EVALUATION OF A TEST MEASURING MATHEMATICAL MODELLING COMPETENCY FOR INDONESIAN COLLEGE STUDENTS

Background and Purpose: Mathematical modelling competency is one of the vital characteristics in mathematics education. Educational researchers have updated the benefit of modelling as key factor to the study of complexity and modern science. Since many scholars frequently adopt instrument from one cultural background to another, they also offer proof on the issue of validity and reliability. The present paper aimed at validating a mathematical modelling test for secondary prospective mathematics teachers.   Methodology: We utilized a survey approach to examine the factor structure of mathematical modelling test for 202 secondary prospective mathematics teachers, selected by cluster random sampling. Mathematical modeling test was adapted to measure the desired constructs. More importantly, we used exploratory factor analysis (EFA), confirmatory factor analysis (CFA) using AMOS 18 and Rasch measurement model with Winstep version 3.73 to analyze the data.   Findings: The EFA and CFA technique verified that a mathematical modelling test was acceptable for Indonesian prospective mathematics teachers. In addition, Rasch analysis also confirmed that all items fit the criteria well and implied that all items are valid in measuring student mathematical modelling competency. This finding concludes that the mathematical modelling test of Indonesian prospective mathematics teachers have an eight-dimension structure.    Contributions: This present research contributes towards psychometric measure on the reliability and validity of a mathematical modelling test in mathematics education programs.   Keywords: Confirmatory factor analysis, mathematical modelling competency, Rasch measurement model.   Cite as: Hidayat, R., Qudratuddarsi, H., Mazlan, N. H., & Mohd Zeki, M. Z. (2021). Evaluation of a test measuring mathematical modelling competency for Indonesian college students.  Journal of Nusantara Studies, 6(2), 133-155. http://dx.doi.org/10.24200/jonus.vol6iss2pp133-15

Physics education with interactive computational modelling

UID/CED/02861/2019The development of knowledge and cognition in physics and other fields of contemporary science, technology, engineering and mathematics (STEM) is based on modelling processes increasingly requiring advanced methods of scientific computation. Physics education for STEM education should then involve learning sequences featuring modelling activities with computational knowledge and technologies. Such sequences should manifest epistemological and cognitive balance between theory, experimentation and computation, be interactively collaborative, and ensure the development of meaningful knowledge in physics, mathematics and scientific computation, appropriately considering the diversity of STEM contexts. To address this challenge we have proposed an approach based on the creation of sequences of interactive engagement learning activities with computational modelling that explore different kinds of modelling, introduce scientific computation progressively, generate and resolve cognitive conflicts in the understanding of physics and mathematics, and comparatively analyze the various complementary representations of the mathematical models of physics. In this work we discuss a learning sequence about fluid mechanics for introductory physics students of STEM university courses, during which they built and explored in the computer mathematical physics models and animations helping them resolve difficulties persisting after theoretical lectures and problem-solving paper and pen activities.publishersversionpublishe

An ethnomathematical perspective of STEM education in a glocalized world

An Ethnomathematics-based curriculum helps students demonstrate consistent mathematical processes as they reason, solve problems, communicate ideas, and choose appropriate representations through the development of daily mathematical practices. As well, it recognizes connections with Science, Technology, Engineering, and Mathematics (STEM) disciplines. Our pedagogical work, in relation to STEM Education, is based on the trivium curriculum for mathematics and ethnomodelling, which provides communicative, analytical, material, and technological tools to the development of emic, etic, and dialogic approaches that are necessary for the elaboration of the school curricula. STEM education facilitates pedagogical action that connects ethnomathematics; mathematical modelling, problem-solving, critical judgment, and making sense of mathematical and non-mathematical environments, which involves distinct ways of thinking, reasoning, and developing mathematical knowledge in distinct sociocultural contexts. The ethnomathematical perspective for STEM education proposed here provides a transformative pedagogy that exposes its power to transform students into critical and reflective citizens in order to enable them to transform society in a glocalized world

