Andreas Obersteiner

Andreas Obersteiner
Technische Universität München | TUM · TUM School of Social Sciences and Technology

Prof. Dr.

About

85
Publications
21,248
Reads
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965
Citations
Citations since 2017
49 Research Items
788 Citations
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Introduction
Andreas Obersteiner is a full professor at the Technical University of Munich. He is holding the Heinz Nixdorf Chair of Mathematics Education. Much of his research focusses on understanding and supporting mathematical thinking and learning processes, and on connecting basic cognitive research with educational practice. To that end, he uses a variety of research methods, including traditional methods as well as measures of reaction times and eye movements.
Additional affiliations
October 2020 - March 2021
Pädagogische Hochschule Ludwigsburg
Position
  • Professor (Full)
March 2017 - March 2018
University of Wisconsin–Madison
Position
  • Research Associate
April 2016 - October 2020
Freiburg University of Education
Position
  • Professor (Full)

Publications

Publications (85)
Article
Many studies have used fraction magnitude comparison tasks to assess people’s abilities to quickly assess fraction magnitudes. However, since there are multiple ways to compare fractions, it is not clear whether people actually reason about the holistic magnitudes of the fractions in this task and whether they use multiple strategies in a flexible...
Article
Full-text available
Beim Übergang von natürlichen Zahlen zu Bruchzahlen müssen Lernende einen Conceptual Change vollziehen, da manche der von den natürlichen Zahlen vertrauten Eigenschaften weiterhin gültig sind, während andere ihre Allgemeingültigkeit verlieren. In der vorliegenden Analyse wurden drei Schulbuchreihen der Klassen 5 bis 7 daraufhin untersucht, ob und i...
Article
Full-text available
To assess individual students’ abilities and misconceptions in mathemat- ics, teachers need diagnostic competencies. Although research has addressed the quality of teachers’ diagnostic competencies in recent years, it is not very clear how to foster these competencies effectively in the course of prospective teachers’ university education. Research...
Chapter
Full-text available
Analyzing students’ documents (e.g., their homework) can serve as a basis for diagnosing students’ learning status and thus also for adaptive teaching. When making diagnostic judgments about students’ learning status in mathematics, teachers may benefit from using theoretical models of mathematical competence because such models illustrate what tas...
Article
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Simulation-based learning is often used to facilitate complex problem-solving skills, such as collaborative diagnostic reasoning (CDR). Simulations can be especially effective if additional instructional support is provided. However, adapting instructional support to the learners' needs remains a challenge when performance is only assessed as the o...
Chapter
Many children and adults experience fractions as a challenging mathematical content. Behavioral studies have extensively documented typical errors in fraction tasks and identified various factors that contribute to their occurrence. However, the cognitive mechanisms of fraction processing and fraction learning are still not fully understood. In rec...
Conference Paper
Full-text available
Teachers' diagnostic competence includes the ability to identify misconceptions in student solutions and to respond adaptively to these solutions. According to current models of diagnostic competence, teachers need pedagogical content knowledge (PCK) about typical student misconceptions and they need to use this knowledge effectively when respondin...
Article
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An important aspect of mathematics teachers’ diagnostic competences is the ability to judge the difficulty of a mathematical task. The process of judging task difficulty includes the perception and interpretation of task characteristics that are potentially challenging for students. Such judgement processes are often quick and difficult to assess....
Article
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Research in universities and other organizations is often conducted within established disciplines that are historically based and highly arbitrary (Campbell, 2014). However, emergent phenomena fail to fit into disciplinary boundaries, making cross-disciplinary research necessary, often involving corresponding collaboration (Hall et al., 2008). On...
Article
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Self-efficacy is an important predictor of learning and achievement. By definition, self-efficacy requires a task-specific assessment, in which students are asked to evaluate whether they can solve concrete tasks. An underlying assumption in previous research into such assessments was that self-efficacy is a one-dimensional construct. However, empi...
Article
People are often better at comparing fractions when the larger fraction has the larger rather than the smaller natural number components. However, there is conflicting evidence about whether this “natural number bias” occurs for complex fraction comparisons (e.g., 23/52 vs. 11/19). It is also unclear whether using benchmarks such as 1/2 or 1/4 enha...
Article
Full-text available
