Modelling of multiplicative structures in a B10B program

Multiplication is a key operation in m1thmetic. Teachers utilize a range of resources to help children make sense of the conceptual basis of this operation. Despite this, many children experience difficulty in solving multiplicative problems. In recent times, teachers and teacher educators have tumed to ICT-based resources in order to provide a more effective learning environment in which to explore multiplication. While this change in teaching strategy has received considerable support, it is based on the assumption that teachers who are already in practice and those who are being trained to become teachers draw on a well-developed knowledge of the multiplicative process, and could exploit the ICT appropriately with the view to helping children construct deeper understandings about multiplication. The aim of the study reported here was to examine the quality of coment knowledge of multiplication developed by a group of prospective elementary mathematics teachers in the context of an ICT-based software (B]()B Program). Analysis of data showed the existence of gaps in the prospective teachers' knowledge base of multiplication. Specifically, the participants' repertoire of models of multiplicative process was found to be limited. I discuss these results in terms of primary teachers' skills and knowledge and the use of ICT for the construction of appropl1ate models of multiplication. Introduction Children's informal understandings of whole numbers begin with their pre-school experiences. The development of this understanding is supported in the classroom through various exploratory activities that focus on numeration and operations involving numbers. The four fundamental operations of whole numbers are addition, subtraction, multiplication and division, and these are regarded as being 'central to knowing mathematics' (National Council of Teacher of Mathematics, 2000:41). The importance of understanding these operations lies principally in their utility in solving a multitude of real-life problems. While the teaching of the above operations of arithmetic, in general, tend to begin with addition and subtraction, it has been sll;ggested that the sequence of learning experiences provided to children must attempt to make explicit the connections among these operations (Putnam, Lambert & Peterson, 1990). These connections provide children with perspectives about what they mean and how they are related to one another. The noted mathematics educator, Richard Skemp (1976), made a powerful statement about the difference between two forms of mathematical understanding: relational and instrumental. Relational understanding involves understanding structures and connections within concepts, whereas instrumental understanding shows ability to manipulate formulas and carry out operations. Skemp's articulation of mathematical understanding in this manner has been having a significant impact on the strategies that primary teachers adopt in constructing effective learning environment for their children. The modelling of abstract concepts is one such strategy, and this approach in teaching has been suggested as an appropriate way to bring about relational understanding of mathematics among young children (English and Halford, 1995). In this study I address the question of how teachers can utilize an Internet-based software to model multiplication, and explore its links with other operations with their children.