Visualization is the most important skill that teachers need to help children develop in their early years.
Writing numerals are an abstract representation of numbers. Before children are ready to work with writing model of numbers they need to have experiences with concrete and visual models.
According to Jerome Bruner's CPA Approach, children develop concepts of the number system in three stages.
They moved from working with concrete representations of object (such as blocks, unifix cubes, tangram, their fingers) to visual representations (such pictorial drawings) and finally to the abstract conventional number symbols or models
It seemed that most mathematically competent learners in the class had developed in their mind strong visual images of numbers or models. Learners are engaged in the folding or cutting of paper to develop such models. Some time learners were given pencil and paper to work out a problem.
They drew shapes, different symbols, then progressively to drawing arbitrary marking for tens and ones, lines or circles to representing tens. These symbolic images helped learners to develop mental images
Abstract model using conventional numbers symbols were only useful for learners with strong visual image of numbers.
In preparing and planning the lesson; according to Zoltan Dienes' theory of Varability, teacher needs to preamp and expect different responses and perceptual variant
Following the child’s lead, if we watch closely and listen uncritically young children will tell us much about how they think.