Mathematical Test Research Articles

ChatGPT’s performance in university admissions tests in mathematics

ChatGPT’s performance in university admissions tests in mathematics

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.

Mathematical connection skills of junior high school students in solving system of linear equations in two variables problems

Students mathematical connection skills are valuable dimension that teachers must put into consideration so that students can develop and link their mathematical skills with knowledge beyond Mathematics. This research aimed to analyze the mathematical connection skills of Junior High School students when solving the System of Linear Equations in Two Variables (Sistem Persamaan Linear Dua Variabel/SPLDV) problem. Students mathematical connection skills are valuable dimension that teachers must put into consideration so that students can develop and link their mathematical skills with knowledge beyond Mathematics. This research aims to analyze the mathematical connection skills of Junior High School students when solving the SPLDV problem. This research made use of Qualitative approach by which 18 students of grade VIII from SMP Argopuro 1 Panti Jember, East Java, participated. Mathematical connection skill test and interview guideline were conducted for this research. Data triangulation technique was used to process and compile data for the research report. The findings of the research discovered that students with high level of mathematical connection skills were able to relate and implement their knowledge to different kinds of situations, and students with medium level of mathematical connection skills were only able to apply their knowledge to simple situations, meanwhile students with low level of mathematical connection skills were unable to relate and implement their knowledge to a variety of situations.

Educational outcomes school year nine in children treated for acute lymphoblastic leukemia: A nationwide registry-based study from Sweden.

Acute lymphoblastic leukemia (ALL) constitutes approximately 25% of pediatric cancers, and with contemporary protocols, the 5-year survival rate is over 90%. Despite improved survival, neurocognitive impairments from treatment raise concerns. This registry study aimed to explore the impact of ALL treatment on educational outcomes from school year nine in Swedish children. A population-based cohort of 503 children diagnosed with ALL from 1990 to 2010 was identified from the Swedish Childhood Cancer Registry and matched with five controls each. Assessed variables were delayed graduation, high school eligibility, total merit value, school grades in Swedish, English, mathematics, and physical education, and results in national tests. Analyses were performed between cases and controls and by sex, age at diagnosis, and risk group. Our results showed that, compared to controls, cases had higher odds for delayed graduation, poorer results in physical education, and higher rates of absence in national tests in English and mathematics. Children in the standard-risk group (treated with first-line chemotherapy only) exhibited similar results to matched controls whereas children in the high-risk group (treated with cranial irradiation, hematological stem cell transplantation, or/and for ALL relapse and thus likely received also radiotherapy) had lower total merit value compared to controls. We conclude that Swedish children diagnosed with ALL between the years 1990-2010 mainly exhibited comparable educational outcomes to controls, although children in the high-risk group had lower results. These findings highlight the importance of evaluating especially children with high-risk ALL in order to identify those requiring educational support and for designing targeted interventions.

Writing PISA-Like Mathematics Items: The Case of Tertiary Mathematics Instructors from a State University in the Philippines

<p style="text-align:justify">Mathematics test items in International Large-Scale Assessments (ILSAs) such as the Programme of International Student Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS) are nested in contexts defined in their assessment framework (e.g., the Personal, Occupational, Societal, and Scientific contexts in PISA). This study followed the item-writing activities of four tertiary mathematics instructors in the Philippines as they constructed context-based mathematics items. They were tasked to write four items each, following a set of specifications for PISA content and context categories. The data consisted of transcripts from the focus-group discussion which was conducted days after the task. The transcripts were then analyzed using thematic analysis. The results of this study showed that the phenomenon of item-writing in the context of writing PISA-like mathematics items had two themes: the phases of item-writing and the dimensions of item-writing. Findings showed that the respondents struggled to find realistic contexts and that they engaged in a problem-solving task likened to solving a puzzle as they attempted to satisfy the content, context, and process categories in the table of specifications (TOS). This study contributes to filling in the research gap on item-writing activities, particularly those of mathematics teachers in the Philippines- a country whose recent mathematical performance in the PISA 2018, TIMSS 2019, and PISA 2022 was nothing short of dismal.</p>

Analyzing Student’s Mathematical Critical Thinking Ability of Concept Newman’s Error Analysis Review from Habits of Mind