Enhancing science and mathematics education with computational modelling

The development of knowledge in science and mathematics involves modelling processes where theory, experiment and computation are dynamically interconnected. For education in these fields to be in contact with their rapid progress and closer to the nature of research, it is crucial that both curricula and learning environments from high school to university manifest effectively a balanced interplay between theoretical, experimental and computational elements. We present an approach to improve the integration process of computational modelling in the science and mathematics high school and university curricula while respecting the cognitive balance between theoretical aspects, experimentation and scientific computation. As strategy, we propose the creation of learning activities built around exploratory and expressive computational modelling experiments which are presented in digital documents where the fundamental concepts and problem solving processes are explained using interactive text, images and embedded movies. To design the activities, special emphasis is given to cognitive conflicts in the understanding of scientific and mathematical concepts, to the manipulation of multiple representations of mathematical models and to the interaction between analytical and numerical solutions. We discuss illustrative examples constructed with Modellus which are relevant for the high school and undergraduate university curricula in mathematics and physics

How do future teachers model area and perimeter situations? The role of units and formulae

[EN] This study explores those skills associated with modeling that preservice primary and secondary teachers develop when working with measure. The sample was made up of a total of 12 master's degree students and 13 primary school teacher students, who worked in groups to solve a task, which was specically designed to develop skills associated with measure through modeling. The analysis of the models produced by the prospective teachers revealed a great wealth of ideas and evidence of the dependence on formulae for the calculation and estimation of areas. Results also indicate relationship between the model's closeness to the real situation and the tendency of participants to validate it, as well as the importance of the layout of the task on the produced models.[ES] Se presenta una investigación que explora el tipo de modelo que los futuros profesores de educación primaria y secundaria desarrollan cuando trabajan en situaciones de medida. La muestra empleada estuvo compuesta por un total de 12 alumnos de máster de formación de profesorado y 13 estudiantes del grado en educación primaria, que resolvieron en grupos una tarea diseñada específicamente para trabajar la medida a través de la modelización. El análisis de los modelos producidos por los futuros profesores reveló gran riqueza de ideas y evidenció limitaciones al uso de fórmulas para el cálculo y estimación de áreas. Los resultados también indican relación entre la cercanía del modelo con la situación en contexto y la tendencia de los participantes a validarlo, así como la importancia del formato de la tarea empleada sobre los modelos producidos.Montejo-Gámez, J.; Fernández-Ahumada, E.; Adamuz-Povedano, N. (2019). ¿Cómo modelizan los futuros profesores en situaciones de área y perímetro? El papel de las unidades y de las fórmulas. Modelling in Science Education and Learning. 12(1):5-20. https://doi.org/10.4995/msel.2019.11001SWORD520121Ärlebäck, J. B. (2009). Exploring the solving process of group solving realistic Fermi problems from the perspective of the Anthropological theory of didactics. En M. Pytlak, T. Rowland y W Swoboda (eds.), Proceedings of the Seventh Conference of European Research in Mathematics Education (CERME 7), (pp. 1010-1020). CERME: Rzeszów (Poland).Blomhøj, M., y Højgaard, T. