A framework for assessing middle school students' thinking in conditional probability and independence

Based on a synthesis of research and observations of middle school students, a framework for assessing students thinking on two constructs--conditional probability and independence--was formulated, refined and validated. For both constructs, four levels of thinking which reflected a continuum from subjective to numerical reasoning were established. The framework was validated from interview data with 15 students from Grades 4-8 who served as case studies. Student profiles revealed that levels of probabilistic thinking were stable across the two constructs and were consistent with levels of cognitive functioning postulated by some neo-Piagetians. The framework provides valuable benchmarks for instruction and assessment.