Understanding Students' Modelling Skills

Haines, Chris; Crouch, Rosalind; Davis, James F.

doi:10.1533/9780857099655.5.366

Cited by 47 publications

(32 citation statements)

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“…Modeling competence A modeling test was constructed which assessed modeling competence in a multiple-choice format as suggested and empirically evaluated by Haines, Crouch and Davies (2001).…”

Section: Student Levelmentioning

confidence: 99%

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

Mischo

Maaß²

2013

Journal of Education and Training Studies

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This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and findings from mathematics education. Teacher beliefs about mathematics, learning and self-efficacy were expected to have a major impact on their classroom practices. We therefore assessed teacher beliefs about the usefulness of mathematics, learning (constructivist and socio-constructivist beliefs) and teacher self-efficacy when teaching modeling (teacher or class level variable). The student level variables assessed were modeling competence and other individual factors, such as basic mathematical skills and cognitive abilities.The effectiveness of the intervention was measured in a pre-post control group design using multilevel structural equation modeling. The results showed no direct effect of the intervention on student modeling competence. However, they did reveal that the intervention had a significant effect on teacher beliefs about learning (constructivist and socio-constructivist view) and an effect of these teacher beliefs about learning on student modeling competence. Further, the results showed that students' gains in modeling competence is not only mediated by teacher beliefs, but also influenced by individual factors. Implications for teaching as well as limitations of the study are discussed.Keywords: teacher beliefs, teacher education, mathematical modeling, teacher training Theoretical Background IntroductionMathematical modeling means solving complex, realistic and open problems with the help of mathematics. Although mathematical modeling became part of the national German curriculum in 2004 and has been discussed among mathematics educators for decades, it is still rare in day-to-day teaching practice (Blum, 2002).In the present study, we wanted to know whether specially designed (written) curriculum materials for teachers support the development of students' modeling competences. We focused on the design of curriculum materials because materials -other than long-term teacher training -can reach many teachers easily and effectively. We designed mathematical modeling teaching materials for the target group of six grade students (age 11) because modeling is part of the curriculum for this grade. Teachers were asked to use these materials over a period of one school year. The effectiveness of the materials was evaluated in a pre-post control group design by means of a standardized test to assess student competences in mathematical modeling. We also assessed teacher beliefs before and after the intervention because it was expected that their beliefs play a mediating role in the effectiveness of the written materials.The main research questions of the study were:1. Does teacher use of curriculum materials directly influence student modeling competen...

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Section: Student Levelmentioning

confidence: 99%

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

Mischo

Maaß²

2013

Journal of Education and Training Studies

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“…Haines et al (2001) have shown how closed items testing modelling competencies can be designed. In the TIMS-study, for example, students had to complete tasks in multiple choice format as well as in open answering format.…”

Section: Construction Of the Modelling Testmentioning

confidence: 99%

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

Maaß

Mischo

2010

J Math Didakt

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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.

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“…Araştırmacılar üniversite öğrencilerinin modelleme yeterliklerini değerlendirmek için kısmi yaklaşıma göre hazırlanmış çoktan seçmeli bir test geliştirmişlerdir (Haines, Crouch & Davis, 2001). Kısmi modelleme yeterliklerini (i) matematiksel model oluşturmak için varsayımda bulunma, (ii) gerçek modelin amacını açığa çıkarma, (iii) problem durumunu formüle etme, (iv) değişkenleri, parametreleri ve sabitleri belirleme, (v) matematiksel terimleri formüle etme ve (vi) matematiksel model üzerine yansımalarda bulunma olarak ele almışlardır.…”

