Abstract
<p class="apa">This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model, comprising of 2 layers of explanatory variables-Matrix Multiplication, Performance and Semantic Explanations; and one layer of evidential variables containing 9 evidential variables-was developed. With the simulating data, 9 students’ Performance and Semantic Explanation evidences were recorded. The results indicated that the hierarchical Bayesian assessment effectively traced and recorded students’ learning trajectories; and assessed students’ learning dynamically and diagnostically.</p>
Highlights
This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication
This study is to explore an effect assessment procedure to describe cognitive trajectories and diagnose the learning problems, the problems graduate students have in their matrix operation problem solving opportunities
It is important to develop an effective assessment procedure to recognize the problems in the matrix operation processes
Summary
The Mastery of matrix operations was a necessary step for graduate students in education and other social sciences to understand the data analytical techniques in their quantitative research designs and data analyses (Poole, 2011; Stevens, 2009). Some graduate students and doctoral candidates registered in their programs with different educational backgrounds coupled with insufficient preparation in research design and data analysis. They lack adequate knowledge of advanced linear algebra, such as matrix operations, which are fundamentals in quantitative research method learning. From learning science point of view, a cognitive process model is required to both improve learning proficiency and provide effective assessment information. The Bayesian network is an appropriate method hierarchically used to represent the structure of the cognitively diagnostic assessment model. Cognitively diagnostic assessment model with Bayesian network representation is an appropriate description of this study
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