Eye tracking is an increasingly popular method in mathematics education. While the technology has greatly evolved in recent years, there is a debate about the specific benefits that eye tracking offers and about the kinds of insights it may allow. The aim of this review is to contribute to this discussion by providing a comprehensive overview of th...
Article
Full-text available
Research has identified two core difficulties many students have with fractions: first, they often struggle with processing fraction magnitudes, and second, they rely on natural number concepts in fraction problems ["Natural Number Bias" (NNB)]. Yet, the relation between these two difficulties is not well-understood. Moreover, while most studies of...
Conference Paper
Ein Verständnis für den Bruchzahlbegriff gilt als zentrales Lernziel im Inhaltsbereich Zahl und als Erfolgsindikator für spätere mathematische Leistungen. Jedoch sehen sich zahlreiche Schülerinnen und Schüler beim Erlernen des Bruch-zahlbegriffs großen Schwierigkeiten gegenüber. Auf Grund ihrer "Schlüsselrolle" für das Lernen von Mathematik stellen...
Article
Full-text available
Diagnostic competences are an essential facet of teacher competence. Many studies have investigated the quality of teachers’ judgments of students’ competences. However, little is known about the processes that lead to these judgments and about the ways to promote these processes in the early phase of teacher training. The aim of the research proje...
Article
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We propose a conceptual framework which may guide research on fostering diagnostic competences in simulations in higher education. We first review and link research perspectives on the components and the development of diagnostic competences, taken from medical and teacher education. Applying conceptual knowledge in diagnostic activities is conside...
Article
Das Arbeiten mit Funktionen gehört zu den zentralen Kompetenzbereichen des Mathematikunterrichts. Kompetenzen sind dabei als individuelle Ausprägungen kognitiver und auch affektiv-motivationaler Dispositionen, wie Selbstwirksamkeitserwartungen, zu verstehen. Für die Identifikation von Kompetenzprofilen bei linearen Funktionen fehlen bislang jedoch...
Conference Paper
Eyetracking nimmt in der mathematikdidaktischen Forschung mittlerweile eine prominente Rolle ein. Studien nutzen dabei zahlreiche technische, methodische und theoretische Ansätze zur Beantwortung von Fragestellungen aus diversen Inhaltsbereichen. Es stellt sich die Frage, welchen spezifischen Beitrag Eyetracking dabei für die mathematikdidaktische...
Article
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Affect and mathematical competence are each multifaceted constructs. Accordingly, the studies in this Special Issue address multiple pathways between the two in young children. This commentary highlights the variability of these pathways and asks how affective variables are specifically related to core mathematical activities such as problem solvin...
Chapter
Many students face difficulties with fractions. Research in mathematics education and cognitive psychology aims at understanding where and why students struggle with fractions and how to make teaching of fractions more effective. Additionally, neuroscience research is beginning to explore how the human brain processes fractions. Yet, attempts to in...
Chapter
Large-scale studies assess mathematical competence in large samples. They often compare mathematical competence between groups of individuals within or between countries. Although large-scale research is part of empirical educational research more generally, it is also linked to more genuine mathematics education research traditions, because sophis...
Article
Full-text available
Professional knowledge is highlighted as an important prerequisite of both medical doctors and teachers. Based on recent conceptions of professional knowledge in these fields, knowledge can be differentiated within several aspects. However, these knowledge aspects are currently conceptualized differently across different domains and projects. Thus,...
Conference Paper
An understanding of fraction concepts is a key facet of mathematical literacy. There is empirical evidence that understanding fractions is predictive of later achievement in higher mathematics such as algebra (Bailey, Hoard, Nugent, & Geary, 2012). Unfortunately, many students struggle with learning of fraction concepts as well as with higher mathe...
Article
Full-text available
Recent studies have tracked eye movements to assess the cognitive processes involved in fraction comparison. This study advances that work by assessing eye movements during the more complex task of fraction addition. Adults mentally solved fraction addition problems that were presented on a computer screen. The study included four types of problems...
Article
Mathematics education is a scientific discipline that has close connections to other disciplines. Psychology is one of these related disciplines, but the specific nature of the relationship between psychology and mathematics education is a matter of debate. This special issue aims at contributing to this debate, by presenting studies that rely on t...
Chapter
Full-text available
This chapter focuses on the neuro-cognitive, cognitive and developmental analyses of whole number arithmetic (WNA) learning. It comprises five sections. The first section provides an overview of the working group discussion. Section 7.2 reviews neuro-cognitive perspectives of learning WNA but looks beyond these to explain the transcoding of numeral...