Section: Introductionunclassified

“…Dolayısıyla bu çalışmada diğerlerinden farklı olarak öğrencilerin modelleme yeterlikleri kısmi yaklaşım çerçevesinde ele alınmaktadır. Kısmi yaklaşım çerçevesinde gerçekleştirilen uluslararası çalışmalarda ise modelleme yeterlikleri modelleme sürecinin basamakları çerçevesinde teker teker değil gruplandırılarak incelenmektedir (Blomhøj & Hojgaard Jensen, 2003;Brand, 2014;Grünewald, 2012;Haines, Crouch & Davis, 2001;Kaiser & Grünewald, 2015). Bu çalışmada öğrencilerin her bir modelleme yeterliği birbirinden bağımsız olarak ele alındığı için çalışmanın kuramsal temelini Blum ve Kaiser'in (1997) modelleme yeterlikleri çerçevesi oluşturmaktadır.…”

Section: Introductionunclassified

Modelleme Yeterlikleri ile Sınıf Düzeyi ve Matematik Başarısı Arasındaki İlişkilerin İncelenmesi

Dede¹

2017

İlköğretim Online

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Ayşe Tekin Dede, Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi, ayse.tekin@deu.edu.tr ÖZ. Çalışmanın amacı ortaokul öğrencilerinin modelleme yeterlikleri ile sınıf düzeyi ve matematik başarıları arasındaki ilişkileri ve öğrencilerin modelleme yaklaşımlarını incelemektir. Çalışmaya 5., 6., 7, ve 8. sınıfta eğitim gören toplam 311 öğrenci katılmıştır. Öğrencilerin modelleme yeterliklerini belirlemeyi amaçlayan sorulara verdiği yanıtlar bir rubrik aracılığıyla analiz edilirken söz konusu ilişkileri belirlemek için istatistiksel analizler gerçekleştirilmiştir. Sınıf seviyesi arttıkça doğrulama dışındaki tüm yeterlik düzeyleri artmış ve matematik dersi başarısı yüksek olan öğrencilerin modelleme yeterlik düzeyleri de yüksek çıkmıştır. Öğrencilerin verilen probleme uygun varsayımları seçerek gerçek modeller oluşturdukları görülmüştür. Farklı gösterim şekillerinden faydalanarak matematiksel modeller oluşturan öğrenciler matematiksel modelleri çözerken hatalar yapmışlardır. Gerçek yaşamlarında karşılaşabilecekleri bir durumu yorumlamaya çalışan öğrenciler, doğrulama yaparken varsayımları, matematiksel modelleri ve ulaşılan sonuçların anlamlılığını değerlendirmişlerdir. Anahtar Sözcükler: Kısmi Yaklaşım, Matematik Başarısı, Modelleme Yeterliği, Sınıf Düzeyi ABSTRACT. The purpose of the study is to investigate the relationship between the elementary school students' modelling competencies and their class level and mathematics achievements, and examine their modelling approaches. 311 students from 5th, 6th, 7th and 8th grades participated in the study. While the responses of the students to the questions aiming at determining the modelling competencies were analysed by means of a rubric, the statistical analyses were performed to examine the relationships. As the class level increased, all the competency levels except the validity of the solution increased, and the students with high mathematics achievement level had higher level of modelling competencies. It was seen that they constructed real models by choosing appropriate assumptions. The students who constructed mathematical models by taking advantage of different forms of representations made mistakes in solving the models. The students who tried to interpret a situation that they could encounter in their real life assessed the assumptions, the mathematical models and the obtained results while validating. Keywords: Atomistic Approach, Mathematics Achievement, Modelling Competence, Class Level SUMMARY Purpose and Significance: Mathematical modelling is a process in which real life problems are brought into the mathematical world and solutions are developed, and the obtained mathematical solutions are returned to the real life context and validated and verified. The modelling competencies need to be improved in order for students to be successful in this process. Research suggests two different approaches as atomistic and holistic for the development of modelling competencies. While the majority of studies were holistic in the modelling process, the lack of studies ca...

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Understanding Students' Modelling Skills

Cited by 47 publications

References 1 publication

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

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

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

Modelleme Yeterlikleri ile Sınıf Düzeyi ve Matematik Başarısı Arasındaki İlişkilerin İncelenmesi

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