Benjamin Rott | Universität zu Köln (original) (raw)

Papers by Benjamin Rott

for the learning of mathematics, 2020

Frontiers in Psychology, Jul 13, 2023

The use of student drawings to assess their experiences and beliefs about teaching and learning o... more The use of student drawings to assess their experiences and beliefs about teaching and learning of mathematics has become almost a regular research methodespecially when working with young students who may not express themselves well, for example, in self-report questionnaires. These methods, nevertheless, need to be improved regarding their objectivity and validity. By building on the existing research, in this study, we focus on objectivity and validity issues in drawing-based methods. We use a drawing-based instrument: Draw A Mathematics Classroom (DAMC) and present 104 fourth-grade students to draw a picture of their regular mathematics lessons. We especially aim to develop and validate a data coding manual with lowinferent categories; that is, well-operationalizable categories that can be used with high interrater-reliability like the presence of teachers, the arrangement of student desks, and teacher-student interactions. The results reveal that almost half of the participating students perceive their lessons as teacher-centered. The results also confirm the reliability and validity of the methodological approach. For example, in pictures where the teacher is depicted larger than the students, the teacher is also depicted in the center, and students are pictured working alone. Classroom observations support students' perceptions, and all these show that the manual used in this study is useful to getting insights into young students' perceptions of their mathematics classroom.

for the learning of mathematics, 2020

Research in Mathematics Education, Jun 9, 2020

Connections of Working Backwards and Reversing Lines o f Thought-Some Theoretical Considerations.

Der vorliegende Beitrag befasst sich mit der Identifikation intuitiven Verhaltens innerhalb mathe... more Der vorliegende Beitrag befasst sich mit der Identifikation intuitiven Verhaltens innerhalb mathematischer Problemlöseprozessen von Schüler*innen. Sowohl in der Kreativitätsforschung als auch innerhalb der Mathematikdidaktik wird vor allem begabten Schüler*innen ein solches Verhalten attestiert. Im Rahmen einer Pilotierung wurde dazu der Bearbeitungsprozess einer Schülerin zu einer bestimmten Problemaufgabe beobachtet und mit Hilfe eines darauffolgenden Einzelinterviews ausgewertet. Erste Ergebnisse lassen Ansätze eines intuitiven Verhaltens anhand von zuvor aufgestellten Indikatoren erkennen. Daran anknüpfend wird die Ausarbeitung und Präzisierung des Untersuchungsdesigns vorgestellt. Hierbei geht es insbesondere um mögliche Aufgabentypen, die intuitives Verhalten begünstigen könnten, und Erhebungsmethoden, mit denen man entsprechendes Verhalten erfassen kann.

HAL (Le Centre pour la Communication Scientifique Directe), Feb 6, 2019

Most studies that deal with possible influences of the social context related to students’ abilit... more Most studies that deal with possible influences of the social context related to students’ abilities on the connection between beliefs and practices involve only a small number of participants (e.g., 1 – 3 teachers). Thus, we have designed a new quantitative questionnaire (named TBTP) which is intended to examine these influences for a larger number of teachers (here: N = 43). Then, for a further qualitative investigation, we interviewed and observed lessons of three of those teachers. The results show that the 43 teachers distinguish their style of teaching in different contexts of students’ abilities. The correlation between beliefs about mathematics and the styles of teaching can be seen in the context of low ability students rather than in the context of high ability students. In the further investigation, this correlation is supported by the three teachers’ descriptions of their general teaching of mathematics and their real practices in classes containing many low ability students.

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

The number line is an important external representation in primary education and research has sho... more The number line is an important external representation in primary education and research has shown that performance in number line tasks correlates with general mathematical achievement. A promising tool for gaining insights into students' strategies-in number line and other tasks-is eye tracking. However, previous eye-tracking research has predominantly addressed students' use of strategies on an empty number line, whereas students' strategy uses and eye movements on the marked number line have hardly been explored. This paper presents an exploratory study that investigates student strategies in locating numbers on a marked number line. In this paper, we present students' strategies in naming and placing numbers on the number line as well as differences in the use of strategies between students with short and long response times, indicating the use of more or less efficient strategies.