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and its Applications, 22(3), 123‐139.Blum, W. y Leiss, D. (2007). How do students' and teachers deal with modelling problems? En C. Haines et al. (Eds), Mathematical Modelling: Education, Engineering and Economics. (pp. 222-231). Chichester: Horwood.Blum, W. y Borromeo-Ferri, R. (2009). Mathematical Modelling: Can It Be Taught And Learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.Borromeo-Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38 (2), 86-95.Bukova-Güzel, E. (2011). An examination of pre-service mathematics teachers' approaches to construct and solve mathematical modelling problems, Teaching Mathematics and Its Applications 30, 19-36Burkhardt, H. (2004). Establishing Modelling in the Curriculum: Barriers and Levers. En H.W.Henn y W. Blum (Eds.), ICMI Study 14: Applications and Modelling in Mathematics Education: Pre-Conference. Dortmund, Germany: ICMI.Cabassut, R. y Ferrando, I. (2017). Difficulties in Teaching Modelling: A French-Spanish Exploration. En G.A., Stillman, W. Blum, y G. Kaiser (Eds.), Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education (pp.223-232) Springer International Publishing.Chevallard, Y. (1989). Le passage de l'arithmétique à l'algébrique dans l'enseignement des mathématiques au collège - Deuxième partie: Perspectives curriculaires : la notion de modelisation. Petit X, 19, 45-75.Chevallard, Y., Bosch, M. y Gascón, J. (1997). Estudiar matemáticas. El eslabón perdido entre la enseñanza y el aprendizaje. Barcelona: ICE/Horsori.Colwell, J. y Enderson, C. M. (2016). "When I hear literacy": Using pre-service teachers' perceptions of mathematical literacy to inform program changes in teacher education. Teaching and Teacher Education 53, 63-74Comisión Europea/EACEA/Eurydice (2012). El desarrollo de las competencias clave en el contexto escolar en Europa: desafíos y oportunidades para la política en la materia. Informe de Eurydice. Luxemburgo: Oficina de Publicaciones de la Unión Europea.De Lange, J. (2003). Mathematics for literacy. En B.L. Madison, y L.A. Steen (Eds.), Quantitative literacy. Why numeracy matters for schools and colleges (pp. 75−89). Princeton, NJ: The National Council on Education and the Disciplines.Doerr, H. (2007). What Knowledge do teachers need for teaching mathematics through applications and modelling?. En Blum, Galbrait, Henn y Niss (Eds). Modelling and applications in mathematics education. The 14 th ICMI Study. (pp. 69-78). New York: Springer.Freudenthal, H. (1973). Mathematics as an Educational Task. Dordrecht, The Netherlands: Riedel Publishing Company.Gallart, C., Ferrando, I., García-Raffi, L. M. (2014). Implementación de tareas de modelización abiertas en el aula de secundaria, análisis previo. En M. T. González, M. Codes, D. Arnau, T. Ortega, Investigación en educación matemática (pp. 327-336). Salamanca: SEIEM.Garcia, F. J., Gascón, J., Ruiz, L., y Bosch, M. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM, 38(3), 226-246.Gravemeijer, K. y Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39 (1-3), 111-129.Hıdıroğlu, Ç. N., Dede, A. T., Kula-Ünver, S. y Bukova-Güzel, E. (2017). Mathematics Student Teachers' Modelling Approaches While Solving the Designed Eşme Rug Problem. EURASIA Journal of Mathematics Science and Technology Education, 13 (3), 873-892Huincahue Arcos, J., Borromeo-Ferri, R., y Mena-Lorca, J. (2018). El conocimiento de la modelación matemática desde la reflexión en la formación inicial de profesores de matemática. Enseñanza de las ciencias, 