In the first part of this investigation we highlight two, seemingly irreconcilable, beliefs that suggest an impending crisis in the teaching, research, and practice of—primarily state-supported—mathematics: (a) the belief, with increasing, essentially faith-based, conviction and authority amongst academics that first-order Set Theory can be treated as the lingua franca of mathematics, since its theorems—even if unfalsifiable—can be treated as ‘knowledge’ because they are finite proof sequences which are entailed finitarily by self-evidently Justified True Beliefs; and (...) (b) the slowly emerging, but powerfully rooted in economic imperatives, belief that only those Justified True Beliefs can be treated as ‘knowledge’ which are, further, categorically communicable as Factually Grounded Beliefs—hence as comprehensible pre-formal ‘mathematical truths’—by any intelligence that lays claims to a mathematical lingua franca. We argue that this seeming irreconcilability merely reflects a widening chasm between an increasing under-estimation of the value to society of ‘semantic arithmetical truth’, and an increasing over-estimation of the value to society of ‘syntactic set-theoretical provability’; a chasm which must be narrowed and bridged explicitly. We thus proffer a Complementarity Thesis which seeks to recognize that mathematical ‘provability’ and mathematical ‘truth’ need to be interdependent and complementary, ‘evidence-based’, assignments-by-convention to the formulas of a formal mathematical language; where (a) the goal of mathematical ‘proofs’ may be viewed as seeking to ensure that any mathematical language intended to formally represent our pre-formal conceptual metaphors and their inter-relatedness is unambiguous, and free from contradiction; whilst (b) the goal of mathematical ‘truths’ must be viewed as seeking to ensure that any such representation does, indeed, uniquely identify and adequately represent such metaphors and their inter-relatedness. Our thesis is that, by universally ignoring the need to introduce goal (b) in our curriculum, the teaching of, and research in, mathematics at the post-graduate level cannnot justify its value to society beyond the mere intellectual stimulation of individual minds. In the second part we appeal to some recent—and hitherto unsuspected—unarguably constructive Tarskian interpretations, of the first-order Peano Arithmetic PA, which establish PA as both finitarily consistent, and categorical. Since we also show that the second order subsystem ACA0 of Peano Arithmetic and PA cannot both be assumed provably consistent, we conclude that there can be no mathematical, or meta-mathematical, proof of consistency for Set Theory. Hence the theorems of any Set Theory are not sufficient for distinguishing between (i) what we can believe to be a ‘mathematical truth’; (ii) what we can evidence as a ‘mathematical truth’; and (iii) what we ought not to believe is a ‘mathematical truth’; whilst the theorems of the first-order Peano Arithmetic PA are sufficient for distinguishing between (i), (ii) and (iii). We conclude from this that the holy grail of mathematics ought to be ‘arithmetical truth’, not ‘set-theoretical proof’. (shrink)

