REiD (Research and Evaluation in Education) ISSN 2460-6995 REiD (Research and Evaluation in Education), 3(1), 2017, 64-76 Available online at: http://journal.uny.ac.id/index.php/reid Research Article A construct of the instrument for measuring junior high school mathematics teacher’s self-efficacy * 1 Rachmadi Widdiharto; 2 Badrun Kartowagiran; 3 Sugiman *Centre for the Development and Empowerment of Mathematics Teachers and Educational Personnel (PPPPTK Matematika) of Yogyakarta Jl. Kaliurang Km. 6, Sambisari, Condong Catur, Depok, Sleman 55281, Yogyakarta, Indonesia *Email: rachmadiw@yahoo.com Submitted: 06 April 2017 | Revised: 15 July 2017 | Accepted: 15 July 2017 Abstract The aim of this study was to develop a construct of the instrument for junior high school mathe- matics teacher self-efficacy and its mapping in the Special Region of Yogyakarta. The population was 816 junior high mathematics teacher, and a sample of 274 teachers was selected through proportionate random sampling technique. The data were analyzed using Confirmatory Factor Analysis (CFA), using Lisrel 8.80 software through the first order and the second order stages. The result of data analysis toward four dimensions obtained: 11 fit items for dimension of per- sonal efficacy (PE), 12 fit items for dimension of general teaching efficacy (GTE), 13 fit items for dimension of subject matter teaching efficacy (STE), and 8 fit items for dimension of out- come efficacy (OE). Afterward, the result of selecting 54 items in the first order stage was examined for the second order CFA, which shows the model is fit to the data and obtains 25 fit items. The loading factors for each dimension PE, GTE, STE, and OE consecutively were: 0.46; 0.84; 0.89, and 0.92, and the mapping of mathematics teacher self-efficacy level shows: 43.07% in low category, 55.47% in medium category, and 1.46% in the high category. Keywords: self-efficacy, construct, mathematics, junior high school How to cite item: Widdiharto, R., Kartowagiran, B., & Sugiman, S. (2017). A construct of the instrument for measuring junior high school mathematics teacher's self-efficacy. REiD (Research and Evaluation in Education), 3(1), 64- 76. doi:http://dx.doi.org/10.21831/reid.v3i1.13559 Introduction Increasing and improving teacher qual- ity is continually implemented by the govern- ment through the fulfillment of academic qualification of S-1/D-IV, teacher certifica- tion, block grant for the continuation of the study, the revitalization of Teachers Working Group (Kelompok Kerja Guru/KKG) for elementary school teachers, Subject-matter Teacher Forum (Musyawarah Guru Mata Pe- lajaran /MGMP) for junior and senior high school teachers, and program BERMUTU (Better Education through Reformed Man- agement and Universal Teacher Upgrading) (Jalal et al., 2009, p. 124). However, the government's efforts still failed to give satis- factory results when the condition of teacher teaching practices do not support the ability of students in mathematics achievement. The results of TIMSS (Trends in Inter- national Mathematics and Science Study) Video Study 2007 (Leung & Ragatz, 2010, p. 33) states that most junior high school math- ematics teachers in Indonesia use 76% of their time to the problem activity and 24% for non-problem, while in Japan, 82% for prob- lem activiy and 18% for non-problem, and mailto:farida_as@uny.ac.id http://dx.doi.org/10.21831/reid.v3i1.13559 REiD (Research and Evaluation in Education) A construct of the instrument for measuring junior high school... - 65 Rachmadi Widdiharto, Badrun Kartowagiran, & Sugiman Hong Kong 85% of problem activity and 15% for non-problem activity. The Report of Training Need Assess- ment and Recruitment (PPPPTK Matematika, 2007, p. 46) of a sample of 268 teachers in 15 provinces showed approximately 61.78% of the teachers had difficulty learning mathema- tics associated with problem solving. In a fur- ther interview with the respondents, there was a tendency for them to avoid delivering learn- ing materials considered difficult. In terms of having no choice and a must to deliver the stated material, they lacked confidence in their performance or in their teaching practice. Sumardyono (2011, p. 244) in a study of math anxiety to 89 participants of mathema- tics teachers training in PPPPTK Matematika in 2010, from the District of Banjarmasin, South Kalimantan, showed that adapting Mathema- tics Anxiety Rating Scale (MARS), increased the level of anxiety gradually from the higher education in which teachers teach to the low- er education. It means that the high school teacher had a low level of anxiety compared to the junior high school mathematics teach- ers or primary school teachers. Meanwhile, preliminary research con- ducted by the researchers to 38 junior high school mathematics teachers in Java, who attended PPPPTK Matematika training activ- ities in 2012, by adopting Teacher Efficacy Scale (TES) from Tschannen-Moran, Hoy, and Hoy (1998), reported that 13.16% of