Power management of variable capacitors in electrical grid systems according to the criterion of mini-mum energy loss

The aim is to manage the transmitted reactive power in electrical grids using variable capacitor batteries according to the criterion of minimum energy loss under different annual reactive load schedules and different numbers of variable capacitor sections. The main theoretical relations were obtained by the methods of mathematical modelling and integral calculus using the theory of optimal control. The influence of the power and number of sections in a capacitor battery on energy losses in the grid was estimated using computational experiments. Dependencies for energy losses in a capacitor battery, as well as for reducing energy losses in the grid, were obtained. These expressions are valid for linearized load schedules. It is shown that the dependences of energy losses in a capacitor battery and the reduction of losses in the grid on the section power have inflection points and pass through a maximum. The presence of inflection points is associated with a change in the number of capacitor sections operating throughout the year. The presence of a maximum is explained by the fact that, with an increase in the power of the capacitor battery, its operating time decreases under the complete number of variable sections. It is established that the batteries of static capacitors with two variable sections can reduce energy losses when transmitting reactive power by over 90%. For three- and four-section static capacitors, the loss reduction is close to 100%. The reduction in energy losses increases when approaching maximal levels of annual reactive load. Energy losses in electrical grid systems can be reduced by capacitor batteries with no more than three or four variable sections. In most cases, this can be achieved by two-section capacitor batteries.

Student’s mathematical connection ability through GeoGebra assisted project-based learning model

Several previous studies related to mathematical connection abilities and GeoGebra-assisted project-based learning models, but this research focuses on improving students' mathematical connection ability in the Integral Calculus course. This study examines the improvement of mathematical connection abilities through a project-based learning model assisted by GeoGebra. The research method used was a quasi-experimental design with a pretest-posttest nonequivalent multiple group design. The population is students of the Mathematics Education Study Program at the University in West Java, Indonesia. 1A and 1B students, which are used as samples. The technique of taking the research subject uses purposive sampling. The instrument consisted of a mathematical connection ability test with three essay questions. The test in this study used a pretest and posttest students' mathematical connection ability and the Group Embedded Figure Test (GEFT). The data analysis technique used an independent sample t-test and a two-way ANOVA test. The results showed that the improvement of students' mathematical connection ability who obtained the GeoGebra-assisted project-based learning model was better than students who obtained the project-based learning model. There is no interaction effect of learning models and cognitive styles on the achievement and improvement of students' mathematical connection abilities. The implication of this research is to provide significant changes in student learning habits in integral calculus courses to use technology and foster high self-regulated learning. This research has implications for universities implementing project-based learning models combined with other technology applications in other subjects.

Pengembangan Video Pembelajaran Kalkulus Untuk Memahamkan Konsep

This research is motivated by the difficulty of students understanding the concept of integration techniques through bold learning, so that a concept understanding-based learning video is needed for flat area material. This study aims to develop learning videos and determine the validity and practicality of the videos produced. This type of research is in the form of ADDIE model development research (Analysis, Design, Development, Implementation, Evaluation). The research subjects were class B students, batch 2020, the Ahmad Dahlan University Mathematics Education study program. The results of the assessment from material experts obtained an average score of 4.77 with very good criteria, from material experts obtained an average score of 4.55 with very good criteria, and from student responses a score of 3.50 was obtained with good criteria so that it can be concluded that the video Integral calculus learning is valid and practical to use. Keywords: integral calculus, learning videos, trigonometric functions

Exploring Students’ Learning of Integral Calculus using Revised Bloom’s Taxonomy

<p>Integral calculus is one of the topics involved in mathematical courses both at secondary and tertiary level with several applications in different disciplines. It is part of gateway mathematical courses at universities for many majors and important for the development of the science. Several studies had been undertaken for exploring students’ learning of integral calculus, both at the secondary and tertiary level, using a variety of frameworks (e.g., Action-Process-Object-Schema (APOS) theory (Dubinsky, 1991). However, students’ learning of integral calculus has not been explored in terms of metacognitive experiences and skills, and the number of studies which have explored metacognitive strategies in relation to the students’ learning of integral calculus is limited. Therefore, this study used Revised Bloom’s Taxonomy (RBT) (Anderson et al., 2001), Efklides’s metacognition framework (Efklides, 2008), and an adaptation of VisA (Visualization and Accuracy) instrument (Jacobse & Harskamp, 2012) for exploring students’ learning of integral calculus. A multiple case study approach was used to explore students’ learning of the integral-area relationships and the Fundamental Theorem of Calculus in relation to the RBT’s factual, conceptual, and procedural knowledge, and the facets of metacognition including metacognitive knowledge, experiences, and skills. The study sample comprised of nine first year university and eight Year 13 students who participated in individual semi-structured interviews answering nine integral calculus questions and 24 questions related to the RBT’s metacognitive knowledge. Integral calculus questions were designed to address different aspects of RBT’s knowledge dimension and activate RBT-related cognitive processes. A think aloud protocol and VisA instrument were also used during answering integral calculus questions for gathering information about students’ metacognitive experiences and skills. Ten undergraduate mathematics lecturers and five Year 13 mathematics teachers were also interviewed in relation to the teaching and learning of integral calculus to explore students’ difficulties in the topic. The entire teaching of integral calculus in a first year university course and a Year 13 classroom were video recorded and observed to obtain a better understanding of the teaching and learning of integral calculus in the context of the study. The study findings in terms of the RBT’s factual knowledge show several students had difficulty with notational aspects of the Fundamental Theorem of Calculus (FTC) (e.g., Thompson, 1994) whereas this issue was not dominant for the definite integral. In relation to the RBT’s conceptual and procedural knowledge for both topics, conceptual knowledge was less developed in students’ minds in comparison to procedural knowledge (e.g., students had not developed a geometric interpretation of the FTC, whereas they were able to solve integral questions using the FTC). The obtained results were consistent with previous studies for these three types of knowledge. The study contributes to the current literature by sharing students’ metacognitive knowledge, experiences and skills in relation to integral calculus. The findings highlight some student learning, monitoring, and problem-solving strategies in these topics. A comparison between University and Year 13 students’ results showed students across this transition had different factual, conceptual, procedural, and metacognitive knowledge in these topics. For instance, University students in the sample use online resources more often than Year 13 students, are more interested in justifications behind the formulas, and have more accurate pre and post-judgments of their ability to solve integral questions. The information obtained using questions based on RBT and the metacognition framework indicates that these two together may be very useful for exploring students’ mathematical learning in different topics.</p>