J. N. (Jitendra Nath) Mohanty (1928–2023). -/- Professor J. N. Mohanty has characterized his life and philosophy as being both “inside” and “outside” East and West, i.e., inside and outside traditions of India and those of the West, living in both India and United States: geographically, culturally, and philosophically; while also traveling the world: Melbourne to Moscow. Most of his academic time was spent teaching at the University of Oklahoma, The New School Graduate Faculty, and finally Temple University. Yet (...) his preeminent work in Husserlian phenomenology developed alongside his eminent work in Indian philosophy: describing his interests as “a fusion of disparate horizons.” -/- J. N. Mohanty was born September 26, 1928, in Cuttack (Odisha, East India). After graduating from high school, he went on to study both Indian and Western philosophy in Calcutta, earning bachelor’s and master’s degrees. There he read Whitehead and Kant’s First Critique; although he wanted to include mathematics in his curriculum, he was led instead to include Indian philosophy and Sanskrit. On the shelves of his teacher, Ras Vihar Das, he came upon a copy of the English translation (Ideas I, 1931) of Edmund Husserl’s classic Ideen I (1913), which presented Husserl’s ground-breaking conception of phenomenology. In 1952–1954 he left India for the first time, reaching Göttingen to study mathematics and philosophy, which earned him a doctorate in mathematics and “philosophy of mathematical sciences” (in his own words). In Göttingen, Mohanty found the powerful mathematical world that Husserl himself had earlier interacted with, where several Husserl students had formed the Göttingen school of phenomenology. During these years Mohanty studied primarily mathematics, alongside Kant and also Vedic Sanskrit. From his friend Günter Patzig, interpreter of Aristotle and Frege, Mohanty was drawn to Frege in relation to mathematical logic. He attended lectures of Heidegger, intrigued by his ontological thinking. Yet, despite the Husserlian legacy, Mohanty was completely self-taught in his studies of Husserl (as he has reported). With a doctorate in mathematics, and ideas from Kant and Frege in his philosophical background, Mohanty set about crafting his own conception of philosophy grounded in phenomenology, drawing on Husserl’s extensive work, critically sifting through Husserl’s texts and their emerging concepts of intentionality, meaning, subject, intersubjectivity, and world. In between he wrote his first book-length study: on phenomenological insights in Nicolai Hartmann and A. N. Whitehead (1958). -/- Over many decades Mohanty formulated and argued, in analytical detail, for a conception of phenomenology and its place in philosophy, later presented in a clear and concise book titled Transcendental Phenomenology: An Analytic Account (1989). Over these very decades the same scholar explored classical and recent Indian philosophy, thinking through kindred ideas of consciousness, self, and knowledge drawn from the Indian philosophical contexts. While writing on Nyāya theory of truth, he also pondered whether the world and finite individual are illusory or real, and whether Marx, Arendt, Gandhi (whom he heard speak in Calcutta), or Vinoba Bhave (with whom he marched across India for the land-grant movement) could best navigate post-Independent India’s social and svarāj or self-rule reforms. The two Mohantys, thinking through a vision of self and world, turned out to be “non-different” or “non-dual” as they each practiced critical phenomenology from both inside and outside the respective philosophical and cultural traditions. Numerous students, fellows, and colleagues or collaborators have benefited immensely from this infusion and unified approach to diversity in philosophical thought. In the 2000s, moving into retirement, Mohanty wrote two long books devoted to his understanding of Husserl and phenomenology and the calling of philosophy itself. This two-volume study shows Mohanty himself thinking through Husserl, critically, in The Philosophy of Edmund Husserl: A Historical Introduction (2008), and Edmund Husserl’s Freiburg Years: 1916–1938. As Mohanty worked on Husserl, he carefully indicated where he agreed and where he rejected or changed ideas, all part of his practice in phenomenology of “description and interpretation.” It was the same pattern he used in addressing the thought of Husserl vis-à-vis Kant or Frege or even Quine. -/- As Mohanty developed his understanding of phenomenology over the years, he wrote books on theory of meaning and the concept of intentionality, developing a model of ideal meaning and its foundation in intentionality, drawing on Husserl’s results. He followed these with the book Husserl and Frege (1982), linking the thought of those foundational figures for the “continental” and “analytic” traditions, respectively, in twentieth-century Western philosophy. Over his long career Mohanty addressed both traditions in his clear and accessible writing style. While developing his views on phenomenology, Mohanty regularly looked to “Husserl and his others,” evaluating views in Heidegger, Sartre, Merleau-Ponty, Ricoeur, and then Derrida and others in the wake of Husserl. With his background in Kant, Mohanty also looked toward Heidegger and Hegel in relation to Husserl’s later work in the Crisis (1935–38). Similarly, he looked to contemporary analytic philosophers, adjudicating his own, oft-wise Husserlian views in relation to Frege, Nagel, and others. Amid his active scholarly career, Mohanty co-founded the journal Husserl Studies, and was editorial advisor to Philosophy & Phenomenological Research, Philosophy East & West, Journal of Indian Philosophy, Sophia, among others. -/- Yet all this while Mohanty was also thinking and writing about Indian philosophy and its relation to phenomenology. In his own retrospective, Indian philosophy is “the permanent background” of his Husserlian thinking, while Kant is the recurrent Western background of his Husserlian phenomenology. Mohanty’s form of “transcendental phenomenology” evolved, in his own perspective, against the background of his studies of Navya-Nyāya on logic and Vedānta on consciousness, in Indian philosophy, and against the background of Kant’s First Critique on the transcendental, in Western philosophy. Accordingly, Mohanty’s study of logical form and of the intentionality of consciousness seeks a fusion of East and West in the conception of transcendental phenomenology. (Cf. Mohanty’s apt response to critics in The Empirical and the Transcendental (2000).) Even in the context of North American Husserl scholarship, Mohanty has exercised an earnest fusion of East and West. For the so-called East Coast and West Coast interpretations of Husserl’s crucial notion of noema both find a sympathetic spirit in J. N. Mohanty’s careful and nuanced interpretation of Husserlian transcendental phenomenology. With Mohanty the two faces of the noema are the logical (Fregean) and the phenomenal (Kantian), and these views of intentional structure join in consciousness—in a way resonant with Indian thought. -/- - David Woodruff Smith (UC Irvine) and Purushottama Bilimoria (SFSU, San Francisco; University of Melbourne) -/- For photo of Prof Mohanty visit APA online memorial_minutes2023 Courtesy of APA Memorial Minutes (& Proceedings) 2023 . (shrink)

