Mathematical Problem-solving Test Research Articles

Exploring Sources of Bias to Improve the Universal Design of Mathematical Problem-Solving Tests

ABSTRACT Advancement of testing of mathematical problem-solving skills calls for open-ended, realistic tasks particularly susceptible to bias, compromising the score validity and fairness of tests. Informed by universal design principles, this study framed 360 prototype items developed for the Problem-solving Measures Grades 6–8 Computer Adaptive Tests as a bounded case to illuminate sources of bias in middle-school mathematics assessment. Experts’ shared understandings of potential sources of bias were collected using an iterative Delphi technique. Four themes in sources emerged from a thematic analysis of 201 sources of bias identified: assumed lived experiences, language use, item presentation, and stereotypes. These sources potentially placed subgroups of students from certain sociocultural backgrounds (e.g. culture, gender, race/ethnicity, socioeconomic status) at a disadvantage by challenging them in ways unrelated to mathematical problem solving. Recommendations for minimizing potential sources of bias in test development to achieve equitable K-12 mathematics problem-solving tests are discussed.

Analysis of Mathematic Problem-Solving Ability in Solving Pythagoras Theorem Problems

Problem solving is about finding a solution to a problem, so learning mathematics involves solving problems that relate to everyday life. The method of research used is qualitative descriptive research aimed at describing and explaining the methods of solving problems of Pythagoras's theorem students, as seen from the analysis of student's ability to solve mathematical problems. Information obtained from the work or written answers (tests) that have been completed. In this study, 30 students participated in the 2022/2023 academic year in the eighth grade of Delitua Private High School. The highest percentage value was 98.04% for the indicator of problem understanding, while the lowest percentage was 33.34% for the re-examination indicator. Overall, the average percentage score was 69.51%, which is high. This means that the ability of the students of the eighth grade of Delitua Private High School to solve mathematical problems using the material of Pythagoras's theorem is very competent. The students' responses to the statement in the mathematical problem-solving test were effective because all the statements were answered positively by ≥ 90% of students

PENGEMBANGAN INSTRUMEN EVALUASI BERBASIS KEMAMPUAN PEMECAHAN MASALAH PADA MATERI EKSPONEN DI TINGKAT SMA

The purpose of this research is to produce a test instrument to measure mathematical problem-solving ability by looking at the development procedures and the quality of the mathematics problem solving instruments developed. The research used is the type of research (R&D) that is the development of test instruments to measure the ability to solve mathematical problems. The development model of this research instrument is developed on the basis of the Tessmer model which is the formative type of evaluation, i.e. (1) preliminary stage, (2) self evaluation stage, (3) prototyping stage (expert reviews, one-to-one and small group) and (4) field test stage. The test subject of the experiment were X Students of SMAN 2 Bayah which amounted to 25 students. Based on the results of experiments conducted, it is found that: (1) math problem solving test instrument has been said "valid" because based on the CVR results are 1 and meet the criteria of ≥ 0.99 and CVI is 1 with a category perfectly suitable or in the range 0,68-1,00 (2) mathematical problem-solving test instrument is said to be reliable with a value of 0.754 with high category, and is in the range of 0.60 < r11 < 0,80 (3)instrumen test the math problem solving device has a level of difficulty good then the average level of difficulty obtained is 0.58 with the medium category that is in the range of 0.31 to 0.70. (4) instrumen test math problem solving devices has a power a good differentiator and the average distinguishing power obtained is 0.35 with sufficient category or is in the range Dp > 0.2. As a result, the produced instrument is appropriate for assessing pupils' mathematical problem-solving abilities

The Effect of Implementing Learning Models Cycle 7e on Mathematical Problems-Solving Ability

This research was motivated by the low mathematical problem-solving abilities of students at Batanghari 15 State Junior High School, Jambi. This research aims to determine the effect of the Learning Cycle 7e learning model on students' mathematical problem abilities at Batanghari 15 State Junior High School. This research uses the quasi-experimental method, using a post-test-only control design. There are two groups, each of which is chosen randomly. The population of this research is all students in class VIII of Batanghari 15 State Junior High School for the 2023/2024 academic year, totalling 90 students and divided into four classes. In this research, the sample used was 50 students divided into two classes (experimental and control classes). The sample was determined using the Random Sampling technique. The data collection techniques used in this research were observation and mathematical problem-solving tests. This research indicates that the Learning Cycle 7e learning model is more effective in influencing problem-solving abilities than the direct learning model.

