ABSTRACT
The first half of this chapter briefly describes some of the most significant philosophical foundations of models and modeling (M&M) perspectives. Then, in the second half, a two-column table format is used to describe a variety of ways that we believe a models and modeling perspective moves beyond constructivist foundations for thinking about the nature of children’s developing mathematical knowledge and abilities–and about mathematics teaching, learning, and problem solving. The left hand column identifies significant contributions that constructivism (in many variations) has made to the field of mathematics education (Steffe & Thompson, 2000). The right hand column briefly describes some of the most important points that have been described in greater detail throughout the chapters of this book concerning: (a) the nature of children’s developing mathematical knowledge, (b) the nature of real life situations (beyond school) where elementary-but-powerful mathematical constructs are useful, (c) the nature of mathematical understandings and abilities that contribute to success in the preceding problem solving situations, and (d) the nature of teaching and learning situations that contribute to the development of the preceding understandings and abilities. … Overall, the table is organized around the following questions.
What Does It Mean To Be a Constructivist?
What is Different About Assembly-ists, Constructivists and CONSTRUCT-ivists?
Do Constructs Need To Be Discovered Independently By Students?
What is the Relationship Between the Mastery of Basics Skills and the Development of Deeper and Higher Order Understandings and Abilities?
What is the Nature of “Real” Experience?
Can We Know What is in the Mind Of Another Person?
In What Ways Do M&M Perspectives Go Beyond Piagetian Views About Students’ Developing Mathematical Constructs?
In What Ways Do M&M Perspectives Go Beyond Cognitively Guided Instruction?
In What Ways Do M&M Perspectives Go Beyond Ladder-Like Stages of Development?
In What Ways Do M&M Perspectives Go Beyond Research on Situated Cognition?
In What Ways Do M&M Perspectives Go Beyond Research On Vygotsky’s Zones of Proximal Development?
In What Ways Do M&M Perspectives Go Beyond Social Constructivism?
In What Ways Do M&M Perspectives Go Beyond Current Research On Students’ Learning Trajectories?
In What Ways Do M&M Perspectives Go Beyond Current Research on Representation and Semiotic Functioning?
In What Ways Do M&M Perspectives Go Beyond Research on What is Needed for Success Beyond School of Education in a Technology-Based Age of Information?
In What Ways Do M&M Perspectives Go Beyond Traditional Research on Problem Solving-And Information Processing?
In What Ways Do M&M Perspectives Go Beyond Current Research on Metacognition and Higher Order Thinking?
In What Ways Do M&M Perspectives Go Beyond Constructivist Research on Teacher Development?
