Based on a synthesis of the literature and observations of young children over two years, a framework for assessing probabilistic thinking was formulated, refined and validated. The major constructs incorporated in this framework were sample space, probability of an event, probability comparisons, and conditional probability. For each of these constructs, four levels of thinking, which reflected a continuum from subjective to numerical reasoning, were established. At each level, and across all four constructs, learning descriptors were developed and used to generate probability tasks. The framework was validated through data obtained from eight grade three children who served as case studies. The thinking of these children was assessed at three points over a school year and analyzed using the problem tasks in interview settings. The results suggest that although the framework produced a coherent picture of children's thinking in probability, there was 'static' in the system which generated inconsistencies within levels of thinking. These inconsistencies were more pronounced following instruction. The levels of thinking in the framework appear to be in agreement with levels of cognitive functioning postulated by Neo-Piagetian theorists and provide a theoretical foundation for designers of curriculum and assessment programs in elementary school probability. Further studies are needed to investigate whether the framework is appropriate for children from other cultural and linguistic backgrounds.
- Prof Dev