In response to paradigm shifts in education, teacher education institutions have increasingly adopted flexible learning modalities such as online courses, blended learning approaches, and personalized instruction to meet the diverse needs of students and prepare educators for the demands of modern classrooms. This study used a mixed-method research design to gain a comprehensive understanding of the flexible teaching and learning modalities it brought to mathematics teacher educators (MTEs) and learners in a state university in West Philippines. Since ethical (...) considerations preclude random sampling, the study comprised nonrandom participants using purposive sampling, where 189 learners were surveyed, and six MTEs and 16 learners were interviewed. A researcher-made interview guide was prepared to describe the flexible teaching and learning modalities and opportunities of the MTEs. Also, a researcher-made questionnaire was used to describe the learners’ general assessment of the flexible teaching and learning modalities in mathematics education. Quantitative data were gathered online, while qualitative data were gathered through interviews. Results showed that flexible teaching-learning approaches have implications for education, overcoming barriers, and promoting engagement. The findings highlight the importance of technology integration, inclusive assessment modalities, infrastructure support, and professional development opportunities in enhancing the quality and accessibility of flexible teaching and learning, ultimately leading to inclusive educational environments. Therefore, the educational institution must adopt flexible instructional modalities, emphasize diverse assessment methods, and personalize the learning experience by integrating online platforms and various assessments for effective mathematics instruction. (shrink)

The emergence of the COVID-19 pandemic initiated major disruptions to higher education systems. Physical spaces that previously supported interpersonal interaction and community were abruptly inactivated, and faculty largely took on the responsibility of accommodating classroom structures in rapidly changing situations. This study employed interviews to examine how undergraduate Science, Technology, Engineering, and Mathematics (STEM) instructors adapted instruction to accommodate the mandated transition to virtual learning and how these accommodations supported or hindered community and belonging during the onset of the (...) pandemic. Interviews with 25 STEM faculty at an undergraduate Hispanic Serving Institution revealed a wide range of accommodations they made to their courses and how they managed communication with students. Faculty strived to support student belonging with responses ranging from caring to crisis management, though some faculty expressed feelings of powerlessness when unable to accommodate certain challenges. The case of a responsive and flexible instructor is presented to highlight a productive response to a crisis. These retrospective findings point to strategies to support faculty teaching in virtual learning environments in the future; increasing opportunities for student–student and student–faculty interaction, supporting faculty in learning technologies that support these interactions and addressing faculty’s feelings of powerlessness. (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)

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

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)

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

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

The purpose of this paper is to critically analyse and discuss the views of constructivism, on the teaching and learning of mathematics. I provide a background to the learning of mathematics as constructing and reconstructing knowledge in the form of new conceptual networks; the nature, role and possibilities of constructivism as a learning theoretical framework in Mathematics Education. I look at the major criticisms and conclude that it passes the test of a learning theoretical framework but (...) there is still a gap between theory and mathematics classroom practice. (shrink)

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late nineteenth century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis (in the sense of the infinitesimal calculus) received much attention in the nineteenth century. They helped instigate what Hans Hahn called a “crisis of intuition”, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this (...) “crisis” as follows: Mathematicians had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof... (p. 67) Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called “logicization”, “when the discipline requires nothing but purely logical fundamental concepts and propositions for its development.” On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals to visual representations. This would be a radical reformation of past practice, necessary, according to its advocates, for avoiding “unclarities and mistakes” like the one exposed by Peano. (shrink)

Metacognitive skills are essential to be developed by the students to help improve their academic performance. This study was conducted with the aim of determining whether the use of problem-solving strategies can increase students' metacognitive skills. Students of the Mathematics in the World course offered at a local college in the Philippines were selected to participate in this study. Using an independent sample t-test, results revealed that students who were the recipients of problem-solving strategies scored statistically higher in formal (...) examinations compared to those students who were taught using conventional strategies. The researchers concluded that students who were taught using the problem-solving strategy enhanced their metacognitive skills based on their scores in the test of metacognitive skills during the post-test. The researchers suggested that teachers should incorporate problem-solving strategies into their lessons since this research demonstrates this to be an effective strategy for enhancing students' metacognitive skills essential to their learning. (shrink)

