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Mathematical modelling in the primary school
 In
, 2004
"... Changes in society and the workplace necessitate a rethinking of the nature of the mathematical problemsolving experiences we provide our students across the grades. We need to design experiences that develop a broad range of futureoriented mathematical abilities and processes. Mathematical modell ..."
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Changes in society and the workplace necessitate a rethinking of the nature of the mathematical problemsolving experiences we provide our students across the grades. We need to design experiences that develop a broad range of futureoriented mathematical abilities and processes. Mathematical modelling, which has traditionally been reserved for the secondary school, serves as a powerful vehicle for addressing this need. This paper reports on the second year of a threeyear longitudinal study where a class of children and their teachers participated in mathematical modelling activities from the 5th grade through to the 7th grade. The paper explores the processes used by small groups of children as they independently constructed their own mathematical models at the end of their 6th grade. Our everchanging global market is making increased demands for workers who possess more flexible, creative, and futureoriented mathematical and technological skills (Clayton, 1999). Of importance here is the ability to make sense of complex systems (or models), examples of which appear regularly in the media (e.g., sophisticated buying, leasing, and loan plans). Being able to interpret and work with such systems involves important mathematical processes that are underrepresented in the mathematics curriculum, such as constructing, describing, explaining, predicting, and representing, together with quantifying, coordinating, and organising data. Dealing with systems also requires the ability to work collaboratively on multicomponent projects in which planning, monitoring, and communicating results are essential to success (Lesh & Doerr, 2003). Given these societal and workplace requirements, it is imperative that we rethink the nature of the mathematical problemsolving experiences we provide our students — in terms of content covered, approaches to learning, ways of assessing learning, and ways of increasing our children's access to quality learning. One approach to addressing these issues is through mathematical modelling (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003). Mathematical modelling has traditionally been reserved for the secondary school
Mathematical modeling with 9yearolds
 In
"... This paper reports on the mathematical modelling of four classes of 4thgrade children as they worked on a modelling problem involving the selection of an Australian swimming team for the 2004 Olympics. The problem was implemented during the second year of the children's participation in a 3ye ..."
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This paper reports on the mathematical modelling of four classes of 4thgrade children as they worked on a modelling problem involving the selection of an Australian swimming team for the 2004 Olympics. The problem was implemented during the second year of the children's participation in a 3year longitudinal program of modelling experiences (i.e., grades 35; 20032005). During this second year the children completed one preparatory activity and three comprehensive modelling problems. Throughout the two years, regular teacher meetings, workshops, and reflective analysis sessions were conducted. The children displayed several modelling cycles as they worked the Olympics problem and adopted different approaches to model construction. The children’s models revealed informal understandings of variation, aggregation and ranking of scores, inverse proportion, and weighting of variables.
MODELING WITH DATA IN CYPRIOT AND AUSTRALIAN PRIMARY CLASSROOMS
"... This paper addresses the mathematical developments of two classes of ten year old students in Cyprus and Australia as they worked on a complex modeling problem involving interpreting and dealing with multiple sets of data. Modeling problems require students to analyse a realworld based situation, ..."
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This paper addresses the mathematical developments of two classes of ten year old students in Cyprus and Australia as they worked on a complex modeling problem involving interpreting and dealing with multiple sets of data. Modeling problems require students to analyse a realworld based situation, pose and test conjectures, and construct models that are generalizable and reusable. Our findings show that students in both countries, with different cultural and educational backgrounds and inexperienced in modeling, were able to engage effectively with the problem and, furthermore, adopted similar approaches to model creation. The children progressed through a number of modeling cycles, from focusing on subsets of information through to applying mathematical operations in dealing with the data sets, and finally, identifying trends and relationships.
DEVELOPMENT OF 10YEAROLDS ’ MATHEMATICAL MODELLING
"... This paper addresses the developments of a class of fifthgrade children as they worked modelling problems during the first year of a 3year longitudinal study. In contrast to usual classroom problems where students find a brief answer to a particular question, modelling activities involve students ..."
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This paper addresses the developments of a class of fifthgrade children as they worked modelling problems during the first year of a 3year longitudinal study. In contrast to usual classroom problems where students find a brief answer to a particular question, modelling activities involve students in authentic case studies that require them to create a system of relationships that is generalisable and reusable. The present study shows how 10yearolds, who had not experienced modelling before, used their existing informal mathematical knowledge to generate new ideas and relationships, and how these developments were fuelled by significant social interactions within small group settings.
SeventhGraders ’ Mathematical Modelling on Completion of a ThreeYear Program
"... This paper addresses 7thgrade children's mathematical modelling at the end of a 3year program. The children and their teachers participated in a series of mathematical modelling activities from the 5th grade through to the 7th grade. The problems involve authentic situations that need to be i ..."
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This paper addresses 7thgrade children's mathematical modelling at the end of a 3year program. The children and their teachers participated in a series of mathematical modelling activities from the 5th grade through to the 7th grade. The problems involve authentic situations that need to be interpreted and described in mathematical ways. We examine the mathematical understandings and mathematisation processes that the children used in constructing their models for the final problem (Summer Reading). We report on the nature of the problem factors that the children chose to consider, the operations they applied, the types of transformations they made through these operations, and the representations they used in documenting their models. In a technologybased age of information, educational leaders from different walks of life are emphasizing a number of key understandings and abilities for success beyond school. These include the ability to make sense of complex systems through constructing, describing, explaining, manipulating, and predicting such systems (such as sophisticated buying, leasing, and loan plans); to work on multistage and multicomponent projects in which planning, monitoring, and communication processes are critical for success; and to
HARDY’S LEGACY TO NUMBER THEORY
 J. AUSTRAL. MATH. SOC. (SERIES A) 65 (1998), 238–266
, 1998
"... Ths is an expanded version of two lectures given at the conference held at Sydney University in December ..."
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Ths is an expanded version of two lectures given at the conference held at Sydney University in December
DERIVATION OF A SPATIALLY CONTINUOUS TRANSPORTATION MODEL1
"... Abstract—A geographically continuous movement model can be deduced from the quadratic transshipment problem by considering the transportation network as a discrete mesh. The resulting system of coupled Helmholz equations can be considered to solve simultaneously the spatially continuous versions of ..."
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Abstract—A geographically continuous movement model can be deduced from the quadratic transshipment problem by considering the transportation network as a discrete mesh. The resulting system of coupled Helmholz equations can be considered to solve simultaneously the spatially continuous versions of the traffic “distribution ” and “assignment ” problems. The associated Lagrangian functions are similar to the potentials of classical flow theory. Numerical methods implement the procedure. This work uses a sequence of elementary discrete geographic movement models to lead to an equivalent spatially continuous version, which then involves potential fields describable by a system of partial differential equations. One departure from classical results is that there is a different potential for gross and for net movements, the one allowing for simultaneous movement in more than one direction at each place. The models solve the “distribution ” and “assignment” problems of transportation and traffic engineering. The irregular and awkward geographic topologies encountered in practice require that numerical methods be used for solution of the system of equations. To start, consider a simple journeytowork problem. Assume that the territory of interest is