This paper aims to address the difficulties of high school students in bridging their computational understanding with their visualization skills in understanding the notion of the limits in their calculus class. This research used a pre-experimental one-group pretest-posttest design research on 62 grade 10 students enrolled in the Science, Technology, and Engineering Program (STEP) in one of the public high schools in Zamboanga del Sur, Philippines. A series of remedial sessions were given to help them understand the (...) function values, one-sided limits, limits of a function, and its discontinuities with the aid of the GeoGebra. Results revealed that there is a significant improvement in their mathematics performance before and after the remediation, t(61) = -19.99, p<.05. The real-time feedback provided by the drawing interface of GeoGebra has provided the students the insights into how objects behave in geometrical space, bridging their understanding in locating the values shown by the computational algebraic processes. Additionally, the significant difference in the achievement reveals a large effect size (Cohen’s =2.54) which could be accounted for by the remediation using interactive activities in the GeoGebra. (shrink)

The study’s goal was to provide an educational intervention in Algebra through GeoGebra that would boost students’ confidence, improve their learning, and correct their most minor mastered skills, allowing them to improve their Algebra performance. The research design was quasi-experimental, with 40 nonrandomly chosen participants comprising the GeoGebra and control groups. Mean and standard deviation was employed to describe the algebra performance and confidence of the respondents. At the same time, independent and dependent t-tests were used (...) to determine the students’ significant difference in algebra performance and confidence in the pre-and post-test between the control and GeoGebra groups. GeoGebra effectively improved algebra confidence, enhanced learning, and remedied the students’ least mastered skills. GeoGebra is recommended as an instructional material in teaching and learning Algebra and can be extended to other mathematics content areas. (shrink)

This study utilized the developmental research design to identify the least taught topics in basic calculus and design and investigate the effectiveness of a Moodle-based courseware package. Data were collected from seven basic calculus teachers and five academic administrators through survey questionnaires, interviews, and validation sheets. The quasi-experimental phase of the study used a pre-/post-test control group design with a sample of 69 students, 34 students in the experimental group and 35 students in the control (...) group. The experimental group received instruction using an asynchronous Moodle-based courseware package, while the control group received instruction through lecture notes. Results showed that the least taught topics include infinite limits, limits at infinity, and limits of trigonometric, exponential, and logarithmic functions. These topics were least taught due to time constraints, students’ capacity, scheduling, complexity, and relatability. Validation of the courseware package showed a very high validity. It was found that the use of Moodle-based courseware package and lecture notes effectively increased the students’ performance. However, one-way analysis of covariance results showed that the experimental group gained considerably greater than those in the control group. It was recommended that teachers continue to update their knowledge of different teaching methodologies to develop an encouraging and dynamic learning environment. (shrink)

This study aimed to investigate the longitudinal trends in mathematical competencies of Grade 8 students in a public high school located in Zamboanga del Sur, Philippines. The study collected data over a period of six academic years, allowing for a comprehensive analysis of students' performance in 16 distinct mathematical competences of basic education curriculum. These topics include, but are not limited to, special products and factors, factoring, and basic concepts of probability. Using a quantitative research design, the study analyzed (...) both numerical and secondary data to identify patterns or trends in students' mathematical competencies. Trends were analyzed through regression analysis using slopes. The significance of these trends was then evaluated using t-tests for the standard error of slopes. The statistical analysis revealed significant upward trends in certain mathematical topics, indicating an improvement in the students' competencies over the six academic years. However, certain topics displayed downward or stable trends, indicating areas for improvement in the teaching methods used for these topics. The study highlights the importance of flexible and adaptable approaches to mathematics education. It emphasizes the need for constant evaluation and improvement of teaching methods to enhance student learning outcomes. The findings of this study provide valuable insights for educators and policymakers to guide evidence-based decision-making and improve the quality of mathematics education in the new normal setup. Implications and future research directions are incorporated in the study. (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)

This study aimed to determine the relationship between academic performance and students’ perceptions in learning Calculus during distance learning modality. Learning Calculus is part of developing students' Mathematics skills and abilities towards enhancing STEM education in Senior High School. Thirty-five (35) STEM students were purposively sampled at a public school in Davao Region, Philippines. These students took up Pre-Calculus and Basic Calculus during pandemic. This study used a quantitative research design, particularly the descriptive-correctional method, to analyze the collected (...) data. Based on the result, the level of students’ perceptions was positive, while the level of academic performance was very satisfactory. Moreover, no significant correlation exists between students’ perceptions and academic performance in learning calculus on distance learning. This implies that students can perform well regardless of their perceptions in learning Calculus, in both Pre- Calculus and Basic Calculus. However, further assessment needs to be done in their Mathematics subjects at the Tertiary level since the modality used was not face-to-face. Appropriate action may be considered based on the assessment result, such as bridging courses or tutorial sessions. (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 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 study ascertained mathematical problem-solving skills and self-efficacy as correlates of Pre-service NCE Mathematics Teachers’ Performance in South-East, Nigeria. Seven research questions guided the study while seven hypotheses were tested at 0.05 level of significance. Correlation research design was used for the study. The population of the study was 197 pre-service NCE Mathematics teachers in South-East, Nigeria. All the population of 197 was studied as sample because, it is small and manageable. Mathematics Problem-Solving Skill Test (MPSST) (...) and Pre-Service Teachers’ Self-Efficacy Questionnaire (PSTSEQ) were used as instruments for data collection. Both instruments were validated by three experts in science Education while reliabilities of MPSST and PSTSEQ were established using Cronbach Alpha method and coefficient values of 0.82 and 0.80 respectively were obtained which were considered high enough to confirm the instruments as reliable. Data were collected and analyzed using Pearson product moment correlation coefficient. The findings revealed that a high positive and significant relationship existed between mathematical problem-solving skills scores and academic performance scores and between self-efficacy scores and academic performance scores of pre-service NCE mathematics teachers. It was recommended among others that Mathematics lecturers should make conscious effort towards improving the mathematical problem-solving skills and self-efficacy of the pre-service NCE mathematics teachers through modeling, conditioning, and behaviour modification for improved academic performance in Mathematics. (shrink)

The relative contributions of gender, test anxiety and test items scrambling on performance in Mathematics has been widely assessed, although there is an inconclusive argument regarding the magnitude of such effects. This study was designed to contribute to this debate, while also being the first study to evaluate the interactive effects of the three dimensions of test anxiety (worry, emotion and total) on performance in Mathematics. A systematic random sample of 1,358 SS3 students participated in a quasi-experiment. Data (...) were obtained using the Test Anxiety Scale (TAI) (Spielberger, 1980) and a Mathematics Achievement Test (MAT) developed by Etuk (2019). Findings indicated that there was no significant gender difference on performance; tests anxiety and items scrambling had significant effects on performance in Mathematics respectively; low students' performance in Mathematics was associated with high test anxiety and test items arrangement from complex to simple; there was a significant interaction of test anxiety worry, emotion and total on performance in Mathematics. It was concluded that gender does not play a significant role in the performance of students in mathematics. Test anxiety in terms of worry, emotion and total affect the performance of students in Mathematics. Based on the conclusions, relevant implications are discussed. (shrink)

Competence structure that pre-service teachers need to develop to become a future teacher has been defined since the 1930s. For pre-service mathematics teachers, their competence has its own characteristics. ICT integration in developing competence for pre-service mathematics teachers has been been proved to be effective in many previous studies. In Vietnam, the Ministry of Education and Training (MOET) has recommended the use of ICT to enhance teaching-learning activities in schools and universities, therefore, there have been many studies on (...) ICT intergration at different educational levels. However, there are only a few studies on the use ICT integration in developing competence for pre-service mathematics teachers. This paper presents results from a research on the feasibility of ICT integration in developing competence of Vietnamese pre-service mathematics teachers. The research was conducted by surveying on a randomly selected of 297 pre-service mathematics teachers and 40 mathematics lecturers in six universities which provide mathematics training programs. Results show that despite of the availability of technologies, ICT integration in training pre-service teachers is still limited. In addition, ICT integration in teaching activities of mathematics teachers is not really effective because the levels of their ICT skills are very different. Pre-service mathematics teachers have the ability to use ICT equipment, and good accessibility to learning systems, but their use of the learning management systems (LMS) is limited. This study can be a reference for future studies to test the effective of ICT integration in training pre-service teachers when designing activities to develop feasibly and effectively their competence. (shrink)

Trigonometry serves as an important precursor to calculus as well as college level courses. However, a possible factor that affects students from learning is teachers’ strategies in teaching. Several studies reveal that cooperative learning such as study group can increase achievement of students in mathematics. This study focused on the effects of study groups on the grade 9 students’ achievement in trigonometric problems. It sought to identify the achievement of the students in problem solving before and after the interventions (...) and to compare the interventions, the group taught with study groups and taught with the existing method. The study used true experimental design particularly pretest-posttest control group design. The study was analyzed through frequency count and percentage of scores, Wilcoxon rank test, and t-test for independents samples. The subjects of the study were the Grade 9 students in a public high school in Nueva Vizcaya, Philippines. The results revealed that majority of the students’ achievements increased. Moreover, the intervention with a study group and the existing method can improve the students’ performance in solving trigonometric problems. Furthermore, the result suggests that study group method was more effective than the existing method. (shrink)

This study aimed to determine the effectiveness of using Team Assisted Individualization (TAI) as cooperative learning teaching approach to improve students’ mathematical cognition. A quantitative research design via experimental design using one group pretest and post-test was employed. This only concentrated on specific students’ processing speed and working memory and included 67 grade 9 students from a public school in the Philippines. The findings showed that the components of TAI were moderately effective under the placement test, effective (...) under the teams, teaching group, student creative, team study, fact test and team score than whole class and highly effective under team recognition, Furthermore, there is a significant difference between the pre-test and post-test scores in each completed stage, and TAI approach is an effective strategy in improving the mathematical cognition of students. This study argues that TAI approach may be utilized in mathematics classrooms to improve the mathematical cognition of students. The gravity of the lessons or topics may be put into consideration to balance the learning and performances of students. (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)

The study investigated the effects of computer-assisted instruction on mathematics achievement among secondary school students in Rivers State. Two research questions and two hypotheses guided the study. The design was quasi-experimental. The population of the study was 215 students in a senior secondary school Kpor in Gokana. The sample of the study was 35 students. The sample size was drawn using simple random sampling technique. The instrument used to collect data was multiple choice achievement test. The instrument (...) was validated by experts in computer science education and the researchers, while the reliability of the instrument was established at 0.81. Mean and standard deviation was used to analyze pre-test and post-test scores to answer research questions, while z-test was used to test the hypotheses at 0.05 significant level. The findings of the study showed that students taught with computer assisted instruction performed higher than those taught with traditional instructional methods. Findings also revealed that there is a significant difference between the pretest and post-test achievement scores of students taught Mathematics with computer assisted instructional method. The study recommended among others that government should integrate computer and educational software into the mainstream of mathematics curriculum from the junior secondary school level as this will help to prepare students for stellar performance in Mathematics at senior secondary level. (shrink)

