Problem-solving Test Research Articles

Mathematical Creativity, Mathematics Self-Efficacy, and Mathematics Problem-Solving Performance of High School Students in Different Curricular Programs

This descriptive-correlational study generally aimed to determine if mathematics self-efficacy and mathematical creativity can predict mathematics problem-solving performance of high school students. Further, it also aimed to determine the level of mathematics self-efficacy, level of mathematical creativity, and level of problem-solving performance of high school students as a whole and when classified according to curricular program. The respondents of this study were the two hundred twenty-four (224) high school students enrolled in a national high school in Iloilo. Cluster sampling was used to determine the participants in the study. Three researcher-made instruments were used in this study: the Mathematics Self-Efficacy Rating Scale (MSERS), the Mathematical Creativity Test (MCT), and the Mathematics Problem-Solving Test (MPST). These instruments were content-and face-validated by a panel of three experts and were pilot tested to determine their administrability. Mean and standard deviation were employed for the descriptive analysis of the study. The inferential statistical tools employed were the Oneway Analysis of Variance (ANOVA), Pearson’s Product-moment Correlation Coefficient (Pearson’s r) and the Stepwise Multiple Linear Regression Analysis, all set at .05 alpha level of significance. This study found that the participants’ level of mathematics self-efficacy and mathematics problem-solving performance when taken as an entire group was average, while their level of mathematical creativity, as a whole and in terms of fluency, flexibility, and originality, was moderately low. It was also found out that there existed a significant difference in self-efficacy; creativity in terms of fluency, flexibility, and originality; and mathematics problem- solving performance when the participants were classified according to curricular program. In addition, it was found that a moderate positive correlation existed between the participants’ mathematics self-efficacy and their mathematical creativity. Finally, the result of this study revealed that mathematics self-efficacy and mathematical creativity are predictors of mathematics problem-solving performance when participants were taken as a whole group. When classified according to curricular program, mathematics self-efficacy and mathematical creativity are predictors in the Regular Class participants but not in the Special Science Class, School for the Arts, and School of the Future participants. Furthermore, mathematical creativity was found to be the best predictor of mathematics problem solving performance when participants were taken as a whole group and when classified as to curricular program

Hubungan Gaya Kognitif Siswa Dengan Kemampuan Pemecahan Masalah Matematika

This article discusses the relationship between students' cognitive style and mathematical problem-solving abilities in the number pattern material carried out at SMP Negeri 1 Botupingge in the odd semester of the 2021/2022 academic year. The research method used is a survey method with a correlational approach, with a questionnaire instrument to determine students' cognitive style and problem-solving tests to measure students' mathematical problem-solving abilities. The results showed that the correlation coefficient between students' cognitive styles and mathematical problem-solving abilities was 0.60, which means that there is a relationship between students' cognitive styles and mathematical problem-solving abilities at a high level. The coefficient of determination of 0.36 indicates that 36% of the contribution of cognitive style to the improvement of mathematical problem-solving abilities, and the remaining 64% is determined by other factors.

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.

Mathematical Error Patterns to Facilitate Solving Math Problems for Junior High School Students

Mathematical understanding is important in problem-solving. This study aimed to find patterns of mathematical understanding errors in solving mathematics problems for junior high school students. The method used in this study is qualitative. Data collection uses triangulation. Interviews were conducted on three subjects during one month at Islamic Junior High School. Data collection techniques are carried out through triangulation, namely test results, interviews, and observations. The intrusion used is a math problem-solving test. This study found patterns of errors in solving mathematical problems in the field of geometry. From the results, it was found that the biggest error pattern was in calculating the area and perimeter of rectangles and parallelograms. Stakeholders can also use the results of this research in education to encourage understanding of geometric concepts in education at the secondary level. This study offers educational authorities policy options regarding the importance of understanding mathematics in general and geometry in particular for students.

