Piaget and Inhelder (1956) conducted one of the first studies of children’s understanding of infinity. Their study involved geometrical problems such as how to draw the smallest and the largest possible square on a piece of paper, or what would happen if the process of division of a geometrical figure (for instance by two) were to be continued mentally. What would be the form of the final element of such a division? They concluded that in the concrete operational stage of development, the child’s ability to visualize the division of a geometrical figure into smaller parts is limited to a finite number of iterations. Only in the stage of formal logical thinking, at around 11–12 years of age, is a child able to envision subdivision as an infinite process.
One of the main difficulties in children’s understanding of infinity is its abstract nature—the concept of infinity is difficult to link to real-life experiences and is therefore dependent on our ability to visualize mentally.
According to Fischbein et al. (1979), the main source of difficulties which accompany the concept of infinity is the fundamental contradiction between this concept and our intellectual schemes, which are naturally adapted to finite realities.
Monaghan (2001) points out the fact that the real world is apparently finite and there are thus no real referents for discourse regarding the infinite.
The problem in understanding the concept of infinity also stems from the fact that the mathematical world is a non-temporal world where infinite summations can be done without reference to time. Outside of the world of pure mathematics, the expression such as ‘going on forever’ would be meaningless for a child because no process exists which could last forever (Monaghan, 2001).
This summary is from the paper Analysis of factors influencing the understanding of the concept of infinity by Vida Manfreda Kolar & Tatjana Hodnik Čadež published Educational Studies in Mathematics