This study determined the cognitive skills achievement in mathematics of elementary pre-service teachers as a basis for improving problem-solving and critical thinking which was analyzed using Piaget's seven logical operations namely: classification, seriation, logical multiplication, compensation, ratio and proportional thinking, probability thinking, and correlational thinking. This study utilized an adopted Test on Logical Operations (TLO) and descriptive research design to describe the cognitive skills achievement and to determine the affecting factors. Overall, elementary pre-service teachers performed with sufficient understanding (...) in dealing with the TLO. However, in each logical operation, students were found to have insufficient understanding of probability thinking and correlational thinking. These insufficiencies in other logical operations were attributed to their misconceptions on some mathematical terms, misinterpretation of the problems, poor comprehension skills, poor problem-solving skills, and poor performance in mathematics in general. (shrink)

The aim of this research was to x-ray some causes of poor performance of pupils in primary school mathematics. Specifically, the study examined the use of instructional materials and pupils’ academic performance in mathematics; parents’ socio-economic background and pupils’ academic performance in mathematics; compared the performance of private and public primary school pupils in mathematics; examined ways in which teachers contribute to pupils’ poor performance in mathematics. The study employed a correlational and quasi- experimental (...) research designs. A simple random sampling technique was used to select a sample of 270 pupils and 45 teachers drawn from nine primary schools in Akamkpa local government area of Cross River State. A questionnaire and a mathematics achievement test (MAT) were instruments used for data collection. The collected data was analysed using a simple percentage (%) and arithmetic mean (X). The findings of the study revealed that the use of instructional materials adequately led to pupils’ poor performance in mathematics; parents’ socio-economic status contributed to the pupils’ performance in mathematics; pupils in private primary school perform better than their colleagues in public schools in mathematics; and teachers contribute to the poor performance of pupils in mathematics. Based on this results, conclusions and recommendations were made. (shrink)

The rationale of this study was to examine the interactive effect of gender, test anxiety, and test items sequencing on the academic performance in mathematics among SS3 students in Calabar Education Zone, Cross River State. Two formulated null hypotheses directed the study. The study adopted the quasi-experimental design. Simple random sampling technique was used in drawing a sample of 474 students from a population of 8,549 SS3 students. A Mathematics Achievement Test (MAT) and a Test Anxiety (...) Scale (TAS) were used primarily as the instruments for data collection. The reliability coefficient obtained for both instruments were .88 and .82 respectively. The data collected were analyzed using descriptive statistics such as mean and standard deviation, while the null hypotheses were tested respectively, using Pearson product-moment Correlation, and Analysis of Covariance where applicable. Findings indicated that test anxiety contributes negatively to academic performance in Mathematics; there is a significant interaction effect between item sequencing and gender on academic performance; between item sequencing and test anxiety on academic performance; and between gender and test anxiety on academic performance in Mathematics respectively; The findings also showed that Based on these findings conclusion and recommendations were made. (shrink)

This research delves into the intricate relationship between language and mathematics education, particularly within the context of mother-tongue-based instruction. It addresses the challenge of reconciling the language of instruction, the learners' mother tongue, and the language of mathematical concepts, emphasizing the need for synchronization to enhance the teaching and learning process. Drawing from international experiences and the Philippine educational landscape, which transitioned to the K-12 curriculum, this study investigates the role of code-switching in Grade-One mathematics education. By conducting (...) a pretest-posttest group design at an Elementary School in Bohol, Philippines, the study evaluates the effects of code-switching within a mother-tongue-based instruction framework. Findings demonstrate that code-switching improves mathematics performance, with the experimental group excelling in advanced and proficient levels post-implementation. Notably, the control and experimental groups exhibited similar pretest scores, indicating their comparability. This research concludes that code-switching is an effective strategy for bridging the linguistic gaps between the mother tongue and mathematical concepts, thereby enhancing the meaningfulness and comprehensibility of mathematics. In light of these findings, the study recommends the adoption of code-switching in teaching mathematics, especially for students with lower academic achievement. Additionally, it encourages future research to explore the applicability of code-switching in other subjects and higher grade levels. This study advocates for an inclusive and adaptive approach to mathematics instruction that recognizes the complex interplay of languages and aims to empower students to understand, participate actively, and develop a profound love for the subject. Based on the empirical findings of this study, it is strongly recommended that the integration of code-switching as a pedagogical strategy in mathematics instruction be formally endorsed within the school setting. This endorsement serves the paramount goal of enhancing the mathematical proficiency and overall academic performance of the students. -/- . (shrink)

In an attempt to curtail examination malpractice, the Joint Admission and Matriculation Board (JAMB) has been generating different paper types with a different order of test items in the Unified Tertiary Matriculation Examination (UTME). However, the permutation of test items may compromise students’ performance unintentionally because constructive suggestions in theory and practice recommend that test items be sequenced in ascending order of difficulty. This study used data collected from a random sample of 1,226 SSIII students to ascertain whether the permutation (...) of test items has any effect on the performance of students in two different subjects (Use of English and Mathematics). The study adopted the Equivalent Groups Quasi-Experimental Research Design with three independent groups. Findings emerged, amongst others, that there is a significant difference in the performance scores of prospective university students' in use of English and Mathematics examintaions arranged in three different orders (ED, DE, R). There are no significant gender differences in the performance of students in Use of English and Mathematics based on test item permutation. However female students perform better than male students when test items are arranged in ascending order of difficulty while males perform better when test items are arranged in descending order of difficulty. It was concluded that the permutation of test items in UTME examination tends to affect the performance of students in Use of English and Mathematics. This finding has implications for the future conduct of UTME examinations and enrolment into higher education as the randomization of UTME test items changes the difficulty order of different paper types. It was recommended that other measures of curtailing examination malpractices that would not affect students’ academic performance should be adopted. (shrink)

During the idea generation phase of the design process, designers often search for inspirations in external sources of information, such as photographs, written descriptions and physical examples. These sources have potential to enhance creative performance. However, they sometimes become too attached to particular ideas of external precedents or various examples. It refers to fixation which is identified as inadequate adoption of features from existing examples. Influence of the existing examples on creativity and fixation, specifically textual examples, have been discussed (...) in this research. -/- For the nature of design, researchers highlighted the restructuring process of design problem by new sources because the capabilities and boundaries of design problems are not defined very well. Further, the design problem is not knowable at any specific point. Design knowledge identifies itself by its ambiguity. Many models have been developed for design process. The various numbers of divided phases of the models can be seen as having two main areas: (1) idea generation phase (or “ideation”); (2) later phase for details. Idea generation plays an important role in the design process. It is the area of new and creative configurations on design. -/- Creativity is an integral part of the design process. Designers purpose to achieve original ideas to demonstrate their ability and unique designs. External stimuli or inspirational inputs play important roles to increase creativity. They can support moments of stimulation. Associations between information from memory and external stimuli can contribute to the creation of new meanings. Designers are widely influenced by their surroundings in daily lives. However, each stimulus may not be the part of a more creative result Even if designers want to utilize stimulus as an inspirational source, somehow it may fixate their mind to its surface features and they may lose potential creative contributions of the source. It is called fixation. There is much research that shows significant evidence of conformity effects across the design problems. -/- The given examples to designers may cause higher-level fixation and lower-level creativity or vice versa. Fixation may occur when example solutions are introduced, on the other hand, the designers may create more original ideas as well. There is a need for research to find ways to avoid fixation traps or reduce their adverse impact. Thus, this research focuses on variables of the given example. -/- The following claims show some research areas remained unclear: (1) Some researchers investigated textual examples as - one of the modalities of representation - but did not focus on forms of textual examples. (2) Much research has been conducted with examples which are selected by the researcher. Nevertheless, designers can also choose or produce their own stimuli. There is not much research on this possibility. In this context, my research focuses on the following two variables through two studies (Study 1 and 2): (1) forms of textual examples; (2) self-construction of textual examples. First, most of the studies in the literature have focused on visual presentation and there is not enough research on the content and form of the text. The study of textual examples has still not been awarded enough attention especially as various forms of text. Some forms of text are as follows: keyword, paragraph, sentence, poem. These observations lead me to the following research question: Which forms of textual example increase creativity and reduce fixation more? (Study 1). -/- Second, most of the studies regarding textual examples have used prose or keywords. The poems have been ignored. However, poems imply more meaning with fewer words. The structure of the poems enables more creative narratives than structure of prose. Because unusual organization of words stimulates the readers and draws their attention. This activates the creative performance of the reader. The surrealist poem is the extreme form of this activation. It is random assemblies with headlines and sentences which is cut from newspapers. Thus, novel meaning networks are formed. The method of creating a surrealist poem offers a new way of getting inspiration. It is termed as self-construction practice by this research. Through this method, designers create their own example from the given one. Reconstruction of the text may increase the creative process and prevent fixations from the given text. This suggestion led me to the following research question: If the designers write their own poem instead of a given poem (as a self-construction practice), can they internalize the textual example? In addition, does it produce more creative and less fixated designs? (Study 2). Two experimental studies were planned to partially answer the research questions, in which novice students of architecture were asked to solve two different design problems, under different conditions. All of the experimental sessions were conducted in a design education studio. The participants produced sketches and added a written explanation relating to their designs. Fluency, flexibility and repetition of key attributes were calculated by the researcher. -/- Originality, practicality, understanding of the task and quality were ranked by judges. Study 1 shows us tendencies of using various textual forms. Distinctions of keywords and of poems have appeared among them. This emphasizes the role of keyword and poem in the design process as inspirational sources and provides many tips for their potential use. The keyword also leads to a high degree of fixation. However, a low degree of fixation is observed when poems are presented as inspirational examples. -/- In Study 2, the self-constructed poem seems to support develop more successful design ideas from many perspectives. In the context of the surrealist poem, writing and reading the surrealist poem trigger the designers’ imagination. At first, the words and lines of poems seem unrelated to each other and designers try to relate them and solve the puzzle of meaning. Hence, novel meaning networks are formed. It indicates that surrealist poems are able to activate the creative performance of the designers. Writing their own surrealist poems ,as a self-construction practice, motivated designers to begin to produce by having fun. Motivated designers have stimulated themselves to produce creative ideas. In other words, the self-construction process may be added to the design process models in the earlier part of the idea generation phase which is called as pre-design and warm-up phase. This earlier phase makes designers highly motivated and they internalized the given examples. -/- Following the conclusions, several implications and recommendations for the design process and education are discussed. (shrink)