those with high-efficacy scale categories, and approximately 86.84% efficacy scale were in a medium category. The teachers were also test- ed with Mathematics Teacher's Efficacy Belief Instrument (MTEBI) developed by Enoch & Smith (1997) which states that most (almost all) their mathematics belief is in the medium category, and no participant was in the low or high category. Hastuti et al. (2009) mention that teach- er certification improves the welfare and like- ly improves the teachers quality because they can concentrate more and become more mo- tivated. However, he was not convinced by it because increasing the quality and perfor- mance is a matter of personal commitment. Sadtyadi and Kartowagiran, (2014, p. 291) mention that through the assessment done by the time the teacher is teaching, it is difficult to describe the actual performance of teach- ers, because they have a tendency to be better prepared, than when monitoring is not done, in the assessment of its performance. Based on that condition in which the teacher competence is still not optimal, and they themselves lack of confidence in carrying out the tasks they are responsible for, it is a bit difficult to expect they will be able to teach the material to their students well. Pajares (1996, p. 544) refers to Bandura‟s opinion that defines self-efficacy as a belief about their ability to successfully perform certain tasks in certain situations. Self-efficacy is also defined as an assessment of the person's ability to or- ganize and execute courses of actions required to complete a type of work that has been de- termined, primarily for mathematics teachers‟ duties associated with fostering students‟ mathematical power (Kastberg, D‟Ambrosio, McDermot, & Saada, 2005, p. 10). Self-Concept Burn (1984) states that self-concept is a composite image of what we think we are, what we think we can achieve, what we think others think of us, and what would we like to be. Most social psychologists, one of whom, Rokeach, (Burn, 1984, p. 52) agree that self- concept as a set of self- attitudes that consist of four components appear to be embodied: (a) a belief, or knowledge or cognitive compo- nent, (b) an affective or emotional compo- nent, (c) an evaluation, and (d) a predisposi- tion to respond. Attitude organizes a relatively enduring belief in the object or situation around as a person's tendency to respond in various ways that he or she likes. Thus the self-concept is more of a hypothetical con- struct. In other words, it is a concept or a use- ful way to predict the attitude or behavior of a person, but must be careful not to „filter‟ or judge the constructs as a thought that exists in the real world. Self-efficacy Another concept related to the belief of an individual or representation of one's self is the self-efficacy. Bandura in Keller (2010, p. 146) mentions another concept related to the REiD (Research and Evaluation in Education) 66 − REiD (Research and Evaluation in Education, 3(1), 2017 belief in personal agency, i.e self-efficacy, the belief which is typically referred to as a per- son's belief that he or she can succeed in per- forming a given task. In line with this defini- tion, Bandura also mentions self-efficacy as people's judgments on reviews of their abil- ities to organize and execute courses of action required to attain designated types of perfor- mances. Based on those opinions, it might be concluded that self-efficacy is defined as a be- lief or judgment about a person's ability to or- ganize and execute courses of action required to complete a type of work that has been de- termined. Keller (2010, p. 146) states that a person's self-efficacy is comprised of combi- nation of belief related to three questions: Am I capable of doing the things that are neces- sary for success, developing a plan that will lead to success, and persisting in my effort long enough to achieve success? Thus the results of the strength or toughness of self- efficacy can be expected of a person: whether repetition or modification of planned behav- ior, how much effort will be made, and how long one will survive in the face of obstacles and challenging experience. Mathematics Teacher Competency Teacher competence, on Law No. 14 Year 2005 of Republic of Indonesia about Teachers and Lecturers, article 32, states that the promotion and development of the teach- ing profession as referred to in paragraph (1) includes the pedagogical competence, person- al competence, social competence, and spirit- ual competence. In relation to the compe- tence of mathematics teachers, there are some opinions that highlight the mastery of sub- stance, achievement in performing or teaching in the classroom, peers assessment, or prepa- ration of the portfolio. Fennema and Franke (Turnuklu & Yesildere, 2007, p. 2) mention that some of the components of mathematical knowledge to be possessed by a mathematics teacher: knowledge of mathematics, know- ledge representation/math symbols, know- ledge of the