Teaching and Learning Mathematics in Context

Contents Preface v Section 1 WHAT IS MATHEMATICAL MODELLING? 1 Blum, W Mathematical modelling in mathematics education and instruction 3 2 Carr, A Problems and projects for teaching modelling 15 3 Usiskin, Z Conceptions of mathematical modelling and their implications for the future 26 Section 2 EXAMPLES AND ISSUES 2.1 Primary education 4 Neuman,D Exploring numbers through subtraction in primary mathematics 37 5 Gravemeijer, K Modelling two-digit addition and subtraction with an empty number line 51 ii 6 Athanasopoulos, P, Patronis, T, Potari, D, Spanos, D and Spiliotopoulou, V Constructing a village: a cross-curricular activity 62 7 Bell, M Modelling and applications of mathematics in the primary curriculum 71 2.2 Lower secondary education 8 Rouncefield, M Statistical simulations 81 9 Gillespie, J and Phillips, R Interactive video as an aid to modelling 93 10 Abrantes, P Learning activities involving mathematics in real-life situations 103 11 Yanagimoto, A, Mori, Y and Matsumiya, T Mathematics of track and field events - Composite Real Mathematics approach 115 12 Steeg, T and Williams, J Units of mathematics in integrated projects with science and technology 127 2.3 Upper secondary education 13 Kitchen, A and Williams, J Implementing and assessing mathematical modelling in the academic 16-19 curriculum 138 14 Choate, J Iterative models in the secondary mathematics curriculum: some examples 151 iii 15 Money, R Mathematical modelling today and tomorrow 163 2.4 Tertiary education 16 Graham, E Mathematical modelling in an extended engineering course 173 17 Abel, H Industrial applications of mathematics for engineering students 184 Section 3 LOOKING AHEAD - RESEARCH ON MATHEMATICAL MODELLING 18 Haines, C, Izard, J and Le Masurier, D Modelling intentions realised: assessing the full range of developed skills 200 19 Kaiser-Messmer, G Reflections on future developments in the light of empirical research 213 20 da Ponte, J P Necessary research in mathematical modelling and applications 219 21 Tanner, Hand Jones, S Developing metacognition through peer and self assessment 228 22 Garfunkel, S Future of mathematical modelling in the classroom 242