Five-Tier Diagnostic Test Instrument for Uniform Circular Motion Concepts: Development, Validity, Reliability and Limited Trials

Students' understanding on Physics concepts could be different from each other. Based on the conceptual diagnostic test, especially in five-tier format, the students' different understanding can be categorized into several conception levels. One of them is misconception. For example, students consider that all objects moving on a circular trajectory called uniform circular motion (UCM). According to the Physics concept, an object in UCM must meet three criteria: an object travels along a circular path, the radius of the path is always fixed, and the object moves at a constant speed. However, a standardized conceptual diagnostic test instrument in five-tier format is not yet available. This work aims to develop a five-tier diagnostic test instrument for UCM concepts, perform validity and reliability test and use the developed instrument to identify a number of students’ conception level. The research development method was employed to produce 15 valid and reliable questions. The validity test consisted of internal and external (content and construct empirical) aspects. The internal validity obtained was 88% (very valid). The content aspect, i.e. the false positive=4.95% and the false negative=5.59% both met the criteria 10%. The construct aspect obtained by a Pearson product moment correlation was  (5% sig. level). The reliability level of the Alpha Cronbach coefficient  shows that the developed instrument was valid and reliable. The limited trial result shows that the students’ conception levels on the UCM concepts was generally lack of knowledge.


I. INTRODUCTION
Physics is a set of knowledge, way of thinking, and investigation in the form of facts, concepts, principles, theories and models (Astuti, 2015;Fitriani et al., 2017;Ilyas et al., 2020). Based on the 2013 Curriculum framework, Physics learning aims to enable students to master concepts, principles, and skills as provisions for continuing education to a higher level (Kemendikbud, 2014 (Pebriyanti et al., 2017). When viewed using a five-tier diagnostic test, (Anam et al., 2015) called the various understanding on Physics concepts as conception levels. Table 1 summarizes the conception levels proposed by Anam et al., (2015). Table 1. Students' conception levels (Anam et al., 2015) No Conception levels Description

SC (Scientific Conception)
When students answer on the first-tier and the chosen reason on the third-tier are correct. The student is sure with the chosen answers and reasons, and the pictures or conclusions made on the fifth-tier is in accordance with the Physics concept.

ASC (Almost Scientific Conception)
When students answer on the first-tier and the chosen reason on the third-tier are correct. The student is sure with the chosen answers and reasons, but the pictures or conclusions made on the fifth-tier is not completely in accordance with the Physics concept.

LK (Lack of Knowledge)
When only one of the students answers on the first-tier and the chosen reason on the third-tier is correct. The student can be sure or not with the chosen answers and reasons, and the pictures or conclusions made on the fifth-tier is sufficiently in accordance with the Physics concept.

MSC (Misconception)
When students answer on the first-tier and the chosen reason on the third-tier are wrong. The student is sure with the chosen answers and reasons, but the pictures or conclusions made on the fifth-tier is not in accordance with the Physics concept.

NU (No Understanding on Concept)
When students answer on the first-tier and the chosen reason on the third-tier are wrong. The student is not sure with the chosen answers and reasons, and the pictures or conclusions made on the fifth-tier is not in accordance with the Physics concept.
Based on Table 1, misconception becomes one of the levels of conception.
Misconceptions in physics learning often occur (Respatiningrum et al., 2015;Haryono et al., 2020 Edition" (2013:76), it is said that "if a particle travels along a circle path or circular arc of radius r at a constant speed of v, the particle is said to be in uniform circular motion". This means that a particle or object is said to be in UCM when it meets three criteria, namely: 1) the particle or object moves on a circular path, 2) the distance between the particle or object to the center of the circle (r) is always fixed and 3) the particle moving at a constant  (Milenković, 2016).
When the guessed answer is correct, the conclusions about the students' conception level drawn by the examiner could be inaccurate (Ermawati et al., 2019  for assessing students's conception levels when using five-tier diagnostic test. Table 2 provides students' conceptual levels in a fivetier diagnostic test adapted from them. Table   3 shows the description and scores of the answers for fifth-tier question in Table 2.  (Gurel et al., 2015, Amin et al., 2016and Anam et al., 2019.  When there is a "tier" that is not answered by students or they answered more than one option  The validity and reliability tests were performed and the valid and reliable instrument was tested to a number of high school students to obtain their conception levels data in UCM.

II. METHOD
As mentioned, this work adopted the research and development (R&D) method to develop a five-tier diagnostic test (FTDT) on uniform circular motion (UCM) concepts, examined the validity and reliability, and used the valid and reliable instrument to test the conception levels of a number of students.
The following paragraphs explain the works carried out on each (R&D) stage.