A-123 Problem Solving and Mental Workload in Binge and Non-Binge Drinking College Students

Abstract Objective: Chronic sustained alcohol abuse is known to impact cognitive functioning. We examined potential differences in problem solving ability and mental workload in a more short-term population, binge-drinking college students. Method: Binge-drinking (BD) (n = 129) and non-binge-drinking (NBD) (n = 163) college students completed a computerized test of problem solving, a 3-disk and 4-disk version of the Tower of Hanoi (TOH). After each TOH session, they also completed an assessment of mental workload via the NASA-Task Load Index (NASA-TLX). Mental workload was defined as the Mental Demand subscale of the NASA-TLX. Results: No significant group difference was found in mean number of moves to complete the TOH in either the 3-disk version or 4-disk version. For mental workload, no difference was evident for the 3-disk TOH (BD M = 28.81, SD = 21.05 vs NBD M = 27.09, SD = 21.59, p = 0.497), but there was a difference for the 4-disk TOH condition (BD M = 47.22, SD = 21.86 vs NBD M = 41.84, SD = 22.94, p = 0.044). Conclusion(s): While no group differences in test performance were evident, there was a difference in mental workload on the more difficult TOH condition. We propose that mental workload, which is not normally considered in neuropsychology, might be a valuable tool in assessment of cognitive status, especially when there are subtle cognitive differences. In this case, even with similar test performance, cognitive status might not necessarily be the same between the two groups, with the BD group showing greater mental workload.

Can Video Gameplay Improve Undergraduates' Problem-Solving Skills?

In this study, the authors investigated if two distinct types of video gameplay improved undergraduates' problem-solving skills. Two groups of student participants were recruited to play either a roleplaying video game (World of Warcraft; experimental group) or a brain-training video game (CogniFit; control group). Participants were measured on their problem-solving skills before and after 20 hours of video gameplay. Two measures were used to assess problem-solving skills for this study, the Tower of Hanoi and The PISA Problem Solving Test. The Tower of Hanoi measured the rule application component of problem-solving skills and the PISA Problem Solving test measured transfer of problem-solving skills from video gameplay to novel scenarios on the test. No significant differences were found between the two groups on either problem-solving measure. Implications for future studies on game- based learning are discussed.

Applying functional near-infrared spectroscopy and eye-tracking in a naturalistic educational environment to investigate physiological aspects that underlie the cognitive effort of children during mental rotation tests.

Spatial cognition is related to academic achievement in science, technology, engineering, and mathematics (STEM) domains. Neuroimaging studies suggest that brain regions’ activation might be related to the general cognitive effort while solving mental rotation tasks (MRT). In this study, we evaluate the mental effort of children performing MRT tasks by measuring brain activation and pupil dilation. We use functional near-infrared spectroscopy (fNIRS) concurrently to collect brain hemodynamic responses from children’s prefrontal cortex (PFC) and an Eye-tracking system to measure pupil dilation during MRT. Thirty-two healthy students aged 9–11 participated in this experiment. Behavioral measurements such as task performance on geometry problem-solving tests and MRT scores were also collected. The results were significant positive correlations between the children’s MRT and geometry problem-solving test scores. There are also significant positive correlations between dorsolateral PFC (dlPFC) hemodynamic signals and visuospatial task performances (MRT and geometry problem-solving scores). Moreover, we found significant activation in the amplitude of deoxy-Hb variation on the dlPFC and that pupil diameter increased during the MRT, suggesting that both physiological responses are related to mental effort processes during the visuospatial task. Our findings indicate that children with more mental effort under the task performed better. The multimodal approach to monitoring students’ mental effort can be of great interest in providing objective feedback on cognitive resource conditions and advancing our comprehension of the neural mechanisms that underlie cognitive effort. Hence, the ability to detect two distinct mental states of rest or activation of children during the MRT could eventually lead to an application for investigating the visuospatial skills of young students using naturalistic educational paradigms.

