Modes of modelling assessment—a literature review

This paper presents a critical review of literature investigating assessment of mathematical modelling. Written tests, projects, hands-on tests, portfolio and contests are modes of modelling assessment identified in this study. The written tests found in the reviewed papers draw on an atomistic view on modelling competencies, whereas projects are described to assess a more holistic modelling competence but obstacles regarding reliability of assessing projects are identified. The outcome of this investigation also indicates that the criteria used in frameworks or modes of assessment seldom are derived from a theoretical analysis, but more often based on ad hoc constructions, experience from assessment situations or empirical studies of students’ work. Finally, this study suggests that an elaborated view on the meaning of quality of mathematical models is needed in order to assess the quality of students’ work with mathematical models.

[1]  H. Watt Attitudes to the Use of Alternative Assessment Methods in Mathematics: A Study with Secondary Mathematics Teachers in Sydney, Australia , 2005 .

[2]  Frank K. Lester,et al.  Second handbook of research on mathematics teaching and learning : a project of the National Council of Teachers of Mathematics , 2007 .

[3]  Morten Blomhøj,et al.  Teaching mathematical modelling through project work , 2006 .

[4]  Werner Blum,et al.  Advances and perspectives in the teaching of mathematical modelling and applications , 1995 .

[5]  A. O. Moscardini,et al.  Teaching and applying mathematical modelling , 1986 .

[6]  O. Skovsmose Travelling Through Education: Uncertainty, Mathematics, Responsibility , 2005 .

[7]  Morten Blomhøj,et al.  What’s all the Fuss about Competencies? , 2007 .

[8]  Gloria Stillman Applications and Modelling Research in Secondary Classrooms: What Have We Learnt? , 2015 .

[9]  Gloria Stillman The Emperor's New Clothes? Teaching and Assessment of Mathematical Applications at the Senior Secondary Level , 1998 .

[10]  Eva Jablonka,et al.  What makes a model effective and useful (or not) , 1997 .

[11]  Mogens Allan Niss Assessment in Mathematics Education and Its Effects: An Introduction , 1993 .

[12]  Marielle Simon,et al.  Impact of a Content Selection Framework on Portfolio Assessment at the Classroom Level , 2000 .

[13]  Werner Blum,et al.  How do Students and Teachers Deal with Modelling Problems , 2007 .

[14]  Katja Maaß,et al.  What are modelling competencies , 2006 .

[15]  Pauline Vos Assessment of Applied Mathematics and Modelling: Using a Laboratory-Like Environment , 2007 .

[16]  Eva Jablonka,et al.  Theorising in mathematics education research differences in mode and quality , 2010 .

[17]  Jerry Legé “To Model, or to Let Them Model?” That is the Question! , 2007 .

[18]  Qiyuan Jiang,et al.  An Introduction to Cumcm , 2007 .

[19]  Peter Galbraith,et al.  Mathematical Modelling as Pedagogy – Impact of an Immersion Program , 2001 .

[20]  Werner Blum,et al.  Modelling and Applications in Mathematics Education : the 14th ICMI Study , 2007 .

[21]  Dede de Haan 7 – New Applications of the Mathematics A-lympiad , 2003 .

[22]  Anselm L. Strauss,et al.  Basics of qualitative research : techniques and procedures for developing grounded theory , 1998 .

[23]  Ken Houston,et al.  Mathematical modelling in education and culture , 2003 .

[24]  Hans-Wolfgang Henn Why Cats Happen to Fall from the Sky or on Good and Bad Models , 2011 .

[25]  John Izard Assessing Progress in Mathematical Modelling , 2007 .

[26]  A. Bryman Social Research Methods , 2001 .

[27]  Ken Houston,et al.  Modelling and Mathematics Education: ICTMA 9: Applications in Science and Technology , 2002 .

[28]  E. Jablonka,et al.  Mathematisation and demathematisation : social, philosophical and educational ramifications , 2007 .

[29]  Elfi Furtmueller,et al.  Using grounded theory as a method for rigorously reviewing literature , 2013, Eur. J. Inf. Syst..

[30]  Werner Blum Applications and modelling in learning and teaching mathematics , 1989 .

[31]  Dylan Wiliam,et al.  Keeping learning on track: classroom assessment and the regulation of learning , 2007 .