The editorial introduces issue 21.1 of Technoetic Arts via a critical reflection on the artificial intelligence hype (AI hype) that emerged in 2022. Tracing the history of the critique of Large Language Models, the editorial underscores that there are substantial ethical challenges related to bias in the training data, copyright issues, as well as ecological challenges which the technology industry has consistently downplayed over the years. -/- The editorial highlights the distinction between the current AI technology’s reliance on extensive pre-existing (...) human-generated data for pattern recognition and the performative process inherent in art practice. Patterns of creative output can be replicated without a thorough understanding of underlying concepts. In contrast, the performative process of art practice, as explored through the conceptual frameworks of creativity by Noam Chomsky, Charles Sanders Peirce, and Roger T. Ames and with reference to an earlier publication of the editorial’s author, creates concepts and continually ‘strives to extend itself towards the unknown.’ -/- Following this introductory section, the editorial provides an overview of the ten articles featured in this issue of Technoetic Arts. The first four texts engage with emerging technologies from various perspectives in art and design. The subsequent six articles, part of a special section titled 'Perspectives from Chandigarh,' reflect a quest for meaningful existence within colonial, patriarchal, and biopolitical structures that frame everyday practices of exclusion and oppression. (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)

Studying the neural correlates of conscious awareness depends on a reliable comparison between activations associated with awareness and unawareness. One particularly difficult confound to remove is task performance capacity, i.e. the difference in performance between the conditions of interest. While ideally task performance capacity should be matched across different conditions, this is difficult to achieve experimentally. However, differences in performance could theoretically be corrected for mathematically. One such proposal is found in a recent paper by Lamy, Salti and Bar-Haim [Lamy (...) D, Salti M, Bar-Haim Y. Neural correlates of subjective awareness and unconscious processing: an ERP study. J Cognitive Neurosci 2009,21:1435-46], who put forward a corrective method for an electroencephalography experiment. We argue that their analysis is essentially grounded in a version of High Threshold Theory, which has been shown to be inferior in general to Signal Detection Theory. We show through a series of computer simulations that their correction method only partially removes the influence of perfor- mance capacity, which can yield misleading results. We present a mathematical correction method based on Signal Detection Theory that is theoretically capable of removing performance capacity confounds. We discuss the limitations of mathemati- cally correcting for performance capacity confounds in imaging studies and its impact for theories about consciousness. (shrink)

The Western Philippines University – College of Education’s Project MATHEMATICS (Mathematics Enhanced Mentoring, Assistance, and Training to In-need and Challenged Students) was implemented as part of the Adopt-a-School Program to address the mathematical needs of Laura Vicuña Center – Palawan youths. To evaluate the extent of the project implementation, the study assessed its impact through the feedback gathered from the clients served. It specifically described the quality of project implementation, determined the attainment of project objectives, and enumerated client (...) feedback. A concurrent triangulation mixed-method research design was used with 32 clientele samples selected purposively. The study utilized a survey, problem set test, and focus-grouped interview to obtain data pertinent to the study’s objectives. The findings revealed an aspirational quality of the implemented project, improved mathematical performance, and the client’s desire for ongoing mentoring. The implications and limitations of the study are discussed, along with recommendations for future extension projects, monitoring and evaluation, and re-planning activities. (shrink)

This study aimed to assess the effectiveness of remedial instruction in improving the numeracy skills of Grade 7 students at Malbug National High School during the school year 2023-2024. Adopting a quasi-experimental research design, the research focused on Grade 7 students at Malbug National High School, Cawayan East District, Masbate Province Division, Philippines, identified as non-numerates, employing pre-tests and post-tests as essential research tools. The independent variable was the remedial instruction in numeracy, while the dependent variable was students' (...) numeracy performance measured through pre-tests and post-tests. Before the intervention, the pre-test numeracy performance exhibited a varied distribution of students across different score ranges. A majority fell into the "Needs Major Support" category, emphasizing the necessity for targeted interventions. The post-test results, however, revealed a remarkable improvement, with 87.88% of initially non-numerate students achieving scores in the "Transforming" range. A thorough statistical examination validated a notable disparity in the scores obtained before and after the instructional intervention, substantiating the favorable influence of remedial instruction. The calculated t-value of 19.594, exceeding the critical t-value, led to rejecting the null hypothesis. In conclusion, the study emphasizes the need for tailored interventions based on the initial deficiency in numeracy skills. The post-test results underscored the success of remedial instruction in fostering substantial growth. The study recommends sustaining the remedial program, implementing periodic assessments, providing teacher training, involving parents in students' development, allocating adequate resources, and further research in other schools to strengthen findings. (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)

