Kristina Reiss - Academia.edu (original) (raw)

Papers by Kristina Reiss

Zentrum für internationale Bildungsvergleichsstudien (ZIB) Technische Universität München (TUM) B... more Zentrum für internationale Bildungsvergleichsstudien (ZIB) Technische Universität München (TUM) Bibliografische Informationen der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar.

Dieses Skalenhandbuch für das Programme for International Student Assessment (PISA) 2015 umfasst ... more Dieses Skalenhandbuch für das Programme for International Student Assessment (PISA) 2015 umfasst die Dokumentation aller Instrumente, die in der Studie im Jahre 2015 in Deutschland eingesetzt wurden. Neben den Fragen – den sogenannten Items – des Schülerfragebogens, des Elternfragebogens, des Lehrerfragebogens sowie des Schulleiterfragebogens werden die mittleren (internationalen und nationalen) Lösungshäufigkeiten der verwendeten Testaufgaben für die Domänen Naturwissenschaften, Lesen und Mathematik aufgelistet. In der Erhebung 2015 bildete die Domäne Naturwissenschaften zum zweiten Mal die Hauptdomäne. Es werden sowohl die internationalen Fragen als auch Fragen abgebildet, welche nur in Deutschland erhoben worden sind. (DIPF/Verlag)

Methodological knowledge is an important component of proof competence. In this paper, we argue t... more Methodological knowledge is an important component of proof competence. In this paper, we argue that three different aspects of methodological knowledge may be distinguished, which we describe as proof scheme, proof structure, and chain of conclusions. These theoretical aspects guided part of an interview study on secondary students’ methodological knowledge, which serves as a qualitative supplement of a large-scale quantitative study. We present some results of this investigation in which the students had to evaluate correct and incorrect proofs.

ZDM, 2015

ABSTRACT Understanding contingency table analysis is a facet of mathematical competence in the do... more ABSTRACT 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 children’s strategy use, and to explore the extent to which psychological theories of intuition and inhibition help better understand the cognitive mechanisms underlying these strategies. In an initial study, we investigated 231 second-graders’ performance on various types of contingency table problems in a paper-and-pencil test. In a second study, we asked 45 second- and fourth-graders to give reasons for their decisions on contingency table problems in an interview situation. Results of both studies suggest that ignoring relevant information and referring to additive rather than multiplicative relationships between cell frequencies were among the children’s primary strategies. These strategies can be explained by intuition, which the children were often not able to inhibit. We discuss the implications of this interpretation from a mathematics education perspective.

Mitteilungen der Deutschen Mathematiker-Vereinigung, 2004

Zentralblatt für Didaktik der Mathematik, 2002

Proof is an important topic in the area of mathematics curriculum and an essential aspect of math... more Proof is an important topic in the area of mathematics curriculum and an essential aspect of mathematical competence. However, recent studies have revealed wide gaps in student's understanding of proof. Furthermore, effective teaching to prove, for example, by Schoenfeld's approach, is a real challenge for teachers. A very powerful and empirically well founded method of learning mathematics, which is also relatively easy to implement in the classroom, is learning through worked-out examples. It is, however, primarily suited for algorithmic content areas. We propose the concept of using heuristic worked-out examples, which do not provide an algorithmic problem solution but offer instead heuristic steps that lead towards finding a proof. We rely on Boero's model of proving in designing the single sub-steps of a heuristic example. We illustrate our instructional idea by presenting an heuristic example for proving that the interior angles in any triangle add up to 180°.

Competence models have been developed to describe levels of competence in mathematics and particu... more 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 description of the five levels of competence in the domain of numbers as proposed in a competence model for the primary school level that was based on theoretical and empirical research. Moreover, we discuss students􏰕 errors on three items to show how such a detailed analysis can provide additional information about how to support students in their development. We suggest that with such a combined empirical-psychological perspective, competence models can provide guidance for instruction.

Cognition and Instruction, 2014

ABSTRACT External number representations are commonly used throughout the first years of instruct... more ABSTRACT 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 counting. We compared first-grade children's performance on two types of computerized enumeration tasks, in which between one and 20 dots were presented in random arrangements or on a twenty-frame. The number of dots was a strong predictor of response times and accuracy rates in the enumeration task with random arrangements but not in the twenty-frame task. Performance on the twenty-frame task was correlated with performance on a number and arithmetic test, even when other cognitive variables were statistically controlled. We discuss these findings in the light of theories on utilizing external representations to support numerical learning. Free Full-text Download: http://www.tandfonline.com/eprint/3w4tZMyzPWb7CdsHEZz3/full

