Students who study at home certainly affect their self-concept. Their study found that knowledge of distance learning affects the perceived usefulness of this process. This study described self-concept has an influence on learning achievement in mathematics. The type of research used in this study was descriptive quantitative research to determine the relationship between students’ self-concept and learning achievement in mathematics. This research was conducted in class 8 of State Junior High School (SMPN) 1 Palasah, Indonesia (...) with 151 students as respondents. The self-concept data was obtained from a study questionnaire that had previously estimated its validity and reliability. This analysis is used to explain the data in the form of standard deviation, average, and low score. Self-concept is categorized into three categories (high, medium, and low). Self-concept is categorized into two kinds, namely positive self-concept, and negative self-concept. Categorization of self-concept can also be divided into three kinds. A high self-concept is also called a more positive self-concept, a moderate self-concept is also called a positive self-concept, and a low self-concept is also called a negative self-concept. Therefore, when students have a positive self-concept, it affects learning achievement positively as students needhaveaves to have a self-concept in learning mathematics. (shrink)

This study aims to describe the learning motivation of students using virtual media when they are learning mathematics in grade 5. The research design applied in this research is classroom action research. The research is conducted in two phases which involve planning, action and observation and reflection. The results of the study revealed that intrinsic motivation to learn is most prevalent in the form of fun to learn mathematics with virtual media. Other forms of intrinsic motivation (...) include curiosity, need and interests, and satisfaction. Extrinsic motivation in the form of awarded and clarity of learning objectives. The most enjoyable learning experience for students was when they feel like they're learning more than they actually are. This level of enthusiasm increases with the level of learning complexity. The students are more active and motivated to learn. This can be evidenced by the increase in motivation to learn after the first phase. Unfortunately, the lack of bandwidth and time allocated for conducting experiments are some of the obstacles in the way of learning through virtual media. This study revealed that the use of virtual media could improve student's motivation for learning. (shrink)

The first learning game to be developed to help students to develop and hone skills in constructing proofs in both the propositional and first-order predicate calculi. It comprises an autotelic (self-motivating) learning approach to assist students in developing skills and strategies of proof in the propositional and predicate calculus. The text of VALIDITY consists of a general introduction that describes earlier studies made of autotelic learning games, paying particular attention to work done at the Law School of (...) Yale University, called the ALL Project (Accelerated Learning of Logic). Following the introduction, the game of VALIDITY is described, first with reference to the propositional calculus, and then in connection with the first-order predicate calculus with identity. Sections in the text are devoted to discussions of the various rules of derivation employed in both calculi. Three appendices follow the main text; these provide a catalogue of sequents and theorems that have been proved for the propositional calculus and for the predicate calculus, and include suggestions for the classroom use of VALIDITY in university-level courses in mathematical logic. (shrink)

The study aimed to determine if differentiated instruction effectively addresses learning gaps in mathematics. In particular, it explored how it can improve the student’s learning gaps concerning mathematical performance and confidence. The study employed a quasi-experimental design with 30 purposively-selected Grade 10 participants divided into differentiated (n = 15) and control groups (n = 15), ensuring the utmost ethical measures. The mean and standard deviation were used to describe the participants’ performance and confidence. Independent samples t-tests were (...) used to determine the significant differences in the performance and confidence between the two groups. In contrast, dependent samples t-tests were used to determine the significant differences in each group’s pre and posttest performance and confidence. Findings bared that the differentiated instruction successfully addressed students’ performance in mathematics even in a short period. It also increased the participants’ confidence when answering fundamental problems. Continuing differentiated instruction activities are recommended since it benefits students who struggle in mathematics, particularly in answering fundamental operations. Differentiated teaching activities in mathematics can boost academic achievement and engagement and prepare students for future success while fostering a positive and inclusive classroom culture that values individual learning needs and preferences. (shrink)

The purpose of this study was to evaluate the differentiated learning training program at the mathematics subject teachers' meeting (MGMP). A descriptive quantitative approach was used to identify the successes of the program and areas that require improvement. The sample included 21 mathematics teachers in Sub Rayon 2 of Lebak District. The instruments used were questionnaires in which data on participants' responses to resource persons, materials, and suggestions for future activities were collected, and the results of direct (...) observations. Data analysis was carried out using descriptive statistical methods to describe the overall evaluation results. Based on the findings, it is expected to provide an in-depth view of the differentiated learning program, contribute to the development of the program in the future, and become a guideline for improving the quality of mathematics learning in the Lebak district. The results of this training program evaluation show that the differentiated learning training activities have been well implemented in MGMP Mathematics Sub Rayon 2 Lebak District. This is evidenced by the level of teacher satisfaction in participating in the training, the majority of which were at scores 4 and 5, namely agreeing and strongly agreeing. This was also the case with the resource persons, materials, and training facilities, and organization. It is hoped that in the future continue to carry out ongoing training related to differentiated learning by current needs and to improve the competence of mathematics teachers in particular, as well as teachers of other subjects in general. (shrink)

This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".