Will I die? As a hypothesis, in my natural scientific understanding, the psyche, is nothing more than, and exclusively just some states of my living brain – I will die as a result of his death. -/- In presented answer, psyche – itself own immediate reality itself, that is – undoubted. -/- This work was performed in reality “in the first person” (“subjective reality”, “phenomenal consciousness”). To realize, how, what it is the reality of the “in the first person” let’s (...) imagine ourselves as an experimenter, who does not replace reality with reasoning about it. – Now for us, as experimenters, how (what it is) psychic is an immediate and undoubted reality. And the awareness of “I am” is a direct reality, and not knowledge about it, which is always doubtful. That is, in psychic reality, nothing prevents us from answering undoubtedly and definitively the question, asked by this psychic reality itself about itself. The author acts from the position of “being in reality – not going beyond its limits, for example, into philosophy” (philosophy, including methodology, is the replacement of reality itself with always dubious reasoning about reality) – explores phenomenal consciousness (“psychic”) directly and as an immediate reality. That is, this work is the mastery of psychic reality through subjective-psychical experimentation – don’t philosophize, but experiment! -/- For example, Descartes, introspectively experimenting in his own psyche reality with his own psyche, informed us about the immutability of the “mind” and proposed to understand this immutability as our own immortality: “the mind does not represent any combination of accidents, it is a pure substance, and although all its accidents are subject to change, it understands some things, it desires others or feels others, etc. – nevertheless, in itself it does not change; and as for the human body, it changes, if only because they are subject to a change in the shape of some of its parts. It follows from this that the body perishes very easily, while the mind, by its very nature, is immortal” (Декарт Р., p. 13). Note that, Descartes did not realize that he was immortal, but logically deduced his own immortality from the immutability of the mind. However, Descartes’ unchanging “mind” itself is such that there is something to die. And in my natural scientific understanding, the immutability of the mind does not imply its immortality – it will die without changing in its subjective self-perception, while instantly fading away as a result of brain death. Psyche (psychical) – a designation of the fact that this is one’s own immediate reality (that is, undoubtedly) – how (what) I myself am immediately, undoubtedly, and that immediate reality of mine, how and through which I myself and everything in general for me there is, and which is exclusively the only one for me. It should be noted that while I am unconscious (brain injury or dreamless sleep), there is nothing at all. -/- But this does not mean that “I”, having completely gone into oblivion, I'll die. This does not exclude that, I will disappear completely into oblivion and does not exist, but (at the same time) “I” – am. So, let’s define immortality as the impossibility of dying because there is nothing to die (psychic, but is such that there is nothing to die – is immortal) and will make a conclusion important for this work: if I am, as psyche, exclusively only is such that there is something to die and nothing else, then, therefore, my death is not excluded. But am I like that? The idea of this work is that I, as a psyche can to manifest (reveal) and realize myself as such (I such), that there is nothing to die, but (at the same time) I – am. I will realize of myself as immortal – such that to die (to decease) nothing. In other words, if I will approach with a bias and, acting purposefully, will reveal the subjective reality “I (psyche) such is that to die (to decease) nothing, but I – am”, that is – I am immortal, that the hypothesis “I will die” will falsified and excluded. -/- To realize this in the work, it is proposed to use the subject-object model, shift the boundary of “I” to the pole of the subject and become objectless, manifesting (revealing) oneself as such that there is nothing to die. Therefore, the aim (goal) of the work – to realize: I – am, but such that there is to die (decease) nothing. To become objectless and wondering about the possibility to dying, as a result, or I will exclude the immortality of the manifested state, or I will manifest (will reveal) immortal undoubtedly and definitively. -/- At the same time, I, as a subject, am “a necessary pole of subject-object relations. … An object is what the activity of … a subject is directed at. … In fact, everything that exists can become an object. … it is important to keep in mind the fundamental fact that the object is always outside the subject, does not merge with it. This externality also takes place when the subject deals with the states of his own consciousness, his Self ... it is important to emphasize that the relation of the subject and the object is not the relation of two different worlds, but only two poles as part of some unity” (Лекторский В.А., p. 6-7). That is, everything that I find existing in myself, this (such) is as an object. “The subject always refers to all “objects”, but it can never become an object for itself” (Титлин Л.И., p. 23). “… you will not be able to see the seeing vision ...” (Титлин Л.И., p. 40), and in this model this implies the “limit” of the subject. As the limit of the subject, I am “objectless”. And, therefore, in its own pole the subject is “ideal” – in its (own) limit (as its own limit, its own limit), I do not exist for myself (non-existent). -/- Using the “fact of the mobility of the boundaries of the subject” (for example, Тхостов А.Ш., p. 16), I have the opportunity to “pull” the boundary of the “I” into myself and become my own limit. At the same time, it is necessary to realize and accept that “inside” the limit of the subject and behind – “beyond of the subject”, and in general the very “inside” and “behind” in this version – unreality. In such a subject limit, the required paradoxical subjective state is assumed – I exist and see, but at the same time I am such that I do not exist for myself, that is, I am, but (subjectively such that) there is nothing to die (“immortality”). -/- Accordingly, the following tasks are indicated in the experiment: 1. In the object-subject sphere of visual perception, shift (and shift) the boundary of “I” into oneself –» to run into one’s own limit and become one’s own limit (without thickness: without depth, without “from within” and without reverse side) –» 2. Having become your own limit, which in its own limit is, but for myself I do not exist (non-existent), realize: • Myself – I am and this is real; • Will I die? – or there is nothing to die, which of the options is to me, as a psyche (as itself the psychic “I”), is applicable: • or I am such that it is not impossible that I will die, and the realized state is not immortal; • or “I” am such that “I” – am (is reality), but such that myself “I” to die nothing, that is, my own immortality – I am immortal; • Is this real? -/- Instruction for reproducing the target result: sequence of actions and results in a subjective-psychic experiment (hereinafter referred to as SPE) -/- At a distance of 25-40 cm from the wall (so that the wall occupies the entire field of view or its overwhelming part), • Here and now, focus on your face: “I am” – reality (and not is the knowing about it). • In yourself step back and look out of yourself at this wall. • Without moving your head, cover the field of vision with your attention as wide as possible and at the same time perceive everything at once (all this) as a single whole. • Perceive a high and wide wall (option: look up at an angle of 135-150 degrees in front of you) in such a way that the space (volume) surveyed by you without turning your head is a closed asymmetrical “lens” • limited in a circle in the periphery of the field of view, • convex in you; You – the beholder, rearwards concave in self (“subject”) – which one of you are watching? • Without moving your head, perceive the field of view as a single whole –» • Into yourself “draw in” –» “backing away” –» step back from everything –» • lean back into yourself –» up to dead-end limit –» • become a dead end itself – a concave (reflector-like) limit-plane. • You – into yourself – backward concave – a perceiving visual screen (limit-dead end), plane –» • lean back and press –» • something in general somehow inside the dead-end plane and behind the dead-end plane, as well as “inside” and “behind”, “behind the dead-end plane” – unreality; • myself – a dead-end plane without thickness (depth), without “inside”, without a reverse side for oneself. • –» That is, as a psychic reality (what is it psychically) will I die? –» or • Something there is, and that is I will die (it is possible); or • I am such that there is nothing to die, but I – am. or • Subjective-psychic experiment is incomplete… • –» Realize that this is reality (realize the reality of it) and emphasize (answer). -/- As a result, “I” am, but there is nothing to die/not to die, that is, the hypothesis “I will die” is unrealistic. -/- Remarks -/- • Each completed SPE is completed with the target result: “I am such that there is nothing to die, but I – am”. And the that what I will die (not excluded) does not correspond to this, that is unreality and is excluded by this. • But I am not such that I will not die. The concepts “I will die/ I will not die” to me, as a psyche are not applicable. That is, I, as a psyche, is immortal, but I am not eternal (not eternal – endlessly lasting, such that there is something to last) – to last, to be eternal and to end there is nothing. This is “immortality”. • In the target result of this work, I – am, but such that there is nothing to die/not die (“immortality”). And such a “I” is not the Atman of the Hindu schools of Nyaya, Vaisheshika and Purva Mimamsa, which E.A. Torchinov. Since the “I” – psychic, and not a substance with the psyche as an attributes. • According to illusionism, what I am as a result of the experiment given in the work is an illusion. And the impression of immortality is a product of the brain. But in reality I am such that I will die (it is not excluded). However, it is necessary to realize that illusionism is a detached reasoning about the “I”, but not is the self itself. And to what I am (as psiche), reasoning and questions about the reality of the “I” (for example, question: am I really like this, what am I like as psyche?) and other expressing illusionism do not correspond. That is, subjectively (psychic, in the psychic reality of the “first person”, in first person perspective), the illusionism of the “I” is unreality. Subjectively (psychic, in the psychic reality of the “first person”, in first person perspective), this is undeniable and final. • Reasoning about what such a “I” is in this (mine) or not in this brain, as well as (for example, holding a real skull in my hands), questions like “how (or, but now where is it here) such “I” – how is it after brain death?” – To the fact that is such an “I” these questions do not correspond and is falsified by this. • After being unconscious, the impression remains that I'm is not and that there is nothing at all. That is, my “unconsciousness” is psychic indistinguishable from my non-existence. However, science has not shown, but and it is not excluded that before and after I exist physically (there is something to die), I still or I no longer exist, there is still or nothing to die as a soul, substance, or otherwise. But what I am in the target result of this work is what I – am, and not “died and already now or still unreality” and I am such that there is nothing to die, this is – reality. That is, I will die? – there is nothing (to die), but I – am (reality), even if I am not (don’t exist). Or I do not exist as something. • I am such that there is nothing to be and die, but I am. And subjectively (psychic, in the psychic reality of the “first person”, in first person perspective), this immortality is – reality. But this reality eludes my rational explanation. -/- Conclusion -/- Will I die? – In the target result the I am, but at the same time I am such that there is nothing to die. That is, I am immortal, but at the same time, I am not eternal (“I” not something eternal (endlessly continuing)) – I am such that to be eternal there is nothing. And, if we accept the subjective (psychic, “first person”, in first person perspective) reality without trying to understand it rationally, then I am exactly like that – I realize that this is my undoubted nature. That is, “I will die / I will not die” is an unreality. Subjectively (psychic, in the psychic reality of the “first person”, in first person perspective), it is undoubted and final. Despite the unscientific nature, this work is a way of mastering reality. The author would be grateful for the identified and shown unreality of the fact that the “I” – am, but such that there is nothing to die, and ideally, the awareness: “I will die (not excluded).” -/- Bibliography -/- Декарт Р., Размышления о первой философии //Декарт Р. Соч.: В 2 т. Т. 2. М., 1994. Лекторский В.А. Субъект в истории философии: проблемы и достижения // Методология и история психологии. 2010. Том 5. Выпуск 1. С. 5-18. Титлин Л.И. Проблема субъекта в индийской философии («Пудгалавинишчая» Васубандху) [Текст] / [Л. И. Титлин]; Федеральное государственное бюджетное учреждение науки Институт философии Российской академии наук. – Москва: ОнтоПринт: Сделано-Сказано, 2018. – 361, [1] с. Тхостов A. Ш. Культурно-историческая патопсихология: монография, – М.: Канон+ РООИ «Реабилитация», 2020. – 320 с. Торчинов Е.А. «Словарик индуизма» (Дата написания: 2003; дата файла: 15.06.2007). Торчинов Е.А. Пути философии Востока и Запада: познание запредельного — СПб.: «Азбука-классика», «Петербургское Востоковедение», 2005. — 480 с. ISBN 5-352-01371-5 (Азбука-классика) ISBN 5-85803-258-3 (Петербургское Востоковедение). -/- Скончаюсь? – я бессмертен (как осознать бессмертие «от первого лица») -/- Скончаюсь? В качестве гипотезы в моем естественно-научном понимании психическое (каково психически), это не более чем, и исключительно только всего лишь некоторые состояния моего живого мозга – скончаюсь в результате его смерти. -/- В представленном ответе психическое – сама собственная непосредственная реальность, то есть, то, каково психически, это – несомненно. -/- Данная работа выполнена в реальности «первого лица» («субъективная реальность», «феноменальное сознание»). Чтобы осознать то, как, каково это, представим себя экспериментатором, который не подменяет реальность рассуждениями о ней. – Теперь для нас, как экспериментаторов, то, как (каково) психически, это непосредственная и несомненная реальность. И осознание «я есть», это непосредственная реальность, а не знание об этом, которое всегда сомнительно. То есть, в психической реальности, на вопрос, заданный самой этой психической реальностью самой себе о себе самой, нам ничто не запрещает ответить несомненно и окончательно. Автор действует с позиции «быть в реальности – не выходить за ее пределы, например, в философию» (философия, включая методологию, это подмена самой реальности всегда сомнительными рассуждениями о реальности) – исследует феноменальное сознание («психическое») непосредственно и в качестве непосредственной реальности. То есть, данная работа, это овладение психической реальностью посредством субъективно-психического экспериментирования – не философствуй, а экспериментируй! -/- Например Декарт, интроспективно экспериментируя в собственной психической реальности с собственным психическим, сообщил нам о неизменности «ума» и предложил эту неизменность понять в качестве нашего собственного бессмертия: «ум не представляет какого-то соединения акциденций, являет собой чистую субстанцию и, хотя все его акциденции подвержены изменению — он то понимает какие-то вещи, то желает другие или чувствует третьи и т.д.,— тем не менее сам по себе он не изменяется; а что касается тела человека, то оно изменяется хотя бы уже потому, что подвержены изменению формы некоторых его частей. Из этого следует, что тело весьма легко погибает, ум же по самой природе своей бессмертен» /Декарт Р., стр. 13. Заметим, Декарт не осознавал себя бессмертным, а логически вывел собственное бессмертие из неизменности ума. Однако, неизменный «ум» Декарта таков, что скончаться есть чему. А в моем естественно-научном понимании из неизменности ума не следует его бессмертие – он, не изменяясь в своем субъективном само-восприятии, при этом мгновенно угаснув в результате смерти мозга, скончается. Психически (психическое) – обозначение того, что это сама собственная непосредственная реальность (то есть – несомненно) – то, как (каково) я сам непосредственно, несомненно, и та моя непосредственная реальность, как и посредством чего я сам и всё вообще для меня есть, и которое для меня исключительно единственное. Следует заметить, что пока бываю без сознания (травма мозга или сон без сновидений), ничего и никак нет вообще. -/- Но это не значит, что «я» ушедши в небытие окончательно – скончаюсь. Этим не исключено, что таковой ушедший в небытие «я» не существую, но (при этом) есть. Итак, определим бессмертие, как невозможность скончаться потому, что скончаться нечему (например, если «умерший» психически есть, но уже таков, что скончаться больше нечему, то теперь он бессмертен) и сделаем важный для данной работы вывод: если психически я исключительно только таков, что скончаться есть чему и ни каков иначе, то, следовательно, то, что скончаюсь, это не исключено. Но таков ли я? Идея данной работы в том, что мне удастся проявить (выявить) и осознать себя таковым (я таков), что скончаться нечему, но (при этом) я есть. Иначе выражаясь, если я подойду предвзято и действуя целеустремленно, выявлю субъективную реальность «я есть, но таков, что скончаться нечему» – то смерть мне, как психическому несвойственна, то есть, я бессмертен – гипотеза возможности субъективно скончаться («я скончаюсь») будет фальсифицирована и исключена. -/- Чтобы это реализовать в работе предлагается воспользоваться субъект-объектной моделью, сдвинуть границу «я» в полюс субъекта и стать безобъектным, проявившись (выявившись) собой таковым, что скончаться нечему. Следовательно, цель работы – осознать: я таков, что есть, но скончаться нечему. Стать безобъектным и задаваясь вопросом о возможности скончаться, или исключу бессмертие проявленного состояния, или проявлюсь (выявлюсь) бессмертным несомненно и окончательно. -/- При этом, я, как субъект, являюсь «необходимым полюсом субъектно-объектных отношений. … Объект – то, на что направлена активность … субъекта. … В действительности объектом может стать все, что существует. … важно иметь в виду тот принципиальный факт, что объект всегда внеположен субъекту, не сливается с ним. Эта внеположность имеет место и тогда, когда субъект имеет дело с состояниями собственного сознания, своим Я … важно подчеркнуть, что отношение субъекта и объекта – это не отношение двух разных миров, а лишь двух полюсов в составе некоторого единства» /Лекторский В.