# A Construction of Diagnostic Tests and Guidelines for Solving Deficiencies in Learning Mathematics on the Topic of Surface Area and Volume for Grade 9 Students

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## Abstract

The purposes of this research were 1. To explore students’ deficiencies in learning mathematics on the topic of Surface Area and Volume, 2. To construct diagnostic tests in learning mathematics on the topic of Surface Area and Volume, and 3. To study guidelines for solving deficiencies in learning mathematics on the topic of Surface Area and Volume. The sample consisted of 420 grade 9 students in the second semester of the academic year 2020 of 8 schools under the Secondary Education Service Area Office, Chaiyaphum, obtained through multistage random sampling. The research instruments were two tests. Test 1 was for finding out learning deficiencies. It was a gap-fill test with 40 items and was given to a sample of 100 students. The results of Test 1 were used to create Test 2 which was a 4-choice test with 40 items and was given to students twice. For the first time, it was given to 150 students to determine the item difficulty and the item discrimination. Then, 10 items were eliminated from Test 2. The 30 items that remained were given to 170 students. This test was later used as the diagnostic test on the topic of Surface Area and Volume for grade 9 students. The target consisted of 5 teachers with expertise in mathematics and 10 grade 9 students from Phukhiao School, Chaiyaphum, obtained through purposive sampling. The instruments were 2 sets of semi-structured interview questions: the first set, consisting of 12 questions, was used with the teachers, and the second set, consisting of nine questions, was used with the students. The statistics employed in data analysis were percentage, the mean, and standard deviation.

The results of the research were as follows:

1. The students’ deficiencies in learning mathematics on the topic of Surface Area and Volume for grade 9 students were: the lack of understanding of three-dimensional shapes’ features, of 3-dimensional visualization, and of the unfolding of three-dimensional shapes; the inability to memorize the formula due to lack of teachers’ demonstration, therefore, the students could not find the area and volume of various shapes; inability to solve the problems on the topic of Surface Area and Volume; and the lack of understanding of the relations between 3-dimensional shapes.

2. The diagnostic test in learning mathematics for grade 9 students was a 4-choice test with 40 items, after being given for the first time to 150 students, it was found that: the item difficulty ranged from 0.12 to 0.77, the item discrimination from -0.18 to 0.72, and the content validity was 1.00. After this step, 30 items were chosen for the test to be given for the second time. After the test was given for the second time to 170 students, it was found that the item difficulty ranged from 0.31 to 0.75, the item discrimination from 0.21 to 0.73; all 30 items were valid, with the reliability of 0.90. Regarding the validity, calculated from the correlation between the score of the second diagnostic test and the students’ mathematics GPA of 5 semesters starting from grade 7, was 0.72, which was statistically significant at the 0.01 level.

3. The guidelines for solving deficiencies in learning mathematics on the topic of Surface Area and Volume for grade 9 students were as follows:

3.1 The teacher must review the previous lesson before introducing a new one in every class.

3.2 The teacher should complete the lesson of both surface and volume of each shape first before moving to the new shape. Also, teaching of a chapter should be completed within that semester.

3.3 At the beginning of the lesson on shapes, the teacher should give a summary that there are 2 types of prisms, pyramids, cylinders, and cones while there is only one type of spherical shapes. Moreover, the teacher should emphasize that quadrilateral shapes with right angles are divided into 3 types.

3.4 The teacher should use songs in teaching to grab students’ attention. In addition, the instructional media should be realia or media that can give vivid images, the example of which is using the GSP program to show the three-dimensional pictures of geometric shapes.

3.5 The class should involve dividing students into groups for sharing knowledge and exchanging of ideas. The students should also be assigned to present or discuss ideas in front of the class.

3.6 There should be remedial teaching for the students with learning deficiencies, determined by the diagnostic test, to help them to achieve higher learning outcomes.

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เนื้อหาและข้อมูลในบทความที่ลงตีพิมพ์ในวารสารการวัดผลการศึกษา มหาวิทยาลัยมหาสารคาม ถือเป็นข้อคิดเห็นและความรับผิดชอบของผู้เขียนบทความโดยตรง ซึ่งกองบรรณาธิการวารสาร ไม่จำเป็นต้องเห็นด้วย หรือร่วมรับผิดชอบใดๆ

บทความ ข้อมูล เนื้อหา รูปภาพ ฯลฯ ที่ได้รับการตีพิมพ์ในวารสารการวัดผลการศึกษา มหาวิทยาลัยมหาสารคาม ถือเป็นลิขสิทธิ์ของวารสารการวัดผลการศึกษา มหาวิทยาลัยมหาสารคาม หากบุคคลหรือหน่วยงานใดต้องการนำทั้งหมดหรือส่วนใดส่วนหนึ่งไปเผยแพร่ต่อหรือกระทำการใดๆ จะต้องได้รับอนุญาตเป็นลายลักษณ์อักษรจากวารสารการวัดผลการศึกษา มหาวิทยาลัยมหาสารคาม ก่อนเท่านั้น

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