students, and knowledge about teaching and decision making. Another opinion from Kulm and Wu (Turnuklu & Yesildere, 2007, p. 3) mentions the beliefs on a reciprocal basis underlying the substance of pedagogical content knowledge. Pedagogical content knowledge comprises of three components: content knowledge, teach- ing practice, and knowledge of the curricu- lum, each of which interacts reciprocally. In the practice of teaching, a teacher must under- stand the thought of his/her students (know- ing students' thinking). The understanding of students‟ thoughts is translated into five com- ponents namely: addressing students' miscon- ception, engaging student learning in math, student learning, promoting student thinking in mathematics, and building on student math idea. Thus, this shows that the conviction of a mathematics teacher will be the basis for the substance of pedagogical knowledge, which will ultimately lead to active student activities, anticipate misconceptions, and build mathe- matical ideas. Mathematics Teacher Self-efficacy Related to teacher efficacy, several stu- dies support the theory that the belief in one's ability is the best predictor for the behavior of the completion of a task (Bandura, 1996, 1997; Pajares, 1996, in Leder, Pehkonen, & Torner, 2002, p. 216). Referring to Bandura‟s concept of self-efficacy as confidence in one's ability to organize and carry out a number of actions needed to generate the expected re- sult, with the same understanding, Philippou and Christou (Leder et al., 2002, p. 217), men- tion that the teaching efficacy can be under- stood as a belief in the ability of teachers to organize and create effective learning environ- ments. The activities and actions of teachers are more dependent on what they believe than on what they know, or the competence they rarely achieve. The same idea is said by Hoy and Spero (2005, p. 29) that teachers 'sense of efficacy as teachers' judgments about reviews their capabilities to promote student learning. Gibson and Debo (Leder et al., 2002, p. 218) classify the teacher's self-efficacy into two factors: general teaching efficacy (GTE) and personal teaching efficacy (PTE). GTE refers to teachers‟ general feeling that their teaching and education system will be able to grow and develop students' academic achieve- ment despite the negative influence of outside REiD (Research and Evaluation in Education) A construct of the instrument for measuring junior high school... - 67 Rachmadi Widdiharto, Badrun Kartowagiran, & Sugiman teachers. Meanwhile, personal teaching effica- cy (PTE) is intended as a reflection of teach- ers conviction on their own to continue the significant learning and student achievement. Furthermore, Philippou and Christou (Leder et al., 2002, p. 217) state that the efficacy of belief about the teaching of mathematics is mostly, but not entirely, shaped by one's expe- rience and knowledge of mathematics and its pedagogy. The process skills of mathematics teachers should also be developed, i.e skills in reasoning, understanding of the concept, the relationship between concepts, representation, communication, and problem solving. In relation to teachers‟ efficacy and competence, Tschannen-Moran et al. (1998) proposed an Integrated Model of Teacher Efficacy Cyclical. Furthermore, with reference to Lee (2009, p. 15) about the teacher's self- concept, as well as the opinion of Gibson and Dembo (1984) about the outcome efficacy, the approach develops a system model as pre- sented in Figure 1. Method Research on the construct of the instru- ment for measuring junior high school mathe- matics teacher self-efficacy is a kind of devel- opmental research (Borg & Gall, 1983, p. 775), to obtain a construct of dimensions or factors in relation to the self-efficacy of math- ematics teachers, especially junior high school mathematics teachers in the Special Region of Yogyakarta. This study was conducted over four months from September to December 2013) in four districts, namely Sleman, Bantul, Kulonprogro, and Gunungkidul regencies, as well as in the municipality of Yogyakarta in the of Special Region of Yogyakarta. Research Design The development of a modified con- struct in this study adapted Borg & Gall‟s model, which was simplified from 10 steps into 6 steps. The development of the modified construct is presented in Figure 2. Figure 1. Development of “The cyclical nature of teacher eficacy” (Tschannen-Moran et al., 1998); “Outcome efficacy” (Gibson & Dembo, 1984; Soodak & Podell, 1996), through the system approach. (Tschannen-Moran et al., 1998) Teacher’s self concept (Lee, 2009) Performance Gibson & Dembo (1984) and Soodak & Podell (1996) Sources of Efficacy information . Cognitive process Analyzing the Teaching Task Assessing Personal Teaching Competence Teacher Efficacy Consequences of Teacher Efficacy Consquences of Performance PROCESS INPUT OUTPUT OUTCOME REiD (Research and Evaluation in Education) 68 − REiD (Research and Evaluation in