This study aimed to access the Grade 8 level of learning modules in mathematics from the City Division and Bohol Division throughout the first and second quarters. The researcher uses document analysis in this study, this technique is the most effective way to identify the module’s quality aspects in terms of objectives, content, face validity, suitability of approach, and clarity of the module in a systematic and precise manner. By employing the document analysis and the material, the researcher (...) found out that the evaluator evaluated the learning modules of the Bohol Division and City Division where it can be determined that the mathematics modules are different. The findings employed the Input-Process-Output (IPO) framework as a model and the assessed learning modules would be employed in the new way of teaching mathematical ideas. With this, the researcher recommends that the learning modules as a material fit for the intended users. (shrink)

The objective of this case study concentrated on examining the learning gap, going through some components of the transformation process, and coming up with some ways for aiding students who were experiencing lost learning. A qualitative research design was utilized by the researchers to understand and solve the cases related to Mathematics learning difficulties. Creswell (2008) asserts that qualitative research can be used to discover and comprehend the significance that certain people or groups assign to social (...) or human issues. The researchers used purposive sampling to determine 15 student participants to understand the cases of learning loss and prescribe better interventions to the students. To solve the problems associated with loss of learning experienced by the learners after remote learning, a case study will be utilized as the strategy of inquiry since it fits the situation that is to focus the said key cases, discuss some transforming process, and develop interventions. After analyzing the interviews, researchers identified three common themes across the three cases which serve to clarify the learners' experiences after the post-remote learning: the learners' learning experiences during remote learning, factors that caused learning loss in Mathematics, and learners' coping strategies. In a deeper analysis, the impact of distance learning on students during the pandemic goes beyond just the difficulties in learning and understanding lessons which resulted in difficulty in learning math during in-person classes. The lack of in-person interaction with classmates and teachers also contributes to a sense of isolation and boredom, negatively affecting students' overall well-being and mental health. (shrink)

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. (shrink)

The high rate of mathematics education students‟ academic performance in universities has become unbearable. In an attempt to proffer solution to this menace, this study assessed Poll Everywhere eLearning platform, test anxiety, and undergraduates‟ academic performance in Mathematics in Cross River State, Nigeria. The study adopted a quasi-experimental research one control group and one treatment group. The population of this study comprised all the fulltime regular undergraduates offering Education Mathematics in the Department of Science Education, University of (...) Calabar, Calabar, Nigeria. Accidental sampling technique was adopted in selecting a sample of 328 undergraduates who are owners of smartphones from the population. Test-Anxiety Inventory and Mathematics Achievement Test (MAT) were used as data collection instruments. The null hypotheses were tested using independent t-tests and simple linear regression. Findings revealed that Poll Everywhere eLearning platform has a significant effect on students‟ test anxiety and academic performance in Mathematics respectively; there is a moderate negative and significant relationship between students‟ test anxiety and their academic performance in Mathematics. Based on the findings of this study, it was concluded that Poll Everywhere eLearning platform could be used for the effective teaching and examination of learners in Mathematics and other science-related disciplines. This can be done through the design and integration of course modules to the Poll Everywhere online platform. (shrink)

The researcher was prompted to conduct this study to give intervention of the alarming situation which there is a low performance in solving problems related to geometry in Grade IV Mathematics. This study was about on how to enhance the mathematical competencies of the grade IV pupils using a downloaded worksheets as a learning activity. This study focused in giving remediation applying the intervention materials. These resources give several approaches to attain mastery using distinct drill cards. The investigation (...) was carried out utilizing quasi-experimental design. During administering the pre-test and post-test, the researcher used the weighted mean and t-test to determine the mean percentage scores of the respondents. The respondents were 56 fourth grade learners enrolled in Marangog Elementary School and Tagnate Elementary School in Hilongos East District for the school year 2019 – 2020. At the end of the study, it was found out the use of downloaded math worksheets were found effective means of improving the mastery level. In addition, based on the results gathered, the downloaded math worksheets which were used in the drills or practice greatly contributed to the elimination of non-numerates, and give significantly increasing the number of pupils who mastered the competencies related to geometry. As a result, a proposed innovative teaching strategy is recommended. -/- . (shrink)

The mental risk poses a high threat to the individuals, especially overseas demographic, including expatriates in comparison to the general Arab demographic. Since Arab countries are renowned for their multicultural environment with half of the population of students and faculties being international, this paper focuses on a comprehensive analysis of mental health problems such as depression, stress, anxiety, isolation, and other unfortunate conditions. The dataset is developed from a web-based survey. The detailed exploratory data analysis is conducted on the dataset (...) collected from Arab countries to study an individual’s mental health and indicative help-seeking pointers based on their responses to specific pre-defined questions in a multicultural society. The proposed model validates the claims mathematically and uses different machine learning classifiers to identify individuals who are either currently or previously diagnosed with depression or demonstrate unintentional “save our souls” (SOS) behaviors for an early prediction to prevent risks of danger in life going forward. The accuracy is measured by comparing with the classifiers using several visualization tools. This analysis provides the claims and authentic sources for further research in the multicultural public medical sector and decision-making rules by the government. (shrink)

Learning mathematics through distance education can be challenging, with the “logical” and “rewarding” nature proving difficult to measure. This article aimed to articulate an argument explaining the “logical” and “rewarding” nature of online mathematics learning, elucidating their causal factors. Existing data from the literature that involving students at Visayas State University, Philippines, were utilized in this study. The study used statistical measures to capture descriptions from the data, and quantile regression analysis was employed to forecast the (...) predictors of the logicality and rewarding nature of learning mathematics at a distance. Results indicate that learning mathematics in the new normal is perceived as “logical” and moderately “rewarding”. The regression and correlation analyses revealed a significant positive association between the perceived “logical” nature and the rewarding experience of learning mathematics. The constructed statistical models depicted that the determinants of logicality in learning mathematics include family income, money spent on the internet, learning environment, household size, social status, and health. Moreover, causal factors such as family income, money spent on the internet, learning environment, leisure activities, social status, and health significantly determine the rewarding nature of learning mathematics online. Conclusively, institution must support college students with their online learning needs. Furthermore, mathematics instructors should create lively and exciting online discussions that boost their logical thinking. Providing problem-solving task that are intrinsically rewarding can contribute to a more fulfilling learning experience. (shrink)

