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Using Rasch Analysis to Identify Difficult Course Outcomes in Linear Algebra


  • SEGi University, Centre of Engineering Education, Universiti Kebangsaan Malaysia, Malaysia
  • Universiti Kebangsaan Malaysia, Malaysia
  • King Abdul Aziz University, Saudi Arabia


Linear Algebra, the second Engineering Mathematics subject for all the engineering students in Universiti Kebangsaan Malaysia contains abstract concepts and difficult for students to understand the subject. This study aimed to identify the tough Course Outcome or topics for the Linear Algebra subject. A total of 282 engineering students from electrical, mechanical, chemical and civil engineering participated in the pre-test. The study based on a set of pre-test questions which covers the entire Course Outcomes of Linear Algebra subject. The content of pre-test questions consists of items based on the level of Bloom Taxanomy (knowledge, comprehension, analysis, synthesis and evaluation). Rasch Measurement Model is used to analyze the result. Summary statistics for questions, summary statistics for persons, fit statistics and item dimensionality test are the output achieved from Rasch analysis. Summary statistics for item indicated a good item difficulty of spread. Summary statistics for person indicated a low person reliability value. This means students provided irregular answers for the pre-test questions. Fit statistics identified two questions as misfit. These questions need to be restructured in future. The item dimensionality test indicates the pre-test questions are within the scope of measuring students’ problem-solving ability. Analysis showed that two Course Outcomes identified as the difficult Course Outcomes in Linear Algebra subject. They are the concepts of vector space, diagonalization, quadratic forms and power series. Questions related to comprehension and application level of Bloom Taxanomy are difficult for students to be solved. This study provides an in-sight view of the Linear Algebra subject by under-pinning the difficult area of the subject. Engineering faculty students should be given more emphasize on the difficult Course Outcome of Linear Algebra subjects. Efforts should be taken by educators to illustrate those topics in a much more simple way.


Course Outcome, Difficult, Engineering Mathematics, Linear Algebra, Rasch Measurement Model.

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