Metacognition-related studies do often give focus on the regulation or experience components but little on the knowledge component. In particular and especially within the Philippine context, not much focus is given with regards to a clear and coherent academic framework that fortifies the metacognitive strategy knowledge in mathematical problem solving amongst students. Using an evolved grounded theory, the purpose of this study is to look closely into the metacognitive strategy knowledge of preservice teacher (...) education students. Twenty-three students participated and initial data were collected using the prepared problem solving test. Subsequently, interviews were conducted to supplement the initial data. Pandit’s grounded theory methodology and the constant comparison method were used to analyze the data collected. Findings revealed an emerging three-phased categorization of metacognitive strategy knowledge thru problem solving: preparatory, production, and evaluation. The multi-distinct yet related categorization were neither linear nor just cyclic in nature but is experienced and underwent by problem solvers with varying degree of creativity and flexibility depending on the problem at hand, beliefs, attitudes, and learning style. The findings shed some light on the distinct role of metacognitive strategy knowledge and some ensuing factors during authentic problem solving. (shrink)

The main purpose of the study is to understand the mathematical problem-solving strategies among student teachers. This study used both quantitative and qualitative type of research. Aside from the semi-structured interviews, data were gathered through participant's actual mathematical problem-solving outputs and the videotaped interviews. Findings revealed that the problem-solving strategies among student teachers in the Problem-Solving subject are cognitive, metacognitive and other strategies. The cognitive strategies used by the student teachers are (...) rehearsal, elaboration, and organization. The metacognitive strategies are critical thinking and self-regulation. Other strategies are overlapping the cognitive and metacognitive strategies. These are prediction/orientation, planning, monitoring, and evaluating. The findings also suggest a significant influence of the strategies to the academic performance of the student teachers. (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)

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)

Elementary preservice teachers (EPTs) substantially impact the quality of mathematics education, and their subject preference and problem-solving performance are essential indicators of their readiness to teach. The study described EPTs’ subject preference and problem-solving performance. Through a sequential explanatory research design, the quantitative inquiry involved 125 random samples, while the qualitative inquiry was participated by 30 non-random samples. Data were obtained by using an online survey and conferencing. Quantitative data were analyzed through descriptive statistics and analysis (...) of variance, whereas qualitative data were themed accordingly. The EPTs displayed unsatisfactory problem-solving performance and preferred to handle subjects other than math. Besides, the analysis found no significant performance differences with the EPTs’ subject preferences. Further, the EPTs who preferred to teach mathematics expressed their confidence in mathematics. Meanwhile, the EPTs who preferred other subjects displayed math avoidance. The study revealed an alarming result indicating that the EPTs are unprepared for teaching. As agents in cultivating the nation’s mathematics education status, these EPTs must be equipped with fundamental content knowledge. It is suggested that educational decision-makers take measures to address the issues identified concerning EPTs’ readiness to teach mathematics successfully. (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)

Proficiency in solving mathematical problems is essential for preservice elementary teachers, as they will teach foundational math concepts and foster problem-solving abilities among young learners. However, many studies found low problem-solving performance among preservice teachers. In line with this, the present study examined how problem-solving disposition relates to the performance of preservice elementary teachers, conducted at a selected higher education institution in Nueva Ecija, Philippines, with 134 participants. The study utilized a mathematical (...) class='Hi'>problem-solving disposition and beliefs scale questionnaire and a problem-solving test scored using the identify, define, explore, act, and look (IDEAL) model. Results indicated an average problem-solving disposition and high problem-solving performance among preservice teachers. Linear regression analysis showed that overall problem-solving disposition is a predictor of performance. Further, stepwise regression analysis revealed that two disposition parameters, mathematical mindset (β = 2.413, p < 0.01) and community of practice (β = 1.866, p < 0.01), significantly predicted problem-solving performance. These findings show the significance of developing a problem-solving disposition, mindset, and learning communities to improve future teachers’ problem-solving ability by providing more learning opportunities, interdisciplinary problems, and social engagements. (shrink)

Math prospective teachers must be able to think creatively and solve problems. The study looked into preservice teachers’ creative thinking and problem-solving abilities in statistics. The investigation was guided by a correlational design in a public university in the Philippines. Stratified random sampling was used to select the 103 study participants from two teacher education programs. Through google forms, data were collected using Torrance et al. (2008)’s tests of creative thinking and researcher-made statistics problem test. The (...) findings revealed that preservice teachers have commendable creative thinking, particularly fluency, flexibility, and elaboration skills. Still, they lack problem-solving skills in statistics, specifically with central tendency, dispersion, and position measures. The correlational analysis revealed no link between creative thinking and problem-solving. Still, creative thinking and problem-solving courses are recommended to help preservice teachers develop their fundamental skills as mathematics educators. (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)