One notable component to look at in the teaching-learning process is the way the subject is taught because one way or another, students are greatly affected by it. Viewing students’ perspectives on the use of the different teaching methods, this study determined the frequency of use of these teaching methods and their level of satisfaction. Through a systematic investigation, the findings from a critical questionnaire administered to first-year BS Hospitality Management college students at Ifugao State University were (...) analyzed and summarized. The frequency of use of the indicated instructional strategies was shown to have a significant relationship with student satisfaction in this study. Furthermore, the data reveal a substantial difference in student satisfaction with instructional approaches utilized before and during the pandemic. Students, on the other hand, prefer the teaching techniques employed before the outbreak to those utilized during the pandemic. (shrink)

This study aimed to trace the 2015 to 2019 MAME graduates in the College of Teacher Education for Graduate Studies of the University of Northern Philippines in terms of their personal profile, their work-related profile before and after taking their master’s degree, reasons of taking up the program, competency level before and after taking the program, appraisal of the most useful courses offered in the program, evaluation on the contribution of the program to their personal and professional growth and assessment (...) on the features of the program and suggestions of how to improve the program. The researcher utilized mixed method of research. The subjects were the MAME graduates, and a questionnaire and open-ended questions were sent to them thru various online flat forms. Based on the findings of the study, the following conclusions are derived: pursuing graduate studies chooses no sex, civil status or age as long as there is a will to improve one's self; students have math- related educational background and finished the program within the prescribed number of years; having master’s degree could contribute greatly in landing a permanent teaching job in public schools; professional and personal growth and development is the strongest drive to pursue advance education; the program offers subjects that are useful which enhanced the teaching competencies of the graduates and consequently contribute to the holistic development of the graduates; and that there are areas needing improvement in the MAME program. (shrink)

The main aim of the study was to determine the levels of Adversity Quotient and problem solving skills in Mathematics of BISU - MC students taking BSEdMathematics in the school year 2021-2022. It sought to find if there was a significant difference in the respondents’ levels of AQ and problem solving skills in Mathematics across their age, gender and year level as well as their level of AQ as a significant predictor of their level of problem solving skills (...) in Mathematics. It also aimed to develop a plan of action that would be proposed to improve these two aspects of their being. The total number of actual respondents was 163. Purposive sampling was used. The study utilized the quantitative type of study. It made use of the descriptive design to describe the characteristics of the population being studied and the regression design to infer the relationship between the independent variable and dependent variable. The Online AQ Profile was used for determining the respondents’ level of AQ and a 10-item test was used for determining their level of problem solving skills in Mathematics. Both inquired their profile. The data provided by the respondents were collected and subjected to statistical treatment through IBM SPSS Statistics Trial software. Data revealed that the age of the respondents ranged from 18 to 22 years old. Females numerically dominated the analyzed field. Majority of the respondents were from the first and fourth year levels. Their AQ was below average while their problem solving skills in Mathematics was satisfactory. The age, gender and year level of students did not matter in identifying their level of AQ. On the other hand, the older students had a higher level of problem solving skills in Mathematics than the younger ones and the students in the higher year level had a higher level of problem solving skills in Mathematics than those in the lower year level. Finally, their level of AQ gave a positive influence on their level of problem solving skills in Mathematics. The education system should be aligned with the profile of the students. The teachers would let the students read the book of Paul G. Stoltz, PhD titled “Adversity Quotient: Turning Obstacles into Opportunities”. The students would also reflect on the word of God. Also, the teachers would let the students study the book by George Polya titled “How To Solve It”. The students would also continue to solve various routine problems. Regardless of age, gender and year level, the family and friends of the students should encourage them in every way they can for their better future as they overcome their adversities. Mathematics curriculum makers and teachers work together to improvise teaching and learning Mathematics specifically problem solving for the younger students and those in the lower year level. Future researchers could replicate the study to further verify the results. Research could focus specifically on the CORE dimensions of AQ predicting the level of problem solving skills in Mathematics. (shrink)

