การสร้างแบบวัดทักษะและกระบวนการทางคณิตศาสตร์ เรื่อง สถิติ สำหรับนักเรียน ชั้นมัธยมศึกษาปีที่ 3 สังกัดสำนักงานเขตพื้นที่การศึกษามัธยมศึกษา เขต 21 โดยการประยุกต์ ใช้ทฤษฎีการสรุปอ้างอิงความน่าเชื่อถือของผลการวัด

Abstract

The objectives of this research were: 1) to create and develop a test of mathematical skills and processes. on statistical literacy, 2) to examine and verify the developed test, and 3) to create a user manual for a test of mathematical skills and processes on statistical literacy for Mathayomsuksa 3 students by applying Generalizability theory (G-theory). A sample group, selected through multi-stage sampling, consisted of 160 participants who were drawn from the population of 7,805 Mathayomsuksa 3 students under the Secondary Educational Service Area Office 21. The instrument was a 10-item subjective test of mathematical skills and processes. Data were analyzed by using percentage, mean, standard deviation, item difficulty, discriminative index, reliability, variance, relative coefficient, absolute coefficient, and content validity.                                                 The results of the research were as follows:                                                                                                                        1. The test of mathematical skills and processes was a subjective test on statistical literacy consisting of: 1) mathematical problem-solving abilities, 2) abilities to communicate and produce meaningful communication in mathematics, 3) connecting various bodies of mathematical knowledge, 4) reasoning abilities, and 5) creative thinking abilities.                                                                                                                                    2. The test of mathematical skills and processes on statistical literacy for Mathayomsuksa 3 students was qualified with item difficulty (p) from 0.69 to 0.77, discriminative index (r) from 0.33 to 0.44, and the reliability of 0.63.                                                                                                                                                                                                3. The test of mathematical skills and processes on statistical literacy for Mathayomsuksa 3 students was assessed by three raters using a holistic assessment. The results revealed that the variance (I) of scoring rating was at the highest level of 57.02 (50.30%) which indicated that the score differences were consistent with the scoring reviews, followed by a student variance (P) of 44.51 (39.30%) which indicated that the score differences were relevant to interpreting different student abilities. In addition, the students and the raters had the lowest interaction effects of 0.06 (0.10%). The relative coefficient was found to be 0.91 with the absolute coefficient of 0.58, which indicated that the test of mathematical skills and processes on statistical literacy was reliable in accordance with the Generalizability Theory.                                                                                    4. The user manual of the test of mathematical skills and processes on statistical literacy for Mathayomsuksa 3 students by applying the Generalizability Theory (G theory) was detailed as follows: 1) definitions of the test of mathematical skills and processes on statistical literacy, 2) objectives, 3) a test structure, 4) a test quality, 5) testing methods, and 6) scoring reviews and examination results of the user manual were validated by five experts containing the content validity index (CVI) of 0.83.