Research in second language learning has identified the absence of metacognition among learners as one of the major problems contributing to students’ inability to comprehend listening texts. Moreover, the shift to remote teaching due to COVID-19 has made it more crucial for teachers and learners to adapt to new modes of teaching and learning. This accentuates the need for effective listening strategy instruction. This study conducted at a university in Oman, is unique in two ways: first, it seeks out (...) teachers’ perceptions of metacognitive strategy instruction in remote teaching; and second, the intervention in the form of explicit metacognitive strategy instruction is offered online. This paper presents the findings of the study, which focused on the following: teachers’ perception of students’ listening difficulties; teachers’ perceptions of metacognitive strategies and their explicit instruction; the role of metacognitive strategy awareness and instruction in improving student participation and skills in listening; challenges encountered in teaching listening during remote teaching; and overcoming challenges of teaching metacognitive strategies in remote teaching. This mixed-method study collected data through questionnaires and interviews with 10 faculty members and 75 students. The findings show that teachers face several challenges, such as time limitations, shortened semesters, unfamiliar coursebook contexts, and assessment practices. For strategy instruction, teachers utilized collaborative lesson planning and resources and virtual flipped classrooms, among others. We conclude that metacognitive strategy instruction can provide better scaffolding during listening instruction and recommends further exploration of students’ use of metacognitive strategies in other academic contexts. (shrink)

This correlational study investigated the relationship between preservice teachers’ math self-concept, self-efficacy, and attitude with their math achievement. Participants were chosen using stratified random sampling from BEEd and BSEd mathematics majors (n = 117). From the findings, preservice teachers had moderate to high math self-concept, self-efficacy, and attitude. These variables were statistically correlated with each other and with math achievement. The inclusion of training programs for developing the preservice teachers’ math self-concept, self-efficacy, and attitude, as well as designing curricula that (...) engage and encourage them to do mathematics and problem-solving, must be considered among teacher education institutions. (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)

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

The study determined the problem-solving performance and skills of prospective elementary teachers (PETs) in the Northern Philippines. Specifically, it defined the PETs’ level of problem-solving performance in number sense, measurement, geometry, algebra, and probability; significant predictors of their problem-solving performance in terms of sex, socio-economic status, parents’ educational attainment, high school graduated from and subject preference; and their problem-solving skills. The PETs’ problem-solving performance was determined by a problem set (...) consisting of word problems with number sense, measurement, geometry, algebra, and probability. A mixed-method research design was employed. Senior PETs purposively served as a sample where they mostly preferred to teach other subjects than mathematics. PETs who preferred math performed satisfactorily, while prospective teachers who opted for other subjects performed unsatisfactorily. The PETs’ unsatisfactory output indicates the need for remediation to advance the mathematical material skills and enrich the problem-solving abilities of these primary schools' potential teachers. Besides, results showed that subject preference strongly affected and predicted the problem-solving success of the PETs. PETs who preferred to teach mathematics performed significantly better than their counterparts; hence, mathematics as a field of specialization in the Bachelor of Elementary Education program may be considered by teacher education institutions. Further, most PETs displayed lack of problem-solving skills; thus, a Problem-Solving course is recommended for them. (shrink)

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

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)

Computation and Metacognitive skills are essential sub-skills under the domain of Critical Thinking which is a 21 st Century Skill. Having acquired these skills can greatly help students to have a better performance in the Mathematics course. The purpose of this study was to determine whether computation and metacognitive skills are significant predictors of students' performance in Mathematics. Students from four sections of the course Mathematics in the Modern World which was offered during the first semester of the (...) academic year 2018-2019 were selected as the participants of this study which was conducted at Gov. Alfonso D. Tan College, Tangub City, Misamis Occidental, Philippines. The results of this study showed that students' scores in computation and metacognitive test of skills significantly correlate with the students' performance in Mathematics in terms of Grade Point Average (GPA) and a positive direct relationship has been established. Using the Regression Analysis, the result revealed that both computation and metacognitive skills of the students were significant predictors of their performance in Mathematics. These research outcomes affirm that if students acquire these skills, they tend to perform better in Mathematics. This suggests that teachers are encouraged to be more strategic in training the students to acquire and develop computation and metacognitive skills by administering various mathematical problems that encourage students to think critically. (shrink)

This study set out to look into the relationship between metacognitive reading strategies and reading comprehension of Grade 11 Technical-Vocational-Livelihood modular distance learners of Pasay City East. A correlational research design was employed. The Metacognitive reading strategies served as the dependent variable while reading comprehension served as an independent variable. Random sampling was used to select the 116 respondents and MARSI R and McCall Crabbs Reading Proficiech test were the instruments. The findings of this study show a weak (...) relationship between metacognitive awareness of reading strategies and reading comprehension and the unachieved grade level which failed to reject the hypothesis that there was no significant relationship of metacognitive reading strategies and reading comprehension for Global and Problem-Solving reading strategies. It recommended that future researchers should employ other reading comprehension proficiency tests to validate the result of the existing study and include intervention through the utilization of metacognitive reading strategies as the appropriate strategy to address reading comprehension. (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)

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 (...) class='Hi'>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)