Foraging on anthropogenic food predicts problem-solving skills in a seabird

Species and populations with greater cognitive performance are more successful at adapting to changing habitats. Accordingly, urban species and populations often outperform their rural counterparts on problem-solving tests. Paradoxically, urban foraging also might be detrimental to the development and integrity of animals' brains because anthropogenic foods often lack essential nutrients such as the long-chain omega-3 fatty acids eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), which are important for cognitive performance in mammals and possibly birds. We tested whether urbanization or consumption of EPA and DHA are associated with problem-solving abilities in ring-billed gulls, a seabird that historically exploited marine environments rich in omega-3 fatty acids but now also thrives in urban centres. Using incubating adults nesting across a range of rural to urban colonies with equal access to the ocean, we tested whether urban gulls preferentially consumed anthropogenic food while rural nesters relied on marine organisms. As we expected individual variation in foraging habits within nesting location, we characterized each captured gulls' diet using stable isotope and fatty acid analyses of their red blood cells. To test their problem-solving abilities, we presented the sampled birds with a horizontal rendition of the string-pull test, a foraging puzzle often used in animal cognitive studies. The isotopic and fatty acid profiles of urban nesters indicated a diet comprising primarily anthropogenic food, whereas the profiles of rural nesters indicated a high reliance on marine organisms. Despite the gulls' degree of access to urban foraging habitat not predicting solving success, birds with biochemical profiles reflecting anthropogenic food (less DHA and a higher carbon-13 ratio in their red blood cells) had a greater probability of solving the string-pull test. These results suggest that experience foraging on anthropogenic food is the main explanatory factor leading to successful problem-solving, while regular consumption of omega-3s during incubation appears inconsequential.

Development of BioPhy Magazine Containing Local Wisdom to Improve Problem Solving Ability and Promote Environmental Awareness Campaign

The purpose of this study was to describe the validity and effectiveness of BioPhy Magazine based on local wisdom, which was developed to improve problem-solving skills and encourage students to conduct environmental awareness campaigns. This type of research was development research with the Tessmer formative evaluation model. The small group trial subjects are Chemistry Tadris students who are taking Basic Physics courses in the 2021/2022 academic year. Data were obtained through validation sheets, problem-solving tests, and poster assessment sheets. The data were then analyzed using the Aiken formula, N-gain, effect size, and Wilcoxon test. The results of the analysis showed that the developed magazine was valid from the aspect of content, presentation, and language. Magazines were also effective in improving problem-solving skills, with an N-gain score on the small group test of 0.90 with a high category and an effect size of 3.34 with a strong influence category. In addition, based on the Wilcoxon test, it was known that Asymp. Sig. (2-tailed) of 0.005, which meant that there was a significant difference in problem-solving ability between before and after learning. In addition, magazines could encourage students to carry out environmental awareness campaigns as indicated by the average student environmental poster score of 95.38. So, BioPhy Magazine was valid, effective, and successful in encouraging students to carry out environmental awareness campaigns

PROFIL PEMECAHAN MASALAH TEOREMA PYTHAGORAS DITINJAU DARI PERBEDAAN GAYA KOGNITIF SISWA

One of the abilities to be achieved through learning mathematics is the ability to solve problems. The problem is not just found in mathematics but also in their daily activity. The student needs to know how to solve a problem because there are many problems in the future that they must solve. Problem-solving in every student is different. The cause is the cognitive style that the student has. The student receives, manages, and makes the conclusion according to their cognitive style. The study aims to describe students' mathematical problem-solving abilities on the Pythagorean theorem material concerning field-independent and field-dependent cognitive styles. The method uses a qualitative descriptive approach with problem-solving test instruments, interview guidelines, and GEFT tests. Determination of the subject using the GEFT test to obtain a subject with an independent field of cognitive style and independent field of 2 subjects each. Problem-solving tests and interviews were used to obtain data on the subject's problem-solving abilities. The problem-solving indicator used is based on Polya's theory. The results showed that the subject with independent field cognitive style was able to do problem-solving well. While the subject with a field-dependent cognitive style is quite capable of solving problems, this is because there are some mistakes in writing answers. However, based on the interview, it was found that the subject was able to solve the problem but was in a hurry to solve the problem.