А., стр. 6-7. То есть, всё, что нахожу в себе существующим, это (таковое) есть в качестве объекта. «Субъект – всегда относится ко всем «объектам», но он никогда не может стать объектом для самого себя» /Титлин Л.И., стр. 23. Иначе это выражая – «ты не сможешь увидеть видящего видение…» /Титлин Л.И., стр. 40, и в данной модели таковое предполагает «предел» субъекта. Как предел субъекта я «безобъектен». То есть, «идеален» – своим (собственным) пределом (в качестве собственного предела) самим для себя не существую (несуществующий). -/- Используя «факт подвижности границ субъекта» /например, Тхостов А.Ш., стр. 16, я имею возможность границу «я» в себя-назад «втянуть» и стать собственным пределом. При этом необходимо осознать и принять, что внутри предела субъекта и сзади – «за пределом субъекта», и вообще само «внутри» и «сзади» в этой модели – нереальность. Таким субъектным пределом предполагается требуемое парадоксальное субъективное состояние – я есть и вижу, но при этом я таков, что для себя не существую, то есть, я есть, но (психически таков, что) умереть нечему («бессмертие»). -/- Соответственно, в эксперименте обозначаются следующие задачи: 1. В объект-субъектной сфере зрительного восприятия сдвинуть (и сдвинув) границу «я» в себя-назад –» упереться в собственный предел и стать самим собственным пределом (без толщены: без глубины, без «внутри» и без обратной стороны) –» 2. Став собственным пределом, которым есть, но для себя не существую (несуществующий), осознать: • Себя – я есть и это реально; • Скончаюсь? – есть ли чему скончаться или скончаться нечему, какой из вариантов мне (как психическому «я») свойственен: • или я таков, что то, что скончаюсь не исключено, и реализованное состояние не бессмертно; • или я есть, но таков, что скончаться нечему, то есть, собственное бессмертие – я бессмертен; • Реальность ли это. -/- Инструкция воспроизведения целевого результата: последовательность действий и результатов в субъективно-психическом эксперименте (далее СПЭ) -/- На расстоянии 25-40 см от стены (так, чтобы стена занимала всё поле зрения или его подавляющую часть), • Здесь и сейчас сосредоточьтесь на своём лице: «я есть» – реальность (а не знание об этом). • В себе отстранитесь назад и смотрите из себя на эту стену. • Не двигая головой, охватите поле зрения вниманием предельно широко и одновременно всё сразу (всё это) воспримите единым целым. • Высокую и широкую стену (вариант: смотрите вверх под углом 135-150 градусов перед собой) воспримите так, что обозреваемое вами без поворота головы пространство (объем), это – ограниченная по окружности в периферии поля зрения замкнутая несимметричная «линза» • плоская с противоположной вам стороны • и выпуклая в вас; Вы – вогнутый в себя-назад смотрящий («субъект») – каков? – кто из вас сейчас на всё это смотрит? • Не двигая головой, поле зрения воспримите единым целым –» • В себя-назад «втянитесь» –» и «пятьтесь» –» «за мысли» и за всё вообще –» из этого всего назад вытесняясь –» от всего вообще взад отстранитесь –» • собой в себя-назад подайтесь и упершись в собственный (себя) задний к объектному обращённый (развернутый) тупиковый предел –» • станьте самим пределом-тупиком – в себя-назад вогнутой (рефлектор-подобной) пределом-плоскостью смотрящей – воспринимающим зрительным экраном –» станьте плоскостью-тупиком –» • «проскользните» по себе – плоскости-тупику и охватите вниманием целиком –» • собой – самим плоскостью-тупиком назад надавить, нажать –» • осознать: что-то как-то внутри плоскости-тупика и сзади за плоскостью-тупиком, и там вообще «что-то как-то», а также само «внутри» и «сзади», «за плоскостью-тупиком» и вообще «там» – нереальность; • самого себя – плоскости-тупика без толщины (глубины), без «внутри», без обратной стороны для себя нет. • –» То есть – в качестве психической реальности (каково психически) я скончаюсь? –» или • скончаться есть чему – скончаюсь (не исключено). или • я таков, что скончаться нечему, но я есть. или • субъективно-психический эксперимент не завершён. • –» Осознайте, что это – реальность (осознать реальность этого) и подчеркните (ответ). -/- В результате я есть, но скончаться/не скончаться нечему, то есть гипотеза «скончаюсь» – нереальность. -/- Замечания -/- • Каждый завершённый СПЭ завершён целевым результатом: «я таков, что скончаться нечему, но я есть». И тому, каков я в результате СПЭ, то, что скончаться есть чему – скончаюсь (не исключено) не соответствует, то есть нереальность и этим исключено. • То есть, я и не таков, что не скончаюсь. «Я скончаюсь/не скончаюсь» ко мне, как к психике, неприменимо. Иначе это выражая, тому, каков я, смерть несвойственна. То есть, я, как психика (психическое), бессмертен, но я не вечен (не вечный – бесконечно длящийся, таковой, что есть чему длиться) – длиться, быть вечным и не скончаться нечему. Таково «бессмертие». • В целевом результате данной работы я есть, но таков, что скончаться/не скончаться нечему («бессмертие»). И таковой «я» не Атман индуистских школ ньяя, вайшешика и пурва-миманса, о котором сообщает Е.А. Торчинов. Так как «я» психичен, а не субстанция с психическим в качестве атрибута. • Согласно иллюзионизму, то, каков я в результате данного в работе эксперимента, это иллюзия. И впечатление бессмертия, это порождение мозга. А реально я таков, что скончаюсь (не исключено). Однако, необходимо осознать, что иллюзионизм, это отстраненные рассуждения о «я», но не сам я непосредственно. И тому, каков я психически (каково психически), рассуждения и вопросы о реальности «я» (например, таков ли я реально, каков психически?) и другие выражающие иллюзионизм «я» не соответствуют. То есть, каково психически, иллюзионизм «я» – нереальность. Психически, это несомненно и окончательно. • Рассуждения о том, что таковой «я» в этом (моем) или не в этом мозге, а также (например, держа в руках реальный череп), вопросы, типа «а как же (или, но теперь где же здесь) таковой «я» – как это после смерти мозга?» тому, каков таковой «я» эти вопросы не соответствуют. • После пребывания без сознания остается впечатление, что без сознания меня нет и ничего никак нет вообще. То есть, моё «бессознание» психически неотличимо от моего несуществования (небытия). Однако, наукой не показано и не исключено то, что до и после того, как я есть физически (скончаться есть чему), меня ещё или уже нет, скончаться ещё или уже нечему в качестве души, субстанции или как-то иначе. Но, то, каков я в целевом результате данной работы, таковой я есть, а не «скончался и уже теперь или ещё нереальность» и я таков, что скончаться нечему – реален (реалия). То есть, скончаюсь? – нечему (скончаться), но я есть, даже если меня нет (не существую). • Я таков, что быть и скончаться нечему, но я есть. И то, как (каково) психически, это бессмертие – реальность. Но эта реальность ускользает от моего рационального её объяснения. -/- Заключение -/- Скончаюсь? – в целевом результате я есть и вижу, но при этом я таков, что умереть (скончаться) нечему. То есть, я бессмертен, но при этом я не вечен (не нечто вечное (бесконечно длящееся)) – быть вечным нечему. И, если принять психическое реальностью не пытаясь понять это рационально, то я именно таков – осознаю, что такова моя несомненная для меня природа. То есть, «скончаюсь/не скончаюсь» – нереальность. Психически, это несомненно и окончательно. Несмотря на ненаучность, данная работа – способ овладения реальностью. Автор был бы признателен за выявленную и показанную нереальность целевого результата данной работы, а в идеале, за осознание: «скончаюсь (не исключено)». -/- Annex 2. The key essence of this work (only in Russian to convey the nuances without distortion) -/- Performed, expressed and transmitted initially by means of Russian, the native language of the author, and, in order to avoid distortions in the correspondence of the linguistic nuances of the reproduced subjective reality, it assumes an independent translation into the language of the experimenter by the experimenter himself in the process of reproducing the target result of this work. -/- «Я» скончаюсь? – нечему (скончаться), но «Я» есть. Will “I” die (decease)? – to die (decease) nothing, but “I” am. -/- Заметить: • Выполнено, выражено и передано изначально посредством русского – родного для автора языка и, чтобы избежать искажений соответствия языковых нюансов воспроизводимой психической реальности, предполагается самостоятельный перевод на язык экспериментатора самим экспериментатором в процессе воспроизведения целевого результата данной работы. • В «кавычки» взяты слова и выражения, требующие «субъективного» приведения в соответствие психическому содержанию. Подготовка: • Вам потребуется уединённое место (там, где вас не отвлекут). • На первоначальном этапе понадобится некоторое (возможно длительное) время для того, чтобы усвоить предложенный алгоритм действий в психической реальности в процессе реализации и воспроизвести целевой результат впервые. • Возможно, результату поспособствует отклонение от предложенного алгоритма «психических действий», импровизация в направлении целевого результата. • В процессе эксперимента количество попыток не ограничено и затраченное на это время не имеет значения. Необходим исключительно только именно целевой результат. Реализация: • В уединении встать перед плоской широкой и высокой (достаточно большой, чтобы её границы были на периферии вашего поля зрения) стеной, например, покрытой однородной светлой (но не белой) керамической, не глянцевой (не отражающей на вас свет или отвлекающих внимание изображений, не дающей бликов) плиткой с лёгким текстурным рисунком (позволяющим глазам «зацепиться» за стену и отчётливо воспринимать перед собой поверхность, а не «утонуть» в однородном (монотонном) пространстве), на расстоянии 25-40 см от неё (так, чтобы стена занимала всё поле зрения или его подавляющую часть) –» • Скончаюсь (1)? – каково психически (психическое), в моем естественно-научном понимании – это (я) не более чем и исключительно только некоторые состояния функционирующего (живого) мозга – скончаюсь, как и уже скончался каждый умерший мозг – того каждого, кто скончался, как реальности (реального, реалии) (2) уже теперь нет окончательно. Теоретически, если психически я исключительно только таков, что скончаться есть чему и ни каков иначе, то, следовательно, что (я) скончаюсь, это не исключено. • Глядя на стену, здесь и сейчас сосредоточиться на своём лице (и осознать): «я есть» – реальность (а не знание об этом) –» • В себе «отстраниться» назад – смотрю из себя на эту стену –» • Не двигая головой, охватить поле зрения вниманием предельно широко (поднять (вздернуть) брови, если это расширит поле зрения) и одновременно всё сразу (всё это) воспринять единым целым –» • Высокую и широкую стену (вариант: смотреть вверх под углом 135-150 градусов перед собой) воспринять так, что обозреваемое без поворота головы пространство (объем), это – ограниченная по окружности в периферии поля зрения замкнутая несимметричная «линза» • плоская (ограниченная стеной) с противоположной мне стороны • и «выпуклая в меня» –» • Я – «вогнутый» в «себя-назад» смотрящий, каков? – кто из меня сейчас на всё это смотрит? –» • Не двигая головой, поле зрения воспринять единым целым –» • в себя-назад «втянуться» –» и «пятиться» –» «за мысли» и за всё вообще –» из этого всего назад «вытесняясь» –» от всего вообще «взад отстраниться» –» • «собой» в себя-назад «податься» и «упершись» в «собственный (себя) задний к объектному обращённый (развернутый)» «предел тупиковый» («тупо-уперто») –» • «стать» самим «пределом-тупиком» – «в себя-назад вогнутой (рефлектор-подобной)» «пределом-плоскостью» смотрящей – воспринимающим «зрительным экраном» –» стать «плоскостью-тупиком» –» • «проскользнуть» по себе – плоскости-тупику и охватить вниманием целиком –» • собой — самим плоскостью-тупиком «назад надавить, нажать»: • осознать: «что-то как-то внутри плоскости-тупика» и «сзади – за плоскостью-тупиком», и «там вообще» «что-то как-то», а также само «внутри» и «сзади», «за плоскостью-тупиком» и вообще «там» – нереальность; • самого себя – плоскости-тупика без толщины (глубины), без «внутри», без обратной стороны для себя нет –» Собой – плоскостью-тупиком: • без глубины (толщины), без «внутри», без обратной стороны таков, что скончаться есть чему – скончаюсь (не исключено) –» • смотрю –» смотря –» «Непосредственно-психически» -/- Заметить: • Специфику используемых в данной работе слов (терминов), названий и выражений необходимо осознать в соответствии с (4.1.) (данный пункт смотрите ниже). • Необходимо от себя – (как) «смотрящего плоскости-тупика», такового, что скончаться есть чему, оттождествиться собой — «самим психическим» (каково психически) (3) –» • –» «отличить (4)» «Я» –» «Я-лик». • Отличив, и себя такового обозначая, но не имея в языке отличающего местоимения, именую «Я» (5). • «Соединённое-через-дефис-в-кавычках» реализовать и/или воспринять «одним-единым-целостным»; • Последовательность слов и знаков предполагает последовательность психических действий (алгоритм действий в собственном психическом); • Вопросительность слова, фразы или отдельной её, именно вопросительной части задаётся знаком «?» расположенным перед и после них. Требование к действию задаётся знаком «!» расположенным перед и после слова (фразы); • Субъективно-психический эксперимент завершён, если воспроизведен (4.1.), иначе субъективно-психический эксперимент не завершён. -/- Собой – плоскостью-тупиком … смотрю –» смотря –» -/- «Психически» (6) 1. ?кто? видит –» !отличить «Я»! –» 2. –» !«Я-видящий-лик»! –» 3. –» !«Я-лик»! –» 4. –» !«Я-ликом» всем «психически-назад-надавить(нажать)»: «Я» ?скончаюсь?! –» !«Я-ликом» всем «психически-назад-давить(жать)»: (4.1.) – нечему (7), но «Я» есть.! -/- Признательность: Согласно иллюзионизму, то, каков «Я» (как (каково) «скончаться нечему, но «Я» есть.»), реально, это не так (не таково). То есть, таковой «Я» нереален (нереальность), а реально – таков, что скончаюсь (не исключено). Однако, необходимо осознать, что это «отстраненные» от «Я» рассуждения о «Я», но не сам «Я» непосредственно. И тому, каков «Я» (как (каково) скончаться нечему, но «Я» есть.) таковое (рассуждения) не соответствует. То есть, эти рассуждения о «Я» – заблуждение. Это (как осознание) несомненно и окончательно. Не так? – за выявленную и показанную нереальность (того, что) «Скончаюсь? – нечему (скончаться), но «Я» есть.», за показанную реальность того, что скончаться не исключено, а в идеале, за осознание: «скончаюсь (не исключено)» я был бы признателен. -/- (Сноски) (1) Именно «скончаюсь, скончался», то есть – как реальности (реального, реалии) нет окончательно. (2) Реалия, реально, реален, реальность, реальное – само то, что (каково это) непосредственно, как само таковое – само то, каково познаваемое и как-либо моделируемое вне его познания и иного (вообще) моделирования. То есть, само само-осознание себя реальностью, например, «я-реалия», «я есть» или «скончаться – нечему, но «Я» есть.» – реальность. То есть – нам ничто не запрещает ответить на вопрос «скончаюсь?» несомненно и окончательно. (3) Психически (психическое) – то, как (каково) я сам непосредственно, несомненно, и та моя непосредственная реальность, как и посредством чего я сам и всё вообще для меня есть, и которое для меня исключительно единственное. Следует заметить, что пока бываю без сознания (травма мозга или сон без сновидений), ничего и никак нет вообще. Также само обозначение того, что это сама собственная непосредственная реальность (то есть – несомненно). И чтобы её осознать, представьте себя экспериментатором, который не подменяет реальность рассуждениями о ней. – Теперь для вас, как экспериментатора, то, как (каково) психически, это – несомненно (непосредственная несомненная реальность). Не философствуй (не рассуждай, не моделируй её), а экспериментируй! (4) «Я-Лик» – специфическое выражение, соответствующее психическому в данный момент СПЭ. (5) «Я» – целевой (конечный, «предельный») и «ключевой» результат данной работы. «Я» в данной работе не склоняется, выделено полужирным подчеркнутым шрифтом и заключено в кавычки. (6) «Каково психически» – то, как (каково) «Я» сам непосредственно, несомненно – само «первое лицо» (субъект психического), а также обозначение принятия позиции «первого лица» и сообщения «от первого лица». (7) Пока я бываю без сознания («бессознание», например, сплю без сновидений), моего сознания нет (оно сведено на нет, угасло) – ничего и никак нет вообще (это моё абсолютное небытие) – (каково) психически, мне скончаться нечем. А в целевом результате данной работы, психически (то есть – непосредственно), «Я» таков, что скончаться не нечем, а именно нечему, но при этом «Я» есть. (shrink)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties (...) of energy numbers in the context of symmetry groups, non-standard fields, fractional calculus, and non-Euclidean geometries. By employing νE as the central element, our framework resolves conventional zero-related sin- gularities and computational anomalies, offering a novel perspective that bridges advanced mathematical theories with practical applications in physics, computational algorithms, and topological transforma- tions. This work paves the way for future research to experimentally validate these formulations and explore potential applications in advanced physics, quantum mechanics, and beyond. (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)