We investigate flexibility and problem solving in skilled action. We conducted a field study of mountain bike riding that required a learner rider to cope with major changes in technique and equipment. Our results indicate that relatively inexperienced individuals can be capable of fairly complex 'on-the-fly' problem solving which allows them to cope with new conditions. This problem solving is hard to explain for classical theories of skill because the adjustments are too large to (...) be achieved by automatic mechanisms and too complex and rapid to be achieved by cognitive processes as they are usually understood. A recent theory, Mesh, can explain these results because it posits that skill-specific cognitive abilities develop during skill learning and that control typically involves an interplay between cognitive and automatic mechanisms. Here we develop Mesh further, providing a detailed explanation for these problem solving abilities. We argue that causal representation, metacognitive awareness and other forms of performance awareness combine in the formulation and control of action strategies. We also argue that the structure of control present in this case is inconsistent with Bratman's model of intentions, and that, in the face of high uncertainty and risk, intentions can be much more labile than Bratman recognises. In addition, we found limitations and flaws in problem solving which illuminate the representations involved. Finally, we highlight the crucial role of social and cultural learning in the development of complex skills. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies (...) methods from computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)

This study explores the needs of Senior High School (SHS) Mathematics Teachers in Cabanatuan City’s Schools Division Office, focusing on professional qualifications, familiarity with essential Mathematics knowledge, and employed pedagogical strategies. Using descriptive research approach, the study examines the correlation between respondent profiles, Mathematics knowledge, pedagogical approaches, and the adequacy of educational infrastructure. Results indicate that most respondents demonstrate excellent familiarity with essential Mathematics knowledge, predominantly employing assessment as a pedagogical strategy. No significant relationship exists between respondent profiles and (...) General Mathematics essential knowledge competence. Respondents highly rate the DepEd-issued Teacher’s Guide, and Mathematics materials’ availability and sufficiency in classrooms are satisfactory. The study recommends providing more usable Mathematics tools and materials, emphasizing targeted Mathematics-related seminars for SHS Mathematics teachers in public secondary schools within Cabanatuan City. (shrink)

Much problem solving and learning research in math and science has focused on formal representations. Recently researchers have documented the use of unschooled strategies for solving daily problems -- informal strategies which can be as effective, and sometimes as sophisticated, as school-taught formalisms. Our research focuses on how formal and informal strategies interact in the process of doing and learning mathematics. We found that combining informal and formal strategies is more effective than single strategies. We provide a (...) theoretical account of this multiple strategy effect and have begun to formulate this theory in an ACT-R computer model. We show why students may reach common impasses in the use of written algebra, and how subsequent or concurrent use of informal strategies leads to better problem-solving performance. Formal strategies facilitate computation because of their abstract and syntactic nature; however, abstraction can lead to nonsensical interpretations and conceptual errors. Reapplying the formal strategy will not repair such errors; switching to an informal one may. We explain the multiple strategy effect as a complementary relationship between the computational efficiency of formal strategies and the sense-making function of informal strategies. (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 potential benefits of cognitive skills in enhancing mathematics ability have been claimed by numerous researchers. Since mathematics requires a complete understanding and grasp of abstract concepts, it is essential to explore how learning with metacognitive skills affects mathematics learning. Thus, the study investigates the students' metacognitive awareness and conceptual understanding of integers. A descriptive-correlational method approach was utilized, and it was carried out on 303 seventh-grade students. The data were obtained using a metacognitive awareness inventory and (...) achievement test on integers. It was further revealed that the students have average metacognitive awareness and performed well in the fundamental operation of integers. Follow-up qualitative analysis revealed that students who were high achievers had the best understanding, average achievers had corrected or incomplete understanding, and low achievers had a functional misconception of integers. Moreover, the student's metacognitive awareness was significantly related to their conceptual understanding of integers. This indicates that student's higher-order thinking skills, such as metacognition, are essential since they are associated with building conceptual skills. Thus, teachers should encourage students' metacognitive awareness to improve students' conceptual understanding of integers. The study provides relevant information for educational managers on the potential factors to be considered in improving mathematics education practices, particularly in promoting metacognition among high school students. (shrink)

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

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)

Mathematical confidence and critical thinking are essential in preparing preservice teachers. Thus, this study explored the perceived confidence and critical thinking levels in mathematics of elementary and secondary preservice teachers. A descriptive-correlational-comparative research design was employed, with a sample of 107 randomly selected preservice teachers enrolled in the Bachelor in Elementary and Secondary Education programs of a state university in West Philippines. The study used arithmetic mean, standard deviation, Spearman’s rank-order correlation, and independent samples t-test to analyze and draw conclusions (...) from the data. The findings revealed that the preservice teachers have high confidence and critical thinking skills. Their program significantly correlates with their perceived critical thinking and confidence level. Besides, the preservice teachers’ confidence levels and perceived critical thinking skills significantly correlate. Further analysis found significant confidence and critical thinking differences favoring the secondary over the elementary preservice teachers. These findings provide insights that would benefit mathematics educators in providing priority programs to enhance the preparation of future math teachers. (shrink)

In today’s fast-changing educational settings, technology integration offers the opportunity to enhance mathematics instruction. This study determines the significant socio-cognitive factors among preservice mathematics teachers (PMTs) affecting their behavioral intention toward the use of technology. A descriptive-correlational research design was employed with 130 participants. Revised UTAUT construct items and behavioral intention scales were utilized through survey forms. Findings revealed that the participants were more inclined to use technology in their pedagogical approach. The only socio-cognitive factors significantly affecting the participants’ positive (...) inclination to utilize educational technology were performance expectancy, effort expectancy, and social influence. However, when controlling for the effects of the participants’ willingness to use technology, social influence became insignificant. Developing favorable impressions of technology’s effectiveness and ease of use may encourage greater technology integration in mathematics education. (shrink)

