Using Rule Space and Poset-based Adaptive Testing Methodologies to Identify Ability Patterns in Early Mathematics and Create a Comprehensive Mathematics Ability Test
Douglas Clements Principal Investigator
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A new assessment for children ages 3-7 is being developed to provide teachers with diagnostic information on a child's development of mathematics facility on ten domains such as counting, sequencing, adding/subtracting, and measurement. The Comprehensive Research-based Mathematics Assessment (CREMA) is being developed using innovative psychometric models to reveal information about children on specific attributes for each of the 10 domains. The CREMA will produce information based on carefully developed learning trajectories in a relative short period of time by using computer adaptive testing. The project is guided by two goals: 1) to produce a cognitively diagnostic adaptive assessment that will yield more useful and detailed information about students' knowledge of mathematics than previously possible, and 2) subject the developmental progressions to close cognitive diagnosis using cutting-edge psychometric approaches. An item pool of about 350 items is being developed that can be used to identify the level of understanding children ages 3-7 have on the 10 domains that have been identified as foundational to further learning in mathematics. A research team headed by Dr. Douglas Clements at the University of Buffalo is conducting the development work while being assisted by Dr. Curtis Tatsuoka, a statistician at Case Western Reserve University.<br/><br/>The CREMA is being developed using leading-edge psychometric models based on Q-Matrix theory, rule-state models, and posets. The initial item pool includes items from the REMA, a previously developed instrument based on unidemensional IRT models. New items are being piloted with at least 200 students from a group of a total of 800 students evenly distributed among pre-K to grade 2. The successful items then are used to create the new CREMA. The new assessment is being field tested with 300 children, pre-K to grade 2. A random sample of 50 students (at least 10 from each grade) is being video taped as they work the items. Specific criteria of convergence are being used for feedback on how specific items are performing to meet the required specifications. An external evaluator is auditing the process and is doing spot checks of item codings and other analyses performed.<br/><br/>The main product will be the CREMA that will be made widely available. This instrument using computer adaptive testing will provide teachers with ready information on young children's understanding of critical mathematical ideas. The new psychometric models that will be used and developed to process multiple attributes from individual items will make large strives to move forward the field of mathematics assessment of young children. A publisher has expressed interest to make the assessment widely available that increases the likelihood the assessment will have large impact on early childhood mathematics learning.