THE EFFECT OF PHET-COLORADO ASSISTED PROBLEM BASED LEARNING LEARNING MODEL ON LEARNING OUTCOMES AND PROBLEM SOLVING DYNAMIC ELECTRICAL MATERIALS IN JUNIOR HIGH SCHOOLS

This study aims to determine the effect of applying the PhET-Colorado-assisted problem-based learning (PBL) learning model on the learning outcomes and problem solving of junior high school students in class IX on Dynamic Electricity. The study was conducted using experimental quasi pretest-postest in one of the country’s junior high schools on the ground. Sample taking technique using purposive sampling. The research sample consisted of two classes each consisting of 32 students, class IX-J was an experimental class that applied the PhET-Colorado-assisted problem-based learning (PBL) model and class IX-D was a control class that applied study conventional. The research instrument used was a multiple-choice test with 4 answer choices to measure cognitive learning outcomes and description tests for students' problem-solving tests on dynamic material. The average pretest and posttest data on learning outcomes in the experimental class were 49.37 and 80.31, while those in the control class were 51.09 and 66.40, respectively. The average pretest and posttest data on student problem solving in the experimental class were 35.31 and 72.12, while in the control class they were 36 and 66.40, respectively. Data were analyzed using the Manova test (multivariate analysis of variance). Based on the hypothesis test, there are significant differences in learning outcomes and problem solving with the application of the PhET-Colorado-assisted Problem Based Learning (PBL) model on science material in junior high schools, so that there is an effect of the PhET-Colorado-assisted Problem Based Learning (PBL) model on learning outcomes and solving student problems. The percentage increase in N-gain learning outcomes in the experimental class was 62.09 in the medium category and the control class was 30.48 with the medium category, and problem solving in the experimental class was 56.90 with the medium category and the control class was 22 with the low category

Students’ problem-solving ability in number patterns topic viewed from cognitive styles

Mathematical problem-solving skills are essential. However, students’ ability to solve number patterns problems topic has not been optimal. The results of previous studies show different problem-solving skill profiles in students with Field Dependent (FD) and Field Independent (FI) cognitive styles in geometry and algebra. Therefore, this study aims to describe the problem-solving ability of students in number patterns based on cognitive styles. The research used qualitative methods with a descriptive approach. The study involved all students of grade 8 at a public junior high school in Klaten Regency, Central Java, Indonesia. Four students were selected for in-depth analysis by administering the Group Embedded Figure Test (GEFT) test and many patterns problem-solving test. Instruments used in this study included the GEFT test and the problem-solving test of number patterns. Research data was collected through a test, interviews, and documentation. The triangulation was applied to validate the data. Data were processed by reducing data, presenting data, and verifying. The results showed that FI students are better able to solve number pattern problems than FD students. It can be seen that FD students can understand the problem, devise a plan, and carry out the plan. However, FD students have been unable to look back at the solutions. Meanwhile, FI students can understand problems, devise a plan, carry out the plan, and look back at the solutions well. Therefore, it is needed to focus more on enhancing FD students’ ability in the stage of looking back.