In this paper, I defend the metalinguistic solution to the problem of mathematical omniscience for the possible-worlds account of propositions by combining it with a computational model of knowledge and belief. The metalinguistic solution states that the objects of belief and ignorance in mathematics are relations between mathematical sentences and what they express. The most pressing problem for the metalinguistic strategy is that it still ascribes too much mathematical knowledge under the standard possible-worlds model of knowledge and (...) belief on which these are closed under entailment. I first argue that Stalnaker's fragmentation strategy is insufficient to solve this problem. I then develop an alternative, computational strategy: I propose a model of mathematical knowledge and belief adapted from the algorithmic model of Halpern et al. which, when combined with the metalinguistic strategy, entails that mathematical knowledge and belief require computational abilities to access metalinguistic information, and thus aren't closed under entailment. As I explain, the computational model generalizes beyond mathematics to a version of the functionalist theory of knowledge and belief that motivates the possible-worlds account in the first place. I conclude that the metalinguistic and computational strategies yield an attractive functionalist, possible-worlds account of mathematical content, knowledge, and inquiry. (shrink)

This study aimed to determine the levels of pre-service teachers' nature of science (NOS) knowledge, assess their pseudo-scientific beliefs, and examine the relationship between aspects of their NOS knowledge and these beliefs. It also aimed to determine whether NOS knowledge and pseudo-scientific beliefs depended on the discipline and gender. A survey method was conducted in this study. Data were collected from 215 pre-service teachers who are being educated in different fields in a state university. Two different five-point Likert scales were (...) applied. Scale 1, which hasthree factors, measured pseudo-scientific beliefs, while Scale 2, which has seven factors, measured NOS knowledge. As a result, preservice teachers' NOS knowledge was found to be inadequate and their pseudoscientific beliefs were excessive. All factors of Scale 1 were positively correlated with each other, and they were correlated with some components of NOS knowledge. Significant differences were found between disciplines in the analysis of the factors of Scale 2; however, no significant differences were found between genders. (shrink)

COVID-19 and military actions on the territory of Ukraine fundamentally changed the organization of the educational process, forcing educational institutions to transfer classroom learning to virtual space. To organize the educational process remotely, we need to organize an educational environment in which we can ensure the implementation of all types of educational activities, as well as creation and selection of e-resources depending on their types. Having guidelines in the form of modes, forms and learning outcomes, it is necessary to structure (...) the content of educational disciplines, corresponding curricula, to ensure the activity of students during lectures and the implementation of practical tasks with the necessary tools, to determine and carry out the selection of electronic educational resources for the effective organization of the educational process in conditions of open education. First of all, it is important to take into account all types of student activities, namely: those ones, which are usually implemented in class and determine the possibility of their implementation in a remote format using cloud services. The monograph considers the problem of effective use of Microsoft 365 services for the organization of e-learning through the prism of the competency approach. In particular, the study established a correspondence between training activities and M365 services, which can provide tools support for their implementation. Chapter 1 analyzes the components of digital competence and the abilities necessary for the organization of the e-learning process. Based on the analysis, the correspondence between the components of digital competence and M365 services, the possession of which indicates the existing level of digital competence, was established. Chapter 2 of the monograph describes the digital competences necessary for the organization of various types of training using Microsoft 365 services. It studies features of using digital identity cloud services, Microsoft 365 services for digital data management and collaboration, e-learning management, design and creation of digital content, problem solving and innovation, digital communication, cooperation and interaction. Chapter 3 offers a developed model of hybrid educational environment architecture based on Microsoft Teams platform and analyzes digital competences for the organization of asynchronous interaction between students and teachers using MS Teams tools. Chapter 4 is devoted to the results of an experimental study of the effectiveness of the use of Microsoft 365 services for the organization of e-learning and the readiness of teachers and students to use them. (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 descriptive correlational study anchored on Lazarus and Folkman’s Coping Theory identified the pedagogical problems met and the coping strategies adapted by elementary school teachers during the pandemic in one school district in the Division of Aklan during the height of the pandemic in 2021. This also tried to find out the extent of pedagogical problems experienced by the teacher respondents related to curriculum, fellow teachers, learners, school, and parents, and the coping strategies applied to manage the problems they (...) encountered. Forty-six grade school teachers purposively selected in the identified elementary schools in the district participated in the study. A researcher-made survey questionnaire validated by experts was used in the gathering of data. Findings revealed that teacher respondents were between 31-40 years old, mostly female and single, with average monthly income from 10,000 to 20, 000, travel less than 6 km from their homes to the work station, and are proficient in terms of ICT competence. The extent of pedagogical problems experienced by the respondents related to curriculum and fellow teachers was slightly a challenge; and to learners, school-related aspects, and parents as not at all considered as challenges. To cope with these challenges, the respondents’ top three activities were attending webinars for professional growth, enjoying quality time with their families, and going to and praying in the church. These imply that grade school teachers are more particular about improving themselves professionally and strengthening their faith in God than doing other things that affect their physical and mental health. (shrink)

