ABSTRACT
Infants are able to match the number of drumbeats to the number of objects in a visual display, rats can learn how many times they need to press a lever in order to receive a reward, and all known human cultures have developed words for counting. Yet, mathematics is generally considered one of the most difficult subjects at school, and mathematical illiteracy is a worldwide phenomenon (Paulos, 1995). What happens to our natural propensity for mathematics? Researchers speak of insufficient mathematical education, psychological blockage, and fallacious, romantic ideas about mathematics. Psychologists and many mathematics teachers believe there is a problem because there is a divorce between the mathematics involved in day-to-day life and the symbolic representations used when teaching at school. Classroom instruction in mathematics is likened
to learning about an environment by studying guidebooks and maps without ever exploring the actual territory or by studying recipes without ever cooking anything. Ah though symbolic representations can be helpful—even essential in the activities of learning to inhabit environments and as important resources for use in reasoning and communication—they should not replace experience in conceptual environments as the main learning activity that we provide for students. (Greeno, 1991,p. 177)
