Madness and Civilization: A History of Insanity in the Age of Reason

https://www.nber.org/system/files/working_papers/w26946/w26946.pdf

Polarization and Public Health: Partisan Differences in Social Distancing during the Coronavirus Pandemic.

In this article we survey the current debate on modelling and, describe different perspectives on this debate. We relate these perspectives with earlier perspectives and show similarities and differences between these different approaches.

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A global survey of international perspectives on modelling in mathematics education

Mathematical modelling ( the process of translating between the real world and mathematics in both directions ) is one of the topics in mathematics education that has been discussed and propagated most intensely during the last few decades. In classroom practice all over the world, however, modelling still has a far less prominent role than is desirable. The main reason for this gap between the goals of the educational debate and everyday school practice is that modelling is difficult both for students' and for teachers. In our paper, we will show examples of how students and teachers deal with demanding modelling tasks. We will refer both to results from our own projects DISUM and COM² as well as to empirical findings from various other research studies. First, we will present some examples of students' difficulties with modelling tasks and of students' specific modelling routes when solving such tasks (also dependent on their mathematical thinking styles), and try to explain these difficulties by the cognitive demands of these tasks. We will emphasise that mathematical modelling has to be learnt specifically by students, and that modelling can indeed be learned if teaching obeys certain quality criteria, in particular maintaining a permanent balance between teacher's guidance and students' independence. We will then show some examples of how teachers have successfully realised this subtle balance, and we will present interesting differences between individual teachers ' handling of modelling tasks. In the final part of our paper, we will draw some consequences from the reported empirical findings and formulate corresponding implications for teaching mathematical modelling. Eventually, we will present some encouraging results from a recent intervention study in the context of the DISUM project where it is demonstrated that appropriate learning environments may indeed lead to a higher and more enduring progress concerning students' modelling competency.

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Mathematical Modelling: Can It Be Taught And Learnt?

Preface to the Paperback EditionForewordIntroductionIGeneral Views and Inquiries1IIDiscussions on Unconsciousness21IIIThe Unconscious and Discovery29IVThe Preparation Stage. Logic and Chance43VThe Later Conscious Work56VIDiscovery as a Synthesis. The Help of Signs64VIIDifferent Kinds of Mathematical Minds100VIIIParadoxical Cases of Intuition116IXThe General Direction of Research124Final Remarks133App. I137App. II142

The Psychology of Invention in the Mathematical Field

The reconstruction of pupils modelling processes can be found in many empirical studies within the literature on modelling. The empirical differentiations of the phases, which includes putting statements and actions of the pupils in the right phase, has not been reconstructed from a cognitive psychological point of view on a micro level thus far. In this article different modelling cycles are discussed with attention to distinctions in the various phases. The "modelling cycle under cognitive psychological aspects" is specifically emphasized in contrast to the other cycles. On the basis of the results of the COM²-project (Cognitive psychological analysis of modelling processes in mathematics lessons, Borromeo Ferri) the phases of the modelling process are described empirically. Some difficulties in the process of distinguishing the various phases are also pointed out. Kurzreferat: Die Rekonstruktion von Modellie- rungsprozessen bei Lernenden ist in vielen empirischen Studien innerhalb der Literatur zum Modellieren zu finden. Die empirische Unterscheidung der Phasen, was die Einordnung von Aussagen und Handlungen der Lernenden miteinbezieht, wurde bisher noch nicht aus kognitionspsychologischer Sicht auf einer Mikro- ebene rekonstruiert. In diesem Artikel wird nach einer Ubersicht ausgewahlter Modellierungs- kreislaufe der "Modellierungskreislauf unter kognitionspsychologischen Aspekten im Vergleich hervorgehoben. Somit liegt der Fokus auf einer kognitionspsychologischen Perspektive hinsichtlich des Modellierungskreislaufes. Auf der Basis von Ergebnissen des KOM²-Projekt (Kognitionspsycho- logische Analysen von Modellierungsprozessen im Mathematikunterricht, Borromeo Ferri) werden die Phasen empirisch beschrieben und auch Schwierigkeiten bei der Einordnung in diese Phasen verdeutlicht. ZDM-Classification: C30, D10 1. Different modelling cycles - different approaches and aims Looking at the literature on modelling and applications one can find different modelling cycles. These cycles are different, because they are dependent on various directions and approaches of

/pdf/theoretical-and-empirical-differentiations-of-phases-in-the-29xpq332zv.pdf

Theoretical and empirical differentiations of phases in the modelling process

Trends in Teaching and Learning of Mathematical Modelling

Learning how to teach mathematical modeling in school and teacher education , Learning how to teach mathematical modeling in school and teacher education , کتابخانه‌های دانشگاه کردستان

Learning How to Teach Mathematical Modeling in School and Teacher Education

Looking at modelling from a cognitive perspective has largely been neglected in the current discussion regarding modelling. Using the mathematical didactical and cognitive-psychological approach of mathematical thinking styles, this study analyses the modelling performed by teachers and students in context-bounded mathematics lessons. This study is complex, and so are the results. The focus of this paper is on the depiction of reconstructed and so-called individual modelling routes of sixteen-year-old learners working in groups on modelling problems during mathematics lessons. These routes provide an insight into the learners' cognitive procedures during modelling.

Rita Borromeo Ferri

Papers

Theoretical and empirical differentiations of phases in the modelling process

Mathematical Modelling: Can It Be Taught And Learnt?

Trends in Teaching and Learning of Mathematical Modelling

Learning How to Teach Mathematical Modeling in School and Teacher Education

Modelling Problems from a Cognitive Perspective