Complex Thinking: How are Students' Mathematical Problem-Solving Skills in Elementary School?

This study aims to see an overview of students' mathematical problem-solving skills in elementary school. This study uses a quantitative approach with a descriptive method. The subjects in this study amounted to 25 grade 5 students in one of the elementary schools in Bandung with details of 10 male and 15 female students. The data collection technique used is a mathematical problem-solving test instrument based on Polya theory on fractional concept material. The data analysis carried out was to calculate descriptive statistics using Microsoft excel and SPSS version 24 to see an overview of mathematical problem-solving skills, categorization of problem-solving scores based on high, medium, and low, and the achievement of students' mathematical problem-solving indicators. From these data, it is then analyzed in depth and linked with relevant theories. The results of this study showed that based on the categorization of student scores, 4 students were in the high category, 15 students were in the medium category, and 6 students were in the low category. The indicator that has a high percentage of students mastered is understanding the problem at 73%, and the lowest indicator at re-checking is 44%. This research can contribute to efforts to create meaningful learning in mathematics by involving complex thinking skills including mathematical problem-solving skills.
 Keywords: Complex Thinking, Mathematical Problem-Solving Skills, Elementary School

Revolutionizing Math Education: Unleashing the Potential of Web-based Learning Media for Enhanced Mathematical Problem Solving Skills

This research aims to develop web-based mathematics learning media with a focus on enhancing students' mathematical problem-solving abilities. The background of the study is based on the urgent need to address challenges in mathematics education and leverage technology to improve learning outcomes. The research method used is a development research with the ADDIE (Analysis, Design, Development, Implementation, Evaluation) approach. Research instruments include student response questionnaires, media and material validation instruments, and mathematical problem-solving test questions. The research results show that the developed web-based learning media is valid and effective in improving students' mathematical problem-solving abilities, as the paired samples t-test yields a significance score of 0.002 (p < 0.05). Students' response to this learning media is positive, and there is a significant improvement in mathematical problem-solving test scores. The conclusion of this research is that the use of web-based learning media has the potential to enrich mathematics education and enhance student learning outcomes. The implications of the research highlight the necessity of integrating technology in education to optimize learning and meet the learning needs of students in the digital era.

ANALISIS KEMAMPUAN METAKOGNISI MAHASISWA DALAM MEMECAHKAN MASALAH MATEMATIKA DI PRODI PENDIDIKAN MATEMATIKA UNIVERSITAS TIMOR

Qualitative descriptive research that aims to analyze students' metacognition ability in solving mathematical problems. The three components of metacognition ability to be measured are developing a strategy or action plan, monitoring actions and evaluating actions. The data in this study was obtained from problem-solving test sheets, metacognition questionnaires and guidelines for interviews. The subjects in this study were students in semester 1 of the mathematics education study program for the 2022/2023 academic year by taking 3 students representing high, medium, and low ability groups. Based on the results of the study, it was obtained that students with high abilities can solve mathematical problem solving test questions because they already involve 3 components of metacognition ability very well, namely compiling action plans, monitoring actions and evaluating actions, students with moderate abilities have not been able to solve mathematical problem solving test questions because they have not evaluated actions so that there are still wrong final answers even though students Having the ability to strategize actions and monitor good actions, students with low abilities cannot complete mathematical problem solving tests because they have not been able to carry out action plans, monitor actions, and evaluate actions properly.

PROSES BERPIKIR DALAM MEMECAHKAN MASALAH BERDASARKAN TINGKAT KEMAMPUAN MATEMATIKA PADA SISWA KELAS VIII SMP

This study aims to determine the thinking process of students with high, medium and low abilities in solving mathematical problems in the Material of a Two-variable Linear Equation System using Polya theory for class VIII SMP Bina Kusuma in the academic year 2022/2023. Each student has different abilities so the teacher can choose a variety of learning methods according to the student's ability level. The approach used is a qualitative approach. The research subjects were 6 students of class VIII SMP Bina Kusuma Ruteng. Data collection in this study was carried out through tests, interviews and documentation with the research instruments, namely the first-semester report cards of mathematical abilities, problem-solving tests and interviews. The data analysis used is the data analysis model of Miles and Huberman, namely, data collection, data reduction, data presentation and concluding. The results of the analysis of research data show that conceptual thinking processes are only owned by students with high mathematical abilities, while semi-conceptual thinking processes only occur in students with moderate mathematical abilities, and computational thinking processes only occur in students with low mathematical abilities.