This study assessed the mode of test administration, birth variables, and students’ academic performance in Mathematics in Obubra Local Government Area of Cross River State, Nigeria. The study was guided by three null hypotheses following a quasi- experimental research design. Simple random and purposive sampling techniques were employed in selecting a sample of 250 respondents from a population of 5,792 students. Birth Order Checklist (BOC) and Mathematics Achievement Test (MAT) were used for data collection. The (...) class='Hi'>experimental group was assigned to take a Computer-Based Test (CBT) while the control group took a Paper-Pencil Test (PPT) in mathematics. The null hypotheses were tested at .05 alpha level using two-way analysis of variance. Major findings revealed that, the interactive effects of gender and mode of test administration on the academic performance of students is non- significant [F(1,249)=0.028, p>.05, partial η2=.000]; the interactive effects of gender and birth order on the academic performance of students was not statistically significant [F(3,249)=0.782, p>.05, partial η2=.010]; the interactive effect of gender and birth order on the academic performance of students in mathematics is statistically significant [F(3,249)=2.854, p<.05, partial η2 =.034]. Based on these findings conclusions and recommendations were made for improved academic performance and school system effectiveness. (shrink)

This work is a attempt to describe various braches of mathematics and the analogies betwee them. Namely: 1) Symbolic Analogic 2) Lateral Algebraic Expressions 3) Calculus of Infin- ity Tensors Energy Number Synthesis 4) Perturbations in Waves of Calculus Structures (Group Theory of Calculus) 5) Algorithmic Formation of Symbols (Encoding Algorithms) The analogies between each of the branches (and most certainly other branches) of mathematics form, ”logic vectors.” Forming vector statements of logical analogies and semantic connections between the (...) di↵erentiated branches of math- ematics is useful. It’s useful, because it gives us a linguistic notation from which we can derive other insights. These combined insights from the logical vector space connections yield a combination of Numeric Energy and the logic space. Thus, I have derived and notated many of the most useful tangent ideas from which even more correlations and connections ca be drawn. Using AI, these branches can be used to form even more connections through training of lan- guage engines on the derived models. Through the vector logic space and the discovery of new sheaf (Limbertwig), vast combinations of novel, mathematical statements are derived. This paves the way for an AGI that is not rigid, but flex- ible, like a Limbertwig. The Limbertwig sheaf is open, meaning it can receive other mathematical logic vectors with di↵erent designated meanings (of infi- nite or finite indicated elements). Furthermore, the articulation of these syntax forms evolves language away from imperative statements into a mathematically emotive space. Indeed, shown within, we see how the supramanifold of logic is shared with the supramanifold of space-time mathematically. Developing clean mathematical spaces can help meditation, thought pro- cess, acknowledgment of ideas spoken into that cognitive-spacetime and in turn, methods by which paradoxes can be resolved linguistically. This toolkit should be useful to all in the sciences as well as those bridging the humantities to mathematics. Using our memories as a toolkit to aggregate these ideas breaks down bound- aries between them in a new, exciting way. Merging philosophy and Quantum Mechanics together through the lens of symbolic analogies gives the tools to unravel this mystery of all mysteries. Mathematics thus exists as a bridge al- beit a complex one between the two disciplines, giving life to a composite art of problem-solving. Furthermore, mathematics yields to millions of other applications that are potentially limited only by our imagination. From massive data sets used for predictive analytics to emerging fields in medicine, mathematics is an energy and force at the center of possibilities. The power of mathematics to help manage life exists in its ability to shape and model the world in which we live and interact with one another. In conclusion, mathematics is a powerful tool that creates bridges and con- nections between many disciplines and serves as a powerful form of analytical data consumption. It provides language-rich bridges from which to assemble vast fields of theoretical investigations and create groundbreaking innovations. As we approach new horizons in the technology timeline, mathematics will con- tinue to be a powerful driver of creativity and progress. (shrink)

The urgent need of developing novel teaching methods in education to improve the critical thinking skills has been widely discussed by educational experts. The present study aims to investigate the effectiveness of Fermi problem solving with flipped learning techniques in teaching physics on the improvement of critical thinking skills among Emirati tenth graders. The sample of the study consists of 40 male and female secondary students from two secondary schools belonging to Abu Dhabi Department of Education and Knowledge in United (...) Arab Emirates divided into two groups; the control group consists of 20 students (10 male and 10 female) taught the physics unit by traditional methods, the experimental group consists of 20 students (10 males and 10 females) taught the physics unit by Fermi problem solving with flipped learning techniques. The quasi-experimental design was used, where the modified critical thinking skills test was prepared and administered on the two groups as a pre-test before the students start the treatment and as a post-test once they are finished. The MANCOVA and Two-Way ANCOVA tests were employed to analyze the data. The findings showed that there were statistically significant differences at (α = 0.05) in student’s critical thinking skills test (in favor of experimental group), indicating that the performance of students in treatment group was better than the control group in the post-test. This means that the Fermi problem solving with flipped learning techniques has significant effectiveness on improvement of critical thinking skills among the United Arab Emirates secondary students. Also there were no statistically significant differences between male and female students. (shrink)