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

Mathematical problem solving is hard to learn and difficult to teach-esp. for classrooms includin... more Mathematical problem solving is hard to learn and difficult to teach-esp. for classrooms including low-achieving (LA) students. We investigate what difficulties LA students encounter when solving problems and how their problem-solving behavior develops within a period of nine months. Within a broader project, three pairs of LA students have been videotaped four times over a period of nine months. For this contribution, the video data of the first and fourth collection were analyzed. To do so, each problem-solving process was coded using four different codings: episodes, heuristics, selfregulatory activities, and success. We identified three main difficulties that students encounter: basic knowledge, stagnated development of heuristics, and a lack of self-regulation.

International Journal of Mathematical Education in Science and Technology, Mar 27, 2023

Kreativität und mathematische Kreativität werden in der Forschung auf verschiedenste Weise konzep... more Kreativität und mathematische Kreativität werden in der Forschung auf verschiedenste Weise konzeptualisiert – mit Auswirkungen auf Studiendesigns und Forschungsergebnisse. Der Beitrag stellt unterschiedliche Grundannahmen und Konzeptualisierungen von (mathematischer) Kreativität vor, systematisiert diese und leitet Konsequenzen für Studiendesigns empirischer Studien ab.

International Journal of Mathematical Education in Science and Technology, Feb 1, 2023

THE 2ND NATIONAL CONFERENCE ON MATHEMATICS EDUCATION (NACOME) 2021: Mathematical Proof as a Tool for Learning Mathematics

International Journal of Mathematical Education in Science and Technology

Mathematische Problemlösekompetenzen fördern – Tagungsband der Herbsttagung des GDM-Arbeitskreises Problemlösen in Braunschweig 2016

Nicht nur in der Psychologie, sondern auch in der Mathematikdidaktik wurden und werden Konzepte u... more Nicht nur in der Psychologie, sondern auch in der Mathematikdidaktik wurden und werden Konzepte und Maßnahmen zur Förderung der Problemlösekompetenz entwickelt. Teilweise richten sich diese direkt an die Lernen-den, teilweise werden Lehrende geschult, um ihrerseits dann die Kompetenzen von Schülerinnen und Schülern zu fördern. In einem Workshop während der Tagung wurden Fördermaßnahmen zusammengetragen, verglichen und kritisch diskutiert. Dabei wurden insbesondere die folgenden beiden Fragen angesprochen: (1) Welche (Teil-) Konzepte bzw. Maßnahmen haben sich als erfolgreich erwiesen und wie? (2) An welchen Stellen eröffnen sich Verbesserungspotentiale? Ziele des Workshops waren die Entwicklung gemeinsamer Konzeptideen und das Anbahnen von Kooperationen (im Rahmen des Arbeitskreises Problem-lösen und darüber hinaus) zu ihrer Umsetzung. Dieser Beitrag verfolgt zusätzlich das Ziel, die vorgestellten Projekte mithilfe eines Rasters zu sortieren, um einen Vergleich auf verschiedenen Eben...

Zeitschrift für Erziehungswissenschaft

Teacher noticing has become widely accepted as a principal component of teacher competence; it is... more Teacher noticing has become widely accepted as a principal component of teacher competence; it is supported during university teacher education in many activities. However, only a few high-quality standardized measurement instruments exist that capture noticing and allow valid interpretations of how its development depends on factors within university teacher education. The present study is based on a video-based test instrument that has been developed to enable a standardized study of the noticing of practicing mathematics teachers—that is, their perception, interpretation, and decision-making skills—with respect to subject-specific and general pedagogical issues in secondary mathematics classrooms. This study examines how this instrument developed for in-service teachers can be used for pre-service teachers at the master’s degree level. Based on a sample of 313 pre-service mathematics teachers enrolled in six German universities, the study investigates (1) the instrument’s interna...

Teaching Mathematics and Computer Science

In this article, I outline the influence of George Pólya's work on research in different area... more In this article, I outline the influence of George Pólya's work on research in different areas and especially on mathematics education, namely heuristics and models of the problem-solving process. On a more personal note, I will go into some details regarding Pólya's influence on my own work in mathematical problem solving with a focus on the research project for my PhD thesis. Subject Classification: 97xxx