Between 2015 and 2017, a reform of teacher training policies was carried out in Colombia. The process of implementing this normativity is analyzed using the multiple case study methodology with five institutions in Bogotá and the consequences for these programs are examined: higher prices and reduction of students. It is evident that the implementation of the studied reform discouraged the training of teachers in philosophy. The changes implemented showed fractures in the legislation and a failure in the strategy (...) of commodification of education, since in an inequitable context like the Colombian one, solving the problems of education is not enough to regulate the education market. (shrink)

The Universal Formula: Solving the Problem of Free Will Through the Law of Balance By Angelito Malicse Introduction The problem of free will has puzzled humanity for centuries, often viewed as a philosophical or metaphysical enigma. This essay presents a universal formula that resolves this dilemma by focusing on the law of karma and the universal law of balance. It explores the interconnectedness of systems, the critical role of accurate knowledge, and the evolution of emotions in maintaining (...) harmony. By examining real-world examples such as overpopulation, environmental degradation, economic instability, and the flaws of capitalism, this essay demonstrates how the universal formula can guide human decision-making to achieve a balanced and sustainable world. The Law of Karma: Systems and Balance The universal formula begins with the law of karma, which extends beyond cause and effect to encompass the integrity of systems, both natural and man-made. Every system—whether ecological, social, or economic—operates according to the universal law of balance. When imbalances arise, the system becomes dysfunctional, leading to adverse consequences. For example, while humans sit at the top of the food chain, the Earth's ecosystem cannot sustain unchecked overpopulation of our species. Overpopulation leads to the destruction of natural resources as humans consume everything, including plants, animals, and even insects. This voracious consumption damages ecosystems, accelerates deforestation, depletes biodiversity, and disrupts the delicate balance of the natural world. To ensure the sustainability of life on Earth, it is crucial to regulate population growth, conserve natural resources, and refrain from exploiting all animals on land and in the sea. By preserving biodiversity and maintaining the integrity of ecosystems, we protect the foundation of life that supports all species, including humans. Free Will and the Dependence on Correct Knowledge Human free will is not an autonomous force but is entirely dependent on correct knowledge and information. Errors in decision-making, often caused by ignorance, false beliefs, and distorted theories, disrupt the balance of systems. For instance, the failure to regulate overpopulation creates cascading problems, including climate change, pollution, and resource depletion. Without accurate knowledge about the consequences of overpopulation, individuals and societies continue to make decisions that exacerbate these imbalances. Education and government policy play vital roles in addressing these issues. Policies that promote population regulation can maintain a sustainable economy, while education fosters awareness of the need to protect ecosystems and biodiversity. Correct information empowers individuals to make decisions that align with the universal law of balance, preventing errors that destabilize systems. The Flaws of Capitalism and the Need for Balance The efficiency of the capitalistic system increases over time, leading to significant flaws if left unchecked. Private companies continually strive to reduce overhead and operating expenses, often by automating processes and replacing human labor with robotics. While this enhances profitability, it also reduces employment opportunities, suppresses wages, and widens income inequality. These principles, central to the management strategies of most private companies, create systemic imbalances in the economy. The solution lies in adopting a mixed economic system that counterbalances the excesses of capitalism with socialist principles. Governments must play a pivotal role in addressing these imbalances by implementing the following measures: Creating High-Salary Government Jobs: These jobs provide stable income and stimulate local economies. Providing Unemployment Benefits or Universal Basic Income (UBI): These measures ensure that individuals who lose jobs due to automation and efficiency gains still have the purchasing power to meet their needs. Offering Free Healthcare and Education: These fundamental services reduce the financial burden on families, enabling them to invest in other areas of life. Promoting Government Spending: By investing in infrastructure, renewable energy, and public services, governments can create new jobs and maintain the flow of money in the economy. Government spending serves as a balancing mechanism by injecting funds into the economy, which in turn supports private companies through increased consumer demand. This feedback loop creates private-sector jobs, stabilizes the economy, and ensures a balanced flow of resources between public and private sectors. The Role of Emotions in Balancing Systems Human emotions, both positive and negative, serve as essential feedback mechanisms for maintaining balance. Positive emotions, such as love and joy, encourage cooperative behavior and strengthen familial and social bonds. Negative emotions, such as fear and anger, signal imbalances that require corrective action. For example, the unconditional love within a family fosters a nurturing environment that supports the emotional and psychological development of children. This foundation contributes to a high-quality next generation of parents, capable of fostering further generational improvement. Conversely, the absence of such love or a dysfunctional family structure often leads to crime, substance abuse, and other societal problems. These negative outcomes are the effects of systemic imbalances, whether caused by poor parenting, economic hardship, or the lack of a government safety net. Addressing Environmental and Social Imbalances The universal formula underscores the importance of a holistic education system in addressing systemic imbalances. Education must instill values such as cleanliness, discipline, ethics, and good manners while fostering a respect for nature. Teaching children the importance of not harming wildlife and preserving ecosystems is critical to protecting biodiversity and ensuring a harmonious coexistence with other species. Government policies also play a crucial role. Regulations that protect natural resources, reduce pollution, and promote renewable energy can prevent environmental degradation. Policies that provide social safety nets can alleviate poverty and reduce crime by addressing the root causes of economic and social imbalance. The Importance of Holistic Systems Thinking The universal formula emphasizes the interconnectedness of systems, demonstrating that imbalances in one area often ripple through others. For instance, a lack of holistic education contributes to ignorance, which leads to poor decision-making. This, in turn, exacerbates issues such as overpopulation, resource depletion, and social unrest. Producing a high-quality young generation requires a combination of good parenting, access to education, and supportive government policies. By fostering an environment that values balance, discipline, and ethics, societies can produce individuals capable of making decisions that align with the universal law of balance. Conclusion The universal formula offers a comprehensive solution to the problem of free will by integrating the law of karma, the universal law of balance, and the evolutionary role of emotions. By understanding and addressing the root causes of imbalance—whether environmental, social, or economic—humanity can achieve harmony within and across systems. Real-world examples, such as overpopulation, economic instability, environmental destruction, and the flaws of capitalism, highlight the urgent need to apply this formula. Through holistic education, informed policies, and an unwavering commitment to balance, individuals and societies can prevent errors, correct existing imbalances, and create a sustainable and harmonious future. The time to act is now. By embracing the universal formula, humanity can unlock the full potential of free will, ensuring a balanced and equitable world for generations to come. ---. (shrink)