Education, 3(1), 2017 Figure 2. Research design on the development of the instrument of junior high school mathematics teacher self-efficacy There are six stages in this research design. First, a construct was designed. This activity consisted of context analysis, relevant literature review, and prototype designing. At this stage, a preliminary instrument of math- ematics teacher efficacy was developed. It consisted of four dimensions, namely: Person- al Efficacy (PE), General Teaching Efficacy (GTE), Subject-Matter Teaching Efficacy (STE), and Outcome Efficacy (OE) based on the relevant theory and literature. The total number of items in this prototype instrument was 94 items consiting of: PE (25 items), GTE (26 items), STE (33 items), and OE (10 items). Likert scale was used with the rating scale of 1–4. The second stage was validation by experts. This activity was a focus group dis- cussion (FGD) involving eight experts or spe- cialists from universities, consisting of: two mathematics education experts, three psycho- metric experts, one educational psychologist, and two experts on teacher training. The as- pects assessed included: blue-print and indi- cators, clarity of the instruments, and the mo- del development. The FGD results obtained content validity (content validity coefficient) through Aiken validity (Aiken, 1985, p. 132; Azwar, 2013, p. 134) was 0.71, meaning that the instrument could be used for collecting data. The third stage was the limited testing. This activity involved 32 people, consisting of 22 mathematics teachers (of three districts in the province) and seven principals and three supervisors. The results of this readability test obtained a score of 4.13 which means that the instrument could be used. The fourth stage was the revision or im- provement. Based on the expert judgement in FGD and the limited testing, revision was done to improve the instrument in accord- ance with the input and advice from the ex- perts. The fifth stage was the extended test- ing. In this case the test subjects were as many as 274 mathematics teachers in the Special Region of Yogyakarta. The sixth stage was the final product and its use. The data from the extended test- ing were analyzed by using Lisrel 8.80 through the the first order and the second order analy- sis of CFA in order to obtain a suitable con- struct between the model and data. Based on this instrument, the researchers employed it for mapping the level of mathematics teacher self-efficacy. Population and Sample The population of this research was junior high school mathematics teachers, by referring to the data of the Provincial Educa- tion Department of Yogyakarta in 2012. It consisted of 816 junior high school mathema- tics teachers. Using the proportionate random sampling technique (Cohran, 2010, p. 85) the researcher established a sample of 274 teach- ers, consisting of 38 teachers from Yogyakarta City, 85 from Sleman, 70 from Bantul, 38 from Kulonprogro, and 43 from Gunung- kidul. The sample size in the CFA analysis was determined by the number of the ob- served variables or items. According to Hair, Black, Babin, and Anderson (2006), for the sample size, it is recommended to use the esti- mates of the Maximum Likelihood (ML) at 100-200. Construct design: Context analysis, designing prototype Expert Validity: Focus Group Discussion (FGD) Limited testing – Readability test: Math teacher/Principal/ Supervisor Instrument Revision – Initial product Extended testing : junior high school math teacher Final Product of Instrument of junior high school math teacher self-efficacy and its use REiD (Research and Evaluation in Education) A construct of the instrument for measuring junior high school... - 69 Rachmadi Widdiharto, Badrun Kartowagiran, & Sugiman Data Analysis Technique In data analysis, Confirmatory Factor Analysis (CFA) consisting of first-order and second order with the software of Lisrel 8.80 was used. The evaluation criteria for the mo- del fit were by p-value on Chi-square (2) and the Root Mean Square Error of Approxima- tion (RMSEA). The model was declared fit if the p-value was greater than Chi-square (2); was not significant if p-value  0.05, meaning there is no significant difference between the model with the data (Joreskog & Sorbom, 2003, p. 128). The evaluation model with the RMSEA was expected to show the RMSEA value of  0.05 for the model considered as close to or the RMSEA value of  0.08 for a model declared as a good fit model. Further- more, the fit instrument construct was used to map the level of mathematics teacher self- efficacy, referring to the score of Mathematics Teacher Self-efficacy (X): X    1 (low category),   1    X + 1 (medium category), and  + 1  X (high category). Findings and Discussion The First Order Analyisis Dimension of Personal Efficacy (PE) This dimension consists of three indica- tors: mathematics self-concept, math anxiety and internalizing the source of efficacy. PE consisted of 25 items, the number of the items