Using Cognitive Models As The Basis For Diagnostic Assessments In Science And Mathematics

Year: 2015

Author: Vosniadou, Stella

Type of paper: Abstract refereed

Word problems are frequently used to introduce students to algebra because they reflect important relationships between algebraic concepts and mathematical referents expressed in text. However, algebra problem-solving assessment has tended to focus on end-state static measures of success/failure rather than on the cognitive processes involved in learning. We argue that the best way of diagnosing individual abilities in algebra is by employing interactive procedures based on cognitive models underpinning knowledge acquisition within the domain. Dynamic Assessment based on cognitive models is being suggested as a way of providing more fine-detailed information about students’ domain knowledge and their conceptual understanding during the learning process. This presentation will discuss a dynamic assessment procedure employing a series of structured prompts based on a cognitive model of the transition from arithmetic to algebraic reasoning. The model is developed from known conceptual difficulties that lead to problem-solving errors. For example, success in mapping symbolic equations onto word problems depends on the ability to understand the way in which variables can be used to replace unknown values, and on the interpretation of the equals sign as a bidirectional operator of equivalence. Success in algebraic problem-solving cannot be achieved from applying arithmetic procedures (e.g., a uni-directional understanding of the equals sign – a common conceptual error). Dynamic assessment is designed to identify these conceptual difficulties and provide assistance to guide success. The main benefits of this dynamic approach are two-fold. First, it specifies the points in the problem-solving process that may present conceptual difficulties for students. Static assessment measures merely report failure to solve the problem; they do not specify the exact reasons, amongst several possible misunderstandings, that may have led to the failure. In contrast, dynamic measures based on cognitive models reveal all areas of problem-solving difficulty. Second, the assessment provides assistance to guide students towards successful problem-solving as their problem-solving difficulties are recognised and alternative approaches are developed. A study highlighting the value of using dynamic assessment techniques based on cognitive models in algebraic problem-solving will be presented. Algebraic entering competence, algebraic problem-solving ability with assistance, and unassisted algebraic problem-solving performance were assessed in 135 13-year-olds. The results show that the number and type of hints required during the dynamic assessment process significantly predicted algebra competence (indexed by unassisted word problem equation mapping) over and above the contribution of basic mathematics ability and algebra entering competence.