THE RELATIONSHIP BETWEEN MATHS ANXIETY, ATTITUDE TOWARDS MATHEMATICS AND MATHS PROBLEM-SOLVING SKILLS AMONG PRIMARY SCHOOL PUPILS IN KEDAH

Pupils in primary schools faced as much daunting and foreboding experiences in Maths. Maths anxiety and attitude towards Mathematics are psychological indicator of poor Maths problem solving skills. This study investigated the relationship between Maths anxiety, attitude towards Maths and Maths problem-solving skills among primary pupils in Kedah state. A questionnaire was developed based on Math Anxiety Questionnaire Children, Attitudes Towards Problem-Solving Skills and a Mathematical problem-solving test administered to 450 primary school pupils. Data were analysed using IBM Statistics and Smart-PLS version 4 software. Results indicated that Maths anxiety and attitude towards Mathematics had a direct influence on Math problem solving.. This research highlighted Maths anxiety as an important factor on Maths problem solving skills as well as pupils’ attitudes towards Mathematics, and teachers should consider this factor an important construct to consider when examining sources of individual differences in Math problem solving skills.

Assessment of domain-specific prior knowledge: A development and validation of mathematical problem-solving test

Science, technology, engineering, and mathematics (STEM) is a complex problem-solving that depends on the deep structures of domain-specific prior knowledge (DSPK) in mathematics. However, there is a lack of mathematics DSPK tests measuring several mathematics topics in every problem-solving phase in conceptual and procedural knowledge. This study aims to develop a mathematical problem-solving test as a mathematics DSPK test and investigate the content and construct validity. The product of test development is a 30-multiple-choice-item test in six mathematics topics. Every topic underlined all problem-solving phases in conceptual and procedural knowledge in a science or individual context. There were six experts performed the content validity sheets which analyzed using the content validity index (CVI) and intraclass correlation coefficient (ICC). The construct validity was examined using the Rasch model from 175 data of 7th grader students in Indonesia (Mage=12.66, SD=55). The result of content validity revealed overall items were valid (CVI≥83) and reliable (α=863; rxx=513). The construct of all items indicated fit (90≤weigheted MNSQ≤1.16) and were reliable (α=74) with various levels of difficulties and six low discrimination items. The recommendation for improvement is emphasized in language aspects. The absence of knowledge of facts could be an improvement for further study.

Effect of use of metacognitive instructional strategies in promoting mathematical problem solving competence amongst undergraduate students in facing competitive examination

Metacognition-related studies often focus on the knowledge, regulation, and experience components but little on the instructional strategies used. In particular and especially within the Indian context, not much focus is given regard to a clear and coherent academic framework that reinforces the use of metacognitive instructional strategies in mathematical problem solving amongst undergraduate students. Using a quasi-experimental method, the purpose of this study is to look closely into the use of metacognitive instructional strategies by undergraduate students. Eighty-four students participated and initial data were collected using the prepared mathematical problem-solving test based on competitive examinations. Single group pre-test and post-test focus group design and the test comparison method were used to analyze the data collected. Findings revealed undergraduate students in the focus group do differ significantly in their mathematical problem solving competence and use of metacognitive instructional strategies between the pre-test and the post-test. The findings shed some light on the distinct role of metacognitive instructional strategy and some ensuing factors during mathematical problem solving in competitive examinations.

PENCAPAIAN KOMPETENSI MATHEMATICAL MODELING MATHEMATICS SISWA DENGAN GAYA KOGNITIF FIELD INDEPENDENT DAN FIELD DEPENDENT

The purpose of this study was to describe the achievement of mathematical modeling competencies of students with field-independent and field-dependent cognitive styles. The type of research used was a mixed method involving 65 SMP N 7 Muaro Jambi students. The data was obtained through the GETF cognitive style test, a mathematical modeling problem-solving test, and interviews. The results showed that students with the FI cognitive style had reached level 6 in modeling competence, namely, performing the entire process of mathematical modeling to interpret and validate solutions against the context of a given problem situation. Meanwhile, FD students up to level 4 can translate real problems into mathematical problems (mathematical models) but cannot use them correctly in mathematics, even though the quality of the models built by FD students is not appropriate to solve problems.

