Lukas Baumanns

Lukas Baumanns
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Lukas verified their affiliation via an institutional email.
Verified
Lukas verified their affiliation via an institutional email.
  • Dr. rer. nat.
  • Postdoctoral Researcher at TU Dortmund University

About

40
Publications
15,103
Reads
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270
Citations
Current institution
TU Dortmund University
Current position
  • Postdoctoral Researcher
Additional affiliations
October 2023 - present
TU Dortmund University
Position
  • Research Assistant

Publications

Publications (40)
Article
Full-text available
In research on mathematical problem posing, a broad spectrum of different situations is used to induce the activity of posing problems. This review aims at characterizing these so-called problem-posing situations by conducting three consecutive analyses: (1) By analyzing the openness of potential problem-posing situations, the concept of ‚mathemati...
Article
Full-text available
The aim of this study is to develop a descriptive phase model for problem-posing activities based on structured situations. For this purpose, 36 task-based interviews with pre-service primary and secondary mathematics teachers working in pairs who were given two structured problem-posing situations were conducted. Through an inductive-deductive cat...
Article
Full-text available
Insights into the process of mathematical problem posing is a central concern in mathematics education research. However, little is known about regulative or metacognitive behaviors that are essential to understanding this process. In this study, we investigate metacognitive behavior in problem posing. We aim at (1) identifying problem-posing-speci...
Chapter
Full-text available
Understanding problem posing as an inherently mathematical activity has gained importance in recent years within mathematics education. Numerous empirical studies show a wide range of different problem-posing activities. This paper highlights the diversity of problem-posing activities based on considerations on subject-matter didactics. Based on de...
Article
Full-text available
Recognizing patterns is an essential skill in early mathematics education. However, first graders often have difficulties with tasks such as extending patterns of the form ABCABC. Studies show that this pattern-recognition ability is a good predictor of later pre-algebraic skills and mathematical achievement in general, or the development of mathem...
Article
Full-text available
In this paper, images containing mathematical ideas that were generated by different image-generating AI models (DALL-E 2, Leonardo.Ai, and Midjourney) are comparatively interpreted from a mathematics aesthetical perspective. Our exploratory study aimed to scrutinize how AI image models visualize abstract mathematical ideas and whether this imagina...
Article
Full-text available
Aktuelle Diskussionen zum Thema Künstliche Intelligenz (KI) sind auch für das schulische Lehren und Lernen von Bedeutung, und somit auch aus dem Mathematikunterricht bzw. dem Lehren und Lernen von Mathematik nicht mehr wegzudenken. Die mathematikdidaktische Forschungscommunity ist bereits aktiv geworden, wie beispielsweise das Diskussionsforum auf...
Conference Paper
Full-text available
The use of AI tools in the professional development of teachers is evolving into an important part of education. Despite growing interest, there is a gap in understanding how AI, specifically ChatGPT, can support mathematics teachers, for example, when posing problems of varying degrees of difficulty. This study aims to explore how interactions wit...
Article
Full-text available
The use of and research on the large language model (LLM) Generative Pretrained Transformer (GPT) is growing steadily, especially in mathematics education. As students and teachers worldwide increasingly use this AI model for teaching and learning mathematics, the question of the quality of the generated output becomes important. Consequently, this...
Article
Full-text available
Der vorliegende Beitrag hat zum Ziel, die Diskussion über die Chancen und Herausforderungen der KI-Integration im Mathematikunterricht weiterzuführen und aktuelle Einsatzmöglichkeiten von ChatGPT im Licht der jüngsten Entwicklungen zu diskutieren, die für Lehrkräfte und Lernende aktuell zugänglich sind. Insbesondere wird das Text-zu-Bild Modell DAL...
Conference Paper
Full-text available
