History of mathematics in teachers' education: Motivation for and of Discussion Group 2

International audienceDiscussion Group 2 (DG 2), in a sequence of two one-hour sessions, revisits the discussion about the role of history of mathematics in teachers' education – both for pre-service teachers and currently practicing teachers. Activities of DG 2 include a discussion of examples from the literature that propose benefits for teachers and their students when history of mathematics is utilized to teach and learn mathematics. Participants will also share experiences from their own contexts. In particular, DG 2 will draw upon concrete examples from university courses, professional development programs, and projects, and when possible, the observed and/or documented benefits derived from the use of history of mathematics resulting from these examples. Finally, participants will discuss specific tasks or activities that may serve as examples for contexts that do not currently possess a strong history of mathematics dimension within mathematics teacher education programs, or which may provide new examples for those who do.

History of Mathematics in Mathematics Education: Recent devlopments

International audience<p>This is a concise survey on the recent developments (since 2000) concerning research on the relations between History and Pedagogy of Mathematics (the <i>HPM domain</i>). Section 1 explains the rationale of the study and formulates the key issues. Section 2 gives a brief historical account of the development of the <i>HPM domain</i> with focus on the main activities in its context and their outcomes. Section 3 provides a sufficiently comprehensive bibliographical survey of the work done in this area since 2000. Finally, section 4 summarizes the main points of this study.</p

Ask Smart to Get Smart: Mathematische Ausgaben generativer KI-Sprachmodelle verbessern durch gezieltes Prompt Engineering

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 vor und untersuchen ihren Effekt in Modellvalidierungen anhand einer arithmetischen und einer algebraischen Problemlöseaufgabe

Optical Probing of Ultrafast Laser-Induced Solid-to-Overdense-Plasma Transitions

Understanding the target dynamics during its interaction with a relativistic ultrashort laser pulse is a challenging fundamental multi-physics problem involving at least atomic and solid-state physics, plasma physics, and laser physics. Already, the properties of the so-called pre-plasma formed as the laser pulse's rising edge ionizes the target are complicated to access in experiments and modeling, and many aspects of this laser-induced transition from solid to overdense plasma over picosecond time scales are still open questions. At the same time, applications like laser-driven ion acceleration require precise knowledge and control of the pre-plasma because the efficiency of the acceleration process itself crucially depends on the target properties at the arrival of the relativistic intensity peak of the pulse. By capturing the dynamics of the initial stage of the interaction, we report on a detailed visualization of the pre-plasma formation and evolution. Nanometer-thin diamond-like carbon foils are shown to transition from solid to plasma during the laser rising edge with intensities < 10^16 W/cm^2. Single-shot near-infrared probe transmission measurements evidence sub-picosecond dynamics of an expanding plasma with densities above 10^23 cm^-3 (about 100 times the critical plasma density). The complementarity of a solid-state interaction model and a kinetic plasma description provides deep insight into the interplay of ionization, collisions, and expansion

Changes and rigors in systems of mathematical representations within gifted children's problem-solving process

International audienceThe paper shows how two gifted primary school children use rules of an individual system of mathematical representations during a problem-solving task. From a research perspective, transformations within and between various representations lead to new mathematical insights and is fundamental for mathematical experiences. But which processes of using mathematical representations do primary school children go through within problem-solving? What happens descriptively before a new mathematical insight in context of representations? For this purpose, two children (3 rd grade, 9 years old) were confronted with a mathematical problem-solving task. The case of Fred and Mark shows how they develop the means of representation themselves before a new mathematical insight

I Spy with my Little Eye – Teachers’ linkages about historical snippets in textbooks

International audienceThe aim of this explorative survey is to identify teachers’ beliefs about tasks concerning the history of mathematics. This poster proposal will give an insightful view on a pilot study on teachers’ beliefs about historical snippets in textbooks. First results of these pilot study can be discussed at CERME11 and may help to develop the main study