An integrated STEM-based mathematical problem-solving test: Developing and reporting psychometric evidence

Science, technology, engineering, and mathematics (STEM) problem-solving is necessary to be infused into the classroom. Nevertheless, the criticism of underrepresented mathematics in STEM problem-solving assessment is an issue. In this study, we develop and investigate the psychometric evidence of an integrated STEM-based mathematical problem-solving test. The product of the test was a mathematical essay test that contains three scientific scenarios related to the environment in every middle school grade. The mathematical contents were integrated into engineering-based design using the technology. Three experts filled an assessment sheet to assess content validity, which was analyzed using a content validity index (CVI) and intraclass correlation coefficient (ICC). The result of content validity revealed that overall items were valid and reliable. The construct validity was examined using the Rasch analysis from the data of Grades 7–9 students in Indonesia (n = 286). The construct of all scenarios and prompting items indicated fit with various difficulty levels and acceptable discrimination value. Nevertheless, four prompting items were reported as misfit based on unweighted mean square value. The recommendation for improvement is emphasized in the language clarity aspect. The inter-rater reliability was also declared good. A further study is suggested to provide a computer-based test.

Design and Validation of a Test for the Types of Mathematical Problems Associated with Reading Comprehension

Being able to understand a written text is an essential life skill, as is solving a problem, which configures a bidirectional relationship between both skills. With regard to reading comprehension, at least three specific levels are required to achieve a full understanding of a text: literal, inferential, and critical. For its part, mathematics has changed substantially in recent decades, prioritizing problem-solving as the central axis of the teaching process as it constitutes a resource for learning. This study connects both skills and aims to design and validate a mathematical problem-solving test contextualized to the quadratic function, to assess the level of reading comprehension of secondary school students. The study is nonexperimental, cross-sectional, and focused on psychometric aspects since it aims to validate a measurement instrument. It was applied on a pilot basis to three municipal secondary education courses in Chile. The content, construct, discrimination, and reliability validation tests carried out allowed us to demonstrate that the problem-solving test contextualized to the quadratic function is a reliable instrument to produce knowledge in educational research.

The effects of E-learning based on a creatively cooperative method on student’s self-regulation ability in mathematics

This study aims to determine the effect of the creatively cooperative learning method on students’ self-regulation abilities in mathematics. This study employed quantitative research with a One-Group Posttest-only design. The research participants were 93 students from the seventh grade at a secondary school. The data were collected using a mathematical problem-solving test and a self-regulated ability questionnaire. The data were analyzed using linear regression analysis. This study indicates that the implementation of the creatively cooperative learning method positively influences students’ self-regulated abilities in mathematics. This study informs educators about the importance of creatively cooperative learning methods to improve students’ self-regulation abilities in mathematics and achievement. Thus, educators can combine the creatively cooperative learning method to make effective and suitable teaching materials or learning plans. Keywords: mathematics learning; self-regulation ability; creative cooperative; learning methods; students’ creativity

Enhancing Upper Secondary Learners’ Problem-solving Abilities using Problem-based Learning in Mathematics

Developing problem-solving abilities is a major objective of learning mathematics at school. However, learners’ problem-solving abilities are still critical. The main purpose of this study was to investigate how the problem-based learning model could enhance learners’ problem-solving abilities in mathematics. The study used quasi-experimental research with one group pre-test-post-test design. The population in this study consisted of fifty-four grade eleven learners (aged between 16 to 19 years old) from one school in Kayonza District in Rwanda. Data were collected using mathematical problem-solving tests and interviews and were analysed using paired t-tests for dependent sample means and descriptive analysis. The study results indicate that problem-based learning potentially impacts learners’ problem-solving abilities. It is shown from learners’ work in problem-solving that all indicators of problem-solving abilities, namely understanding the problem, planning ways to approach the problem, monitoring the progress while tackling the problem and reviewing the solution process, emerged as being fairly well improved. In addition, based on the interview results from some learners and their teachers, they like the PBL model because embedded tasks helped them to apply the knowledge that can improve their reasoning, creativity and thinking capability. The study recommends that schools encourage teachers to adopt PBL for enhancing learners’ problem-solving abilities. Additionally, researchers are urged to use findings from this study as a reference for further research. Furthermore, researchers could conduct similar research on a large scale using different methodologies.