For early mathematics learning, adaptive strategy use by students at different levels of mathematical achievement is of central importance. For several mathematical tasks, there is evidence that high-achieving students are more able to use strategies adaptively, but not yet for pattern-recognition tasks. This paper presents results from an empirica...
Article
Full-text available
Der Beitrag beschäftigt sich mit den derzeitigen mathematischen Fähigkeiten des generativen KI-Spachmodells ChatGPT in Bezug auf das Lösen mathematischer Probleme. Um für den schulischen Nutzen des Modells die Zuverlässigkeit und Nachvollziehbarkeit von mathematischen Ausgaben zu optimieren, stellen wir im Beitrag unterschiedliche Prompt-Techniken...
Conference Paper
Full-text available
A central concern of mathematics education is to develop students’ understanding of multiplication. To this end, it is necessary to investigate students’ strategies in multiplication tasks. Common representations for multiplication are array representations (AR) (i.e., rectangular arrangement of elements). Previous research has identified strategie...
Poster
Full-text available
In the research project Unlocking the Potential of Generative AI Language Models in Professional Workflows and Education of Mathematics Teachers (GenAI-MT) from the University of Hamburg, together with a group of mathematics education researchers we are exchanging ideas about the possibilities for a productive use of generative AI language models f...
Article
Full-text available
Der Beitrag befasst sich mit den Anwendungsmöglichkeiten und Herausforderungen, die durch die Verwendung von generativen KI-Sprachmodellen wie ChatGPT für den Bereich der mathematikdidaktischen Forschung bestehen. Beitag ist veröffentlicht in den Mitteilungen der GDM, 114, 19-26.
Preprint
Am 30. November 2022 veröffentlichte das US-amerikanische Unternehmen OpenAI die Anwendung ChatGPT seines generativen KI-Sprachmodells GPT-3 (Generative Pre-Trained Performer) und ermöglichte somit der Allgemeinheit die kostenlose Nutzung der Anwendung (erreichbar unter der URL chat.openai.com/chat). Bei ChatGPT handelt es sich um einen auf künstli...
Chapter
Mathematical creativity is an important topic both in research and in practice. Especially in research and practice on secondary school level, it is gaining increasing significance with a growing body of tasks, practices, and empirical studies being developed and conducted. At the same time, the growing field of research on mathematical creativity...
Chapter
Research on creativity, invention, and innovation originates in different scientific disciplines and different decades. This diversity in theoretical backgrounds and definitions can still be seen in recent research, especially in mathematics education (see Joklitschke et al., 2021, for a review on notions of creativity in mathematics education rese...
Conference Paper
Full-text available
Recognizing patterns is an important skill in early mathematics learning. Yet only few studies have investigated how first-grade students recognize patterns. These studies mainly analyzed students’ expressions and drawings in individual interviews. The study presented in this paper used eye tracking in order to explore the processes of 22 first-gra...
Conference Paper
Full-text available
For researchers and practitioners, it is important to identify students at risk of developing mathematical difficulties. The aim of this pilot study was to investigate whether it is possible to identify first-grade students who are at risk of developing mathematical difficulties (RMD) through online measures in arithmetic and pattern tasks. In our...
Article
Full-text available
Angesichts bildungspolitischer Reformbestrebungen, das Schulsystem verstärkt inklusiv auszurichten, stellt sich die Frage, wie sich angehende Lehrer*innen als zukünftige schulische Akteur*innen mit inklusionsspezifischen Anforderungen auseinandersetzen. Mit Bezug zu strukturtheoretischen Bestimmungen pädagogischer Professionalität wird im Rahmen ei...
Chapter
Im vorliegenden Beitrag wird der Versuch einer konzeptuellen Ordnung unterschiedlicher Problem-Posing-Tätigkeiten vorgenommen. Dieses Konzept verbindet drei Konstrukte aus der Forschung zum Problem Posing, Problemlösen und der Psychologie: (1) Problemstellen als Generieren neuer oder Reformulieren gegebener Probleme, (2) das Aufwerfen von Aufgaben...
Conference Paper
Full-text available
