Purpose: Essay test in mathematics, both in the form of restricted-response and extended-response, generally consist of polytomous scored items. However, the essay test used by teachers in Indonesia has not been fully supported by sufficient quality evidence. There have been many studies focusing on the development of the essay test, but not many of them have applied the use of relevant measurement theory for the polytomous data. The evidence of content validity also has not been supported by its alignment with the curriculum. This study used alignment index to
<p style="text-align: justify;">The objective of this research is to analyze the twelfth graders' mathematics critical thinking skills using a mathematics learning model to stimulate fundamental critical thinking abilities of science courses in SMA Negeri, Pacitan Regency, East Java Province, Indonesia. This quasi-experimental research design was used in this study with one group posttest only design using multiple substantive posttests. The sample of 141 students from the total population of six public schools involving the twelfth graders of the natural sciences was selected through purposive sampling technique, data were taken through tests of students' critical thinking skills and interviews. The data analysis consists of five stages, namely an analysis of one sample t-test, an analysis of students' grades, an analysis of problem-solving stages, an analysis of critical thinking abilities indicators, and an analysis of mathematics critical thinking abilities indicators. The results showed (1) The results of the one sample t-test show that the mathematics learning model is effective to stimulate critical thinking, which means that the application of the mathematics learning model is effective to stimulate critical thinking; (2) the overall grades of students that met the minimum mastery criteria; (3) the data analysis of eleven problem-solving stages proves that the criteria for critical thinking abilities are categorized as good and very good. The highest score indicator considers the principle and definition of transformation, while the lowest grade indicator is mainly concerned with the questions on right and coherent steps; (4) the critical thinking skills have seven indicators that highlight the criteria of students' critical thinking abilities categorized as good and very good. The indicators that get the highest score determine the definitions of terms, while the indicators of the lowest score determine the action; (5) the results of the analysis show indicators of mathematics critical thinking skills that have eight indicators. The criteria of students' critical thinking abilities met good and very good categories along with indicators with the highest value score by considering the definitions of terms, while the indicators of the lowest score deal with the habit of caution.</p>
This study aims to design mathematical literacy instruments that have evidence of content and construct validity and are reliable for use as an assessment for learning. The research involved eight experts as instrument validators and 273 eighth-grade students of junior high school in Yogyakarta Province. The results showed that the ten mathematical literacy items developed had the V Aiken coefficient index calculated from 0.781 to 0.906 (> 0.75). The results of adequacy testing of samples with KMO and Bartlett show Chi-Square in the Bartlett test of 608,608, the p-value <0.05 and KMO value of 0.781 (> 0.5). The results of testing of the measurement model with Confirmatory Factor Analysis (CFA) produce a Root Mean Square Error of Approach (RMSEA) value of 0.049 (≤ 0.08), chi-s Square of 33.92 (<2df), the p-value of 0.05004 (≥ 0.05). Nine out of the ten items developed had t-value> 1.96, Standardized Loading Factor (SLF) was greater than the critical limit (> 0.3), and Construct Reliability (CR) of 0.78 (> 0.7). It can be concluded that the developed mathematical literacy instrument can measure what must be measured and nine items significantly reflect the construct or latent variable, as well as the level of consistency of a good score.
The aims of this research are: (1) to measure the difficulty level of grain test of mathematics achievement of third grade student at elementary school, (2) to know the differences of mathematics achievement test for third grade student of elementary school, (3) instrument reliability test of mathematics learning achievement of third grade students of elementary school. The research method used is research development, the data analysis to know the information about grains of mathematics test instrument using ITEMAN program. The results show: (1) the test which developed has difficulty level in the range 0,30 ≤ p ≤ 0,70 with accepted category, (2), the test which developed has differences level in range 0,30 ≤ B ≤ 0,39 and 0,40 ≤ B ≤ 1,00 with accepted category and satisfy, and (3) the test which developed has reliability coefficient of 0,783, show that mathematics test instrument give measuring result that stabile and consistent.
Senior High School (SHS) students need to have advanced mathematical thinking. Its growth can be measured through divergent problem solutions based on the teacher’s scaffolding levels. The problems are: (1) How to identify the levels of scaffolding by the teacher to foster advanced mathematical thinking? (2) How to get the results of the analysis to foster of advanced mathematical thinking of SHS students through divergent problem solutions based on the teacher scaffolding levels? The research method was a qualitative approach. The subject of this study was to take 5-6 students of SHS 1 of Ungaran. Research activities: (1) identifying of scaffolding leveling by teachers to foster the advanced mathematical thinking, (2) analyze the growth of advanced mathematical thinking of students of SMAN 1 Ungaran through divergent problem solutions based on the teacher scaffolding levels, (3) conducting of solution analysis of divergent problems based on teacher scaffolding levels; Interview; data analysis; and triangulation. The results: (1) Identified the level of scaffolding by the teacher how to foster advanced mathematical thinking. (2) Obtained the analysis results to foster of advanced mathematical thinking of high school students through divergent problem solutions based on teacher scaffolding leveling. Recommended advice: Teachers need to train their students to be able to work on divergent mathematical problems and provide tiered scaffolding.
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