might decrease gradually in the the first order analysis for obtaining a fit model. Items V2, V5, V6, V7, V9, and V10 were eliminated because the t-value of the loading factor < 1.96. Items V24 and V25 were also eliminated because of a negative loading factor value. Items V3, V13, V18, V19, V20 and V23 errors were eliminated because they shared a variance among items as the cause of the goodness of fit value was not a significant dimensional construct. The result of the first order analysis of CFA showed that the model was fit to the data by obtaining the Chi-Square = 53.61 df = 44 p-value = 0.15201 and RMSEA = 0.020. The number of items decreased from 25 items into 11 items, with the loading factor of 0.19 to 0.64. So the items on the dimensions of PE were 11 items, namely items V1, V4, V8, V11, V12, V14, V15, V16, V17, V21, and V22. Dimension of General Teaching Efficacy This dimension consited of four indica- tors: pedagogy content knowledge, classroom management, student engagement, and paren- tal involvement. GTE consisted of 26 items, the number of item might decrease gradually in the first order analysis for obtaining a fit model. Items V29 and V30 were eliminated because the t-value of the loading factor <1.96. Items V26 and V43 were also elimi- nated because it had an error value variance greater than the value of the loading factor which caused the goodness of fit value was not significant. The result of the first order analysis of CFA showed that the model was fit to the data by obtaining Chi-Square = 66.59; df = 54, p-value = 0.11670 and RMSEA = 0.029. The number of the items decreased from 26 items into 12 items with the loading factor of 0.22 to 0.71. Thus, the number of the fit items in dimensions of GTE was 12 items, namely items V28, V31, V35, V38, V41, V44, V45, V47, V48, V49, V50, dan V51. Dimension of Subject-matter Teaching Efficacy (STE) This dimension consisted of three indi- cators: knowledge of junior high school math- ematics content, teaching strategies, and fos- tering student mathematical power. STE con- sisted of 33 items, the number of items might decrease gradually in the first order analysis for obtaining a fit model. Items V52, V56, V57, V58, V66, and V67 were eliminated be- cause the value of t loading factor < 1.96. The items that were removed were Items V53, V54, V59, V60, V61, V62, V65, V68, V69, V70, V71, V74, and V78 because the error of variance was much greater than the value of the factor loading, causing the value of good- ness of fit not significant. The result of the first order analysis of CFA showed that the model was fit to the data by obtaining Chi-Square = 24.49; df = 20; p-value = 0.2216, RMSEA = 0.029. The number of the items decreased from 33 items REiD (Research and Evaluation in Education) 70 − REiD (Research and Evaluation in Education, 3(1), 2017 into 13 items with the loading factor from 0.22 to 0.40. Thus, there were 13 items left in STE‟s dimensional. They were items V55, V63, V72, V73, V75, V76, V77, V79, V80, V81, V82, V83, and V84. Dimension of Outcome Efficacy (OE) The dimension of Outcome Efficacy (OE) consisted of three indicators, namely: student achievement, building mathematics attitude, and the continouing study. OE con- sisted of 10 items, and the number might de- crease gradually in the first order analysis for obtaining a fit model. All items had a t-value of loading factor > 1.96 and no negative load- ing factor value. However, items V86 and V91 were eliminated because they had a value of error variance much greater than the value of the loading factor, causing the value of goodness of fit not significant. The result of the first order analysis of CFA showed that the model was fit to the data by obtainng Chi-Square = 14.60; df = 9; p-value = 0.10256; RMSEA = 0.048. The number of the items decreased from 10 items to eight items, with the loading factor from 0.32 to 0.42. Therefore, the number of items was reduced to 8 items, namely V85, V87, V88, V89, V90, V92, V93 and V94. The Second Order Analysis Based on the items obtained in each di- mension in the first order analysis, the second order analysis of CFA was done. Several si- mulations and iterations among these dimen- sions were done for obataining a fit model, such as: PE and GTE; STE and OE; dimen- sions of PE, GTE, and dimension STE. Final- ly, iterations of the next dimensions of PE, GTE, STE, and OE, derived a construct mo- del that was fit to the data, as presented in Figure 3. Figure 3. Path diagram of the second order analysis output REiD (Research and Evaluation in Education) A construct of the instrument for measuring junior high school... - 71 Rachmadi Widdiharto, Badrun Kartowagiran, & Sugiman Table 1. Results of the second order CFA of the instrument of junior mathematics teachers‟ self- efficacy with 25 items Item Loading Factor t-value R2 Result Dimension: PE Item 8 0.40 --- 0.19 Reference Item Item 11 0.61 2.68 0.37 Item Fit Item 14 0.58 2.62 0.30 Item Fit Item 15 0.48 2.47 0.25 Item