论文信息 - A MODELLING APPROACH TO DEVELOPING AN UNDERSTANDING OF AVERAGE RATE OF CHANGE

A MODELLING APPROACH TO DEVELOPING AN UNDERSTANDING OF AVERAGE RATE OF CHANGE

Students’ difficulties in reasoning about change are well documented in the research literature. In this paper, we describe a modelling approach to developing students’ abilities to create and interpret models of phenomena where change is occurring and developing their concepts of rate of change. We describe the design of a model development sequence and its classroom implementation with 33 students just prior to beginning their university studies. The pre/post-test results show that the students made significant gains in their understanding of the concept of average rate of change. We present an analysis of the areas of greatest gains and of the difficulties some students encountered in their interpretations of changing phenomena.

Helen M. Doerr | AnnMarie H. O’Neil | H. Doerr

[1] Patrick W Thompson,et al. Foundational Reasoning Abilities that Promote Coherence in Students' Function Understanding , 2008 .

[2] Richard Lesh,et al. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching , 2003 .

[3] Marilyn P. Carlson,et al. Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study. , 2002 .

[4] Michal Yerushalmy,et al. Functions of Interactive Visual Representations in Interactive Mathematical Textbooks , 2005, Int. J. Comput. Math. Learn..

[5] Claus Michelsen,et al. Functions: a modelling tool in mathematics and science , 2006 .

[6] Jere Confrey,et al. Exponential functions, rates of change, and the multiplicative unit , 1994 .

[7] Helen M. Doerr,et al. A modeling perspective on student's mathematical reasoning about data , 2003 .

[8] Patrick W Thompson,et al. Images of rate and operational understanding of the fundamental theorem of calculus , 1994 .

[9] Gabriele Kaiser,et al. A global survey of international perspectives on modelling in mathematics education , 2006 .

[10] G. A. Miller,et al. THE DEVELOPMENT OF THE FUNCTION CONCEPT , 1928 .

[11] Richard Lesh,et al. Model development sequences , 2003 .