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The purpose of this research was to study Mathayomsuksa V students’ deficiencies in conceptual and procedural knowledge about permutations. Using the stratified random sampling technique, the participants were 95 students who were studying in the second semester of the 2017 Academic Year from three schools run by the Office of the Secondary Educational Service Area District 9, Suphan Buri including Danchangwittaya school, Samchukratanapokaram school and Banharnjamsaiwittaya 1 school. The research instrument was an exam designed by the researchers consisting of 15 items of multiple choice, 9 items of completion and 2 items of essay. The data in this study were students’ responses on the exam. Definitions of conceptual and procedural knowledge were employed as a framework to analyzed and classified students’ conceptual and procedural knowledge deficiencies about permutations
The research findings revealed that the subjects showed their deficiencies in both conceptual and procedural knowledge about permutations. The deficiencies in conceptual knowledge were as follows: 1) selecting definitions, rules or formulas, 2) using definitions, rules or formulas and 3) explaining/giving a reason to each step of problem-solving process. The deficiencies in procedural knowledge included 1) using data, 2) lacking basic knowledge in algebra, 3) computing based on definitions, rules or formulas and 4) completing and sequencing of problem-solving process.
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