This study delved into the perceptions of Mathematics’ student teachers regarding the implementation of gamification in secondary schools at Nasugbu, Batangas. This research investigates the rising global trend of implementing gamification in education, particularly in Mathematics teaching, to address contemporary learner needs by examining student teachers' use of gamified activities, their design factors, encountered challenges, and perceived benefits. Purposive sampling was utilized in a multiple-case study approach to select ten (10) secondary school Mathematics’ student teachers engaged (...) in practice teaching in Nasugbu, Batangas. Qualitative findings revealed common gamified activities employed by student teachers, emphasizing the importance of student-centered design, alignment with learning objectives, student engagement, assessment, and adaptation to the classroom context. Challenges faced by student teachers in integrating gamification included technical limitations, sustaining engagement, time management, and addressing diverse learning styles. Despite these challenges, integrating gamification showed benefits such as increased engagement, improved learning outcomes, reduced math anxiety, and enhanced attitudes towards Mathematics. In conclusion, gamified activities play a significant role in enhancing student engagement and learning outcomes in Mathematics classrooms. The findings suggest student teachers to explore and integrate gamified activities into Mathematics lessons to create engaging environments supporting student success. (shrink)

Mathematics is an important subject taught in primary and secondary schools that equips students with foundational knowledge and skills for organizing their lives. This study determined the Mathematics proficiency level among the Grade Three pupils in Cagayan de Oro City in School Year 2022-2023. Specifically, it sought to determine the respondents’ profile in terms of language used at home, study habits, parental involvement, and attitude towards Mathematics; find out the proficiency level in Mathematics; and determine the (...) significant relationship between the respondents’ proficiency level in Mathematics when grouped according to their profile. Data were gathered from one hundred fifty (150) respondents. The researcher-made questionnaire and Mathematics Test patterned from the Division of Cagayan de Oro Periodical Tests for the School Year 2022-2023 were utilized in the study. It used a descriptive research design to analyze the data using frequency, mean, standard deviation, correlation analysis, and P-value. Findings revealed a significant relationship between respondents’ proficiency level in Mathematics and their study habits, parental involvement, and attitude towards Mathematics. In contrast, no significant relationship exists between the language used at home. It is recommended that teachers incorporate literacy in teaching Mathematics, use game-based strategies, and review Mathematics lessons to increase the chances of obtaining high scores. (shrink)

Mathematics textbooks teach logical reasoning by example, a practice started by Euclid; while logic textbooks treat logic as a subject in its own right without practical application to mathematics. Stuck in the middle are students seeking mathematical proficiency and educators seeking to provide it. To assist them, the article explains in practical detail how to teach logic-based skills such as: making mathematical reasoning fully explicit; moving from step to step in a mathematical proof in logically correct ways; and (...) checking to make sure inferences are logically correct. The methodology can easily be extended beyond the four examples analyzed. (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)

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing (...) the principles that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

This contribution aims to explore the historical predecessors of the Five Percenter model of self-realization, as popularized by Hip Hop artists such as Supreme Team, Rakim Allah, Brand Nubian, Wu-Tang Clan, or Sunz of Man. As compared to frequent considerations of the phenomenon as a creative mythological background for a socio-political struggle, Five Percenter teachings shall be discussed as contemporary interpretations of historical models of self-realization in various philosophical, religious, and esoteric systems. By putting the coded system of the tenfold (...) Supreme Mathematics as one of its core teachings in context with the Pythagorean Tetractys, an arrangement of ten points in four lines, the commonalities between the sequence and concepts attributed to the respective numbers will be demonstrated. (shrink)

Teaching in- effectiveness of most mathematics teachers has been attributed a negative attitude of the teachers and their inability to utilize modern ICT facilities in the teaching of the subject. The study was on the influence of teachers’ attitude towards ICT variables, the utilization of ICT facilities and the teaching effectiveness of mathematics teachers in public senior secondary schools in Cross River State. Two hypotheses were drawn from the stated research questions built around the dependent (...) and independent variables. Literature review was carried out according to the variables in the study. A survey design was adopted based on the descriptive nature of the study, while the random sampling technique was used. Two sets of structured questionnaires, titled; ‘Teacher Effectiveness Questionnaire’ (TEQ) and ‘ICT Evaluation Test Questionnaire’ (ICTETQ) were designed to obtain data from respondents. Data collected were analysed using the t-test statistic for the first hypothesis and Analysis of Variance (ANOVA) statistic for the last hypothesis. The hypotheses were tested at .05 levels of significance. The results of the findings were as follows: There is no significant influence of mathematics teachers’ attitude towards ICT facilities and their teaching effectiveness in public senior secondary schools in Cross River State; facilities utilization has no significant influence on mathematics teachers’ effectiveness in public senior secondary schools in Cross River State. Based on the findings, it was recommended among other things that basic training and other facilities like electricity be made available in schools to stimulate a positive attitude in Mathematics teachers and to able them (mathematics teachers), utilize the available ICT facilities and others facilities that should be provided in schools while at the same time teachers’ attitude should be channelled in the direction of imbibing and integrating ICTs into teaching so as to ensure an effective mathematics teaching in public senior secondary schools in Cross River State. (shrink)