Fit Item 16 0.65 2.63 0.42 Item Fit Item 17 0.66 2.67 0.44 Item Fit Item 22 0.42 2.53 0.21 Item Fit Dimension: GTE Item 28 0.57 --- 0.33 Reference Item Item 31 0.42 6.41 0.18 Item Fit Item 35 0.59 7.20 0.35 Item Fit Item 44 0.55 6.05 0.30 Item Fit Item 45 0.62 6.70 0.38 Item Fit Item 47 0.52 5.48 0.27 Item Fit Item 48 0.64 7.65 0.41 Item Fit Dimension: STE Item 63 0.62 -- 0.39 Reference Item Item 72 0.48 6.04 0.23 Item Fit Item 73 0.56 8.11 0.31 Item Fit Item 75 0.52 7.68 0.28 Item Fit Item 77 0.66 8.71 0.43 Item Fit Item 81 0.56 8.35 0.31 Item Fit Item 84 0.64 8.42 0.41 Item Fit Dimension: OE Item 87 0.52 -- 0.28 Reference Item Item 89 0.78 8.17 0.60 Item Fit Item 90 0.76 8.00 0.57 Item Fit Item 94 0.69 7.31 0.48 Item Fit The results of the tests performed on the measurement model of the second order analysis of CFA on 54 items resulted in p value = 0.12824 (p> 0.05) and RMSEA = 0.019 (RMSEA <0.05). Based on the data, p- value and RMSEA were successfully met so that it could be concluded this model was really fit with the data. The RMSEA value of 0.019 indicates that the model is very fit. In other words, all 25 items are valid indicators for measuring the instrument construct of self-efficacy of junior high school mathema- tics teachers. These results also showed that 25 items measured a latent variable, which was the self-efficacy of mathematics teachers. It was concluded that self-efficacy measure- ment instrument for mathematics teachers met unidimensionality assumptions. Table 1 is the table of all fit items of the results of sec- ond order CFA for measuring of junior high school mathematics teacher self-efficacy. Based on the t-value of the second or- der CFA testing, it was known that all of the items were fit to measure junior high school mathematics teacher self-efficacy because the whole t-value was greater than 1.96. From Table 1, it is also noted that Item 89 has the highest contribution to the measuring instru- ment with the loading factor of 0.78, while Item 15 gives the smallest contribution to the loading fator of 0.38. Mapping of Mathematics Teacher Self-Effica- cy The degree or level of mathematics teacher self-efficacy was obtained from the interpretation of the scores of an individual mathematics teacher as many as 274 teachers within 25 fit items. The scores obtained in the questionaire are raw scores, which need to be converted first into z-standard score, with μ = 0, and  = 1. However, because the standard z-scores allow their negative score, then for the ease of readability and interpretation, they need to be converted into t-score,with μ = REiD (Research and Evaluation in Education) 72 − REiD (Research and Evaluation in Education, 3(1), 2017 50, and  = 10. The result of the conversion of the scoring through a simple program MS Excel, and which referred to the categoriza- tion, as presented in the data analysis, shows the obtained mapping of mathematics teacher self-efficacy for each diemnsion as in Table 2. Meanwhile, the percentage of respondents‟ MTSE level is shown in Figure 4. Discussion The results of the analysis of the second order with Chi-Square = 297.58; df = 271; p- value = 0.12824; RMSEA = 0.019; 25 out of 54 items are with the factor loading () of each dimension PE, GTE, STE, and OE con- secutively being 0.46; 0.84; 0.89 and 0.92. Thus it can be said that the model was fit to the data. Dimension of Personal Efficacy (PE) The dimension of Personal Efficacy contains three indicators, from the initial 11 items (the first order) it decreases to 7 items (the second order). Those three indicators in- clude (a) mathematics self-concept, with item descriptors: efficacy of the ability to provide necessary information known to the students in learning mathematics (V8); (b) mathematics anxiety, item descriptors; efficacy on the read- iness of the teachers when they would teach mathematics (V11), tranquility or comfort du- ring mathematics learning (V14), the level of concern toward the material that was not be acquired (V15), having difficulty in concen- trating while teaching mathematics (V16), and concerns if there were other people observing their teaching (V17); (c) the internalization of the source of efficacy, with efficacy item des- criptor against social persuasion such as: invi- tations, suggestions, and verbal advice from a colleague which can push them to perform task (V22). Table 2. Frequency recapitulation of mathematics teacher self-efficacy (MTSE) level for each dimension Category Dimensions/Factors MTSE PE GTE STE OE Low(L) 82 94 94 93 93 Medium (M) 192 179 181 170 178 High (H) 0 2 4 1 4 Total Number 274 Figure 4. Graphic of Percentage MTSE level 64.96% 33.94% 1.46% REiD (Research and Evaluation in Education) A construct of the instrument for measuring junior high school... - 73 Rachmadi Widdiharto, Badrun Kartowagiran, & Sugiman Dimension of General Teaching Efficacy (GTE) General Teaching Efficacy dimension contains four indicators (from the initial 12 i- tems (the first