36(1), 99-115.Kaiser, G. (2014). Mathematical modelling and applications in education. En Encyclopedia of mathematics education (pp. 396-404). Springer, Dordrecht.Kaiser, G., Blomhøj, M., y Sriraman, B. (2006). Mathematical modelling and applications: empirical and theoretical perspectives. ZDM - Zentralblatt für Didaktik der Mathematik, 38(2), 82-85.Lesh, R. y Harel, G. (2003). Problem solving, modeling and local conceptual development. Mathematical Thinking and Learning, 5, 157-189.Lesh, R., Hoover, M., Hole, B., Kelly, A., y Post, T. (2000), Principles for Developing Thought-Revealing Activities for Students and Teachers, en A. Kelly y R. Lesh (eds.), Research Design in Mathematics and Science Education, Lawrence Erlbaum Associates, Mahwah, New Jersey, 591-646.Mathews, S. y Reed, M. (2007). Modelling for pre-service teachers. En Haines, Galbraith, Blum y Khan (Eds.), Mathematical modelling (ICTMA 12): Education, Engineering and Economics. (pp. 458-464). Chichester: Horwood Publishing.Montejo-Gámez, J., y Fernández-Ahumada, E. (2019). The notion of mathematical model for educational research: insights of a new proposal. Aceptado para CERME 11.Montejo-Gámez, J., Fernández-Ahumada, E., Jiménez-Fanjul, N., Adamuz-Povedano, N., y León-Mantero, C. (2017). Modelización como proceso básico en la resolución de problemas contextualizados: un análisis de necesidades. En J.M. Muñoz-Escolano, A. Arnal-Bailera, P. Beltrán-Pellicer, M.L. Callejo y J. Carrillo (Eds.), Investigación en Educación Matemática XXI (pp. 347-356). Zaragoza: SEIEM.Montoya Delgadillo, E. Viola, F. and Vivier, L. (2017). Choosing a Mathematical Working Space in a modelling task: The influence of teaching. En Dooley, T., y Gueudet, G. (Eds.), Proceedings of the CERME10 (pp. 956-963). Dublin, Ireland: DCU Institute of Education and ERME.Niss, M. (1999). Aspects of the nature and state of research in mathematics education. Educational Studies in Mathematics, 40(1), 1-24.Niss, M. (2003). Mathematical Competencies and the Learning of Mathematics: The Danish KOM Project. En A. Gagatsis y S. Papastavridis (Eds), 3rd Mediterranean Conference on Mathematical Education (pp. 115-124). Athens, Greece: The Hellenic Mathematical Society.Niss, M. (2012). Models and modelling in mathematics education. En Mathematical biology. Degree programs in mathematical biology. (pp. 49-52). Zurich, Switzerland: European Mathematical Society Newsletter.Niss, M., y Højgaard, T. (Eds.) (2011). Competencies and Mathematical Learning: Ideas and inspiration for the development of mathematics teaching and learning in Denmark. Roskilde: IMFUFA/NSM, Roskilde University.NCTM. (2000). Principles and Standards for School Mathematics. School Science and Mathematics, 47(8), 868-279. https://doi.org/10.1111/j.1949-8594.2001.tb17957.xOCDE (2013). Marcos y pruebas de evaluación de PISA 2012: Matemáticas, Lectura y Ciencias. Madrid: MECD.Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press.Sriraman, B. (2006). Conceptualizing the model-eliciting perspective of mathematical problem solving. En M. Bosch (Ed.), Proceedings of the CERME4 (pp. 1686-1695). Sant Feliu de Guíxols: FUNDEMI IQS, Universitat Ramon Llull.Stacey, K. (2015). The Real World and the Mathematical World. En K. Stacey y R. Turner (Eds.), Assessing Mathematical Literacy (pp. 57-84). Zurich: Springer. https://doi.org/10.1007/978-3-319-10121-7Van den Heuvel-Panhuizen, M. y Drijvers, P. (2014). Realistic mathematics education. En S. Lerman (Ed.) Encyclopedia of Mathematics Education (pp. 521-525). Amsterdam: Springer. https://doi.org/10.1007/978-94-007-4978-8.Venkat, H. y Winter, M. (2015). Boundary objects and boundary crossing for numeracy teaching. ZDM Mathematics Education 47, 575-586