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

Indigenous communities have a rich cultural heritage encompassing diverse ways of knowing, learning, and understanding the world around them. This mixed methods study utilized the explanatory sequential design to determine the level and relationship of the IP mathematics teachers' beliefs and teaching practices and gain a deeper insight into these beliefs and attitudes. There are 115 respondents for the quantitative phase, while 10 participants in the qualitative phase. Data were collected through survey and key informant interviews and were (...) analyzed through mean, standard deviation, Pearson product moment correlation, and thematic analysis. Results showed that the IP mathematics teachers possess high levels for both beliefs and teaching practices, and a significant moderate positive relationship exists between the two variables. Qualitative data analysis revealed that teachers' beliefs include the ideal qualities of an effective mathematics teacher, respect for students' culture and background, and a constructivist approach to teaching. Teaching practices include discussing student performance and intervention during meetings, implementing culturally relevant approaches, technology, varied activities, and peer mentoring and coaching. Further, it is concluded that teachers’ belief, which influences teaching practices, is shaped by different environmental factors. It is recommended that IP mathematics teachers continue to participate in personal and professional development activities and strengthen collaboration and reflection. (shrink)

Mathematics educators are constantly searching for new and innovative approaches to teaching with the goal of improving student learning outcomes. This phenomenological study aimed to describe the lived experiences of mathematics teachers in implementing the Claim-Evidence-Reasoning (CER) Approach. The study was participated by 13 mathematics teachers, and data were gathered through in-depth interviews and a focus group discussion. Thematic analysis was used to interpret the data guided by Colaizzi’s method. Findings revealed that participants experienced struggles in (...) instruction and assessment, adapted growth mindset and employed support systems, had milestones in the implementation of the CER Approach, and were open to continuous personal and professional development. Furthermore, the teachers’ resiliency and adaptability in the process and the school’s support helped overcome the issues encountered in implementing the CER Approach. The findings imply that the use of CER Approach have the potential to improve the reasoning skills of students in mathematics. Further, it is recommended that mathematics teachers continue to utilize the approach and that educational institutions should provide proper training to teachers through In-Service Training (INSET). (shrink)

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the (...) mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences. (shrink)

While there are satisfactory answers to the question “How should we teach children mathematics?”, there are no satisfactory answers to the question “What mathematics should we teach children?”. This paper provides an answer to the last question for preschool children (early childhood), although the answer is also applicable to older children. This answer, together with an appropriate methodology on how to teach mathematics, gives a clear conception of the place of mathematics in the children’s world and (...) our role in helping children develop their mathematical abilities. Briefly, children’s mathematics consists of the world of children’s internal activities that they eventually purposefully organize in order to understand and control the outside world and organize their overall activities in it. We need to support a child in mathematical activities that she does spontaneously and in which she shows interest, and we need to teach her mathematics that she is interested in developing through these activities. In doing so, we must be fully aware that the child’s mathematics is part of the child’s world of internal activities and is not outside of it. We help the child develop mathematical abilities by developing them in the context of her world and not outside of it. From the point of view of this conception, the standards established today are limiting and too focused on numbers and geometric figures: these topics are too prominent and elaborated, and other mathematical contents are subordinated to them. Adhering to the standards, we drastically limit the mathematics of the child’s world, hamper the correct mathematical development of a child, and we can turn her away from mathematics. (shrink)