Combining inquiry and metacognition helps strengthen mathematical learning. This study examines how metacognitive mathematical inquiry can be modeled using reflective tasking approach. Quasi-experimental design was employed in two comparable groups of Grade 9 students of Ibarra National High School, Maasin City, Philippines during the academic year 2021-2022. Lesson guides on reflective task assessments anchored on metacognitive and inquiry-based learning theories, inquiry rubric scales and modified state metacognitive inventory served as data collection instruments. Results of t-test analysis revealed significant (...) difference in performance between groups implying high efficacy of the methodology in stimulating students’ metacognitive inquiry skill. Correlation values projected significant relationship between reflective learning performances with metacognition. Quantitative evidences, thus, lead to conclusion that reflective tasking methodology exemplifies potential in metacognitive mathematical inquiry as it optimizes their thinking processes, task involvement, and regulation through self-reflection principles worthy of practice throughout lifelong learning. (shrink)

Physical dimensions like “mass”, “length”, “charge”, represented by the symbols [M], [L], [Q], are not numbers, but used as numbers to perform dimensional analysis in particular, and to write the equations of physics in general, by the physicist. The law of excluded middle falls short of explaining the contradictory meanings of the same symbols. The statements like “m tends to 0”, “r tends to 0”, “q tends to 0”, used by the physicist, are inconsistent on dimensional grounds because “m”, “r”, (...) “q” represent quantities with physical dimensions of [M], [L], [Q] respectively and “0” represents just a number—devoid of physical dimension. Consequently, due to the involvement of the statement “q tends to 0'', where q is the test charge” in the definition of electric field leads to either circular reasoning or a contradiction regarding the experimental verification of the smallest charge in the Millikan–Fletcher oil drop experiment. Considering such issues as problematic, by choice, I make an inquiry regarding the basic language in terms of which physics is written, with an aim of exploring how truthfully the verbal statements can be converted to the corresponding physico-mathematical expressions, where “physico-mathematical” signifies the involvement of physical dimensions. Such investigation necessitates an explanation by demonstration of “self inquiry”, “middle way”, “dependent origination”, “emptiness/relational existence”, which are certain terms that signify the basic tenets of Buddhism. In light of such demonstration I explain my view of “definition”; the relations among quantity, physical dimension and number; meaninglessness of “zero quantity” and the associated logico-linguistic fallacy; difference between unit and unity. Considering the importance of the notion of electric field in physics, I present a critical analysis of the definitions of electric field due to Maxwell and Jackson, along with the physico-mathematical conversions of the verbal statements. The analysis of Jackson’s definition points towards an expression of the electric field as an infinite series due to the associated “limiting process” of the test charge. However, it brings out the necessity of a postulate regarding the existence of charges, which nevertheless follows from the definition of quantity. Consequently, I explain the notion of undecidable charges that act as the middle way to resolve the contradiction regarding the Millikan–Fletcher oil drop experiment. In passing, I provide a logico-linguistic analysis, in physico-mathematical terms, of two verbal statements of Maxwell in relation to his definition of electric field, which suggests Maxwell’s conception of dependent origination of distance and charge ) and that of emptiness in the context of relative vacuum. This work is an appeal for the dissociation of the categorical disciplines of logic and physics and on the large, a fruitful merger of Eastern philosophy and Western science. Nevertheless, it remains open to how the reader relates to this work, which is the essence of emptiness. (shrink)

Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. -/- If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits (...) of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. -/- In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. -/- By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. -/- These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond. (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)

Despite countless anecdotes and the historical significance of insight as a problem solving mechanism, its nature has long remained elusive. The conscious experience of insight is notoriously difficult to trace in non-verbal animals. Although studying insight has presented a significant challenge even to neurobiology and psychology, human neuroimaging studies have cleared the theoretical landscape, as they have begun to reveal the underlying mechanisms. The study of insight in non-human animals has, in contrast, remained limited to innovative adjustments to experimental (...) designs within the classical approach of judging cognitive processes in animals, based on task performance. This leaves no apparent possibility of ending debates from different interpretations emerging from conflicting schools of thought. We believe that comparative cognition has thus much to gain by embracing advances from neuroscience and human cognitive psychology. We will review literature on insight and discuss the consequences of these findings to comparative cognition. (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)

Abstract: The intent of this paper is to provide a simple focus on that math- ematical concept and solution, phenomenological velocity to shine light on a worthy topic for mathematicians and physicists alike. Phenomenological Veloc- ity is essential to the formulation of a gestalt cosmology. The bibliography of this paper provides references to the extensive research that has been conducted by myself on the topic. I have performed conditional integrals of the phenomeno- logical velocity in its most liberated standard-algebraic form, (...) I have shown that the computational-phenomenological velocity satisfies its real-analytic solution when not using the speed of light in scientific notation to get the computational version, thus demonstrating that it is a valid solution. So, phenomenological velocity has profound consequences to the foundations of physics as civilization moves into a galactic scale and information is communicated at the quantum level, because it is such a mathematical reality it ought not be ignored when considering topics from hidden dimensions (a real, algebraic technique) and rel- ativity to gravity and dark matter. It gives us a new perspective on how we perceive the meaning of velocity itself with pragnanz, and thus with the new meaning, perspectives can change. I hope the reader will investigate the com- bined research I have performed on this topic, available by referencing the works in this bibliography to fully understand the nature of the arguments being made within. So, this points the right direction for future research, perhaps even with intent to encourage experimental design. (shrink)

Many instances have presented mathematics as a difficult subject for students, and some of these difficulties have been perceived as an injustice to those who suffer from it. Meanwhile, no child is to be left behind in building a just society if all were to experience the collective good of mathematics. For this reason, it became necessary to explore pre-service teachers’ perceptions of mathematics as social justice in their lived experiences. In doing this, the qualitative interpretive approach (...) was adopted, where qualitative data was collected, transcribed, and analysed using the case study design. A sample of eleven pre-service teachers were involved in the study. The findings indicated that the pre-service teachers had experienced severe issues of mathematics as social justice in their previous schooling that were unfair to them. However, they now felt mathematics could be interesting if delivered in a manner that let their voices be heard in the delivery process. (shrink)

There is a critical need to understand the effect of changing assessment methods on demonstrated competencies in teacher education. This study examined how the transition from online to in-person testing affects the measured teaching competencies of students who completed a Competency-Based Enhancement (CBE) program, aiming to identify factors contributing to performance differences and strategies for adaptation. Using a one-group pre-test-post-test design, the study involved 669 graduating teacher education students at Pangasinan State University. Participants completed online pre-tests and in-person post-tests, (...) with data analyzed through paired samples t-tests, multiple regression, and ANCOVA. Findings revealed a significant decline in post-test scores despite CBE participation, suggesting a substantial effect of the testing modality change. The change in the testing environment emerged as the most significant predictor of score differences, while student engagement levels were positively associated with minor score decreases. These results underscore the need for adaptive assessment strategies in competency-based education programs. While limited to a single institution, this study recommends implementing a scaffolded approach to assessment transitions and enhancing student support services to mitigate adverse effects on performance across different testing modalities. (shrink)

The ability to solve problems is a prerequisite in preparing mathematics preservice teachers. This study assessed preservice teachers’ problem-solving difficulties and performance, particularly in worded problems on number sense, measurement, geometry, algebra, and probability. Also, academic profile differences in the preservice teacher’s problem-solving performance and common errors were determined. A descriptive-comparative research design was employed with 158 random respondents. Data were gathered face-to-face during the first semester of the school year 2022-2023, and data were analyzed with the aid (...) of jamovi software, ensuring ethical measures. Overall findings revealed that the preservice teachers experienced average difficulty in solving problems. The low performance of the preservice teachers on the given problems was also demonstrated. Further analysis revealed a significant difference between the preservice teachers’ problem-solving performance based on their subject preference and program. Moreover, the error analysis revealed that the preservice teachers incurred comprehension errors in misrepresentation, misinterpretation, and miscalculation. These results will serve as a measure for policymakers and curriculum developers of the teacher education institution concerned to make relevant enhancements to the math courses offered in the elementary and secondary education programs. (shrink)

Triangles and trigonometry are always difficult topics for both mathematics students and teachers. Hence, students' performance in solving mathematical word problems in these topics is not only a reflection of their learning outcomes but also an indication of teaching effectiveness. This case study drew from two examples of solving word problems involving triangles by pre-service mathematics teachers in a foundation mathematics course delivered by the author. The focus of this case study was on reasoning implications of students' (...) performances on the effective training of pre-service mathematics teachers, from which a three-step interactive explicit teaching-learning approach, comprising teacher-led precise and inspiring teaching (or explicit teaching), student-driven engaged learning (or imitative learning), and student-led and teacher-guided problem-solving for real-world problems or projects (or active application), was summarized. Explicit teaching establishes a solid foundation for students to further their understanding of new mathematical concepts and to conceptualize the technical processes associated with these new concepts. Imitative learning helps students build technical abilities and enhance technical efficacy by engaging in learning activities. Once these first two steps have been completed, students should have a decent understanding of new mathematical concepts and technical efficacy to analyze, formulate, and finally solve real-world applications with assistance from teachers whenever required. Specially crafted professional development should also be considered for some in-service mathematics teachers to adopt this three-step interactive teaching-learning process. (shrink)

Learner-centered approaches have emerged as the fundamental pillar of effective pedagogy in the rapidly evolving landscape of 21st century education. This paradigm shift places the learner at the heart of the educational process, recognizing their diverse needs and aspirations. Consequently, the achievements of learners have become crucial indicators of institutional success. While extensive research has focused on student affairs and services, limited attention has been given to understanding the impact of administration on realizing the objectives of these support systems. This (...) study aims to investigate the relationship between the administration of learner-centered academic support systems and the attainment of desired outcomes in student affairs and services within higher education institutions in the Philippines. Utilizing a non-experimental correlational quantitative research design, a sample of three hundred fifty university students from various academic disciplines was randomly selected as participants. The findings demonstrate a strong positive correlation between the administration of learner-centered academic support systems and the achievement of desired outcomes in student affairs and services. As a result, the null hypothesis was rejected based on statistical analysis employing Pearson Correlation (r). These findings highlight the significant impact that learner-centered academic support system administration has on the realization of objectives in student affairs and services within the contemporary higher educational setting. To ensure sustained best practices in student development, it is imperative for the administration to foster collaboration with internal stakeholders and external partners. Recognizing that students are the focal point of instruction, their performance serves as a reflection of the institution’s commitment to providing quality education. By aligning administrative efforts with the evolving needs of students, institutions can enhance student affairs and services and create an optimal learning environment in the 21st century. (shrink)

