Implementing Modelling into Day-to-Day Teaching Practice – The Project STRATUM and its Framework

Abstract

This paper presents the framework and methods of the project STRATUM (Strategies for Teaching Understanding in and through Modelling), whose aim it is to design and evaluate teaching units for supporting the development of modelling competencies in low-achieving students at the German Hauptschule. The teaching units are based on the theory of modelling and on results acquired through educational research. We will explain major characteristics of the teaching units and give examples, as well as present the research design and the instruments. A major challenge of the project was the design of a modelling test. We will show how it was tailored to meet the framework of the study. The psychometric quality of the test indicates that it is suitable for the evaluation of our teaching units.Keywords Mathematical modelling · Low-achieving students · Teaching modelling · Professional development · Implementation in day-to-day teaching · Design of teaching materialsWe would like to express our thanks to the Research Association of the Hauptschule Forschungsverbund Hauptschule Baden-Württemberg for their financial support of STRATUM project. K. Maaß ( ) · C. MischoZusammenfassung Dieser Aufsatz stellt das Konzept des Projektes STRATUM (Strategies for Teaching Understanding in and through Modelling) vor, dessen Ziel es war, Unterrichtseinheiten zur Förderung der Modellierungskompetenzen von Hauptschülern zu entwickeln und zu evaluieren. Die Unterrichtseinheiten wurden basierend auf der internationalen Diskussion um Modellierungen und Ergebnissen der fachdidaktischen, psychologischen und erziehungswissenschaftlichen Forschung entwickelt. In diesem Aufsatz werden wir wesentliche Eigenschaften der Unterrichtseinheiten darlegen, Beispiele geben und das Forschungsdesign (inkl. der Erhebungsinstrumente) vorstellen. Eine wesentliche Herausforderung des Projektes war es, einen Modellierungstest für die Zielgruppe zu entwickeln. Wir werden zeigen, wie er gezielt für dieses Forschungsdesign entwickelt wurde. Die psychometrische Qualität des Testes zeigt seine Eignung zur Evaluation unserer Unterrichseinheiten.

German-Speaking Traditions in Mathematics Education Research

“…Katja Maaß focused in her talk on "Mathematical modelling in professional development: Traditions in Germany on professional development courses," addressing topics such as differentiation and assessment when modelling. Based on expert interviews and a desktop analysis, she outlined the most important milestones, thereby showcasing important steps which might be useful for other countries as well (see Maaß & Mischo, 2011). In addition, Katrin Vorhölter gave an overview on "Implementing mathematical modelling in schools" by presenting several projects of the last two decades aiming at the implementation of modelling in Germany.…”

The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling – An Intervention Study

“…Hence, Tillema concluded that the acquisition process in teacher training depends on the preceding or accompanying change of beliefs. Maaß (2011) reconstructed teacher beliefs about teaching and learning in the framework of a professional development course on modeling and identified the static type and the process type. The static type aims to prepare students efficiently for their final exam, while the process type expects students to learn to apply mathematics in real life.…”

“…We followed a structured approach to the introduction of mathematical modeling which (a) accounted for the fact that students and teachers are novices in mathematical modeling, and (b) was appropriate for the student performance level. Thus, in our teaching units, successive competences in carrying out the single steps are developed following the modeling process as described above (for details of the lessons and teaching units see Maaß & Mischo, 2011).…”

“…From these answer options; several had to be ticked as "right" (for more details see Maaß & Mischo, 2011). The modeling task that follows is one of the more simple ones used, as only one variable has to be estimated (number of people per apartment).…”

Ortaokul 3.Sınıf Öğrencilerinin Okuma Yarışması Problemi Üzerinde Bilişsel Modelleme Yeterlikleri

“…Çalışmalarda, öğrencileri bu tür modelleme problemleriyle karşı karşıya getirmenin matematik hakkındaki olumsuz inançların gelişimini engellediği gibi verilen kısa süreli modelleme deneyimlerinin bile öğrencilerin matematiğe karşı inançlarının pozitif yönde değişmesinde önemli bir rol oynadığı (Biccard & Wessels, 2011); tümevarım ve tümdengelimli düşünme becerileri geliştirmesinin yanında problem çözme, hipotez oluşturma ve ispatlama, nedensel ilişkileri ortaya koyma ve değişkenler arasındaki ilişkileri geliştirme yeterliklerini artırdığı (Sekerak, 2010); matematiksel modelleme basamaklarını takip etme prosedürü odaklı öğrenme ortamlarında öğrencilerin model oluşturma etkinlikleri ile çalıştırılması matematiksel modelleme yeterliklerinin kazandırılmasında pozitif etkisi olduğu (Blomhoj & Jensen, 2003;Maaß, 2006;Kaiser, 2007) (Henning & Keune, 2007;Ludwig & Xu, 2010); öğrencilerin yorumlama ve doğrulama yeterliklerinin yeterince gelişmediği (Kaiser, 2007;Maaß, 2006) ve yeterliklerin tam olarak gelişmesinin zaman gerektiren bir süreç olduğu ( Blomhoj & Jensen, 2003;Kaiser, 2007); düşük sosyo-ekonomik ailelerden gelen düşük performanslı öğrencilerle modelleme öğretimi uygulaması ve bu amaç için öğretim birimleri tasarlanması gerekliliği (Maaß & Mischo, 2011) anlama, yorumlama, yapma ve kullanma becerisi olarak tanımlamaktadır (Niss, 2004). Yani yeterlik sadece beceri ve yetenekten ibaret olmayıp ayrıca bunların gerçek yaşama yansımış kullanımları ile bu beceri ve yeteneklerin istekli biçimde eyleme aktarımını da kapsamaktadır (Maaß, 2006).…”