This study aims to find out how high the level and trends of student misconceptions experienced by high school students in Indonesia. The subject of research that is a class XI student of Natural Science (IPA) SMA Negeri 1 Anjatan with the subject matter limit function. Forms of research used in this study is a qualitative research, with a strategy that is descriptive qualitative research. The data analysis focused on the results of the students' answers on the test essay subject (...) matter limit function with the number of students by 16 (sixteen). Data collection techniques used are shaped test methods essay, interview method to students who have misconceptions, and methods of documentation of the test answers. Examination of the validity of the data using a triangulation technique that compares the data written test results with data from interviews. The results of this study can be described as follows; (1) The level of misconceptions experienced by students belonging to the category of low, amounting to 12.18%. However, students who do not understand the concept quite high at 40.38%, and the others are students who understand the concept that is equal to 47.44%. (2) The misconception most experienced students lie in subconcepts explain the meaning of limit function at one point through the calculation of values around that point, that is equal to 20.51%. The tendency misconceptions experienced by students is located on errors and operating concepts that misconceptions students that there should be no limit in the completion of the writing of the emblem and misconceptions about the limit students to conclude if the limit value of 0 is no limit to the value of the function. (shrink)

This study investigated the impact of collaborative learning on mathematics achievement and attitudes in sixth-grade students, comparing it to traditional didactic teaching. A quasi-experimental research design was utilized in which sixth-grade students were randomly assigned to either control or experimental groups. Pre- and post-tests assessed mathematics achievement using curriculum-aligned tests. In addition, attitudes toward mathematics were measured using the ‘attitude towards mathematics’ inventory developed by Tapai and Marsh in 2004. Both groups exhibited similar pre-test levels. (...) The experimental group received collaborative learning, while the control group received traditional teaching. Post-tests after a 12-week intervention showed significant improvements in the experimental group’s mathematics achievement, regardless of initial achievement levels. Positive changes in attitudes toward mathematics were also observed in the experimental group, with some progress in the control group. Collaborative learning appears promising for enhancing mathematics achievement and nurturing positive attitudes in elementary students. (shrink)

The broad range of emotional factors that affect learning on the sudden change of the learning modality in Mathematics led to this study. This study aimed to compare the level of support factors that greatly affect the students’ learning in mathematics in a blended learning approach. Sex, age, and relationship status were considered grouping variables on the individual, motivational, and social support factors towards learning mathematics in the blended learning mode of (...) thirty education students at the tertiary level. This study used a quantitative approach, particularly descriptive-comparative design. It utilized descriptive statistics such as means, standard deviations, and frequency and percent to describe the level of support factors. T-test for independent samples/ Mann Whitney U test was used to compare the level of support factors when grouped by the profile variables. Repeated Measures Analysis of Variance was used to compare the three support factors. The results revealed that the students’ level of support factors is high. Moreover, the level of support factors towards learning the subject in the blended learning mode of delivery of the students is the same regardless of their sex, age, and relationship status except in individual factors. Older students are influenced by their self-esteem or study habits more than younger students in learning mathematics in a blended approach. The students are eager to learn Mathematics in a blended learning approach because they are more motivated or are supported by their peers or their self-esteem. (shrink)

his study aims to determine whether the application of brain-friendly learning through whole brain teaching gives a positive effect on the creative character of students, to know the response of the students against the application of brain-friendly learning through whole brain teaching, and to find out if the student response against the application of brain-friendly learning through whole brain teaching correlates positively with the creative character of students in learning mathematics. The research method used that (...) is quantitative. The instruments used, namely the now student response related application of brain-friendly learning through whole brain teaching, and sheets of observation about the creativity of students in learning mathematics after implementing this method. The correlation analysis with the results of the study showed that the value of the larger significance of the alpha values (5%) which means accepting and rejecting H0 Ha which means student response against the application of brain-friendly learning through whole brain teaching not correlated positively with the creative character of students in learning mathematics. The average student response score against this method is found on very good i.e. amounted to 85%. As for the observations of the creative character of the students, after this method is applied, the average score of 68% is found quite creative. (shrink)

The purpose of this study was to determine whether the application of learning brain-friendly through the whole brain teaching a positive effect on the character of creative students, to study the response of the students, and to determine whether the students' response to the application of learning brain-friendly through the whole brain teaching positively correlated with the character of creative students in mathematics. The research method used is quantitative. The instruments used are student questionnaire responses related to (...) the application of brain-friendly learning through the whole brain teaching and observation sheet on student creativity in the learning of mathematics after the implementation of this method. Results of research with correlation analysis show that the greater significance of the alpha value (5%), which means accepting and rejecting H0 Ha which means students' response to the application of brain-friendly learning through the whole brain teaching is not positively correlated with the creative character of students in the learning of mathematics. The average score of the students' response to this methodology very well categorized in the amount of 85%. The results of the observation of the creative character of the students after the implementation of this method, the average score of 68% were categorized quite creative. (shrink)

