Modes of representation of ideas, computers and learning styles in K-6 mathematics

Constructivist theories of mathematics learning suggest that learners personally negotiate meaning by creating different mental representations of mathematical knowledge. They may then progress towards relational understandings of mathematical ideas by making connections between the different modes of representation. Partnerships between concrete materials and computer software offer a way of enhancing the value of both approaches and have benefits in making learning more powerful by the integration of concrete, pictorial and symbolic modes of representation. This thesis investigates the use of the computer as a transition device in linking different modes of representation of mathematical knowledge. A particular software package was chosen and three teaching treatments were devised, corresponding to three different modes of representation of knowledge. Computers were used to provide a pictorial treatment, Dienes' Base 10 Arithmetic Blocks were used to provide a treatment which was predominantly concrete, and teacher exposition provided a treatment which conformed to symbolic instruction. Quantitative analysis of the data collected found no significant statistical differences in achievement outcomes of any treatment groups. The findings of this investigation do not support the contentions that the computer is a necessary link between concrete and symbolic modes of representation of knowledge, or that programs in which teaching style is matched to the preferred learning style of students lead to increased attainment by student