Developing mathematical problem-solving skills in primary school by using visual representations on heuristics

Developing students’ skills in solving mathematical problems and supporting creative mathematical thinking have been important topics of Finnish National Core Curricula 2004 and 2014. To foster these skills, students should be provided with rich, meaningful problem-solving tasks already in primary school. Teachers have a crucial role in equipping students with a variety of tools for solving diverse mathematical problems. This can be challenging if the instruction is based solely on tasks presented in mathematics textbooks. The aim of this study was to map whether a teaching approach, which focuses on teaching general heuristics for mathematical problem-solving by providing visual tools called Problem-solving Keys, would improve students’ performance in tasks and skills in justifying their reasoning. To map students' problem-solving skills and strategies, data from 25 fifth graders’ pre-tests and post-tests with non-routine mathematical tasks were analysed. The results indicate that the teaching approach, which emphasized finding different approaches to solve mathematical problems had the potential for improving students’ performance in a problem-solving test and skills, but also in explaining their thinking in tasks. The findings of this research suggest that teachers could support the development of problem-solving strategies by fostering classroom discussions and using for example a visual heuristics tool called Problem-solving Keys.

Mindset and Levels of Conceptual Understanding in the Problem-Solving of Preservice Mathematics Teachers in an Online Learning Environment

Mindset plays a vital role in tackling the barriers to improving the preservice mathematics teachers’ (PMTs) conceptual understanding of problem-solving. As the COVID-19 pandemic has continued to pose a challenge, online learning has been adopted. This led this study to determining the PMTs’ mindset and level of conceptual understanding in problem-solving in an online learning environment utilising Google Classroom and the Khan Academy. A quantitative research design was employed specifically utilising a descriptive, comparative, and correlational design. Forty-five PMTs were chosen through simple random sampling and willingly took part in this study. The data was gathered using validated and reliable questionnaires and problem-solving tests. The data gathered was analysed using descriptive statistics, analysis of variance, and simple linear regression. The results revealed that the college admission test, specifically numerical proficiency, influences a strong mindset and a higher level of conceptual understanding in problem-solving. Additionally, this study shows that mindset predicts the levels of conceptual understanding in problem-solving in an online environment where PMTs with a growth mindset have the potential to solve math problems. The use of Google Classroom and the Khan Academy to aid online instruction is useful in the preparation of PMTs as future mathematics teachers and problem-solvers. Further studies may be conducted to validate these reports and to address the limitations of this study.

The Effect of Problem-Based Learning on Students' Problem-Solving and Self-Learning Abilities in Acid-Base

This study aimed to determine students' problem-solving and independent learning on acid-base and involved 30 students of class XI MIA SMA Negeri 4 Maluku Tengah. The students were divided into two classes (experimental and control groups), and the chemistry teaching was conducted online because of the Covid-19 pandemic. Data were collected using problem-solving tests and self-learning ability questionnaires. The results showed that the experimental group (problem-based learning class) had better problem-solving and independent learning abilities than the control group (conventional method class). This result implies that problem-based learning improved students' problem-solving abilities and helped them provide appropriate solutions. Problem-based learning also helps students to learn more independently.

Kemampuan Spasial Siswa SMP Laki-Laki Maskulin dan Perempuan Feminin dalam Memecahkan Masalah Geometri

This study aims to describe the spatial ability of masculine male and feminine female students in solving geometric problems. The subjects of this study are one masculine male gender and one feminine female gender junior high school students who had the same mathematical ability. The subject selection was carried out using the Bem Sex Role Inventory instrument and Middle Semester Assessment scores, followed by conducting TPM (Problem Solving Test) and TPM-based interviews. The data collected from the TPM results and TPM-based interviews were then analyzed by applying the following steps: categorization, reduction, data presentation, interpretation, and conclusion. The results showed that subject-1 satisfied five indicators of spatial ability, namely spatial perception, visualization, spatial rotation, spatial relations, and spatial orientation so that it can be said to have high spatial abilities. On the other hand, subject-2 only meets three indicators of spatial ability, namely spatial rotation, spatial relation, and spatial orientation, so it can be said that female students have moderate spatial abilities. It is expected that the results of this study will be useful for future research and the mathematics learning process in schools

Blended Learning for Developing Problem-solving Skill, Learning Motivation, and Student Engagement in Mathematical Physics II Course During the COVID-19 Pandemic