[32]  Morten Blomhøj,et al.  Modelling Competency: Teaching, Learning and Assessing Competencies – Overview , 2011 .

[33]  A. O. Moscardini,et al.  Mathematical Modelling Courses , 1988 .

[34]  D.N.P. Murthy A first course in mathematical modelling: F. R. Giordano and M. D. Weir. Brookes-Cole, Belmont, Calif. (1985). XVII + 328 pp. , 1987 .

[35]  Miriam Amit,et al.  Assessing a Modeling Process of a Linear Pattern Task , 2010 .

[36]  Werner Blum,et al.  Applied mathematical problem solving, modelling, applications, and links to other subjects — State, trends and issues in mathematics instruction , 1991 .

[37]  Morten Blomhøj,et al.  Developing mathematical modelling competence: conceptual clarification and educational planning , 2003 .

[38]  Gabriele Kaiser,et al.  A global survey of international perspectives on modelling in mathematics education , 2006 .

[39]  Ian Huntley,et al.  Mathematical Modelling: Methodology, Models, and Micros , 1986 .

[40]  Peter Galbraith,et al.  Modelling and Applications in Mathematics Education , 2007 .

[41]  Katja Maaß Modelling in Class: What Do We Want the Students to Learn? , 2007 .

[42]  Troels Lange Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education , 2007 .

[43]  K. Stacey,et al.  Learning Mathematics for Life: A Perspective from PISA , 2009 .

[44]  Gabriele Kaiser,et al.  Modelling and Modelling Competencies in School , 2007 .

[45]  Eva Jablonka,et al.  Meta-Analyse von Zugängen zur mathematischen Modellbildung und Konsequenzen für den Unterricbt , 1997 .

[46]  Werner Blum,et al.  Trends in Teaching and Learning of Mathematical Modelling , 2011 .

[47]  Zheng Tong,et al.  8 – “Mathematics Contest in Modelling” Problems from Practice , 2003 .

[48]  Ross Turner,et al.  Modelling and Applications in Pisa , 2007 .

[49]  Stefan Ufer,et al.  Assessing Modelling Competencies Using a Multidimensional IRT Approach , 2011 .

[50]  Ken Houston Assessing the “Phases” of Mathematical Modelling , 2007 .

[51]  O. Skovsmose Travelling Through Education , 2008 .

[52]  Peter Galbraith,et al.  Mathematical modelling : teaching and assessment in a technology-rich world , 1998 .

[53]  Francisco Javier García,et al.  Mathematical modelling as a tool for the connection of school mathematics , 2006 .

[54]  Peter Frejd,et al.  First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies , 2009 .

[55]  Herbert Henning,et al.  Levels of Modelling Competencies , 2007 .

[56]  Peter W. Airasian Classroom Assessment: Concepts and Applications , 1991 .

[57]  Christopher Haines,et al.  Mathematical Modelling and Applications: Ability and Competence Frameworks , 2007 .

[58]  Lieven Verschaffel,et al.  Modelling Competencies — Overview , 2007 .

[59]  Søren Antonius Modelling Based Project Examination , 2007 .

[60]  Rita Borromeo Ferri,et al.  Theoretical and empirical differentiations of phases in the modelling process , 2006 .

[61]  Werner Blum,et al.  Teaching of Mathematical Modelling and Applications , 1991 .

[62]  Roger Brown 11 – Formulating and Assessing a Mathematical Modelling Problem in a Technological Environment , 2001 .

[63]  Geoff Wake,et al.  MODELLING AND FORMATIVE ASSESSMENT PEDAGOGIES MEDIATING CHANGE IN ACTIONS OF TEACHERS AND LEARNERS IN MATHEMATICS CLASSROOMS , 2010 .

[64]  Jonas Bergman Ärlebäck,et al.  Mathematical modelling in upper secondary mathematics education in Sweden , 2010 .

[65]  Norbert M. Seel,et al.  Encyclopedia of the sciences of learning , 2012 .

[66]  Peter Galbraith Assessment and Evaluation - Overview , 2007 .

[67]  Christopher Haines,et al.  Remarks on a Modeling Cycle and Interpreting Behaviours , 2010 .

[68]  T. Jensen,et al.  Assessing Mathematical Modelling Competency , 2007 .

[69]  Peter Frejd An investigation of mathematical modelling in the Swedish national course tests in mathematics , 2011 .