This study sought to examine the factors affecting the Science, Technology, Engineering and Mathematics (STEM) students’ Mathematics performance in a modular distance learning at Notre Dame Village National High School (NDVNHS). In particular, the researcher was interested to determine if these factors had a significant effect on the students’ Pre-Calculus and General Mathematics performance considering the number of hours spent in modular learning. The period covered by the study was during the first semester of the (...) school year 2020-2021. The respondents were all 67 Grade 11 STEM students of NDVNHS. A quantitative research design was utilized particularly using Multivariate Analysis of Covariance (MANCOVA). The findings of the study revealed that majority of the STEM students had a good performance in their Mathematics subjects for the first semester. Also, the factors specifically type of motivation (intrinsic or extrinsic) and support system (parents, siblings, relatives, friends, or classmates) had statistically significant effect on their mathematics performance in the new normal considering the amount of time they spent in learning using modules. Moreover, there were statistically significant differences in both Pre-Calculus and General Mathematics performances between the type of motivation and support system when adjusted for the number of hours spent in modular learning. Based on the findings, the study concluded that the students’ motivation and support system can greatly affect their mathematics performance when controlling for the allocated time in modular learning. Especially in Pre-Calculus and General Mathematics, motivation and support system are important factors in learning using modules. In the new normal education, the students should increase their level of motivation as well as exposure in self-learning and be given full support towards the processes in the modular approach of distance learning. (shrink)

In the recent years, problem-solving become a central topic that discussed by educators or researchers in mathematics education. it’s not only as the ability or as a method of teaching. but also, it is a little in reviewing about the components of the support to succeed in problem-solving, such as student's belief and attitude towards mathematics, algebraic thinking skills, resources and teaching materials. In this paper, examines the algebraic thinking skills as a foundation for problem-solving, and learning (...) cycle as a breath of continuous learning. In this paper, learning cycle to be used is a modified type of 5E based on beliefs. (shrink)

The prediction potential of the model "emotional intelligence and self-reliance" to students' mathematical performance was investigated in this study. This research was conducted in the third and fourth quarters of the academic year 2021-2022. The quantitative research design, specifically comparative and regression analysis, was used in this study. The comparative design was utilized to assess the differences in emotional intelligence and self-reliance between male and female students, and the regression analysis was performed to see if the model "emotional intelligence and (...) self-reliance" can predict students' mathematical performance. In terms of emotional intelligence and self-reliance, the findings show no significant difference between male and female students. Furthermore, the student's emotional intelligence and self-reliance were strong predictors of mathematics performance. It implies that emotional intelligence and self-reliance are essential factors in better math learning. The study suggested that teachers may improve their students' emotional intelligence and self-reliance by integrating social and emotional learning programs into their classes. (shrink)

In these days, there is an increasing technological development in intelligent tutoring systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that help students understand the basics of math and that helps a lot of students of all ages to understand the topic because it's important for students of adding and subtracting. Through which the student will be able to study the course and solve related problems. An (...) evaluation of the intelligent tutoring systems was carried out and the results were encouraging. (shrink)

The study determined the influence of innate mathematical characteristics on the number sense competencies of junior high school students in a Philippine public school. The descriptive-correlational research design was used to accomplish the study involving a nonrandom sample of sixty 7th-grade students attending synchronous math sessions. Data obtained from the math-specific Learning Style and Self-Efficacy questionnaires and the modified Number Sense Test (NST) were analyzed and interpreted using descriptive statistics, Pearson’s Chi-Square, and Simple Linear Regression analysis. The research instruments (...) and statistics were all validated and tested for reliability. The analysis revealed that the students are visual learners, had no or slight self-efficacy, and their number sense competency level is poor. They encountered difficulty in all the components and domains of the NST. Moreover, the students’ mathematical self-efficacy is significantly related and may influence their number sense competency level. Building upon the learners’ self-efficacy to further their understanding and skills in number sense is necessary. (shrink)

The purpose of this study was to determine the form of teacher readiness and difficulty when implementing the mathematics curriculum in high school, measured from four teacher competency assessments. Schools in Indonesia are still 50% learning from home until 2022, this situation has an impact on the achievement of student learning outcomes. In 2020, the ministry conducted a survey of 4000 students and the results of the survey and out of 100% of the participants, 58% were of (...) the opinion that online learning was ineffective, 38% lacked attention from the teacher, 35% had poor communication, 62% had poor internet access, and 80% had difficulty learning mathematics online. The method in this research is descriptive qualitative. The technique of collecting data is by means of field observations, interviews and collecting documentary evidence. Data analysis techniques by presenting data, data reduction and intersecting data are drawn into conclusions. The number of people who were observed was 2 with a total of 58 and 13 people interviewed sources. Findings, difficulties arise from unprepared pedagogic competence and professional competence. Teachers have no self-constructed modules, difficulty writing symbols and mathematical proofs online. Students provide an assessment of teacher competence online, from 100% of respondents 80% disagree with pedagogic and 90% disagree with professional competence. This is due to the lack of readiness of the two competencies. In conclusion, online learning is expected by students and teachers to have their own modules. Students argue that the teacher's difficulties when writing symbols, providing examples of questions and proving mathematical formulas can be written in modules and modules can be given to students to study at home. (shrink)

This study assessed students’ perception of teachers’ effectiveness and learning outcomes in mathematics and economics in secondary schools of Cross River State, Nigeria. Two null hypotheses were formulated to direct the study. The factorial research design was adopted for the study. Cluster and purposive sampling techniques were however employed in selecting a sample of 1,800 students from the three education zones in Cross River State. “Students’ Perception of Teachers Effectiveness Questionnaire (SPTEQ)”, Mathematics Achievement Test (MAT), and Economics (...) Achievement Test (EAT) were used as instruments for data collection. Reliability estimates of .86, .91, and .81 were obtained for the three instruments using Cronbach alpha. Collected data were analysed using descriptive statistics while the research question was answered and the null hypothesis tested using Pearson Correlation matrix and multiple regression analyses (where applicable), with the aid of Minitab v18. Findings revealed amongst others that, there is a significant composite influence of students’ perception of teachers’ motivational skills, teaching methods, relationship with students, and communication level on learning outcomes in Mathematics (F = 142.46, p < .05) and Economics (F = 150.31, p < .05) respectively. It was recommended amongst others that secondary school teachers should adopt motivational techniques such as praises, rewards, and smiles, in strengthening the interest of learners during mathematics and Economics lessons. Keywords:. (shrink)