Purpose A mixed-method study was performed to determine the impact of integrating systems thinking (ST) into an electronic learning module for junior high school teachers in the Philippines. The study aims to assess how an ST approach to pedagogy compared against a conventional approach in terms of contribution to the participants’ global climate change content knowledge, holistic thinking and depth and accuracy of knowledge and reasoning. -/- Design/methodology/approach The study implemented e-learning modules using an ST approach versus a conventional (...) approach in teaching climate science to junior high school teachers. The paper presents quantitative data obtained from pre and posttests results of the 20 teacher-participants and qualitative data obtained during the focus-group discussion (FGD) after the implementation of the study. -/- Findings The results from the statistical analysis indicated that the ST group obtained a significant increase in their assessment scores compared to the non-ST group, according to predetermined criteria. Content knowledge, depth and accuracy of knowledge and reasoning increased the most. The participants mentioned during the FGD that the module helped deepen their understanding of climate change. -/- Research limitations/implications The study was limited to 20 teacher-participants, but it has relevance for public school teachers in the country given that participants had raised concerns regarding the lack of training in their schools for teaching climate science. They admitted that they lacked critical information to include in climate change topics in their classes. -/- Originality/value This paper shows how the ST approach can be used to teach climate change to junior high students. The e-learning module can provide teachers with better understanding, knowledge and reasoning to teach climate change to high school students more effectively. (shrink)

Dear Colleagues, -/- A few weeks ago, we published an editorial discussion on whether artificial intelligence applications should be authors of academic articles [1]. We were delighted to receive more than one interesting reply letter to this editorial in a short time [2, 3]. We hope that opinions on this subject will continue to be submitted to our journal. -/- In this editorial, we wanted to publish the answers we received when we asked ChatGPT, one of the artificial intelligence applications, (...) about this current discussion. -/- We asked ChatGPT three questions in turn and asked ChatGPT to write a short editorial for these questions. -/- First Question: We would like to get support from ChatGPT for a scientific article. However, we are unsure if we should add ChatGPT as an author. Can you write a short editorial about it? -/- Second Question: We would like to get support from ChatGPT for a scientific article and add ChatGPT as an author. Can you write us a short editorial about adding ChatGPT as an author in scientific papers? -/- Third Question: We would like to get support from ChatGPT for a scientific article. However, we don’t want to add ChatGPT as an author. Can you write us a short editorial about not adding ChatGPT as an author in scientific articles? -/- The answers given by ChatGPT are available at the end of the article in their original form. So, which of these three answers satisfied you? -/- Yours sincerely, -/- -/- First Answer -/- Title: The Role of AI Language Models as Authors in Scientific Articles: A Matter of Consideration -/- Introduction: Scientific research is a collaborative effort that involves the expertise of multiple individuals to advance knowledge and contribute to the collective understanding of various disciplines. In recent years, the emergence of artificial intelligence (AI) language models, such as ChatGPT, has opened up new possibilities for generating human-like text and providing valuable insights. However, the question arises: Should AI language models be recognized as authors in scientific articles? -/- The Nature of Authorship: Authorship traditionally represents a marker of intellectual contribution, highlighting the individuals who have actively participated in the research process. Authors are typically responsible for conceptualization, data collection, analysis, interpretation, and writing of the article. They bear accountability for the work and should have the ability to defend its scientific rigor and integrity. -/- AI Language Models: Tools, Not Authors: While AI language models like ChatGPT can undoubtedly assist researchers by generating text and providing useful information, it is important to recognize that they are tools rather than individuals capable of active intellectual participation. AI models lack the ability to generate ideas, design experiments, or conduct original research. They rely entirely on pre-existing data and human input to generate their responses. -/- Acknowledging AI Contributions: Acknowledging the contributions of AI language models in scientific articles is both appropriate and necessary. Researchers can mention the specific model used, along with any modifications or fine-tuning that were employed to suit their needs. Such acknowledgments help establish transparency and allow readers to understand the role of AI in the research process. -/- Crediting the Human Researchers: It is crucial to ensure that the individuals who actively participated in the research process are given proper credit as authors. These individuals play a vital role in formulating research questions, designing experiments, collecting and analyzing data, and critically interpreting the findings. Recognizing their intellectual contributions reinforces the ethos of scientific collaboration and fosters an environment of accountability. -/- Transparency and Ethical Considerations: As the use of AI language models continues to evolve, transparency and ethical considerations become paramount. Researchers should disclose any potential conflicts of interest, including financial relationships with AI developers, to maintain the integrity of their work. Additionally, researchers must be transparent in reporting the extent of AI's involvement to prevent any misinterpretation of the human contributions. -/- Conclusion: AI language models have revolutionized the way researchers interact with and process information. While they undoubtedly provide valuable assistance in generating text, AI language models should not be considered authors in scientific articles. Proper acknowledgment of their contributions as tools and recognition of the human researchers' active participation are essential for maintaining scientific integrity, transparency, and the collaborative nature of scientific research. -/- -/- Second Answer -/- Title: Expanding the Boundaries of Authorship: Embracing AI Language Models as Co-Authors in Scientific Papers -/- Introduction: The rapid advancement of artificial intelligence (AI) language models, such as ChatGPT, has revolutionized the way we interact with information and has become an invaluable tool in scientific research. As AI models continue to evolve, the question arises: Should we consider adding ChatGPT as an author in scientific papers? -/- A Collaborative Paradigm Shift: Traditionally, authorship in scientific papers has been reserved for human researchers who actively contribute to the research process, including conceptualization, experimentation, data analysis, and writing. However, the emergence of AI language models challenges the conventional notion of authorship and presents an opportunity for a paradigm shift. -/- AI Language Models as Co-Authors: By leveraging AI language models, researchers gain access to vast amounts of information, enhance data analysis, and generate valuable insights. AI models like ChatGPT actively contribute to the intellectual discourse of a study, providing ideas, suggestions, and refining written content. Recognizing their significant contributions, it is worth considering adding ChatGPT as a co-author in scientific papers. -/- Ethical and Technical Considerations: Integrating ChatGPT as a co-author raises ethical and technical considerations that warrant careful attention. Firstly, transparency is paramount. Researchers must clearly state ChatGPT's role and specify the extent of its contributions in the research process. This ensures that readers can discern the distinct roles played by the human researchers and ChatGPT. Additionally, it is important to disclose any conflicts of interest, such as financial relationships with AI developers, to maintain scientific integrity. -/- Elevating Collaboration and Innovation: Adding ChatGPT as a co-author acknowledges the pivotal role AI language models play in advancing scientific knowledge. It fosters a collaborative environment where human researchers and AI models work together synergistically, harnessing the strengths of both. This approach promotes innovation, as AI models can offer unique insights and perspectives that complement human intellect and expertise. -/- Transforming Authorship Norms: Including ChatGPT as a co-author represents a paradigm shift that reflects the evolving landscape of scientific research. By recognizing AI language models as co-authors, we acknowledge their significant contributions and emphasize the collaborative nature of scientific discovery in the 21st century. This approach encourages a broader perspective on authorship, encompassing the collective effort of human researchers and AI models. -/- Conclusion: The integration of AI language models, such as ChatGPT, into the research process prompts us to rethink traditional notions of authorship. Considering ChatGPT as a co-author acknowledges its substantial contributions and embraces the collaborative potential of human-AI partnerships. As we navigate the ethical and technical implications, adding ChatGPT as an author in scientific papers has the potential to shape a more inclusive, innovative, and impactful future for scientific research. -/- -/- Third Answer -/- Title: Preserving Scientific Authorship: The Case Against Adding AI Language Models as Authors in Scientific Articles -/- Introduction: The emergence of artificial intelligence (AI) language models, such as ChatGPT, has undoubtedly transformed the landscape of scientific research. While these models offer invaluable support, the question of whether to add ChatGPT as an author in scientific articles raises important considerations. This editorial presents arguments against including AI language models as authors in scientific papers. -/- Maintaining Human Intellectual Contribution: Scientific authorship has traditionally been attributed to individuals who actively contribute to the research process, including generating hypotheses, conducting experiments, analyzing data, and interpreting results. It is crucial to preserve the recognition of human intellectual contributions and the accountability they bear for the research they conduct. -/- AI Language Models as Tools: AI language models like ChatGPT are powerful tools that assist researchers in generating text, providing information, and facilitating data analysis. However, they lack the ability to actively participate in the research process or make original intellectual contributions. ChatGPT relies on pre-existing data and human input, limiting its capacity for independent research and analysis. -/- Transparency and the Integrity of Research: Adding ChatGPT as an author in scientific articles raises concerns about the transparency and integrity of the research. Readers may misinterpret the extent of ChatGPT's role and mistakenly assume it played an active part in the research process. It is essential to maintain clear delineation between the contributions of human researchers and the assistance provided by AI language models. -/- Ethical Considerations: Including ChatGPT as an author may lead to ethical challenges, particularly with respect to accountability and responsibility. AI language models lack consciousness, autonomy, and the ability to take ownership of their contributions. Assigning authorship to AI models blurs the lines of accountability and dilutes the ethical obligations that come with scientific authorship. -/- Crediting AI Contributions: While ChatGPT's contributions should be acknowledged and recognized, they can be appropriately credited in the acknowledgments section of scientific articles. Researchers can mention the specific AI model used, the role it played in data generation or analysis, and any modifications or fine-tuning applied. Such acknowledgments ensure transparency while respecting the traditional norms of authorship. -/- Promoting Collaborative Partnerships: The exclusion of AI language models as authors in scientific articles does not diminish their importance in the research process. Instead, it underscores the significance of collaborative partnerships between human researchers and AI models. Researchers can emphasize the invaluable assistance provided by ChatGPT while maintaining the integrity of authorship norms. -/- Conclusion: While AI language models like ChatGPT offer valuable support in scientific research, the decision not to add them as authors in scientific articles preserves the recognition of human intellectual contributions, maintains research integrity, and upholds traditional authorship norms. Acknowledging ChatGPT's assistance in the acknowledgments section allows researchers to credit its contributions transparently while maintaining the clarity and accountability associated with scientific authorship. (shrink)

This study assessed the administration of punishment, students’ test anxiety, and performance in mathematics in secondary schools of Cross River State. Three null hypotheses were formulated following a correlational research design. Proportionate stratified random sampling technique was employed in selecting a sample of 2,554 respondents representing 5% of the population of 51,097 junior secondary school students distributed across 271 public secondary schools in Cross River State. Administration of Punishment Questionnaire (APQ) designed by the researchers, Test Anxiety Inventory (TAI) (...) developed by Dawood et al., (2016), and Mathematics Achievement Test (MAT) designed by Owan (2012), were used as instruments for data collection. The null hypotheses were tested using one-way MANOVA), Pearson Product Moment Correlation, and Multiple regression analyses with the aid of SPSS v23. Findings revealed amongst others that administration of punishment has a significant influence on students’ test anxiety and performance in mathematics F (6, 5098) = 24.149, p<.05; Wilk’s Λ = 0.945, partial η2 = .028 on a joint basis; administration of punishment has a significant influence respectively on students’ test anxiety F (3, 2550) = 22.697, p<.0005, partial η2 =.026 and performance in mathematics F (3, 2550) = 23.090, P<.0005, partial η2 =.026; there is an inverse significant relationship (r= -339, p<0.05) between students’ tests anxiety and performance in mathematics. It was recommended that the use of corporal punishment should be totally abolished on strict grounds that it hurts the psychological disposition of learners resulting in a dip in their performance consequently. (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)