A. Research stage
What is meant by the research stage here is that the author did literature studies on the UCM concepts from some Physics textbooks, i.e. "College Physics, 9 th Edition" (2010) by   ( ) depends only on the radius of the path ( ) and the rotation period of the object ( ). Thus, the object's mass ( ) has no effect on linear velocity ( ).
object's will rotate slower.

Period ( )
In UCM concepts, period of an object revolving in a circle is the time required for one complete revolution (Giancoli, 2014:111) and given in Equation (2): = ( 2) Based on the Equation (2), the number of fan blades rotation ( ) is inversely proportional to the period ( ).
Students assumed that the number of fan blades rotations ( ) is directly proportional to its period ( ) because the more turns that are taken, the resulting period is also greater. Equation (3) was occupied to calculate % of the internal validity (Arikunto, 2016), while Table 5 provides score ranges and interpretation of the internal validation results calculated using the Eq. (3) and Table 8 shows the internal validity results.
where % is % of internal validity, is the total score given by the validator, is the maximum score for the indicator, is the number of indicators for each validity aspect and is the number of validator (2). and % false negative (FN) and these were calculated using Eq. (4) and (5) (Jannah & Ermawati, 2020). FP is the answer combination of correct-sure-wrong-surewrong (i.e. the option No. 6 in Table 2).
While FN is the answer combination of wrong-sure-correct-sure-wrong (i.e. No. 9 in Table 2).
Where is the sum of FP, is the sum of FN, is the number of questions (15 questions) and is the number of students who involved in the external validity and reliability test (31 students). According to Kirbulut and Geban (2014), the content aspect is valid when % FP and FN each < 10%.
where is the correlation between the and , x is the difference between the number of correct answer scores for each question in the first-and third-tier with the average score of the correct answers for all the questions; y is the difference between the total score for sure answers in the second-and fourth-tier questions with the average score correct answers for all questions. Table 10 provides   the result of the construct aspect for each question. An instrument is valid when the value of > ℎ . In this work, the chosen ℎ value was 0.355 with a 5% significance level considering that the number of students was 31. Figure 1   The reliability of the instrument was calculated by the Alpha Cronbach coefficient as in Eq. (7) (Sugiyono, 2015).
11 is the Alpha Cronbach reliability coefficient, is the number of questions and 2 is the number of variants of each question. The variance value of each question calculated by Equation (8) while the total variance value calculated by Equation (9) (Sugiyono, 2015).

Significance
Value N where 2 is the variance value of each question, is the student's answer for each question, is the number of students. 2 is the total variance value and is the total student answer for each question.
The Alpha Cronbach reliability coefficient ( 11 ) in Eq. (7) was compared with the Alpha Cronbach reliability coefficient criteria in Table 6 to determine whether the instrument is reliable or no. An instrument is reliable when the Alpha Cronbach reliability coefficient ( 11 ) exceeds the ℎ ( 11 > ℎ ) . Table 11 shows the reliability of the Draft 3 (FTDT) on the UCM concepts.

The limited trials
The limited trial was conducted on 10 students at one of public high schools in Sidoarjo who had already taught the UCM concepts at the previous semester. The results that were analyzed using Table 2 are shown in     Table 7 is a multiple-choice question that consists of   Table 8, the average % of internal validity is 88% which is very valid (see Table 5). is therefore valid and reliable.  (Jannah & Ermawati, 2020); (Arikunto, 2016); and according to the reliability criteria of an instrument according to (Sugiyono, 2015), the Draft 3 (FTDT) developed in this work is valid and reliable.    Table 2 Sub-concept: a = UCM characteristics, b = angular displacement, c = the relationship between angular displacement and the length of the path, d = linear velocity, e = the relationship between linear velocity and angular velocity, f = the relationship between the linear velocity and the radius of the path, g = the effect of object's mass on the linear velocity, h = period, i = frequency, j = relationship between frequency and angular velocity, k = angular acceleration, l = value of centripetal acceleration, m = direction of centripetal acceleration, n = relationship between centripetal acceleration and linear velocity, o = effect of object's mass on centripetal acceleration. MSC (P) = preconception, MSC (H) = humanistic thinking, MSC (A) = associative thinking, MSC

A. Conclusion
The development of a FTDT with 15 question on the UCM concepts has been completed. The instrument is valid and reliable. The limited test given to 10 students shows that the instrument successfully identified the conception levels for each student on the UCM concepts, i.e. almost 50% of the students suffered lack of knowledge.

B. Suggestion
The FTDT on the UCM concepts can be used to test the conception levels of students from other schools. By doing so, the teacher has the data on the students' learning difficulties and can find appropriate treatments to solve it.