In the present time, the ecological crisis is one of the gravest challenges being faced by humanity. There is a serious concern that our planet may fail to remain a sustainable biosystem in the long run. Though human beings are seen as the most intelligent life form on Earth, yet they are responsible for almost all the environmental damage done to the planet. Sikh theology emphasizes that recognizing the sacred relation between human beings and the environment is crucial for (...) preserving the health of our planet and our survival. Furthermore, Sikh doctrines emphasize that humility, surrender to the divine spirit, and maintaining a harmonious relationship with all are crucial for humanity to find a way out of its current predicament. (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 August 2022, only a few months before ChatGPT was released, Barry Smith, well-known contemporary philosopher, together with Jobst Landgrebe, artificial intelligence entrepreneur, published a book entitled Why Machines will Never Rule the World: Artificial Intelligence without Fear (Landgrebe and Smith 2022). In this important, dense and far-reaching work, Landgrebe and Smith argue from the mathematical theory of complex systems, and a sophisticated analysis of the capabilities of human intelligence, that AGI— at the level of human intelligence—will never be possible. (...) In broad outline, Landgrebe and Smith claim that intelligent human behaviour is a facility that develops from a complex world and for a complex world; that the complexities of the real world and our behaviour in it can never be fully specified or simulated mathematically; that digital systems can only execute what can be simulated mathematically; and that therefore human-level intelligence will never be manifested by a digital system. The present collection of articles is in response to and inspired by Landgrebe and Smith. It provides reflections from a variety of perspectives and disciplines on the possibility of AGI, as well as on the transformations that AI technology is already bringing even in its current incarnation. (shrink)

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

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

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

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)

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)

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)

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

I analyse the 2014 policy to promote 'British values' in schools from the perspective of the two main positions in contemporary liberal theory, comprehensive liberalism and political liberalism. I highlight in what ways comprehensive and political liberal defences of the policy are unsatisfactory, before briefly sketching a possible alternative position – ‘thin comprehensive liberalism’ – and discussing its potential for justifying a substantive education in liberal values. In light of this theoretical perspective, I suggest some ways that the existing British (...) values policy might be amended in practice so as to bring it more in line with the liberal ideal. (shrink)

Impulse and momentum are basic concepts of mechanics introduced in the K to 12 curricula. Despite its basic concepts, students still have difficulties understanding the topic, especially when they are out of school due to the pandemic. After reopening the gates for face–to–face classes in the Philippines, the researchers found a significant reason to conduct a lesson study to improve teaching strategies on the topic. Lesson study is a development process wherein teachers work collaboratively to improve teachers teaching (...) capacity. This study was conducted at Plaridel National High School with 23 participants from Grade 9 Newton (Set A and B). The research was conducted in two cycles using a four – phase lesson study. The research lesson was implemented using a 4A Model lesson plan and the results were taken from the analysis of the lesson study observation sheets, along with the class proficiency level. The researchers used the following strategies to improve teaching, namely; (1) showing mastery of subject matter, (2) reviewing basic mathematical operations, (3) contextualizing the lesson, (4) allowing students to answer questions in mother tongue, (5) using collaborative activities, (6) giving rewards, and (7) applying proper time management. However, the findings still showed that both sets of students achieved beginning proficiency level. Despite the implementation of these strategies, the students still lack basic knowledge of the topic and mathematical operations, and they struggle to understand it. Thus, it is recommended to plan the lesson effectively, utilize other research instruments, and collect feedback from the students. (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)

While practical efforts in the field of artificial intelligence grow exponentially, the truly scientific and mathematically exact understanding of the underlying phenomena of intelligence and consciousness is still missing in the conventional science framework. The inevitably dominating empirical, trial-and-error approach has vanishing efficiency for those extremely complicated phenomena, ending up in fundamentally limited imitations of intelligent behaviour. We provide the first-principle analysis of unreduced many-body interaction process in the brain revealing its qualitatively new features, which give rise to rigorously defined (...) chaotic, noncomputable, intelligent and conscious behaviour. Based on the obtained universal concepts of unreduced dynamic complexity, intelligence and consciousness, we derive the universal laws of intelligence applicable to any kind of intelligent system interacting with the environment. We finally show why and how these fundamentally substantiated and therefore practically efficient laws of intelligent system dynamics are indispensable for correct AI design and training, which is urgently needed in this time of critical global change towards the truly sustainable development. (shrink)

The present crisis of truth, the "post-truth" crisis, puts the philosophy of truth in a new light. It calls for a reexamination of the tasks of the philosophy of truth and sets a new adequacy condition on this philosophy. One of the central roles of the philosophy of truth is to explain the importance of truth for human life and civilization. Among other things, it has to explain what is, or will be, lost in a post-truth era. Clearly, (...) the deflationist answer that the role of truth is to serve as a tool of generalization and oblique endorsement will not do. My account of truth in this paper addresses this task. Truth, I argue, is first and foremost a human value. Its importance to our life/civilization lies, not exclusively, but principally, in the centrality of this value to our humanity. I investigate the ramifications of this answer to the issues discussed in the contemporary philosophy of truth, and I end with a comparison of the substantivist and deflationist approaches to truth in light of this new perspective. (shrink)

