Exploring Multiple Strategic Problem Solving Behaviors in Educational Psychology Research by Using Mixture Cognitive...

Area of Science:

• Psychometrics
• Educational Measurement
• Cognitive Science

Background:

• Cognitive diagnosis models (CDMs) are essential for understanding student knowledge states.
• Existing CDMs often assume a single strategy for solving problems, limiting their applicability to complex tasks.
• Individual differences in strategy selection and its impact on item response require further investigation.

Purpose of the Study:

• To propose a novel mixture cognitive diagnosis model (MMS-DINA) to investigate individual differences in response category selection for multiple-strategy items.
• To provide a robust statistical framework for diagnostic testing that accommodates multiple problem-solving strategies and varying difficulty levels.
• To develop methods for model estimation and selection in the context of multiple-strategy assessments.

Main Methods:

• Development of the mixture multiple strategy-Deterministic, Inputs, Noisy "and" Gate (MMS-DINA) model.
• Implementation of a Markov Chain Monte Carlo (MCMC) algorithm for parameter estimation.
• Conducting four simulation studies to assess the MCMC algorithm's performance.
• Computation of two Bayesian model selection criteria to compare single-strategy and multiple-strategy DINA models.

Main Results:

• The proposed MMS-DINA model effectively investigates individual differences in strategy selection for multiple-strategy items.
• The MCMC algorithm demonstrated reliable performance in parameter estimation for the MMS-DINA model across simulation studies.
• Bayesian model selection criteria provided guidance for choosing between single-strategy and multiple-strategy DINA models.
• The model was successfully applied to analyze fraction subtraction data, illustrating its practical utility.

Conclusions:

• The MMS-DINA model offers a significant advancement in cognitive diagnosis by incorporating multiple strategies and individual differences.
• The MCMC estimation and Bayesian model selection methods provide a sound statistical foundation for applying the MMS-DINA model.
• This approach enhances the precision of diagnostic testing, particularly for complex skills requiring varied problem-solving approaches.