The focus is on the education of mathematics course leaders in Germany, who were all teachers. In order to support them in taking up their role and run courses on (IBL), a course leader seminar following design research was developed. The course aimed at course leaders’ learning on two levels: (1) as mathematics teachers about IBL and (2) as course leaders about running PD on IBL. A small scale retrospective interview study gives insights into the needs the participants face when learning about IBL as teachers and when learning as future course leaders. It also illuminates in which way participants took up their role as a course leader. These insights suggest how to optimize the course following design research.
This paper addresses a particular aspect of 21st century skills: the potential of STEM (science, ... more This paper addresses a particular aspect of 21st century skills: the potential of STEM (science, technology, engineering and mathematics) to support students in developing skills for citizenship, life and careers. In this respect, including connections to the world of work in mathematics and science classes seems to be indispensable. Therefore, in this paper we outline the necessity of including such connections in education and the related theoretical background. We then present an international research study of long-term professional development courses involving inquiry-based learning and connections to the world of work. The course was designed on an international level for use in 13 countries and was subsequently implemented in these countries. The results of the pre-post study across all these countries show that such a course can indeed lead to the desired outcomes concerning the teachers and their teaching, but also that these outcomes are associated with teachers’ beliefs as well as their perceptions of policy support, classroom management and time issues.
Mathematical and scientific knowledge are integral to preparing our population to be actively eng... more Mathematical and scientific knowledge are integral to preparing our population to be actively engaged and responsible citizens. Science and mathematics education, however, has mainly focused on concepts and skills detached from societal implications. In this paper we present an interdisciplinary international design research study in which we developed teaching and professional development materials connecting mathematics and science education to citizenship education. We outline the design research process, its theoretical basis as well as the design products. The study shows that it is indeed possible to develop such approaches supporting active citizenship and thereby the development of 21st century skills in mathematics education, thus strengthening the role of mathematics education in the STEM field.
This paper presents an international research study of long-term professional development courses... more This paper presents an international research study of long-term professional development courses on modelling. It addresses the question of scaling-up professional development. So far, there has been much research on small-scale professional development courses, but we know very little about what it means to scale up such a course and to reach out to large numbers of teachers. Therefore, our study researches the impact of a scaled up professional development course on teachers and their teaching, as perceived by the teachers themselves and their students. The course was designed on an international level for use in 12 countries. The results show that such a course can indeed lead to desired outcomes concerning the teachers and their teaching, and the research therefore adds to our understanding of scaling-up.
Inquiry-based learning (IBL) is a more student-centered approach to mathematics teaching that is ... more Inquiry-based learning (IBL) is a more student-centered approach to mathematics teaching that is recommended by many policy and curriculum documents across Europe. However, it is not easy for teachers to change from a more teacher-centered way of teaching to inquiry-based teaching as this involves a change of their role in class. Professional development courses are one way to help teachers with this endeavor. Within the discussion of effective professional development, beliefs are often named as an important influencing factor. In this respect, much research has been carried out on how beliefs on mathematics teaching impact the outcomes of the course. However, there has been much less research on what beliefs mathematics teachers develop on inquiry-based learning and how this might impact their (perceived) classroom teaching. Therefore, this paper presents an international research study carried out within the European Project Primas, in which professional development courses on in...
In the following, I will comment on the chapter by Haines on “Drivers for Mathematical Modelling:... more In the following, I will comment on the chapter by Haines on “Drivers for Mathematical Modelling: Pragmatism in Practice” in this volume. The examples described by Haines exemplify in an expressive way that modelling can be quite challenging and many reality-related problems can be only dealt with at tertiary level. Subsequently, it may be questioned if modelling is possible in lower secondary school and even in primary school. When it comes to lower secondary level, this has been widely accepted (see e.g. Blum and Leiß 2007). Additionally, modelling is also possible at primary level, when appropriate tasks for children are chosen (see, e.g. Biembengut 2007).
Abstract Modelling and application are regarded as an important topic for maths lessons. But so f... more Abstract Modelling and application are regarded as an important topic for maths lessons. But so far the concept 'modelling competencies” has not been described in a comprehensive manner. The aim of this paper is to supplement former descriptions of modelling competencies based on empirical data. An empirical study was carried out which aimed at showing the effects of the integration of modelling tasks into day-to-day maths classes. Central questions of this study were - among others: How far do math lessons with focus on modelling enable students to carry out modelling processes on their own? What are modelling competencies? The paper describes the theoretical and the methodological approach, the classroom settings, and the results of the study.
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