The present crisis of foundations in Fundamental Science is manifested as a comprehensive conceptual crisis, crisis of understanding, crisis of interpretation and representation, crisis of methodology, loss of certainty. Fundamental Science "rested" on the understanding of matter, space, nature of the "laws of nature", fundamental constants, number, time, information, consciousness. The question "What is fundametal?" pushes the mind to other questions → Is Fundamental Science fundamental? → What is the most fundamental in the Universum?.. Physics, (...) do not be afraid of Metaphysics! Levels of fundamentality. The problem №1 of Fundamental Science is the ontological justification (basification) of mathematics. To understand is to "grasp" Structure ("La Structure mère"). Key ontological ideas for emerging from the crisis of understanding: total unification of matter across all levels of the Universum, one ontological superaxiom, one ontological superprinciple. The ontological construction method of the knowledge basis (framework, carcass, foundation). The triune (absolute, ontological) space of eternal generation of new structures and meanings. Super concept of the scientific world picture of the Information era - Ontological (structural, cosmic) memory as "soul of matter", measure of the Universum being as the holistic generating process. The result of the ontological construction of the knowledge basis: primordial (absolute) generating structure is the most fundamental in the Universum. (shrink)

The sudden shift in the education system during the pandemic and its subsequent evolution during the post-pandemic era have been pivotal in fostering significant educational development and growth. However, this paradigm shift has not been without challenges. This paper aims to investigate the challenges faced by 68 mathematics teachers in four public elementary schools in the Philippines. The respondents were purposively selected to answer the study’s instrument. Using a descriptive survey research methodology, this study explored the five domains in (...) teaching mathematics, namely planning lessons, executing lessons, assessment, mathematical knowledge, and using technology tools. This paper revealed that novice, experienced, and highly experienced teachers alike had moderate difficulty enriching mathematical knowledge and utilizing technology in teaching the subject matter. Moreover, teachers with more than five years’ experience had moderate difficulty in the five domains of teaching mathematics in the post-pandemic era. This finding emphasizes the widespread impact of the education shift for teachers of all levels of experience. The paper further emphasizes the importance of supporting experienced teachers during this transformative phase of formulating innovative learning activities and adapting to reimagined pedagogical concepts. Consequently, this study underscores the need for additional training interventions to enhance their mathematical knowledge and use of technology as an integral teaching tool. (shrink)

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

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

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)

The deep crisis in modern fundamental science development is ever more evident and openly recognised now even by mainstream, official science professionals and leaders. By no coincidence, it occurs in parallel to the world civilisation crisis and related global change processes, where the true power of unreduced scientific knowledge is just badly missing as the indispensable and unique tool for the emerging greater problem solution and further progress at a superior level of complex world dynamics. Here we reveal (...) the mathematically exact reason for the crisis in conventional science, containing also the natural and unified problem solution in the form of well-specified extension of usual, artificially restricted paradigm. We show how that extended, now causally complete science content provides various "unsolvable" problem solutions and opens new development possibilities for both science and society, where the former plays the role of the main, direct driver for the latter. We outline the related qualitative changes in science organisation, practice and purposes, giving rise to the sustainability transition in the entire civilisation dynamics towards the well-specified superior level of its unreduced, now well understood and universally defined complexity. (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)

The Philippine educational system established alternative delivery modes of education, such as the Modified Work and Study Program, to eradicate student dropout incidence. This phenomenological study aims to probe the challenges and explore the coping mechanism of MWSP students in studying mathematics. The study was conducted at a public high school offering the program. Six students were chosen to participate in the study. Focus group discussion was utilized for the data gathering of the study. Results showed that mediocrity of (...) resources and conspicuous learning environment were the leading challenges that MWSP students encounter. Moreover, the coping mechanisms include good classroom management, utilization of concrete examples, time scheduling, steward support, motivational encouragement, and recreational and body relaxation. It is recommended that MWSP mathematics teachers integrate innovative strategies, provide more concrete contextualized examples, intensify the development of learning kits, and reinforce teaching and learning through supplementary materials. (shrink)