This study aimed to identify the effects of teaching Mathematical Physics II (FIS1221) through blended learning during the COVID-19 pandemic on problem-solving skills, learning motivation, and student engagement at Ganesha University. The study followed a pre-experimental approach. The research subjects consisted of 27 fourthsemester students. The pre- and post-test data on the problem-solving ability were collected through a problem-solving test, while the learning motivation data were gathered using a questionnaire. Data on learning engagement were collected only post-test using a questionnaire. Data analysis was done descriptively, and t-test was used for analysing the problem-solving ability and learning motivation. Additionally, data on learning engagement were analyzed using the Wilcoxon Signed Rank Test. The results showed (1) a significant difference between the average score of the pre- and post-test problem-solving abilities; (2) a significant difference between the average score of the pre- and post-test learning motivation; and (3) a difference in student engagement scores with standard scores specified (a passing grade). Therefore, blended learning is an effective approach for developing problem-solving skills, learning motivation, and student engagement.
 Keywords: blended learning, problem-solving skill, learning motivation, student engagement

Analisis Kesalahan Siswa Sekolah Menengah Atas dalam Memecahkan Masalah Geometri

Problem solving in everyday life is closely related to mathematics. However, there are still many students who have not been able to solve the problem mathematically. This research is a qualitative descriptive study that aims to examine the mistakes made by high school students in solving problems on the subject of geometry based on Polya's problem solving steps. The subjects of this study were 19 grade 12 high school students who had completed their study period and were in the period of participating in the college selection. Research data obtained from problem solving tests and interviews on the subject. Based on the results of the research conducted, the mistakes that are mostly made by students are in planning problem solving and implementing problem solving plans. Errors made by students are caused by a lack of understanding of students in mastering the material and linking various materials so that they cannot solve problems logically and correctly. The results of this study recommend teachers to provide examples of problems and practice solving more complex problems so that students can minimize errors in solving problems. Keywords: Error Analysis, Problem Solving, Geometry, Senior High School Student

The effect of distance education on the problem-solving success of university students taking algebra and students' opinions on the practice

This study aims to examine the effect of distance education in formal education on the success of university students taking algebra in solving algebraic problems and to determine students' opinions on practice. The research design was determined as a posttest quasi-experimental design with a control group. The data collection tools of the research consist of the Algebra Problem Solving Test (APST) consisting of open-ended questions and the Semi-Structured Interview Form (SSIF). SPSS software package version 22.0 was used in the analysis of the data. As a result of the independent samples t-test, it was observed that there was no statistically significant difference between the posttest scores of the experimental and control groups obtained from APST. The qualitative data of the research were analyzed by content analysis. When the opinions of the experimental group students about the practice were examined, it was seen that they stated that distance education had various advantages, but they mostly experienced various difficulties. Students stated the disadvantages of distance education as not being able to ask questions, not feeling like in the classroom, not being motivated to the lesson, not being disciplined due to the comfort of a home environment, internet-related difficulties, inadequate communication, and socialization.

TRANSFORMATION OF PRE-SERVICE MATHEMATICS STUDENT'S ALGEBRA AND CALCULUS THINKING IN SOLVING DIFFERENTIAL EQUATION PROBLEMS

This study aims to analyze the transformation of algebraic thinking and calculus of preservice the mathematics students based on SOLO taxonomy in solving differential equations problems. The research subjects were 86 students in the mathematics education study program. Subject selection uses purposive sampling (students who take courses in differential equations). Data were collected using problem-solving tests and interviews which were then analyzed using the descriptive qualitative method with the following stages: (1) transcribing test and interview data, (2) coding segmentation, (3) analyzing student thinking transformations, and (4) concluding. The results showed that the transformation of algebraic and calculus thinking was used by students at each level of thinking to solve problems. The higher the level of thinking achieved, the better and the maximum transformation of algebraic and calculus thinking used by students. These results indicate that students need to be well supported and facilitated in problem-solving to achieve higher levels of thinking, such as the relational and extended abstract levels.