This study aims to analyze and describe the mistakes made by students in completing mathematical critical thinking skills in terms of habits of mind (HOM) with three categories, namely limited, developing, and proficient. The review was also analyzed from the factors that led to the occurrence of errors based on error analysis according to Newman. This research uses qualitative research methods. The data collection techniques used are questionnaires, tests, and interviews. The instruments used are HOM questionnaires and mathematical critical thinking ability tests. The selection of the study subject was carried out purposively with the consideration that the subject had a HOM category. A total of 25 students who filled out the HOM scale and mathematical critical thinking ability test, 3 students were selected to be interviewed based on the HOM category classification. The data analysis techniques used in this study are data reduction, data presentation, and drawing conclusions. Based on the results of the study, students with limited HOM were only able to solve questions up to indicator 1 because they made mistakes in reading and process skills. Students with HOM develop, only able to solve problems up to indicator 2 due to Comprehension and transpormation errors. Students with proficient HOM, are able to solve questions up to indicator 3 because they make mistakes in the skill and encoding process.

Computational Thinking Readiness Level of First-Year Students of Mathematics Education

The main objective of this study was to measure the level of computational thinking readiness in prospective first-year mathematics education students. In addition, this study also aims to identify factors that influence their level of readiness towards computational thinking. This research is qualitative and descriptive in nature. This study describes first-year mathematics education students' mathematical computational thinking ability based on the theory of mathematical computational thinking. This study was conducted on first-year mathematics education students in the academic year 2023/2024. There were 16 first-year mathematics education students, all of whom were taken as samples in this study, to obtain more in-depth information about the computational thinking ability of first-year mathematics education students for further research development. The instruments used to collect data on first-year mathematics education students' mathematical computational thinking ability are (1) a mathematical computational thinking ability test and (2) an interview. The data obtained were calculated using statistical tests, and the results will be explained in depth. The mean score of the first-year mathematics education student's computational thinking ability test was 59.68, indicating that students generally have a fairly good level of computational thinking ability.

Dimensional versus Categorical Approach: A Comparative Study of Mathematical Cognition

BackgroundResearchers have employed two distinct methods to understand the cognitive underpinnings of mathematical ability: categorical and dimensional. These two methods have different underlying assumptions. However, to the best of our knowledge, research to date has not empirically tested which method can better predict variance in mathematical ability. Method104 children from Indian public schools in the 3rd and 4th grades completed a mathematical ability test. For the categorical approach, participants were categorized into two groups: mathematical learning difficulty and high math achieving. For the dimensional approach, the data of all participants were considered. The cognitive abilities measured included approximate number system, working memory, inhibitory control, and spatial ability. ResultsMixed factorial ANOVA and hierarchical regressions revealed that the dimensional approach demonstrated better predictive power for mathematical ability than the categorical approach. ConclusionsThe dimensional approach offers a more comprehensive insight into mathematical cognition, enabling greater control over the predictors.

Mathematics Self-Efficacy and Study Habit as Predictors of Achievement of Senior Secondary School Students

This study therefore looked at Mathematics Self-Efficacy and Study Habit as Predictors of Academic Achievement of Senior Secondary School Students in Ijebu Ode Local Government Area, Ogun State, Nigeria. Three hypotheses that were examined at the 0.05 significance level served as the study's compass. Descriptive survey was used, 500 students sampled from 10 senior secondary schools in Ijebu ode using simple random sampling techniques. mathematical achievement test, study habit scale, and self-efficacy scale constitute the instruments, validated and demonstrates reliability coefficients of 0.78, 0.81 and 0.86. The results shows that self-efficacy and study habit will accurately forecast students' academic success in mathematics (F =38.328, p < 0.05 & F =35.011, p < 0.05) and jointly predict students' proficiency in mathematics (F = 49.136, p < 0.05). The conclusion derived is that both Study habits and self-efficacy are significant predictors of academic achievement of senior secondary school students in mathematics.

Structural and transcriptional signatures of arithmetic abilities in children

Arithmetic ability is critical for daily life, academic achievement, career development, and future economic success. Individual differences in arithmetic skills among children and adolescents are related to variations in brain structures. Most existing studies have used hypothesis-driven region of interest analysis. To identify distributed brain regions related to arithmetic ability, we used data-driven cross-validated predictive models to analyze cross-sectional behavioral and structural MRI data in children and adolescents. The gray matter volume (GMV) of widespread brain regions reliably predicted arithmetic abilities measured by the Comprehensive Mathematical Abilities Test. Furthermore, we applied neuroimaging-transcriptome association analysis to explore transcriptional signatures associated with structural patterns of arithmetic ability. Structural patterns of arithmetic ability primarily correlated with transcriptional profiles enriched for genes involved in transmembrane transport and synaptic signaling. Our findings enhance our understanding of the neural and genetic mechanisms underlying children’s arithmetic ability and offer a practical predictor for arithmetic skills during development.