This study employed an Interpretative Phenomenological Analysis (IPA) which aimed to explore the lived experiences, challenges, and coping mechanisms of teachers in the public school both in elementary and secondary schools in Malolos, Bulacan. The findings of this study revealed that most teachers are significantly challenged with the poor internet connection, multitasking and multitudes of paperwork to be submitted, communication with the parents and teachers and the different modalities of learning which are cited as the contributing factors of stress (...) and anxiety. As to the experiences of the teachers, they became a module writer, online teacher, reporter while doing the online classes and juggling with the work at home as a homemaker. However, the good experiences of this pandemic brought realization to the teachers that they were able to unleash their potential and utilized the skills needed to survive in this difficult time. Moreover, teachers coped up with the situations through prayers, listening and watching motivational videos, yoga and others became farmers too just to avoid stress. Finally, the teachers also gave their suggestions to further help other teachers also who are struggling during this pandemic. Majority of the participants gave emphasis to focus on stabilizing mental health. Others also highlighted the need to seek the assistance of other people who are knowledgeable in terms of ICT. Continuing innovation and researching to update oneself was also one of the suggested ways to deal with the current paradigm shift in education. (shrink)

Mathematical thinking skills are very important in mathematics, both to learn math or as learning goals. Thinking skills can be seen from the description given answers in solving mathematical problems faced. Mathematical thinking skills can be seen from the types, levels, and process. Proportionally questions given to students at universities in Indonesia (semester I, III, V, and VII). These questions are a matter of description that belong to the higher-level thinking. Students choose 5 of 8 given problem. Qualitatively, (...) the answers were analyzed by descriptive to see the tendency to think mathematically used in completing the test. The results show that students tend to choose the issues relating to the calculation. They are more use cases, examples and not an example, to evaluate the conjecture and prove to belong to the numeric argumentation. Used mathematical thinking students are very personal (intelligence, interest, and experience), and the situation (problems encountered). Thus, the level of half of the students are not guaranteed and shows the level of mathematical thinking. (shrink)

Aims: The purpose of this study is to identify the factors associated with the academic performance of Grade 10 students during their First Quarter of school as well as the significant correlation between the factors and student academic performance in Mathematics. -/- Study Design: Descriptive Correlation Design. -/- Place and Duration of Study: The study was conducted at Agusan National High School in Cagayan de Or City's East 1 District during the school year: 2022 – 2023. -/- Methodology: The (...) respondents were Two hundred thirty-one (231) students in Grade 10 at Agusan National High School in Cagayan de Oro City's East 1 District. This study used a researcher-made questionnaire that underwent validity and reliability testing and the academic performance of the students. -/- Results: The results showed that students agree with routines related to mastering Mathematics at a high level. Furthermore, there is no correlation between student study habits and Mathematics performance in terms of self-confidence, but there is a substantial positive association between the student's study habits and performance in terms of attitude. The study habits and learning techniques used by students were found to be important determinants of how well they performed in Mathematics. The researcher strongly suggested using the enhancement plan in teaching Mathematics to Junior High school students. -/- Conclusion: Students have a very positive attitude toward their study habits when learning Mathematics. Students felt that studying and learning Mathematics was essential. Students' success and academic growth depend heavily on their Mathematics performance. It is essential for pupils to master and comprehend its concepts. Students' study habits in terms of attitudes have an impact on how they learn Mathematics. (shrink)

This study primarily assessed students' achievement in mathematics using a mobile educational application to help them learn and adapt to changes in education. The study involved selected Grade 9 students at a public high school in Nueva Vizcaya, Philippines. This study used a quasi-experimental method, particularly a post-test control group design. Descriptive statistics such as frequencies, percent, mean, and standard deviation were used to describe the achievement of the students in mathematics. A t-test for independent samples was also (...) computed to determine if there is a significant difference between the students’ achievement in mathematics after using the mobile educational application by the control and experimental groups. Results revealed that students' achievement in mathematics was very proficient after using the application. Moreover, the usage of educational mobile applications has a better impact on students' achievement in mathematics than the traditional approach to teaching. Teachers are encouraged to place priority on solving problems. Overall, the use of the mobile educational application can enhance learning in mathematics, thus the continued use of the said application is advised. (shrink)

Prediction-based decisions, which are often made by utilizing the tools of machine learning, influence nearly all facets of modern life. Ethical concerns about this widespread practice have given rise to the field of fair machine learning and a number of fairness measures, mathematically precise definitions of fairness that purport to determine whether a given prediction-based decision system is fair. Following Reuben Binns (2017), we take ‘fairness’ in this context to be a placeholder for a variety of normative egalitarian (...) considerations. We explore a few fairness measures to suss out their egalitarian roots and evaluate them, both as formalizations of egalitarian ideas and as assertions of what fairness demands of predictive systems. We pay special attention to a recent and popular fairness measure, counterfactual fairness, which holds that a prediction about an individual is fair if it is the same in the actual world and any counterfactual world where the individual belongs to a different demographic group (cf. Kusner et al. (2018)). (shrink)

