Abstract
This paper examines 6th grade children's local conceptual development and mathematization processes as they worked a comprehensive mathematical modeling problem (creating a consumer guide for deciding the best snack chip) over several class periods. The children and their teachers were participating in a 3-year longitudinal teaching experiment in which sequences of mathematical modeling problems were implemented from the 5th grade (10 years of age) though to the 7th grade. In contrast to traditional problem solving, mathematical modeling requires children to generate and develop their own mathematical ideas and processes, and to form systems of relationships that are generalizable and reusable. Reported here is a detailed analysis of the iterative cycles of development of one group of children as they worked the problem, followed by a summary of the mathematization processes displayed by all groups. Children's critical reflections on their models are also reported. The results show how children can independently develop constructs and processes through meaningful problem solving. Children's development included creating systems for operationally defining constructs; selecting, categorizing, and ranking factors; quantifying quantitative and qualitative data; and transforming quantities.
Similar content being viewed by others
References
DaPueto, C. and Parenti, L.: 1999, ‘Contributions and obstacles of contexts in the development of mathematical knowledge’, Educational Studies in Mathematics 39, 1–21.
Doerr, H.M. and English, L.D.: 2001, ‘A modeling perspective on students' learning through data analysis’, in M. Heuvel-Panhuizen (ed.), Proceedings of the 25th conference of the International Group for the Psychology of Mathematics Education, Utrecht University, pp. 361–368.
Doerr, H.M. and English, L.D.: 2003, ‘A modeling perspective on students' mathematical reasoning about data’, Journal for Research in Mathematics Education 34, 110–136.
Elbers, E.: 2003, ‘Classroom interaction as reflection: Learning and teaching mathematics in a community of inquiry’, Educational Studies in Mathematics 54, 77–99.
English, L.D.: 2002a, ‘Promoting learning access to powerful mathematics for a knowledge-based era’, in D. Edge and Y.B. Har (eds.), Mathematics Education for a Knowledge-based Era, Association of Mathematics Educators, National Institute of Education, Singapore, pp. 100–107.
English, L.D.: 2002b, ‘Development of 10-year-olds' mathematical modeling’, in A. Cockburn and E. Nardi (eds.), Proceedings of the 26th International PME Conference, University of East Anglia, Norwich, pp. 329–336.
English, L.D.: 2003, ‘Reconciling theory, research, and practice: A models and modeling perspective’, Educational Studies in Mathematics 54, 225–248.
English, L.D. and Watters, J.J.: 2005, ‘Mathematical modeling in third-grade classrooms’, Mathematics Education Research Journal 16, 59–80.
Freudenthal, H.: 1973, Didactical Phenomenology of Mathematical Structures, Kluwer, Boston.
Gainsburg, J.: 2006, ‘The mathematical modeling of structural engineers,’ Mathematical Thinking and Learning 8, 3–36.
Galbraith, P.L., Blum, W., Booker, G. and Huntley, I.D.: 1998, Mathematical Modeling: Teaching and Assessment in a Technology-Rich World, Horwood Publishing Ltd, West Sussex.
Gravemeijer, K.: 1999, ‘How emergent models may foster the construction of formal mathematics’, Mathematical Thinking and Learning 1, 155–177.
Greer, B.: 1997, ‘Modeling reality in mathematics classrooms: The case of word problems’, Learning & Instruction 7, 293–307.
Hamilton, E., Lesh, R., Lester, F. and Yoon, C.: In press, ‘The use of reflection tools in building personal models of problem solving’, in R. Lesh, E. Hamilton, and J. Kaput (eds), Models & Modeling as Foundations for the Future in Mathematics Education, Mahwah, New Jersey.
Jones, G., Langrall, C., Thornton, C. and Nisbet, S.: 2002, ‘Elementary school children's access to powerful mathematical ideas’, in L.D. English (ed.), Handbook of International Research in Mathematics Education, Erlbaum, Mawah, NJ, pp. 113–141.
Lesh, R.: In press, ‘Foundations for the future in engineering and other fields that are heavy users of mathematics, science, and technology’, in R. Lesh, E. Hamilton, and J. Kaput, (eds.), Models & Modeling as Foundations for the Future in Mathematics Education, Lawrence Erlbaum, Mahwah, New Jersey.
Lesh, R.A. and Doerr, H.: 2003, ‘Foundations of a Models & Modeling Perspective on Mathematics Teaching and Learning’, in R.A. Lesh and H. Doerr (eds.), Beyond constructivism: A models and modeling perspective on mathematics teaching, learning, and problem solving, Erlbaum, Mahwah, NJ, pp. 3–34.
Lesh, R.A. and English, L.D.: 2005, ‘Trends in the evolution of models and modelling perspectives on mathematical learning and problem solving’, in H. Chick and J. Vincent (eds.), Proceedings of the 29th International Group for the Psychology of Mathematics Education, University of Melbourne, pp. 192–196.
Lesh, R.A. and Kelly, A.E.: 2000, ‘Multi-tiered teaching experiments’, in R. Lesh and A. Kelly (eds.), Handbook of Research Design in Mathematics and Science Education, Erlbaum, Mahwah, NJ, pp. 197–230.
Lesh, R. and Zawojewski, J.: In press, ‘Problem solving and modeling’, in F. Lester, (ed.) Handbook of Research on Mathematics Teaching and Learning, Information Age Publishers, Greenwich.
Lesh, R., Zawojewski, J.S. and Carmona, G.: 2003, ‘What mathematical abilities are neded for success beyond school in a technology-based age of information?’, in R. Lesh, and Doerr, H. (eds.), Beyond constructivism: A Models and Modeling Perspective on Mathematics Problem Solving, Learning, and Teaching, Lawrence Erlbaum, Mahwah, New Jersey, pp. 205–222.
Prediger, S.: 2005, ‘Developing reflectiveness in mathematical classrooms-An aim to be reached in several ways’, International Reviews on Mathematical Education 37, 250–257.
Stevens, R.: 2000, ‘Who counts what as mathematics: Emergent and assigned mathematics problems in a project-based classroom’, in J. Boaler (ed.), Multiple Perspectives on Mathematics Teaching and Learning Ablex Publishing, Westport, CT, pp. 105–144.
Streefland, L.: 1993, ‘The design of a mathematics course. A theoretical reflection’, Educational Studies in Mathematics 25, 109–135.
Van den Heuvel-Panhuizen.: 2003, ‘The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage’, Educational Studies in Mathematics 54, 9–35.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
English, L.D. Mathematical Modeling in the Primary School: Children's Construction of a Consumer Guide. Educ Stud Math 63, 303–323 (2006). https://doi.org/10.1007/s10649-005-9013-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10649-005-9013-1