Teachers’ health and the students’ academic achievement: A systematic review of literature.

The purpose of this review was to synthetize available evidence on the relationship between school teachers’ health and students’ academic achievement. Methods. Systematic searches were conducted, through electronic searches until June 2017. Nine articles fit criteria for analysis. Results. Regarding teachers’ health, all studies investigated variables related to teachers’ mental health, such as: stress, mathematics anxiety, burnout, depression and wellbeing. As a measure of academic achievement, mathematic tests were the most common outcomes. Eight studies reported that students in classes with teachers suffering from mental health problems have lower scores on standardized tests. Conclusions. When teachers suffer mental health problems, they can negatively impact students’ academic achievement. Further research is needed to understand the causes of mental health problems in teachers and to establish the best alternatives to prevent these issues.

Dispersal of optimal foragers in a patchy environment: Simulations with a mathematical model and tests of predictions in field experiments

To predict the effect of density on the dispersal of foraging parasitoids, we developed a spatially explicit individual-based model in which parasitoids move among host patches at random but use an optimal decision-rule about when to leave these patches. We used a simple decision rule where an individual forager exploits a patch as long as the instantaneous attack rate is higher than the average attack rate it has experienced in the environment. Such a rule implies that foragers compute and remember attack rates as they forage. Simulations with different combinations of patch distribution, host density, mutual interference, and parasitoid density predicted that dispersal distance should increase with parasitoid density. To test this prediction, we used data from two field experiments in which we released either few or many adults of the aphid parasitoid Aphelinus asychis in replicated sites, and subsequently assessed dispersal from the spatial distribution of parasitoid offspring. In the first experiment, we did not to detect a relation between the number released and dispersal distance, but in the second experiment, dispersal distance increased with initial density, as predicted by our model. We propose two hypotheses to explain the discrepancy between the experiments. Different levels of environmental variability among experiments, resulting from differences in experimental designs, could cause differences in statistical conclusions. However, there could be a threshold density below which dispersal is not density-dependent, and this threshold may have been exceeded in the second experiment where large releases involved many more individuals than in the first experiment. In any case, our approach linked individual behavior and spatial distribution, and our results show that the insect distributions in the field can be predicted, qualitatively, from theory about individual behavior.

Student composition, equity, and mathematics learning outcomes during a time of educational reforms in Ethiopia

ABSTRACT This paper assesses the extent to which the implementation of a complex educational reform in Ethiopia was associated with changes in mathematics test scores for Grade 4 pupils from 2012–13 to 2018–19. During this period, while mathematics teachers’ educational qualifications and teacher content knowledge in mathematics improved, students in 2018–19 achieved, on average, lower test scores in mathematics than those in 2012–13. However, they also showed, on average, greater progress in mathematics test scores. Progress in mathematics test scores over the school year was associated with teacher content knowledge, but the magnitude of this association was larger in 2018–19 and was especially important for weaker students. The key to reconciling these paradoxical findings is to recognise that the reforms that underpin these improvements in school quality may well be working in multiple ways, changing the composition of the student body who attend school as well as increasing the amount of learning that takes place in the classroom, particularly among disadvantaged students.

Development of domino media to improve problem solving and mathematical communication for Islamic boarding school students

Mathematical problem solving and communication skills are important factors in learning mathematics. Therefore, it is necessary to develop learning media, especially in Islamic boarding school curricula where the learning load is greater than the regular curriculum. On this basis, the aim of this research is to develop domino card media to improve problem solving and mathematical communication skills of Islamic boarding school students. Development was carried out at Al-Izzah IIBS Batu Middle School, Malang, using the ADDIE model. Data obtained from documents, observations, questionnaires and tests were analyzed using qualitative and quantitative approaches. Based on the results of the validation analysis, the domino card media was declared valid from the aspects of design, material, curriculum, consistency, language, practicality, problem solving development and mathematical communication. Meanwhile, the effectiveness of using domino card media in learning is classified as effective, if seen from the results of the problem solving ability test with an N-Gain score of 76.79%, and the results of the mathematical communication ability test with an N-Gain score of 61.79%. Many factors cause this non-optimality, including a lack of mathematics lesson hours, a busy lesson schedule that is less suited to conditions, many demands on students, and the learning load in the curriculum.