Complexity in the modelling process of a statistics task

[EN] In this paper we present the qualitative analysis of the modelling process ofa 15-16 years old students teams working in a statistics activity with real data. We identify the di erent phases of the modelling process using the modelling cycle proposed by (Blum, Leiss, 2007) and we discuss the results from the perspective of the di culties founded during the analysis and the complexity of the modelling process analyze[ES] En este artículo presentamos un analisis cualitativo del proceso de modelizacion de un grupo de trabajo formado por alumnos de 15-16 años trabajando en una actividad estadística con datos reales.En concreto, identicamos las fases del proceso de modelizacion siguiendo el ciclo de modelizacion de Blum and LeiB (2007) y discutimos los resultadosdesde la perspectiva de las dicultades encontradas durante el analisis y la complejidad del proceso de modelizacion analizadoAymerich Restoy, À.; Albarracín Gordo, L. (2016). Complejidad en el proceso de modelización de una tarea estadística. Modelling in Science Education and Learning. 9(1):5-24. doi:10.4995/msel.2016.4121.SWORD52491Albarracín, L., & Gorgorió, N. (2013). Problemas de estimación de magnitudes no alcanzables: una propuesta de aula a partir de los modelos generados por los alumnos. Modelling in Science Education and Learning, 6, 33. doi:10.4995/msel.2013.1836Albarracín, L., & Gorgorió, N. (2014). Devising a plan to solve Fermi problems involving large numbers. Educational Studies in Mathematics, 86(1), 79-96. doi:10.1007/s10649-013-9528-9Arleback, J. B. (2009). On the use of realistic fermi problems for introducing mathematical modelling in school. The Mathematics Enthusiast, 6 (3), 331-364.Barbosa, J. C. (2009). Modelagem e modelos matematicos na educac~ao cientca. Alexandria: Revista de Educaçao em Ciencia e Tecnologia, 2 (2), 69-85.Batanero, C. (2000). Hacia donde va la educación estadística. Blaix, 15 (2), 13.Blum, W. (2002). Educational Studies in Mathematics, 51(1/2), 149-171. doi:10.1023/a:1022435827400Blum, W., & LeiB, D. (2007). Mathematical modelling (ictma 12): Education, engineering and economics. In W. B. S. K. C. Haines P. L. Galbraith (Ed.), (pp. 222-231). Elsevier.Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95. doi:10.1007/bf02655883Gal, I. (2002). Adults’ Statistical Literacy: Meanings, Components, Responsibilities. International Statistical Review, 70(1), 1-25. doi:10.1111/j.1751-5823.2002.tb00336.xGeiger, V. (2011). Factors Affecting Teachers’ Adoption of Innovative Practices with Technology and Mathematical Modelling. Trends in Teaching and Learning of Mathematical Modelling, 305-314. doi:10.1007/978-94-007-0910-2_31Lesh, R. (2010). Tools, researchable issues & conjectures for investigating what it means to understand statistics (or other topics) meaningfully. Journal of Mathematical Modelling and Application, 1 (2), 16-48.Lesh, R., & Harel, G. (2003). Problem Solving, Modeling, and Local Conceptual Development. Mathematical Thinking and Learning, 5(2-3), 157-189. doi:10.1080/10986065.2003.9679998Levitt, S. D., & Dubner, S. J. (2005). Freakonomics: A rogue economist explores the hidden side of everything (Vol. 61). William Morrow.NCTM. (2003). Principios y estandares para la educacion matematicas. Sevilla: SAEM Thales.Palm, T. (2007). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67(1), 37-58. doi:10.1007/s10649-007-9083-3Perrenet, J., & Zwaneveld, B. (2012). The many faces of the mathematical modeling cycle. Journal of Mathematical Modelling and Application, 1 (6), 3-21.Pollak, H. O. (1979). The interaction between mathematics and other school subjects. New Trends in Mathematics Teaching IV, Paris.Sol, M., Giménez, J., & Rosich, N. (2011). Trayectorias modelizadoras en la ESO. Modelling in Science Education and Learning, 4, 329. doi:10.4995/msel.2011.3100Villa-Ochoa, J., Bustamante, C., & Berrio, M. (2010). Sentido de realidad en la modelacion matematica. ALME 23. Comite Latinoamericano de Matematica Educativa-Colegio Mexicano de Matematica Educativa.Vorhölter, K., Kaiser, G., & Borromeo Ferri, R. (2014). Modelling in Mathematics Classroom Instruction: An Innovative Approach for Transforming Mathematics Education. Advances in Mathematics Education, 21-36. doi:10.1007/978-3-319-04993-9_