AKM content: developing a mathematical problem-solving test based on Islamic context at MTs

The low utilisation of mathematical problem-solving tools makes students need additional skills. Multiple schools/madrasahs do this. Islamic schools like madrasas should also teach Islamic ideals. However, mathematical tools must show this integration. This project aims to create an Islamic-based mathematics problem-solving test for AKM at the Madrasah Tsanawiyah level. This research follows Thiagarajan's five-step R&D approach. A test instrument comprising 30 essay tests in four packages was created. This study involved Mts class VIII or IX pupils. The research shows that the Islamic context-based mathematics problem-solving ability test instrument for Madrasah Tsanawiyah AKM content is good. Experts and students evaluate this quality. Expert reviews indicate that the device fits mathematical content, Islamic settings, and language. Student testing results reveal that the test equipment is valid and trustworthy. However, the test questions' difficulty level should be better dispersed and discussed.

Mathematical problem-solving ability of junior high school students

Mathematical problem solving is the process of using students' knowledge to find solutions to problems. Students are This study aims to describe the ability of mathematical problem solving in circle content. This research focuses on solving problems based on 4 stages of Polya, namely the ability to solve problems, organize, plan, and check results. This research uses descriptive qualitative method. The research subjects were 6th grade students of SMPN 1 Meureudu as many as 6 people. The selection of subjects was done by purposive sampling with the criteria that students who were recommended by mathematics’ teachers based on the best grades and had participated in at least one Math Olympiad. The research instrument used mathematical problem-solving tests and interviews. Data analysis technique is done by analyzing student work data, interpreting, and concluding. The results of data analysis showed that students' mathematical problem-solving abilities were still low. The low problem-solving ability is seen based on indicators of problem-solving ability that cannot be achieved by most students

Development of the Mathematical Problem-Solving Ability Using Applied Cooperative Learning and Polya’s Problem-Solving Process for Grade 9 Students

The purposes of the study were 1) to investigate the effectiveness of the applied cooperative learning and Polya’s problem-solving process on grade 9 students’ mathematical problem-solving ability, 2) to compare grade 9 students’ learning achievement before and after learning through the applied cooperative learning and Polya’s problem-solving process, and 3) to study the students’ satisfaction toward learning through the applied cooperative learning and Polya’s problem-solving process. The participants were 18 grade 9 students in a Thai secondary school selected by the stratified random sampling method. The instruments were 1) an applied cooperative learning and Polya’s problem-solving process learning management, 2) a mathematical problem-solving test, 3) a learning achievement test, and 4) a satisfaction questionnaire. The data were analyzed using percentage, mean score, standard deviation, one-sample t-test, paired-samples t-test, and effectiveness test with the criteria of 70. The results of the study indicate that 1) the learning management designed using the applied cooperative learning and Polya’s problem-solving process was effective in developing students’ mathematic problem-solving ability, 2) the students’ learning achievement of surface area and volume in the posttest was higher, and 3) the students were satisfied with learning with the lesson plans using the applied cooperative learning and Polya’s problem-solving process. The results could be applied in both mathematics classrooms and similar research studi area of mathematics instruction.

UPAYA MENINGKATKAN KEMAMPUAN PEMECAHAN MATEMATIS SISWA MELALUI PEMBELARAN BERBASIS IT (GEOGEBRA)

The industrial revolution 4.0 is a formidable challenge for the world of education, one of which is learning mathematics. Moreover, in the current Covid-19 condition, which requires that learning be carried out by e-learning, the level of students' mathematical problem solving abilities is getting lower. To overcome this problem, this study applied an IT-based learning model (geogebra). The objectives of this research are to know the improvement of students' mathematical problem solving, the improvement of students' mathematical learning activities, and the improvement of the teacher's ability to manage learning. This type of research is Classroom Research. The analytical technique used is descriptive. The results of this study seen from the results of students' mathematical problem solving tests increased by 33.33%. Student activity in learning increased by 23.43%. The ability of teachers to manage learning increased by 36%. So the results of this study show that the IT-based learning model (geogebra) can improve students' mathematical problem solving, student activities in class X Multimedia I SMK Negeri 4 Padangsidimpuan.