This investigation aims at developing a framework for identifying metacognitive behaviour in problem-posing processes and illustrating the potential of such a framework for assessing the quality of problem posing. For this purpose, 36 task-based interviews were conducted with pairs of student teachers. On these, an inductive category development ha...
Article
Full-text available
This article aims to develop a framework for the characterisation of problem-posing activities. The framework links three theoretical constructs from research on problem posing, problem solving, and psychology: (1) problem posing as an activity of generating new or reformulating given problems, (2) emerging tasks on the spectrum between routine and...
Article
Full-text available
The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching setti...
Conference Paper
Full-text available
Bazo (gesprochen [baˈzu] und Akronym der Ellipse Brüche am Zahlenstrahl ordnen) ist ein im Rahmen eines Studienseminars entstandenes produktives Übungsspiel für die Bruchrechnung. Im Besonderen soll die Fähigkeit des Platzierens von Brüchen an der Zahlengeraden (vgl. MSW, 2007, S. 21) spielerisch und produktiv geübt werden. Inwieweit Bazo diese Fäh...
Conference Paper
Full-text available
In der Problemlöseforschung ist die Unterscheidung mathematischer Aufgaben in Routineaufgaben und Probleme weitgehend etabliert. Ein Review zur ergänzenden Tätigkeit des Problem Posings hat ergeben, dass die Unterscheidung zwischen dem Aufwerfen von Routineaufgaben bzw. Problemen auch beim Problem Posing fruchtbar ist (Baumanns & Rott, im Review)....
Chapter
Mathematisches Problemlösen erfreut sich bis heute eines großen Interesses innerhalb der fachdidaktischen Forschung. Die Relevanz für das Lernen von Mathematik spiegelt sich in der Präsenz dieser Tätigkeit in den Kernlehrplänen und Bildungsstandards des Faches Mathematik wider. Um über Forschungserkenntnisse zu dieser zentralen Tätigkeit in Austaus...
Conference Paper
Full-text available
Schwerpunkt der vorliegenden Studie ist die Entwicklung eines deskriptiven Prozessmodells von Problem-Posing-Prozessen. Dazu wurden 17 Prozesse erhoben, in denen Lehramtsstudierende in Paaren neue Probleme zum sogenannten NIM-Spiel aufwerfen sollten. Aus der Analyse dieser Prozesse wurden fünf inhaltstragende Episodentypen abgeleitet, mit denen sic...
Conference Paper
Full-text available
In this article, we take an in-depth look at research on the intersection of problem posing and creativity in order to present its current state of research in a systematic review. A full search in top journals from mathematics education and the Web of Science revealed only 15 articles from different genres, of which 11 were included in the analysi...
Conference Paper
Full-text available
In this literature review, we critically compare different problem-posing situations used in research studies. This review reveals that the term "problem posing" is used for many different situations that differ substantially from each other. For some situations, it is debatable whether they provoke a posing activity at all. For other situations, w...
Poster
Full-text available
Probleme sind das Herz der Mathematik (Halmos, 1980, S. 524). Dabei steht bei der Beschäftigung mit mathematischen Problemen nicht alleine das Problemlösen im Zentrum, sondern auch das Aufwerfens mathematischer Probleme, das sogenannte Problem Posing. Dieser Tätigkeit schreibt die Mathematik eine zentrale Bedeutung zu, und doch liegt auf ihr kein F...
Chapter
The University of Potsdam hosted the 25th ProMath and the 5th WG Problem Solving conference. Both groups met for the second time in this constellation which contributed to profound discussions on problem solving in each country taking cultural particularities into account. The joint conference took place from 29th to 31st August 2018, with particip...
Chapter
The University of Potsdam hosted the 25th ProMath and the 5th WG Problem Solving conference. Both groups met for the second time in this constellation which contributed to profound discussions on problem solving in each country taking cultural particularities into account. The joint conference took place from 29th to 31st August 2018, with particip...
Conference Paper
Full-text available
Der vorliegende Beitrag befasst sich mit der Tätigkeit des Aufwerfens mathematischer Probleme, dem sogenannten Problem Posing. Im Rahmen einer Pilotstudie wurden 13 Problem-Posing-Prozesse bei 5 Studierenden und einem Mathematiker beobachtet und analysiert. Dabei wurden die Proband*innen zum strukturierten Problem Posing aufgefordert, bei dem neue...

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