LOGO, mathematics and upper primary school children
This study was set up to assess the contribution that a computer modelling approach using the language LOGO could make to the quality of mathematics learning in primary school children. Following a constructivist theory of mathematical learning it is argued that many problems children have with their mathematics results from instrumental learning without understanding, rather than relational learning. LOGO was developed, in part, to provide a learning environment for children to investigate mathematical ideas and thus develop their own understanding. Previous research has not provided much evidence that this happens, nor specified what mathematical learning could be expected to take place and what pedagogic approach could bring it about. Other questions relating to the maturity of the children and their aptitude for programming have similarly been neglected. This study was set up to identify the mathematical ideas intrinsic to Turtle Geometry and to explore the conditions under which this learning could best be fostered. The study was carried out in three phases. The first phase considered the constraints of maturity and the need to program on the learning of 9 and 11 year old children. The second phase of the study followed up the programming of the older children, to see what mathematics they were encountering, and what sort of activities encouraged them to think mathematically. Pre and post tests were used to identify the mathematical learning which was taking place. In Phase III a control group was used to identify the particular mathematical learning which could be attributed to LOGO experience, and to assess the transfer of mathematical learning from the LOGO context to novel problem solving. The first two phases revealed considerable mathematical activity intrinsic to Turtle Geometry. The need to learn some simple programming apparently did not present a barrier to mathematical investigation. The test results in the third phase showed that the children had deepened their understanding of angles, variables and general process aspects of mathematics through using LOGO. The performance of the children on the computers was monitored and was found to be revealing of their current mathematical understanding.