Kompetenzdiagnostik

ABSTRACT

Förderung des Nachwuchses In Technik und Naturwissenschaft, 2009

ABSTRACT Der letzte Bildungsbericht der Organisation for Economic Cooperation and Development (OE... more ABSTRACT Der letzte Bildungsbericht der Organisation for Economic Cooperation and Development (OECD)1 hat genauso wie die entsprechenden Berichte der vergangenen Jahre gezeigt, dass die laufenden Reformbemühungen nicht ausreichen, um einem Mangel an Akademikerinnen und Akademikern im naturwissenschaftlichen und technischen Bereich vorzubeugen. Dabei lassen sich die Probleme mit einfachen Zahlen belegen. So ist zwischen 2000 und 2006 im OECD-Durchschnitt der Anteil erfolgreicher Hochschulabsolventinnen und -absolventen an einem Altersjahrgang von 28 auf 37 Prozent gestiegen. Im gleichen Zeitraum stieg zwar auch die Akademikerquote in Deutschland, allerdings wesentlich geringer, nämlich von 18 auf 21 Prozent. Dieser eklatante Mangel ist in einigen Fächern und Ausbildungsgängen besonders stark zu spüren. Dazu gehören die Lehramtsstudiengänge genauso wie Ingenieurwissenschaften und andere technisch-naturwissenschaftliche Studiengänge. So werden in vielen OECD-Ländern 4,4 Prozent der Abschlüsse in einem ingenieurwissenschaftlichen Fach gemacht, während es in Deutschland nur 3,2 Prozent sind. In der Folge wird es nicht möglich sein, in den kommenden Jahren aus dem Arbeitsmarkt ausscheidende Personen in diesen Bereichen durch junge Menschen in ausreichender Zahl zu ersetzen. Darüber hinaus ist trotz einer ansteigenden Abiturientenquote die Anzahl der Studienanfängerinnen und Studienanfänger zurückgegangen, insbesondere liegt Deutschland in Bezug auf den Hochschulzugang deutlich unter dem OECD-Durchschnitt.

ZDM, 2008

... In these classrooms, the teacher developed geometric proofs in a teacher-students-interaction... more ... In these classrooms, the teacher developed geometric proofs in a teacher-students-interaction at the black board in a whole class ... Reasoning and proof in geometry ... is heavily dependent on an active role of the learner who should take part in the process of doing mathematics. ...

Learning and Instruction, 2008

This field experiment tested whether a special type of worked-out examples (i.e., heuristic examp... more This field experiment tested whether a special type of worked-out examples (i.e., heuristic examples) helps learners develop better conceptual knowledge about mathematical proving and proving skills than a control condition focussing on mathematical contents. Additionally, we analysed the benefits of self-explanation prompts and completion requirements in a 2 Â 2-design. The participants' (N ¼ 111 student teachers) proving skills and their conceptual knowledge were significantly better when learning with heuristic examples as compared to the control condition. Completion requirements impaired learning especially in combination with self-explanation prompts. The sole provision of self-explanation prompts, in contrast, fostered conceptual knowledge as well as skills.

Journal of Computer Assisted Learning, 2008

Learning from worked-out examples has been shown to be very effective in initial cognitive skill ... more Learning from worked-out examples has been shown to be very effective in initial cognitive skill acquisition. In order to fully exploit the potential of example-based learning, teachers should, however, know how to effectively employ such examples in classroom instruction. Therefore, we have designed a computer-based learning environment in which mathematics and science teachers learn how to effectively employ worked-out examples. The learning environment was developed according to approved design criteria. The topics that are addressed in the learning environment were chosen in response to the results of a needs assessment that analysed schoolbooks and classroom videos, and took interviews with teachers into account. In experiments as well as in several teacher trainings on example-based learning, the computerbased learning environment was evaluated and improved accordingly. On a more general level, our research and development project showed that a computer-based learning programme could be a sensible tool that supports follow-up work in teacher training contexts.

Erziehungswissenschaft, 2011

An der Technischen Universitat Munchen fand im Oktober 2009 die Inauguration der TUM School of Ed... more An der Technischen Universitat Munchen fand im Oktober 2009 die Inauguration der TUM School of Education, einer neuen Fakultat fur Lehrerbildung und Bildungsforschung, statt. [...] Organisatorisch tragt die TUM School of Education die Verantwortung fur die Lehrerbildung an der Technischen Universitat Munchen. Wie Strukturen und Aufgaben der School of Education gefasst sind, wird im zweiten Abschnitt dieses Beitrags ausgefuhrt, bevor dann im dritten Teil wesentliche Elemente des Lehrerbildungsprogramms vorgestellt werden. Der Beitrag beginnt mit einer Skizze von Zielvorstellungen fur eine zukunftsorientierte und verantwortungsbewusste Lehrerbildung, die aktuelle Herausforderungen aufgreift. (DIPF/Orig.)