A Review on the Progress of QbD Approach in Nanosystems Optimization: Current Updates and Strategic Applications

: Nanotechnology has made great strides in developing targeted drug delivery systems over the past few decades. These systems have garnered attention for their unique biological properties and ability to deliver drugs in a stable and sustainable manner. Despite these advances, there are still concerns about quality, efficacy, and safety. Many fabrication techniques still need to be refined to address the complex structures and non-standard manufacturing processes that can impact the quality of drug delivery systems. Recently, optimization techniques such as Quality by Design (QbD) have gained popularity in the pharmaceutical industry. QbD is a structured approach that addresses many technological and trait-related issues by providing a deep understanding of the product and its operations. This review examines the current state of QbD in the design of various nano-drug delivery systems, including lipid nanoparticles, lipid carriers, nano micelles, beaded drug delivery systems, nanospheres, cubosomes, and novel cosmeceuticals. Various mathematical models and statistical tests have been used to identify the parameters that influence the physical characteristics of these nanosystems. Critical process attributes such as particle size, yield, and drug entrapment have been studied to assess risk factors during development. However, critical process parameters are often identified through trial and error. This review highlights common material attributes and process parameters that affect the quality of nano-drug delivery systems. Hence, this survey has disclosed the various material attributes and process parameters, quality variables of different nano-drug systems. QbD designs such as Central drug composite, Design of experiment, D-optimal Design, Box-Benkhen Design, and Face center Design in optimizing the nanosystems have also been added. Conclusively, QbD optimization in nano drug delivery systems is expected to be a time-honored strategy in the forthcoming years.

Students' Critical Thinking in Solving Numeracy Problems: A Case Study of Students with High Self-Efficacy

Critical thinking is a 21st century skill that allows students to think reflectively and reason in making decisions. Students' critical thinking influences success in solving numeracy problems. This study aims to explain the ability to think critically in solving numeracy problems with high self-efficacy. The study employed a qualitative approach and phenomenological method. Data collection involved the use of the Group Embedded Figures Test (GEFT), self-efficacy questionnaires, and numeracy assessments in mathematics, specifically on topics related to cubes and rectangular prisms. Data analysis comprised data condensation, data presentation, and conclusion drawing. Based on GEFT and self-efficacy questionnaire results, one class V-B student with a field-dependent cognitive style and high self-efficacy was selected for further critical thinking skills assessment. Based on the results the student with a field-dependent cognitive style and high self-efficacy demonstrated notable strengths. In the process of basic clarification, the student met the indicators for analyzing arguments and formulating statements, effectively presenting their arguments. When providing reasons for decisions, the student showed the ability to consider the credibility of sources by selecting appropriate problem-solving strategies. However, she occasionally made calculation errors due to inaccuracy. In the process of concluding, the student met the indicators for making and evaluating decisions, successfully composing conclusion sentences that aligned with the problems and final answers. Students with field dependent cognitive style and high self efficacy are able to fulfill all indicators of critical thinking by using their ability to solve critical thinking problems. He excelled in verbal ability at the time of the interview by explaining the argument of the problem and the answer, but his weakness is less thorough in working so that the results obtained are less precise.

Development of an Instructional Model to Enhance Mathematical Literacy for Secondary Students

This study aims (1) to develop an instructional model to enhance mathematical literacy for secondary students and (2) to examine the effects of using this instructional model. The sample group consisted of students from Lampabpla Wittayakarn School, under the jurisdiction of the Surin Secondary Educational Service Area Office in Thailand by using cluster random sampling, during the second semester of the 2021 academic year. Fifteen students from Grade 9/2 were selected as the experimental group, and 15 students from Grade 9/1 were selected as the control group. The data collection tools: 1) interviews; 2) focus group discussion; 3) mathematical literacy tests; and 4) student satisfaction questionnaires. The statistics used for data analysis include percentage, arithmetic mean, standard deviation, dependent and independent t-test. The research findings revealed that (1) the instructional model to enhance mathematical literacy for secondary students comprises six components: 1) principles and basic theoretical concepts, 2) objectives of the model, 3) instructional management procedures, 4) social system, 5) principles of response, and 6) support system. (2) results of using the instructional model showed that: 1) the experimental group of students had markedly higher mathematical literacy after the intervention compared to before, at the .05 significance level; 2) the experimental group had significantly higher mathematical literacy than the control group, at the .05 significance level; and 3) the experimental group reported the highest level of satisfaction with the instructional model to enhance mathematical literacy for secondary students, with an average score of 4.50 and a standard deviation of 0.17.