Mathematics is considered one of the most challenging courses for many elementary pre-service teachers (EPTs). In hopes for improvement, teacher educators have been incorporating a jigsaw strategy to equip future teachers with the necessary competencies. Hence, the study aimed to determine the effectiveness of the jigsaw strategy with EPTs’ level of mathematics achievement and interest in an online cooperative learning environment. The research utilized a pre-experimental design with 40 participants. The researchers used pretest and posttest questions covering (...) fraction operations and a mathematics interest questionnaire before and after the intervention. With the implementation of the jigsaw strategy, results showed that the EPTs’ mathematics achievement improved while their interest in mathematics improved to some extent. Likewise, a significant difference between the pre-and post-intervention concerning the EPTs’ mathematics achievement and interest in mathematics was found. Furthermore, correlation analysis revealed that study time is negatively related to mathematics achievement, as is the overall level of interest in mathematics. These findings imply that a jigsaw strategy is a useful tool in teaching mathematics online. However, several modifications may be considered to recognize that the EPTs’ interest in mathematics varies from one person to another. Teacher education institutions are encouraged to apply this strategy not only for EPTs to increase their mathematical know-hows but also to serve as an example for them to employ in their future teaching careers. (shrink)

Elective mathematics has been an extra mathematics subject for pilot students of Eduardo Barretto Sr. National High School for quite some time now. Through this, many alumni testified how this helped them understand senior high school and college math. However, the teachers have also been struggling with the resources for specific areas of mathematics, such as Business Math, Statistics, Analytic Geometry, Trigonometry, and Calculus. When the pandemic hit the Philippines, contextualized learning material aligned with the Most (...) Essential Learning Competencies (MELC) helped elective mathematics teachers. The contextualized learning material was developed from April to August 2020 and was first validated in February 2021 by the students who participated in the pilot testing. However, following the due process, it was suggested that I revalidate the IDEA-formatted Analytic Geometry and Trigonometry instructional material. It examines Eduardo Barretto Sr. National High School mathematics teachers and SDO Calamba City experts' evaluation of the content's topics, objectives, concepts, directions, and activities and the format's prints, illustrations, design, and layout. Participants' perceptions of learning material were assessed using a 4-point Likert Scale survey. Hence, descriptive quantitative design. Participants were surveyed using a 4-point Likert Scale to assess their learning content impression. The findings reveal that the participants found the format and content of the developed learning material to be very satisfactory. The indicators "localized" and "can be done independently" were viewed as Fair and Satisfactory, respectively. The learning material was enhanced by localizing the activities and giving directions that could facilitate self-learning. (shrink)

Mathematical cognition is one of the most important cognitive functions of human beings. The latest brain and cognitive research have shown that mathematical cognition is a system with multiple components and subsystems. It has phylogenetic root, also is related to ontogenetic development and learning, relying on a large-scale cerebral network including parietal, frontal and temporal regions. Especially, the parietal cortex plays an important role during mathematical cognitive processes. This indicates that language and visuospatial functions are both key to mathematical (...) cognition. All of those advances have important implications for basic mathematical education. (shrink)

Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, machine learning (...) results in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities. (shrink)

This study aimed to understand how secondary mathematics teachers engage with learners during the teaching and learning process. A sample of six participants was purposively selected from a population of ordinary level mathematics teachers in one urban setting in Zimbabwe. Field notes from lesson observations and audio-taped teachers’ narrations from interviews constituted data for the study to which thematic analysis technique was then applied to determine levels of mathematical intimacy and integrity displayed by the teachers as they (...) interacted with the students. The study revealed some inadequacies in the manner in which the teachers handled students’ responses as they strive to promote justification skills during problem solving, in particular teachers did not ask students to explain wrong answers. The teachers indicated that they did not have sufficient time to engage learners in authentic problem-solving activities since they would be rushing to complete syllabus for examination purposes. On the basis of these findings, we suggest teachers to appreciate the need to pay special attention to the kinds of responses given by learners during problem-solving in order to promote justification skills among learners. (shrink)

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it [1]. The second, Shannon information, takes events as belonging to ensembles and quantifies the information resulting from observing the given event in terms of the number of alternate events that have been ruled out [2]. The third, statistical (...) class='Hi'>learning theory, has introduced measures of capacity that control (in part) the expected risk of classifiers [3]. These capacities quantify the expectations regarding future data that learning algorithms embed into classifiers. Solomonoff and Hutter have applied algorithmic information to prove remarkable results on universal induction. Shannon information provides the mathematical foundation for communication and coding theory. However, both approaches have shortcomings. Algorithmic information is not computable, severely limiting its practical usefulness. Shannon information refers to ensembles rather than actual events: it makes no sense to compute the Shannon information of a single string – or rather, there are many answers to this question depending on how a related ensemble is constructed. Although there are asymptotic results linking algorithmic and Shannon information, it is unsatisfying that there is such a large gap – a difference in kind – between the two measures. This note describes a new method of quantifying information, effective information, that links algorithmic information to Shannon information, and also links both to capacities arising in statistical learning theory [4, 5]. After introducing the measure, we show that it provides a non-universal analog of Kolmogorov complexity. We then apply it to derive basic capacities in statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. A nice byproduct of our approach is an interpretation of the explanatory power of a learning algorithm in terms of the number of hypotheses it falsifies [6], counted in two different ways for the two capacities. We also discuss how effective information relates to information gain, Shannon and mutual information. (shrink)

