Research on curriculum resources in mathematics education: a survey of the field - Rezat, Sebastian (ZDM – Mathematics Education)

Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings - Werth, Gerda

Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe - Werth, Gerda (mathematik lehren)

Mathematik – Lesen – Lernen: Ein Vorlesungskonzept zur Förderung mathematischer Lesekompetenz - Rezat, Sebastian; Malik, Sara Naseem; Leifeld, Markus (Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main)

Verstehen schriftlicher Rechenverfahren durch algorithmisches Denken am Beispiel der schriftlichen Subtraktion - Leifeld, Markus; Rezat, Sebastian (Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main)

Herausforderungen anwendungsbezogener Aufgaben - eine curriculare Perspektive auf den Forschungsstand - Malik, Sara Naseem; Rezat, Sebastian (Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main)

Toward student agency in the selection and use of digital resources for learning and studying mathematics - Pepin, Birgit; Kock, Zeger-jan; Rezat, Sebastian (Handbook of Digital Resources in Mathematics Education)

Meta-Resources: Supporting the design of mathematics teaching and learning - Gueudet, Ghislaine; Pepin, Birgit; Rezat, Sebastian (Handbook of Digital Resources in Mathematics Education)

The role of digital technologies in transforming student learning landscapes - Rezat, Sebastian; Geiger, Vince (Handbook of Digital Resources in Mathematics Education)

Geometrie: Leitidee Raum und Form - Hattermann, Mathias; Rezat, Sebastian; Sträßer, Rudolf (Handbuch der Mathematikdidaktik)

Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings - Werth, Gerda (Beiträge zum Mathematikunterricht)

Linguistic features of word problems that cause difficulties for learners across the curriculum: A literature review - Malik, Sara Naseem; Rezat, Sebastian (Proceedings on the Twelfth Congress on the European Society for research in Mathematics Education (CERME 12))

Scaffolding Close Reading of Mathematical Text in Pre-service Primary Teacher Education at the Tertiary Level: Design and Evaluation - Rezat, Sebastian; Malik, Sara Naseem; Leifeld, Markus (International Journal of Science and Mathematics Education)
Abstract Even in the digital age, learning mathematics at an academic level still requires much reading of mathematical text. Research has shown that reading mathematical text requires readers to engage with all the structures of the book and with its pedagogical voice, making connections, and plausible reasoning. Specific practices and strategies that support the close reading of mathematical text have been suggested; however, descriptions and empirical evaluations of materials designed to support these activities are rare. We present the design and first evaluation cycle of materials developed in a design research project that aims to scaffold close reading of mathematical text. The materials were designed and evaluated in a German university course on elementary geometry for first-year teacher education students who study mathematics to become primary teachers. The reading strategies were explained and modeled for students in reading-strategy videos. Additionally, close reading of mathematical text was scaffolded by close-reading tasks and homework tasks and problems that build on the reading strategies and were specifically designed to foster understanding of the mathematical text. Survey data were collected from 296 students to evaluate their use of and attitude toward the different materials. The quantitative results indicate that students used the materials and were generally able to learn the course content by themselves. From all provided materials, they found the close-reading tasks most helpful. A qualitative analysis of answers to open questions revealed issues with different materials, particularly with the script, and requests for additional materials. The issues with the script were categorized inductively. The categories are presented as a qualitative result of the study and discussed.
Keywords: General Mathematics; Education

Mathematics textbooks and curriculum resources as instruments for change - Rezat, Sebastian; Fan, Lianghuo; Pepin, Birgit (ZDM – Mathematics Education)
Abstract In this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources as instruments for change from a theoretical perspective; (2) The design of curriculum resources to mediate the implementation of reform ideas and innovative practice; (3) Teachers’ influence on the implementation of change through curriculum resources; (4) Students’ influence on the implementation of change through curriculum resources; and (5) Evidence of curriculum resources yielding changes in student-related factors or variables. We claim that, whilst textbooks and curriculum resources are influential, they alone cannot change teachers’ teaching nor students’ learning practices in times of curricular change. Moreover, more knowledge is needed about features of curriculum resources that support the implementation of change. We contend that curriculum innovations are likely to be successful, if teachers and students are supported to co- and re-design the relevant curriculum trajectories and materials in line with the reform efforts and their own individual needs.
Keywords: General Mathematics; Education

Challenges of making sense of tasks and automated feedback in digital mathematics textbooks - Rezat, Sebastian; Schacht, Florian; Häsel-Weide, Uta (Mathematics Education in the Digital Age. Learning, Practice and Theory)

How automated feedback from a digital mathematics textbook affects primary students’ conceptual development: two case studies - Rezat, Sebastian (ZDM Mathematics Education)
Abstract One of the most prevalent features of digital mathematics textbooks, compared to traditional ones, is the provision of automated feedback on students’ solutions. Since feedback is regarded as an important factor that influences learning, this is often seen as an affordance of digital mathematics textbooks. While there is a large body of mainly quantitative research on the effectiveness of feedback in general, very little is known about how feedback actually affects students’ individual content specific learning processes and conceptual development. A theoretical framework based on Rabardel’s theory of the instrument and Vergnaud’s theory of conceptual fields is developed to study qualitatively how feedback actually functions in the learning process. This framework was applied in a case study of two elementary school students’ learning processes when working on a probability task from a German 3rd grade digital textbook. The analysis allowed detailed reconstruction of how students made sense of the information provided by the feedback and adjusted their behavior accordingly. This in-depth analysis unveiled that feedback does not necessarily foster conceptual development in the desired way, and a correct solution does not always coincide with conceptual understanding. The results point to some obstacles that students face when working individually on tasks from digital mathematics textbooks with automated feedback, and indicate that feedback needs to be developed in design-based research cycles in order to yield the desired effects.
Keywords: General Mathematics; Education

Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge - Schumacher, Jan; Rezat, Sebastian (Zeichen und Sprache im Mathematikunterricht)
Diagrammatisches Schließen wird im Zusammenhang mit dem Lernen von Mathmematik und ihrer Symbolsprache als wesentliche Theorie der Wissenskonstruktion diskutiert. Dabei wird häufig davon ausgegangen, dass die Wissenskonstruktion im Sinne diagrammatischen Schließens erfolgt. Deskriptive Rekonstruktionen diagrammatischen Schließens bei Lernenden stellen jedoch ein Desiderat der mathematikdidaktischen Forschung dar. Der vorliegende Beitrag befasst sich mit der Fragestellung, wie sich diagrammatisches Schließen bei Lernenden rekonstruieren lässt. Als mögliche Werkzeuge für eine solche Rekonstruktion werden Toulmins Argumentationsschema und Vergnauds Schema-Begriff exemplarisch angewandt, um das diagrammatische Schließen eines Schülerpaars beim Einstieg in die Subtraktion negativer Zahlen zu rekonstruieren. Abschließend wird die tatsächliche Eignung der beiden Ansätze zur Rekonstruktion diagrammatischen Schließens diskutiert.

Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential der Peirceschen Semiotik - Schumacher, Jan

Schulbücher. Werkzeuge zum Üben in den Fächern Deutsch und Mathematik - Rezat, Sara; Rezat, Sebastian (Die Grundschulzeitschrift 320)

Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen - Schumacher, Jan; Rezat, Sebastian (Zeichen und Sprache im Mathematikunterricht: Semiotik in Theorie und Praxis)

Mathematiklernen mit digitalen Schulbüchern im Spannungsfeld zwischen Individualisierung und Kooperation - Rezat, Sebastian (Mobile Medien im Schulkontext)

Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen - Schumacher, Jan (Beiträge zum Mathematikunterricht 2019)

A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers - Schumacher, Jan; Rezat, Sebastian (Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019))
In this paper, we first outline a Hypothetical Learning Trajectory (HLT), which aims at a formal understanding of the rules for manipulating integers. The HLT is based on task formats, which promote algebraic thinking in terms of generalizing rules from the analysis of patterns and should be familiar to students from their mathematics education experiences in elementary school. Second, we analyze two students' actual learning process based on Peircean semiotics. The analysis shows that the actual learning process diverges from the hypothesized learning process in that the students do not relate the different levels of the diagrams in a way that allows them to extrapolate the rule for the subtraction of negative numbers. Based on this finding, we point out consequences for the design of the tasks.
Keywords: diagrammatic reasoning; hypothetical learning trajectory; induction extrapolatory method; integers; negative numbers; permanence principle; semiotics

Proceedings of the Third International Conference on Mathematics Textbook Research and Development: 16-19 September 2019 Paderborn, Germany

Mathilde Vaerting. Deutschlands erste Mathematikdidaktikderin - Werth, Gerda (Beiträge zum Mathematikunterricht)

„...weil man Fermi-Aufgaben so rechnet“. Modelltexte als sprachliche Ressource für das Erklären von Lösungswegen bei Fermi-Aufgaben - Rezat, Sara; Rezat, Sebastian (In: Mathematik differenziert 3/2019)

An Introduction to Grounded Theory with a Special Focus on Axial Coding and the Coding Paradigm - Vollstedt, Maike; Rezat, Sebastian (Compendium for Early Career Researchers in Mathematics Education)

Semiotische Analyse von Sinnkonstruktionsprozessen bei einem innermathematischen Zugang zum Erlernen negativer Zahlen - Schumacher, Jan (Beiträge zum Mathematikunterricht 2018)

Present Research on Mathematics Textbooks and Teachers’ Resources in ICME-13: Conclusion and Perspectives - Rezat, Sebastian; Visnovska, Jana; Trouche, Luc; Qi, Chunxia; Fan, Lianghuo (Research on Mathematics Textbooks and Teachers’ Resources: Advances and Issues)

Textaufgaben verstehen. Lesen und Variieren komplexer Textaufgaben mit sprachlich-mathematischen Strategien. - Topalović, Elvira; Kuzminykh, Ksenia; Rezat, Sebastian (In: mathematik lehren)

Examining peer-interaction during individual work with a digital textbook in a primary mathematics classroom - Rezat, Sebastian; Häsel-Weide, Uta (PROCEEDINGS of the fith ERME TOPIC CONFERENCE (ETC 5) on Mathematics Education in the Digital Age (MEDA))

Sinnkonstruktion beim Erkunden von Mustern und Strukturen - Schumacher, Jan (Beiträge zum Mathematikunterricht 2017)

Subject specific genres and genre awareness in integrated mathematics and language teaching - Rezat, Sara; Rezat, Sebastian (EURASIA Journal of Mathematics, Science & Technology Education 13 (7b))

Erkunden mathematischer Strukturen anstatt Interpretation in Modellen – Ein innermathematischer Zugang zu negativen Zahlen - Schumacher, Jan (Beiträge zum Mathematikunterricht 2016)

Sprachsensibler Umgang mit Textmustern im Mathematikunterricht am Beispiel von Konstruktionsbeschreibungen - Rezat, Sara; Rezat, Sebastian; Janzen, Sabrina (Beiträge zum Mathematikunterricht 2015. Vorträge auf der 49. Tagung für Didaktik der Mathematik vom 09.02.2015 bis 13.02.2015 in Basel. Band 2)

Mathematische Sachaufgaben verstehen und erklären - Rezat, Sara; Rezat, Sebastian (Praxis Deutsch 233)