Building the Foundation: Whole Numbers in the Primary Grades

Description

This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. One of the main challenges of designing the first ICMI primary school study of this kind is the complex nature of mathematics at the early level. Accordingly, a focus area that is central to the discussion was chosen, together with a number of related questions. The broad area of Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems, forms the core content of all primary mathematics curricula. The study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction on the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. As such, this study presents a meta-level analysis and synthesis of what is currently known about WNA, providing a useful base from which to gauge gaps and shortcomings, as well as an opportunity to learn from the practices of different countries and contexts. Front Matter ....Pages i-xxxi Front Matter ....Pages 1-1 Building a Strong Foundation Concerning Whole Number Arithmetic in Primary Grades: Editorial Introduction (Maria G. Bartolini Bussi, Xu Hua Sun)....Pages 3-18 Social and Cultural Contexts in the Teaching and Learning of Whole Number Arithmetic (Maria G. Bartolini Bussi, Xu Hua Sun)....Pages 19-34 Language and Cultural Issues in the Teaching and Learning of WNA (Xu Hua Sun, Maria G. Bartolini Bussi)....Pages 35-70 On Number Language: A Commentary on Chapter 3 (David Pimm)....Pages 71-87 Front Matter ....Pages 89-89 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes (Xu Hua Sun, Christine Chambris, Judy Sayers, Man Keung Siu, Jason Cooper, Jean-Luc Dorier et al.)....Pages 91-124 Reflecting on the What and Why of Whole Number Arithmetic: A Commentary on Chapter 5 (Roger Howe)....Pages 125-135 Whole Number Thinking, Learning and Development: Neuro-cognitive, Cognitive and Developmental Approaches (Joanne Mulligan, Lieven Verschaffel, Anna Baccaglini-Frank, Alf Coles, Peter Gould, Shengqing He et al.)....Pages 137-167 Whole Number Thinking, Learning and Development: A Commentary on Chapter 7 (Pearla Nesher)....Pages 169-179 Aspects that Affect Whole Number Learning: Cultural Artefacts and Mathematical Tasks (Maria G. Bartolini Bussi, Maitree Inprasitha, Ferdinando Arzarello, Hyman Bass, Ulrich Kortenkamp, Silke Ladel et al.)....Pages 181-226 Artefacts and Tasks in the Mathematical Preparation of Teachers of Elementary Arithmetic from a Mathematician’s Perspective: A Commentary on Chapter 9 (Bernard R. Hodgson)....Pages 227-250 How to Teach and Assess Whole Number Arithmetic: Some International Perspectives (Jarmila Novotná, Berinderjeet Kaur, Ann Gervasoni, Mike Askew, Michiel Veldhuis, Catherine Pearn et al.)....Pages 251-286 How to Teach and Assess Whole Number Arithmetic: A Commentary on Chapter 11 (Claire Margolinas)....Pages 287-298 Connecting Whole Number Arithmetic Foundations to Other Parts of Mathematics: Structure and Structuring Activity (Hamsa Venkat, Sybilla Beckmann, Kerstin Larsson, Yan Ping Xin, Alessandro Ramploud, Limin Chen)....Pages 299-324 Structuring Structural Awareness: A Commentary on Chapter 13 (John Mason)....Pages 325-340 Front Matter ....Pages 341-341 Tradition in Whole Number Arithmetic (Ferdinando Arzarello, Nadia Azrou, Maria G. Bartolini Bussi, Sarah Inés González de Lora Sued, Xu Hua Sun, Man Keung Siu)....Pages 343-373 Special Needs in Research and Instruction in Whole Number Arithmetic (Lieven Verschaffel, Anna Baccaglini-Frank, Joanne Mulligan, Marja van den Heuvel-Panhuizen, Yan Ping Xin, Brian Butterworth)....Pages 375-397 Professional Development Models for Whole Number Arithmetic in Primary Mathematics Teacher Education: A Cross-Cultural Overview (Jarmila Novotná, Maria G. Bartolini Bussi, Sybilla Beckmann, Maitree Inprasitha, Berinderjeet Kaur, Xu Hua Sun et al.)....Pages 399-435 Front Matter ....Pages 437-437 The Theory of School Arithmetic: Whole Numbers (Liping Ma, Cathy Kessel)....Pages 439-463 Quantities, Numbers, Number Names and the Real Number Line (Hyman Bass)....Pages 465-475 Low Numeracy: From Brain to Education (Brian Butterworth)....Pages 477-488 Back Matter ....Pages 489-536