The Construction of a Classification Schema as a Foundation for Mathematical Understanding in Young Deaf Children
Kritzer, Karen L., Focus on Learning Problems in Mathematics
While it is known that the mathematics achievement levels of deaf children are substantially below that of their hearing peers, it is not known when or in what capacity these delays begin. It is possible that differences in achievement are also demonstrated in the early thinking skills of these children, for example, the ability to classify. The purpose of this pilot study was to begin to examine the pre-classification skills demonstrated by young deaf children. Findings from this study indicate a possibility that deaf/hard-of-hearing children experience substantial limitations in pre-classification skills as demonstrated through their performance on free-sorting, abstract tasks of the nature used in this study. Limitations in the development of pre-classification skills could impact deaf children's understanding of hierarchical concepts and part/whole relationships thereby influencing their ability to demonstrate adequate understanding of mathematical concepts.
The low performance of deaf students in the area of mathematics has been well documented (Wood, Wood, Griffiths, & Howarth, 1986; Traxler, 2000; Luckner & McNeil, 1994, Ansell & Pagliaro, 2006). Yet while it is known that the performance of deaf students is not up to par, the reason behind and solution for this problem are still unknown. Typically, research in this area has focused on the school age population, including students between the ages of 12 years (Wood et al., 1986) and 19 years (Luckner & McNeil, 1994). These studies have been solely focused on deaf children's mathematics learning in the classroom and/or their abilities to problem solve (Luckner & McNeil, 1994; Ansell & Pagliaro, 2006). An area that has not yet been investigated is the thinking skills, including the ability to classify, that deaf children bring to the classroom with them.
As defined by Piaget (1962), the first step in classification is an ability to make collections. This differs from formal classification in that membership in a collection is dependent upon perceptions, therefore, the members of a set must be physically present (Phillips & Phillips, 1996). Young children are not capable of classification because they are not yet able to abstract out any one attribute to tie a group together. While it may be possible for them to organize groups that differ by one criterion, (e.g., a group of cards that differ only by color), they are not able to do this if there are multiple differences (Lunzer, 1964). The ability to classify develops through practice in making collections (Phillips & Phillips, 1996).
According to Piaget, there are three sequential levels that one must pass through to develop an understanding of classification. The first two levels are pre-classification skills and include the making of graphic and non-graphic collections. True classification is demonstrated in the third level through expression of the understanding of class inclusion and hierarchical relationships (Phillips & Phillips, 1996).
In graphic collections the items to be sorted are viewed independently. A common approach to grouping at this level is to sort items into carefully arranged spatial configurations. For example, the child may create pictures or designs out of the materials to be sorted. A child functioning at the graphical level will examine similarities between items; comparisons however, are made between only two items at a time. S/he is unable to establish a relationship of similarity between individual items and the whole group. Properties of items are not considered as criteria for membership in a group, rather what the total arrangement looks like is the child's primary concern (Phillips & Phillips, 1996).
Unlike graphic collections, in non-graphic collections items are assigned to piles or groups based on similarity. While this is a more sophisticated level of pre-classification, non-graphic collections differ from true classification in that items still need to be within close proximity to each other and their properties must be directly perceptible (i. …