Article
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The results of international comparison studies such as the Program for International Student Assessment (PISA) have initiated intense discussions about educational reforms in Germany. Although in-service and pre-service teachers are an essential part of such reforms, little is known about their attitudes towards PISA studies. The present study aim...
Article
Full-text available
Number sense requires, at least, an ability to assess magnitude information represented by number symbols. Most educated adults are able to assess magnitude information of rational numbers fairly quickly, including whole numbers and fractions. It is to date unclear whether educated adults without training are able to assess magnitudes of irrational...
Article
Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people...
Article
Full-text available
Research suggests that people use a variety of strategies for comparing the numerical values of two fractions. They use holistic strategies that rely on the fraction magnitudes, componential strategies that rely on the fraction numerators or denominators, or a combination of both. We investigated how mathematically skilled adults adapt their strate...
Chapter
Learning environments created to support children’s development of early numeracy often use games. This applies to both formal and informal learning environments. However, there is hardly any empirical research on the effectiveness of games being used in such learning environments. Moreover, it has rarely been discussed whether the games are approp...
Conference Paper
Full-text available
Heuristic worked examples are an effective way to foster students’ mathematical argumentation skills. This study explores how secondary school students make use of different types of representations when working with such kinds of heuristic worked examples. Eye tracking data showed that the students spent more time on pictures than on symbolic or t...
Conference Paper
Full-text available
Competence models have been developed to describe levels of competence in mathematics and particularly in the domain of whole numbers. So far, only descriptions of what competence at different levels actually means are available, but current models do not describe how children can reach the next level. In this article, we propose a fine-grained des...
Article
Full-text available
Understanding contingency table analysis is a facet of mathematical competence in the domain of data and probability. Previous studies have shown that even young children are able to solve specific contingency table problems, but apply a variety of strategies that are actually invalid. The purpose of this paper is to describe primary school childre...
Article
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External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one co...
Article
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Die Ergebnisse der letzten PISA-Studie haben gezeigt, dass 15-Jährige in Deutschland im internationalen Vergleich über gute Leistungen in der Mathematik, im Lesen und in den Naturwissenschaft en verfügen. Doch über ein Länderranking von Schulleistungen hinaus gibt PISA beispielsweise auch Informationen darüber, wie Schülerinnen und Schüler ihren Un...
Article
When school students compare the numerical values of fractions, they have frequently been found to be biased by the natural numbers involved (e.g., to believe that 1/4 > 1/3 because 4 > 3), thereby considering fractions componentially as two natural numbers rather than holistically as one number. Adult studies have suggested that intuitive processe...
Article
Theories of psychology and mathematics education recommend two instructional approaches to develop students’ mental representations of number: The “exact” approach focuses on the development of exact representations of organized dot patterns; the “approximate” approach focuses on the approximate representation of analogue magnitudes. This study pro...
Article
Full-text available
Scientific collaboration between neuroscience and mathematics education has mostly focused on brain imaging trying to inform education. This study aims at meeting expectations of both research fields, thus enhancing the ecological validity. We investigated the influence of age, mathematical competency, and task characteristics (format, complexity)...
Article
Full-text available
This study investigated whether near-infrared spectroscopy (NIRS) can be used to measure the processing of arithmetic problems in school children. Another aim was to assess whether distinct formats of such problems would lead to different neural processing. Two large samples of school children from different age groups were examined while calculati...

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Projects

Projects (5)
Project
The central goal of the Sharp Initiative is to identify conditions for the successful personalisation of learning with simulations in higher education and the derivation of design principles.
Project
We aim to promote German sixth-graders' understanding of fraction magnitude, using a computer-based training tool. Learning gains are analysed on the behavioural level and the neural level (with fMRI).