Development of Learning Achievement and Motivation in Learning Mathematics of Grade 10 Students by Cooperative Learning

This research developed academic achievements to attain a pass rate of 70% and assessed student motivation in studying mathematics. The target group consisted of 40 Grade 10 students during the second term of the 2023 academic year at Sarakham Pittayakhom School under the Mahasarakham Secondary Educational Service Area Office. The tools used in this research included (1) a plan for organising 12 cooperative learning activities, (2) a mathematical achievement test on the topic of logarithmic functions, (3) a measure of mathematical learning motivation and (4) a diary record. Statistical data included percentages, means and standard deviations. Content analysis was employed as qualitative data and the action research model was divided into three cycles as Cycle 1 organized cooperative learning activities using the TAI technique with 40 students. Thirteen students (32.50%) passed the 70% criterion, while 27 (67.50%) did not. The average motivation score was 3.46, indicating moderate motivation among all the students. Cycle 2 implemented the STAD technique with the same group. Twenty two students (55%) passed the 70% criterion, while 18 (45%) did not. The average motivation score increased to 4.24, showing high motivation levels. Cycle 3 utilised the Think-Pair-Share. Thirty nine students (97.50%) passed the 70% criterion, with only one (2.50%) failing. The motivation score further increased to 4.46, suggesting very high motivation levels. After completing the operating circuits, almost all the students met the required academic achievement criterion in mathematics and exhibited high levels of study motivation.

하브루타 토론 활동이 예비유아교사의 수학 교수 효능감과 수학적 태도에 미치는 영향

Objectives This study was conducted to analyze the effects 0f Havruta discussion activities on pre-service early childhood teacher's mathematics teaching efficacy and mathematical attitude. Methods The study was conducted by selecting 13 and 15 students from early childhood education and 3rd graders, respectively, as an experimental group and a comparative group. And mathematics teaching efficacy and mathematical attitude tests were conducted on the study's students through pre and post tests. Results According to the results of this study, First, the experimental group, which was a group of pre-child teachers who conducted Havruta discussion activities, showed significantly higher mathematics teaching efficacy than the comparative group. There was also a statistically significant difference between the results expectation of mathematics teaching and the belief in mathematics teaching ability, a sub-factor of mathematics teaching efficacy. Second, the mathematical attitude of the pre-child teacher group who conducted the Havruta discussion activity was significantly higher than that of the pre-child teacher group who did not. Among the sub-factors of mathematical attitude, the experimental group's score was significantly higher than that of the comparative group in the case of interest in mathematics, motivation for mathematics, and self-concept in mathematics, and the experimental group scored significantly lower than the comparative group in the case of anxiety about mathematics. On the other hand, there was no significant difference in the value of mathematics. Conclusions In summary, the results of this study show that Havruto discussion activities significantly enhance the mathematics teaching efficacy and mathematical attitude of pre-child teachers. These findings demonstrate the value of actively utilizing Havruta discussion activities to enhance the mathematics teaching efficacy and mathematical attitude of pre-child teachers.

The Effectiveness of Mantel Haenszel Log Odds Ratio Method in Detecting Differential Item Functioning Across Different Sample Sizes and Test Lengths Using Real Data Analysis

Objectives: This study aims to determine the effectiveness of the Mantel Haenszel Log Odds Ratio method in detecting Differential Item Functioning (DIF) across gender, while considering variations in sample size and test length. Utilizing real data, the study draws from a sample of tenth-grade students in Jordan who participated in the 2018 PISA International Mathematics Test. Methods: The study employs the experimental methodology, utilizing three levels of sample size and test length: (342, 200, and 100) and (30, 20, and 10), respectively. Nine iterations of the DDFS program were conducted to collect the results, representing nine scenarios resulting from the intersection of sample size and test length levels. Results: The study indicates that variations in sample size and test length significantly affect the Mantel-Hanzel (MH) method. Specifically, it observes an improvement in the MH method’s ability to detect DIF items with larger sample sizes, while maintaining a consistent test length. Conversely, the method’s efficacy declines with longer test lengths, despite maintaining a fixed sample size at a specific level. Conclusion: The study recommends using a large sample size and a short test length for effective detection of DIF items using the MH method.