Learning and thought processes in realistic mathematics instruction

This article deals with the various different approaches to mathematics and the influence that these approaches have had on the teaching of this subject. In addition to the three generally known schools of mathematics instruction - the mechanistic, the structuralistic and the empirical - the article focuses on the realistic school, which has brought about far-reaching changes in mathematics instruction. Realistic mathematics is the most promising of the different schools and has also garnered the most attention internationally. Two factors have had a significant influence on the development of this school: in the first place mathematicians who came to have a different view of mathematics and, in the second place, our knowledge about how children learn mathematics, to a large extent derived from cognitive psychology and the cultural historical school. This article concentrates on mathematics learning and instruction in primary school, using three key concepts: construction, interaction and reflection or metacognition. The article then proceeds to explore which cognitive processes are fundamental to solving mathematics problems, and, finally, discusses developments within the field of educational psychology which may be of relevance to mathematics instruction. Although the theoretical basis for construction, interaction and reflection is quite solid and there is a high level of agreement on the three concepts, more research is needed at al levels of mathematics instruction, in order to increase our understanding of these cognitive processes and the role that they play in mathematics learning and instruction.