order) decreasing to 7 items (the second order)). Those four indicators are: (a) pedagogy content knowledge of mathema- tics, with item descriptors including efficacy of ability to apply appropriate learning strate- gies in classroom practice (V28); (b) class- room management, with item descriptor effi- cacy toward abilities including students‟ drive to obey the rules in class (V31), explanation of the steps that must be performed by stu- dents in learning inside and outside the class- room (V35); (c) students‟ engagement with descriptor item efficacy toward abilities which help students to be actively involved in fun and meaningful learning (V44), maintain or restore the students‟ attention to stay focused on the material presented (V45), enhance stu- dents' understanding (V47) and assure the students that they can perform for completing the lesson task at school well (V48). In GTE dimensions, there actually exist one more indicator, that is promoting the pa- rental involvement in helping their children learning mathematics. At the time of the first- order analysis of GTE, all of the three items representing this indicator exist, but unfortu- nately on the second order CFA three items are forced to be eliminated to fit its models. In this study, the respondents might argue that the indicators were not required to mea- sure mathematics teacher self-efficacy. Thus, in other words, the respondents believed that parental involvement might not help their children learning. The existence of out-of- school learning guidance, additional lesson, or private lesson would replace this role. Dimensions of Subject-matter Teaching Efficacy (STE) The dimensions of STE (Subject-matter Teaching Efficacy) consist of three indica- tors. The initial 13 items (the first order) de- creased to 7 items (the second order). Those three indicators are: (a) the strategy of mathe- matics teaching, with item descriptors being the efficacy toward the ability to guide stu- dents in using a representation of an image, and symbol for mathematics learning (V63); (b) fostering students‟ mathematical power, with item descriptors being the efficacy in abilities to capture gaps between students‟ ca- pability and competencies expected (V72), guiding students in examining the true rela- tionship between one statement and others (V73), guiding students in developing a con- jecture from available premises (V75), design- ing learning that encourages students to ap- preciate the benefits of mathematics (V77), managing the provision of questions to stu- dents (V81), and efficacy toward the ability to provide questions to students relating the idea of mathematics and its applications (V84). In fact, there is one more indicator in STE dimension, that is acquiring mathema- tics content knowledge. At the time of first- order analysis of GTE, there is one out of five items as a representation of this indicator, but in the second order CFA, one item was forced to be eliminated to fit its models. It means that in this study, these indicators were not required to measure mathematics teachers‟ self-efficacy. In other words, acquiring the mathematics content knowledge only by ask- ing thorugh questionaire is not enough. Using a test to measure this domain is more reason- able. The existence of Teacher Competency Testing would support the absence of this indicator. Dimension of Outcome Efficacy (OE) The dimension of Outcome Efficacy (OE) consists of three indicators, the initial eight items (the first order) decrease to four items (the second order). Those three indica- tors include: (a) student achievement, with i- tem descriptor efficacy against the ability to: guide students to succeed in the mathematics contest or mathematics olympiad in district region (V87), (b) bulid a mathematics atti- tudes, with items descriptor belief that mathe- matics learning done by the teacher is to pro- mote students‟ critical logical thinking and to be consistent (V89), efficacy toward the belief that learning is done to guide the students to be honest, disciplined and responsible (V90), (c) continouing study, with item descriptor efficacy toward the belief that learning is done to be able to equip students to practice prob- lem solving in their future life (V94). REiD (Research and Evaluation in Education) 74 − REiD (Research and Evaluation in Education, 3(1), 2017 Based on the discussion, a framework of a construct for junior high school mathe- matics teacher self-efficacy in the Special Re- gion of Yogyakarta could be made, consisting of four dimensions. The first dimension is Personal Efficacy (PE) with a loading factor (=0.41), consisting of indicators including mathematics self-concept, mathematics anxie- ty, and also internalization source of efficacy. The second dimension is General Teaching Efficacy (GTE) with a loading factor ( = 0.84), consisting of indicators including peda- gogy content knowledge, classroom manage- ment, and student engagement. The third di- mension is Subject-matter