A response model that is able to detect guessing behaviors and produce unbiased estimates in low-stake conditions using timing information is proposed. The model is a special case of the grade of membership model in which responses are modeled as partial members of a class that is affected by motivation and a class that responds only according to…

165 students, from the fifth, seventh and ninth grades were asked to solve written problems involving fractions. In the problems a reference quantity (RQ) was multiplied by a fraction (FR), yielding the value of a compared quantity (CQ). The fraction expressed either an part-whole ratio (PW), or a part-part ratio (PP). Six type of problems were…