Using Cryptology to Teach Fundamental Ideas of Mathematics

Cryptology is a very old science and until a few decades it was a science for government, military, secret services, and spies. Nowadays, cryptology is almost everywhere in our lives. This article reports on an epistemological analysis of the question: “Is it possible to teach fundamental ideas of mathematics by using cryptography?” In a first step fundamental ideas of mathematics, which are the basic guidelines for mathematical education are discussed. For the analysis a set of fundamental ideas of mathematics is developed e.g. algorithm, functional dependence, modelling, number, measuring, and ordering. In a second step connections between the set of fundamental ideas and various techniques of cryptology are shown. Some outstanding examples for this part of the analysis are the Fleissner grille or the Diffie-Hellman key exchange.

Traditions in German-Speaking Mathematics Education Research

This open access book shares revealing insights into the development of mathematics education research in Germany from 1976 (ICME 3 in Karlsruhe) to 2016 (ICME 13 in Hamburg). How did mathematics education research evolve in the course of these four decades? Which ideas and people were most influential, and how did German research interact with the international community? These questions are answered by scholars from a range of fields and in ten thematic sections: (1) a short survey of the development of educational research on mathematics in German speaking countries (2) subject-matter didactics, (3) design science and design research, (4) modelling, (5) mathematics and Bildung 1810 to 1850, (6) Allgemeinbildung, Mathematical Literacy, and Competence Orientation (7) theory traditions, (8) classroom studies, (9) educational research and (10) large-scale studies. During the time span presented here, profound changes took place in German-speaking mathematics education research. Besides the traditional fields of activity like subject-matter didactics or design science, completely new areas also emerged, which are characterized by various empirical approaches and a closer connection to psychology, sociology, epistemology and general education research. Each chapter presents a respective area of mathematics education in Germany and analyzes its relevance for the development of the research community, not only with regard to research findings and methods but also in terms of interaction with the educational system. One of the central aspects in all chapters concerns the constant efforts to find common ground between mathematics and education. In addition, readers can benefit from this analysis by comparing the development shown here with the mathematical education research situation in their own country

Problem solving as instruments for the mathematical modeling: “Examples For Real Life”

[EN] Not many years ago that researchers in mathematics education have focused on designing activities based on mathematical modelling of real situations with the conviction to get a better guarantee on profit, by our students, the mathematical learning, and thus teaching by the teachers. The work presented in the context of the SUMMER-2014-Mathematics throughout life, in the Fourth Conference on Mathematical Modelling, intends to use the Problem Solving (PS) as a useful and necessary tool to reach the concept of Mathematical Modelling[ES] No hace muchos años que los investigadores en Educación Matemática han centrado su atención en el diseño de actividades basado en la modelización matemática de situaciones reales con el convencimiento de obtener una mayor garantía en la ganancia, por parte de nuestros alumnos, del aprendizaje matemático, y por ende en la enseñanza por parte de los enseñantes. El trabajo que presentamos, en el contexto del CURSO DE VERANO-2014-Matemáticas a lo largo de la vida, en las IV Jornadas de Modelización Matemática, pretende utilizar la Resolución de Problemas (RdP´s) como un instrumento útil y necesario para llegar al concepto de Modelización Matemática.INGLÉS:Not many years ago that researchers in mathematics education have focused on designing activities based on mathematical modelling of real situations with the conviction to get a better guarantee on profit, by our students, the mathematical learning, and thus teaching by the teachers. The work presented in the context of the Summer-2014-Mathematics throughout life, in the Fourth Conference on Mathematical Modelling, intends to use the Problem Solving (PS) as a useful and necessary tool to reach the concept of Mathematical ModellingRomero Sánchez, S.; Rodríguez, IM.; Benítez, R.; Romero, J.; Salas, IM. (2015). La resolución de problemas como instrumentos para la modelización matemática:Ejemplos para la vida real. Modelling in Science Education and Learning. 8(2):51-66. doi:10.4995/msel.2015.3962SWORD51668