Some people believe that critical thinking is not a modern science, but its roots are old and deeply rooted in the history of philosophy. Its roots date back to Aristotle, the inventor of logic and who was called the first teacher by virtue of this invention. Aristotle was impressed by the language of mathematics and wanted to invent a language to logic similar to the language of Mathematics. What encouraged Aristotle to do so is that Math language is quite (...) different from daily life language. For example , when you say one in Mathematics language, what is this one you mean or intend? That is what is one? Is it a specific man or an animal or something abstract or any creature of the creatures of the natural world? The one we are talking about is neither this nor that and you can use it to talk about one human being or one animal or one creature. Therefore, the concept of the one is something abstract and it is so far from the creatures of the exterior world. Geometry has the same case. Triangle, quarter and rectangle as such are mere geometrical shapes and are far away from real life language. But when we use them in our daily life language we give them specific life meanings. -/- As I said, Aristotle was impressed by the language of Mathematics and wanted to build a similar language for logic .The rationale behind this is to get away from the language of ambiguity caused by the use of daily life language .One word or utterance in a language has many usages in one language or when translated into other languages , and therefore it causes many problems in usage instead of simplifying it and this is what Aristotle tried to avoid. Aristotle chose letters instead of words, the letter is part of the word, and the letter is meaningless unless it is a part of the word. The meaning of a letter depends on its occurrence in the word. If you compose a word from a group of letters and use it , it becomes ambiguous because it becomes part of the used language. -/- However, Aristotle did not combine letters in a word but he used them as abstract letters and gave them meanings in the language of logic where there is no divergence about its use. Aristotle used them in syllogism and they mean the limits of reason . Until recently critical thinking was part of formal logic and learning it means that you have logical background or at least you are familiar with the rules and fundamentals of logic. But critical thinking theorists soon took the initiative to separate it from logic because the latter started to suffer from its rules which are difficult to understand and which require some awareness and thoughts on the part of the scholar to understand. Hence , critical thinking is not supposed to possess a background of logic and it adopts a specific questioning approach where it suggests a number of questions the practitioner of critical thinking has to successively answer since he has to make sure that the opinion he reaches does not rely on any subjective considerations. This is how the skills that are acquired on a continuum of related critical questions are established ,this is not to mention that the concept of critical thinking itself is usually defined in this context as the awareness of such kinds of questions and the ability to arouse and answer them at appropriate times. My paper explains, How to be able to implement these skills in high education and what are the benefits of these skills? The paper includes; Critical Thinking and Logic Socrates `s Approach The impact of critical thinking on teaching methods Questioning How questions are organized in the light of critical thinking? Using Critical Thinking in Problem-Solving Use of Non-Oral language in Critical Thinking. (shrink)

The object of the present study is to propose a technologically-based method for developing Regulation of Cognition (RC) among pre-service teachers in a pedagogical problem context. The research intervention was carried out by two groups during a Teaching Training Workshop, based on the IMPROVE instructional method, which was implemented in the Learning Management System (LMS). The first group (N=53) investigated the pedagogical problems with "dual perspectives (teacher and learner), and the other group (N=47) analyzed the same problems from (...) a teacher perspective only. The triangulated research design provided three sets of data of RC (e.g. statements on Metacognitive Awareness Inventory, Educational Data Mining, and observations on actual teaching). The results were indicative of the advantage that was obtained by the dual perspective group (LMS+2P), which has manifested in most components of RC, as compared with the single based intervention (LMS+1P). (shrink)