It has become a fact that fluency and competency in utilizing the advancement of technology, specifically the computer and the internet is one way that could help in facilitating learning in mathematics. This study investigated the effects of Dynamic Geometry Software (DGS) and Computer Algebra Systems (CAS) in teaching Mathematics. This was conducted in Zamboanga del Sur National High School (ZSNHS) during the third grading period of the school year 2015-2016. The study compared the achievement and attitude (...) towards Mathematics between those students taught with DGS and CAS and those students who were taught without DGS and CAS. A quasi-experimental pretest-posttest control group design was used with two groups which was matched according to their mathematical level. An achievement test was developed and administered to assess the students’ achievement in Mathematics. Aiken’s attitude scale was also used to assess the students’ attitude towards Mathematics. The data were treated with One-Way Analysis of Covariance (ANCOVA) and t-test at 0.05 level of significance. The study revealed a significant difference between the mathematics achievement between students taught with DGS and CAS and those who were taught without it. The integration of DGS and CAS in Mathematics lessons leads to better academic achievement result compared with that of the conventional method of teaching. Moreover, there was no significant difference on the attitude level of the students between the two groups. (shrink)

Throughout this research, imposing the training of an Artificial Neural Network (ANN) to play tic-tac-toe bored game, by training the ANN to play the tic-tac-toe logic using the set of mathematical combination of the sequences that could be played by the system and using both the Gradient Descent Algorithm explicitly and the Elimination theory rules implicitly. And so on the system should be able to produce imunate amalgamations to solve every state within the game course to make better of results (...) of winnings or getting draw. (shrink)

Curriculum integration is frequently promoted as a means of enabling deeper and more authentic learning, with Mathematics often considered a suitable subject for doing so. This review investigates which elements contribute to the effectiveness of Mathematics integration in secondary education. Teacher factors include attitudes towards integrative practices and knowledge of both disciplinary content and curriculum integration theory. Pedagogy factors concern utilising activities that best synthesise concepts from multiple subjects to enhance learning, especially projects. Institutional factors relate (...) to curriculum and assessment requirements as well as school-level variables such as access to planning time and professional development. Limitations in the research literature include a narrow focus on connecting Mathematics with scientific disciplines, a reliance on qualitative methods and small sample sizes, and unknown generalisability to education systems other than those in which studies were conducted. Even so, attempting to navigate the factors involved in effective curriculum integration with Mathematics appears worthwhile. (shrink)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...) they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

The purpose of this study was to investigate the relationships between the students’ self-efficacy, test anxiety and performance on Mathematics of Saint Joseph College, Junior High School Department for SY 2019- 2020. The respondents of the study were randomly chosen junior high school students. Descriptive correlational method of research was used. The data gathered were statistically treated using the Excel and IBM SPSS programs, which summarize the percentage scores, weighted means, correlation coefficients, independent t-test values, and corresponding p-values of (...) relevant statistical tools. Findings indicated that, at average, the students were not confident on their mathematical self-efficacy, moderately anxious on their mathematical test anxiety and satisfactory on their mathematical performance. More findings showed that the following variables have significant relationships: mathematical anxiety and mathematical self–efficacy; mathematical self-efficacy and mathematical performance; and mathematical test anxiety and mathematical performance. The higher the self-efficacy level, the lower the degree of testanxiety; the higher the self-efficacy, the better the mathematics performance; and the lower the test-anxiety, the better the performance. The study recommends regular conduct of diagnostic tests on mathematical self-efficacy and test anxiety and design programs to address the enhancement of learners’ mathematical self-efficacy and reduce their mathematical test anxiety. The researcher recommends Mathematics Learning Development Program (MLDP) as the output of the study. (shrink)

The study sought to identify and evaluate the classroom assessment thoughts, practices, and skills of secondary mathematics teachers in Bulacan. The study revealed that there are no significant relationships between teachers’ thoughts of classroom assessments and practices, and classroom assessment practices and skills. However, there is significant relationship between teachers’ thoughts of classroom assessments and skills. There are no significant differences between the teachers’ thoughts of classroom assessments and their age, educational attainment, teaching experience, number of years in teaching (...) mathematics and in-service training. There is a significant relationship between the teachers’ thoughts of classroom assessment and their classroom assessment skills. In the light of the findings, the researcher recommends that: Secondary mathematics teachers should adopt varied and innovative ways of assessing students’ learning in mathematics. School administrators should ensure that all teachers with appropriate certificates must take more training courses in assessment to improve their skills and use of desirable classroom assessment practices. Further research may focus on the relationship between mathematics teachers’ assessment skills and thoughts, practices and skills, and thoughts and practices. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. (...) A solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

A new AI system, called AlphaGeometry, trained under synthetic data has demonstrated the ability to solve geometric problems at the International Olympiad level. This essay considers the fact that human abilities to learn and do math as well as many other tasks are increasingly augmented with AI. Clearly, smart technologies like AlphaGeometry are redefining a number of concepts and institutions such as learning, schools, education, teacher-student relationships, creativity, etc, which are so fundamental for what we’ve thought of as modern (...) society, economy, and culture. What are we preparing for in mathematics education in the face of the possibility of the continued emergence of disruptive technologies, signaling the beginning of the end, if a new reality of mathematics is not taken into account? (shrink)

