What is the Mathematics in Mathematics Education?

In this paper I tackle the question What is the mathematics in mathematics education? By providing three different frames for the word mathematics. 1. Frame 1: Mathematics as an abstract body of knowledge/ideas, the organization of that into systems and structures, and a set of methods for reaching conclusions. 2. Frame 2: Mathematics as contextual, ever present, as a lens or language to make sense of the world. 3. Frame 3: Mathematics as a verb (not a noun), a human activity, part of one’s identity. After introducing the frames and examining their distinction and their overlap, I discuss their implication with respect to student-centered classroom, context, and culture

Preface

Bharath Sriraman noted in his Editorial for Vol. 10, nos. 1–2 that the first issue of The Mathematics Enthusiast (known then as The Montana Mathematics Enthusiast) published in April 2004 was “the result of four idealistic elementary school teachers believing in the mission of this journal and writing about their attempts to reconcile the mathematics content they were learning in a mathematics for elementary school teachers course with existing mathematics education research found in practitioners’ journals as well as standards imposed by institutions’ framing policy” (p. 2). Ten years later we return to a similar focus

Kinetics of the reduction of Creutzfeldt–Jakob disease prion seeding activity by steam sterilization support the use of validated 134°C programmes

Background Prions are renowned for their distinct resistance to chemical or physical inactivation, including steam sterilization. Impaired efficacy of inactivation poses a risk to patients for iatrogenic transmission of Creutzfeldt–Jakob disease (CJD) via contaminated surgical instruments. Aims Most established prion inactivation methods were validated against scrapie agents, although those were found to be generally less thermostable than human prions. Thus, knowledge gaps regarding steam-sterilization kinetics of CJD prions should be filled and current guidelines reviewed accordingly. Methods Prion inactivation through widely recommended steam sterilization at 134°C was assessed for several holding times by analysing the residual prion seeding activity using protein misfolding cyclic amplification (PMCA). Findings Scrapie 263K was found to be the least thermoresistant prion strain showing no seeding activity after 1.5 min at 134°C, while variant CJD was the most stable one demonstrating some seeding activity even after 18 min of steam sterilization. Sporadic CJD subtype VV2 exhibited residual seeding activity after 3 min, but no detectable activity after 5 min at 134°C. Conclusion Validated steam sterilization for 5 min at 134°C as previously recommended for the routine reprocessing of surgical instruments in contact with high-risk tissues is able to substantially reduce the seeding activity of CJD agents, provided that no fixating chemical disinfection has been performed prior to sterilization and that thorough cleaning has reduced the protein load on the surface to less than 100 μg per instrument.Peer Reviewe

Regionale Auswirkungen des globalen Klimawandels - Variabilität trockenheitsrelevanter atmosphärischer Zirkulationstypen und Veränderung der atmosphärischen Zirkulationsdynamik von langanhaltenden Trockenperioden im Süden von Mitteleuropa

Im bilateralen WETRAX+ Forschungsprojekt wurden trockenheitsrelevante Zirkulationstypen für ein Untersuchungsgebiet im Süden von Mitteleuropa abgeleitet, um die Veränderung der atmosphärischen Zirkulation im Hinblick auf Trockenheit und langanhaltende Trockenperioden im Kontext des Klimawandels zu untersuchen. Diese Arbeit ist aus dem WETRAX+ Projekt hervorgegangen und beschäftigt sich mit Häufigkeits- und Persistenzänderungen sowie mit typinternen Veränderungen trockenheitsrelevanter Zirkulationstypen und der Veränderung der atmosphärischen Zirkulation von langanhaltenden Trockenperioden im südlichen Mitteleuropa im Kontext des Klimawandels. Zudem werden Zusammenhänge zwischen dem Auftreten trockenheitsrelevanter atmosphärischer Zirkulationstypen sowie langanhaltender Trockenperioden mit großräumigen nordhemisphärischen Telekonnektionen betrachtet

Supporting novice mathematics teacher educators teaching elementary mathematics content courses for the first time

In order to be effectively prepared by a teacher education program, prospective elementary teachers (PTs) need to experience high quality mathematics instruction in their mathematics content courses. The instructors of these courses typically consist of individuals (mathematicians and mathematics educators) with ranging experiences, from tenured faculty members to first-year assistant professors or graduate students. This paper explores how to support novice mathematics teacher educators (MTEs) who are teaching elementary content coursework for PTs for the first time. We detail and describe how to implement three systems for supporting novice MTEs: working with a mentor, being provided with educative curriculum materials, and working in a collaborative teaching environment. We close by discussing specific challenges associated with these supports, and call for more institutions to share how they have successfully implemented systems to support novice MTEs

Networking Frameworks: a Method for Analyzing the Complexities of Classroom Cultures Focusing on Justifying

In this paper, we network five frameworks (cognitive demand, lesson cohesion, cognitive engagement, collective argumentation, and student contribution) for an analytic approach that allows us to present a more holistic picture of classrooms which engage students in justifying. We network these frameworks around the edges of the instructional triangle as a means to coordinate them to illustrate the observable relationships among teacher, students(s), and content. We illustrate the potential of integrating these frameworks via analysis of two lessons that, while sharing surface level similarities, are profoundly different when considering the complexities of a classroom focused on justifying. We found that this integrated comparison across all dimensions (rather than focusing on just one or two) was a useful way to compare lessons with respect to a classroom culture that is characterized by students engaging in justifying

Developing Mathematical Content Knowledge for Teaching Elementary School Mathematics

In this paper the authors present three design principles they use to develop preservice teachers\u27 mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2) modeling teaching for understanding, (3) focusing on connections between content knowledge and other types of knowledge. The authors share results of individual research projects and teaching approaches focusing on helping preservice elementary teachers develop such knowledge. Specific examples from different content areas (whole number, fractions, angle, and area) are discussed