In the last 20 years, a stream of research emerged under the label of „complex problem solving“ (CPS). This research was intended to describe the way people deal with complex, dynamic, and intransparent situations. Complex computer-simulated scenarios were as stimulus material in psychological experiments. This line of research lead to subtle insights into the way how people deal with complexity and uncertainty. Besides these knowledge-rich, realistic, intransparent, complex, dynamic scenarios with many variables, a second line of research used (...) more simple, knowledge-lean scenarios with a low number of variables („minimal complex systems“, MCS) that have been proposed recently in problem-solving research for the purpose of educational assessment. In both cases, the idea behind the use of microworlds is to increase validity of problem solving tasks by presenting interactive environments that can be explored and controlled by participants while pursuing certain action goals. The main argument presented here is: both types of systems - CPS and MCS – can only be dealt with successfully if causal dependencies between input and output variables are identified and used for system control. System knowledge is necessary for control and intervention. But CPS and MCS differ in their way of how causal dependencies are identified and how the mental model is constructed; therefore, they cannot be compared directly to each other with respect to the cognitive processes that are necessary for solving the tasks. Knowledge-poor MCS tasks address only a small fraction of the cognitive processes and structures needed for knowledge-rich CPS situations. (shrink)

Real agents rely, when forming their beliefs, on imperfect informational sources (sources which deliver, even under normal conditions of operation, both accurate and inaccurate information). They therefore face the ‘endorsement problem’: how can beliefs produced by endorsing information received from imperfect sources be formed in an epistemically acceptable manner? Focussing on the case of episodic memory and drawing on empirical work on metamemory, this article argues that metacognition likely plays a crucial role in explaining how agents solve the endorsement (...) problem. (shrink)

Rooted in the heart of Vygotsky’s Sociocultural Theory, mediation has recently received considerable attention in the field of TEFL. The existing literature suggests that mediation can play an essential role in language learners’ performance development. In addition, learners need to know about their thinking process which is interpreted as metacognition. This study aimed to investigate the effect of teacher- and peer-assisted evaluative mediation on learners’ metacognitive awareness development. To this end, 40 homogenized intermediate EFL learners were selected using (...) a test of English language proficiency. The participants were then randomly divided into teacher-assisted (n=20) and peer-assisted (n=20) groups. Before the instructional phase, a metacognitive awareness questionnaire was given to the participants. At the instructional phase, the learners in the teacher-assisted group received teacher-assisted mediation. The learners in the peer-assisted group, however, were exposed to mediation provided by their peers. After the instructional phase, the metacognitive awareness questionnaire was given to the participants as the posttest of the study. SPSS was used to analyze the data. The descriptive statistics, the Shapiro-Wilk test of normality, and the Paired Sample T-test for inferential statistics were used to analyze the data. The findings showed that peer-assisted evaluative mediation had positive effects on developing students’ level of metacognitive awareness, whereas teacher-assisted evaluative mediation did not reveal such effects. It could be concluded that peer-assisted evaluative mediation is an effective tool for improving students’ metacognitive awareness. (shrink)

The online-based learning system is a current policy established by the Philippine government in all schools as a result of the COVID-19 pandemic. Shifting face-to-face schools with an online learning-based system creates problems, especially for elementary teachers. This study investigates elementary school teachers' practices in the new normal. The BEED - Generalist researchers employed phenomenological research and purposefully selected participants who were thoroughly knowledgeable to gather essential data about effective methods of virtual delivery. The data was collected through an interview (...) of ten elementary teachers in Magugpo, Pilot, Central Elementary School, using a researcher-made interview guide. Ten essential themes are being gathered, and these are the following: Encountering intermittent internet connection, Observing the struggles of the students, Experiencing increasing student participation, Having doubts about the student's output, Extended extra time to learn the virtual platform, Employed engaging activities, Aligned competencies, and strategies, Demonstrated resiliency, Seeing positive thinking as good mindset, Embracing educational shift and trends, and Adapting positively to changes. The result indicates that the elementary school teachers' practices are effective in virtual classrooms, making students more engaged and actively participating in the class. It is recommended that the result be utilized, improved, and implemented to ensure the effectiveness of handling the online course. (shrink)

This is not a mathematics book, but a book about mathematics, which addresses both student and teacher, with a goal as practical as possible, namely to initiate and smooth the way toward the student’s full understanding of the mathematics taught in school. The customary procedural-formal approach to teaching mathematics has resulted in students’ distorted vision of mathematics as a merely formal, instrumental, and computational discipline. Without the conceptual base of mathematics, students develop over time a “mathematical anxiety” and abandon (...) any effort to understand mathematics, which becomes their “traditional enemy” in school. This work materializes the results of the inter- and trans-disciplinary research aimed toward the understanding of mathematics, which concluded that the fields with the potential to contribute to mathematics education in this respect, by unifying the procedural and conceptual approaches, are epistemology and philosophy of mathematics and science, as well as fundamentals and history of mathematics. These results argue that students’ fear of mathematics can be annulled through a conceptual approach, and a student with a good conceptual understanding will be a better problem solver. The author has identified those zones and concepts from the above disciplines that can be adapted and processed for familiarizing the student with this type of knowledge, which should accompany the traditional content of school mathematics. The work was organized so as to create for the reader a unificatory image of the complex nature of mathematics, as well as a conceptual perspective ultimately necessary to the holistic understanding of school mathematics. The author talks about mathematics to convince readers that to understand mathematics means first to understand it as a whole, but also as part of a whole. The nature of mathematics, its primary concepts (like numbers and sets), its structures, language, methods, roles, and applicability, are all presented in their essential content, and the explanation of non-mathematical concepts is done in an accessible language and with many relevant examples. (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 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)