Many students consider mathematics as the most dreaded subject in their curriculum, so much so that the term “math phobia” or “math anxiety” is practically a part of clinical psychological literature. This symptom is widespread and students suffer mental disturbances when facing mathematical activity because understanding mathematics is a great task for them. This paper described the students’ cognitive skills performance in Basic Mathematics based on the following logical operations: Classification, Seriation, Logical Multiplication, Compensation, Ratio and Proportional (...) Thinking, Probability Thinking and Correlation Thinking as it serves a critical element of teaching and learning, that is determining the current position of the learners’ mathematical capacity. Its implications for mathematics education were also revealed. A descriptive quantitative design was used in this study. The study included 1011 first-year college students from six state universities in the Philippines who were enrolled in the Bachelor of Science of Secondary Education Program during the first semester of the Academic Year 2019-2020. This study made use of the teacher-made test called the Test on Logical Operations. Findings revealed that the cognitive skills achievement of the first year BSE students from different state universities in the Philippines falls under the category of late concrete operational stage. As a result, students are unable to perform the logical operational skills expected of their age. At their age level, they are expected to be under the formal operational stage based on Piaget’s stages of cognitive development. These findings revealed a weak mathematical education foundation among students which requires immediate attention. This reality should be recognized by educational planners and implementers when making curricular and other instructional decisions. (shrink)

This article examines the possibility of philosophizing about mathematics with children. It aims at outlining the nature of the practice of philosophy of mathematics with children in a mainly theoretical and exploratory way. First, an attempt at a definition is proposed. Second, I suggest some reasons that might motivate such a practice. My thesis is that one can identify an intrinsic as well as two extrinsic goals of philosophizing about mathematics with children. The intrinsic goal is related (...) to a presumed inherent importance of presenting children with some philosophical questions about mathematics. The extrinsic goals consist of first the positive effects such a practice can have on mathematical learning and abilities and second the fostering of children's understanding of philosophical method of inquiry and thinking and therefore of their philosophical thinking competences. Third, some examples found in the literature of previously developed ways of practising philosophy of mathematics with children are presented. This article aims at giving a general outlining picture of the issues surrounding the practice of philosophy of mathematics with children and should therefore be read as an encouragement to further development and studies. (shrink)

One is occasionally reminded of Foucault's proclamation in a 1970 interview that "perhaps, one day this century will be known as Deleuzian." Less often is one compelled to update and restart with a supplementary counter-proclamation of the mathematician, David Lindley: "the twenty-first century would be a Bayesian era..." The verb tenses of both are conspicuous. // To critically attend to what is today often feared and demonized, but also revered, deployed, and commonly referred to as algorithm(s), one cannot avoid the (...) mathematical and philosophical legacies of probability. // But attending to these probabilistic or Bayesian legacies must include an undeniable theological legacy in which they remain entangled. // We are not, today, discovering quirky theological metaphors in contemporary technics. It's the other way around. The technologies are mere metaphors of past theologies. (shrink)

Mathematical modeling offers a promising approach to improving mathematics education. This study aims to determine if the concept of metacognitive awareness in the learning process is associated with mathematical modeling. This study also considers the interaction effect of sex and academic year level on both variables. Focusing the study on preservice elementary teachers might address potential issues and targeted intervention in their preparation program concerning their ability to teach and guide young learners in modeling activities. The research sample (...) includes 140 preservice elementary teachers at Central Luzon State University, Philippines. Data collection used an adapted metacognitive awareness inventory and a validated researcher-made mathematical modeling competency test aligned with the K-12 mathematics curriculum in the Philippines. Results revealed that the preservice elementary teachers had a high metacognitive awareness and mathematical modeling competency, ranging from 22 to 31 out of 36 points. Besides, Factorial ANOVA indicates that academic year level positively affects both variables regardless of sex, and stepwise regression analysis unveiled that information management, declarative knowledge, and planning significantly predict 41.4% of the mathematical modeling competency variance. This suggests that developing metacognitive awareness supports preservice elementary teachers in performing modeling tasks that improve their competency level in mathematics. (shrink)

Artificial Psychology (AP) is a highly multidisciplinary field of study in psychology. AP tries to solve problems which occur when psychologists do research and need a robust analysis method. Conventional statistical approaches have deep rooted limitations. These approaches are excellent on paper but often fail to model the real world. Mind researchers have been trying to overcome this by simplifying the models being studied. This stance has not received much practical attention recently. Promoting and improving artificial intelligence helps mind researchers (...) to find a holistic model of mental models. This development achieves this goal by using multiple perspectives and multiple data sets together with interactive, and realistic models. In this book, the methodology of approximate inference in psychological research from a theoretical and practical perspective has been considered. Quantitative variable-oriented methodology and qualitative case-oriented methods are both used to explain the set-oriented methodology and this book combines the precision of quantitative methods with information from qualitative methods. This is a book that many researchers can use to expand and deepen their psychological research and is a book which can be useful to postgraduate students. The reader does not need an in-depth knowledge of mathematics or statistics because statistical and mathematical intuitions are key here and they will be learned through practice. What is important is to understand and use the new application of the methods for finding new, dynamic and realistic interpretations. This book incorporates theoretical fuzzy inference and deep machine learning algorithms in practice. This is the kind of book that we wished we had had when we were students. This book covers at least some of the most important issues in mind research including uncertainty, fuzziness, continuity, complexity and high dimensionality which are inherent to mind data. These are elements of artificial psychology. This book implements models using R software. (shrink)

In these days, there is an increasing technological development in intelligent tutoring systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that help students understand the basics of math and that helps a lot of students of all ages to understand the topic because it's important for students of adding and subtracting. Through which the student will be able to study the course and solve related problems. An (...) evaluation of the intelligent tutoring systems was carried out and the results were encouraging. (shrink)