Teaching Efficacy (STE) with a loading factor (=0.89), consist- ing of indicators including teaching strategies and fostering students' mathematical power. The fourth dimension is Outcome Efficacy (OE) with a loading factor (=0.92), consist- ing of indicators including student achieve- ment, building mathematics attitude, and con- tinuing study. Mapping of Mathematics Teacher Self-Effica- cy Figure 4 shows that the percentage of mathematics teacher self-efficacy is 1.46% in a high category, 64.96% in a medium category, and 33.94% in a low category. With the hope of an ideal efficacy of mathematics teachers reaching high categories, as many as 98.54% of mathematics teachers should be enhanced for high category efficacy. In order to give an idea of the profile of mathematics teacher self-efficacy in these cat- egories and to make it easier to follow up the results of measurements of efficacy in the process of continuing professional develop- ment of mathematics teachers, and refer to the indicators and items of MTSE which have been fit and significant, Table 3 is a general description of MTSE (Mathematics Teacher Self-Efficacy) profile. Table 3. General description of mathematics teacher self-efficacy MTSE Category Description of MTSE Low (Score: 24.96 – 49.92) a. Not sure: the importance of understanding and the role of mathematics self- concept, overcoming math anxiety, and internalization of the sources of self- efficacy, in carrying out the task of teaching responsibility. b. Not sure: able to master knowledge of the pedagogical substance, class-room management, and students engagement c. Not sure: able to perform mathematical learning strategies and fostering students' mathematical power. d. Not sure: able to improve student achievement, students' mathematical attitudes, as well as provisions for the continuation of the study at the next level. Medium (Score: 49.93 – 74.88) a. Sure: the importance of understanding and the role of mathematics self- concept, overcoming math anxiety, and internalization of the sources of self- efficacy, in carrying out the task of teaching responsibility. b. Sure: able to master knowledge of the pedagogical substance, classroom management, and students engagement c. Sure: able to perform mathematical learning strategies and fostering stu-dents' mathematical power. d. Sure: able to improve student achievement, students' mathematical atti-tudes, as well as provisions for the continuation of the study at the next level. High (Score: 74.89 – 100.00) a. Very Sure: the importance of understanding and the role of mathema-tics self- concept, overcoming math anxiety, and internalization of the sources of self- efficacy, in carrying out the task of teaching responsibility. b.Very Sure: able to master knowledge of the pedagogial substance, class-room management, and students engagement c. Very Sure: able to perform mathematical learning strategies and foster-ing students' mathematical power. d. Very Sure: able to improve student achievement, students' mathematical attitudes, as well as provisions for the continuation of the study at the next level. REiD (Research and Evaluation in Education) A construct of the instrument for measuring junior high school... - 75 Rachmadi Widdiharto, Badrun Kartowagiran, & Sugiman Conclusion and Suggestions Based on the findings, some conclu- sions are drawn. First, the results in the se- cond order analysis of the construct of the in- strument for measuring the self-efficacy of ju- nior high school mathematics teachers in the Special Region of Yogyakarta shows the mo- del is fit to the data, indicated by Chi-Square = 297.58; df = 271; p-value = 0.12824; RMSEA = 0.019, from 54 items, 25 items ob- tained with factor loading () each dimension PE, GTE, STE, and OE consecutively are: 0.46; 0.84; 0.89 and 0.92. The construct of the instrument for measuring self-efficacy of junior high school mathematics teachers in the Special Region of Yogyakarta consists of four dimensions. First, the dimensions of Personal Efficacy (PE) with a loading factor (=0.41) with indicators: mathematics self concept, mathematics anxie- ty, and the internalization source of efficacy. Second, the dimensions of General Teaching Efficacy (GTE) with a loading factor ( = 0.84) with indicators: pedagogy content know- ledge, classroom management and students engagement. Third, the dimensions of Sub- ject-matter Teaching Efficacy (STE) with a loading factor (=0.89) consisting of indica- tors: teaching strategies and fostering stu- dents' mathematical power. Fourth, Outcome Efficacy (OE) dimension with a loading fac- tor (=0.92), with indicators: student achieve- ment, building mathematics attitude, and the continouing study. The results of the mapping of the self- efficacy of mathematics teachers in the Spe- cial Region of Yogyakarta show that 43.07% of the teachers are categorized as low, 55.47% are categorized as moderate, and 1.46% are in high category. 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