The demand in the workplace is rapidly changing brought about by the educational reforms and the emergence of disruptive technology. The changes increase the importance of employability skills and literacy that would ensure career success and degree program relevance. On this premise, a study was carried out using a scoping review to examine the existing literature that published information related to employability skills of Teacher Education graduates in the Philippines. The review covered fifteen published articles that qualified in inclusion (...) and exclusion criteria. Results revealed the top employable skills which include communication; information and communication technology; problem-solving and critical thinking; collaboration, cooperation, and teamwork; research; and leadership. This study offers these skills as a framework in the curriculum enhancement of teacher education programs. It was recommended to Teacher Education Institutions to revisit their curriculum and find out if these competencies were given considerable emphasis in instruction. The partially employable skills of graduates from teacher education programs imply the furtherance of the inquiry to confirm if these skills are employable or not. Future tracer studies may take the lens of the framework in evaluating the responsiveness of the curriculum. (shrink)

Crime is a community problem and not just a police problem. The adoption and implementation of Community Policing (CP) in the 1980s, was perceived as departure from the professional ‘police-as- expert’ model of public safety that had been dominant for a long time. The CP approach is designed to engage the community as an equal partner in solving local crime and other security threats within the community. The CP concept was introduced in Kenya in the 1990s.Though it (...) had informally existed in Nairobi County in Ruai and Kasarani estates much earlier.Its formal implementation only gained currency after the Post Election Violence of 2007-2008 in Kenya. Among the factors influencing its implementation in Kenya has received considerable research attention, but challenges impacting on its implementation in Nairobi County have not been adequately documented. This study aimed to fill this research gap by focussing on community factors. The overall research objective sought to determine the influence of community factors in effective implementation of community policing within Nairobi County. The objective of the study was to assess how community factors influence implementation of community policing within Nairobi County. The research findings adds to the body of knowledge, while also benefitting policy makers dealing with issues of community policing. It will also benefit other researchers exploring different aspects of community policing as a strategy to combat crime in city neighbourhoods. The research established that community factors are among the most influential factors that hamper smooth implementation of community policing in Nairobi County. The study recommends that the community needs to be educated on community policing initiatives and how to manage community factors that affect the implementation of CP in Nairobi County. (shrink)

The existing body of knowledge has witnessed gaps arising from the paucity of research literature on the quality of educational research output in higher education. This study shows how the management of data in higher education affects the quality of academic research conducted by university lecturers in South-South Nigeria. The study adopted a factorial research design. The population of this study includes all the Faculty of Education academic staff in both public and private universities situated in South-South Nigeria. Using results (...) of a survey administered to a sample of 602 accessible lecturers during data collection, one research question and one null hypothesis were resolved in the study. Multiple regression was employed in the analysis of data. Findings revealed amongst others that; data storage, data security, data retrieval, data sharing, and data re-use jointly contributed to the total variance in educational research effectiveness in terms of proper citations by 56.25%, problem-solving by 22.14%, knowledge creation by 34.50%, and generation of testable data by 36.88%; and their composite influence on educational research effectiveness in terms of proper citations, problem- solving, knowledge creation, and generation of testable data, is statistically significant. Based on the findings of this study, it was concluded that data management practices play an important role in higher education that significantly influences the quality of research output in universities in South- South Nigeria. It was recommended among others that, there should be an up-to-date database or data warehouse in Ministries of Education where researchers can easily access data in order to increase the quality of researches by eliminating the problems of data fabrication and falsification. (shrink)

Subject matter expertise goes far beyond simply knowing and regurgitating facts. It is a multifaceted ability encompassing a deep understanding of the content, pedagogical knowledge, assessment proficiency, fostering critical thinking and problem-solving skills, and cultivating positive attitudes and values. This transcendental phenomenological study was conducted to understand the lived experiences of SHS out-of-field research teachers in terms of assignment, instruction, and feedback. To grasp the phenomenon's essence, transcendental phenomenology aims to set aside the researcher's preconceived ideas and strive (...) for neutrality. The study was participated by 14 teacher-participants from the selected private senior high schools in Davao City, Philippines. Findings show that in terms of assignment, participants' experiences include adherence and submission to school administrators, consideration of teacher potential, experience, and training, and feelings of anxiety and frustration. With regards to instructional experiences, it includes lack of experience, aptitude, and administrative support; difficulty in establishing authority and checking outputs. With those, participants must be resourceful and creative and engage in professional development activities. In terms of feedback, participants were honest and open-minded and experienced the welcoming nature of the students. The findings elaborate on the complex and multi-faceted nature of out-of-field teaching, which is expected to inspire improved teacher hiring and placement policy. It is recommended that educational institutions should provide professional development programs to help those out-of-field teachers stay updated with best practices. (shrink)