Exploring Students’ Learning of Integral Calculus using Revised Bloom’s Taxonomy

<p>Integral calculus is one of the topics involved in mathematical courses both at secondary and tertiary level with several applications in different disciplines. It is part of gateway mathematical courses at universities for many majors and important for the development of the science. Several studies had been undertaken for exploring students’ learning of integral calculus, both at the secondary and tertiary level, using a variety of frameworks (e.g., Action-Process-Object-Schema (APOS) theory (Dubinsky, 1991). However, students’ learning of integral calculus has not been explored in terms of metacognitive experiences and skills, and the number of studies which have explored metacognitive strategies in relation to the students’ learning of integral calculus is limited. Therefore, this study used Revised Bloom’s Taxonomy (RBT) (Anderson et al., 2001), Efklides’s metacognition framework (Efklides, 2008), and an adaptation of VisA (Visualization and Accuracy) instrument (Jacobse & Harskamp, 2012) for exploring students’ learning of integral calculus. A multiple case study approach was used to explore students’ learning of the integral-area relationships and the Fundamental Theorem of Calculus in relation to the RBT’s factual, conceptual, and procedural knowledge, and the facets of metacognition including metacognitive knowledge, experiences, and skills. The study sample comprised of nine first year university and eight Year 13 students who participated in individual semi-structured interviews answering nine integral calculus questions and 24 questions related to the RBT’s metacognitive knowledge. Integral calculus questions were designed to address different aspects of RBT’s knowledge dimension and activate RBT-related cognitive processes. A think aloud protocol and VisA instrument were also used during answering integral calculus questions for gathering information about students’ metacognitive experiences and skills. Ten undergraduate mathematics lecturers and five Year 13 mathematics teachers were also interviewed in relation to the teaching and learning of integral calculus to explore students’ difficulties in the topic. The entire teaching of integral calculus in a first year university course and a Year 13 classroom were video recorded and observed to obtain a better understanding of the teaching and learning of integral calculus in the context of the study. The study findings in terms of the RBT’s factual knowledge show several students had difficulty with notational aspects of the Fundamental Theorem of Calculus (FTC) (e.g., Thompson, 1994) whereas this issue was not dominant for the definite integral. In relation to the RBT’s conceptual and procedural knowledge for both topics, conceptual knowledge was less developed in students’ minds in comparison to procedural knowledge (e.g., students had not developed a geometric interpretation of the FTC, whereas they were able to solve integral questions using the FTC). The obtained results were consistent with previous studies for these three types of knowledge. The study contributes to the current literature by sharing students’ metacognitive knowledge, experiences and skills in relation to integral calculus. The findings highlight some student learning, monitoring, and problem-solving strategies in these topics. A comparison between University and Year 13 students’ results showed students across this transition had different factual, conceptual, procedural, and metacognitive knowledge in these topics. For instance, University students in the sample use online resources more often than Year 13 students, are more interested in justifications behind the formulas, and have more accurate pre and post-judgments of their ability to solve integral questions. The information obtained using questions based on RBT and the metacognition framework indicates that these two together may be very useful for exploring students’ mathematical learning in different topics.</p>

Identification of Understanding Student in Solving Integral Calculus Based on Mathematical Ability

The purpose of this study was to identify students' lack of understanding in completing integral calculus based on students' mathematical abilities. Integral calculus material here focuses on the material integration techniques. This material is important to identify the lack of understanding experienced by prospective mathematics teacher students because they muhs be able to mahser this material because this material is found at the secondary school level where they will teach. The research method used is descriptive qualitative method. The results of the study are described in a narrative manner based on the data obtained. The subjects in this study were two people with high abilities, two people with moderate abilities, and two people with low abilities. Each ability identified their lack of understanding of integral calculus, especially material on integration techniques. Based on the research that has been done, it is concluded that the identification of students' misunderstandings in solving integral calculus problems, especially the material for integration techniques. High ability students can understand the concept of integration techniques. students with moderate abilities can claMSify integration techniques but do not understand the rational function integral techniques. Low-ability students can only understand the basic concepts of integrals but cannot understand the concepts of integration techniques.

Building Bridges and Breaking Barriers: OER and Active Learning in Mathematics

This article will discuss how open educational resources and instructional technology are used to support student academic success and continuous faculty pedagogical development, as well as reduce barriers to access at an R1 university. This article uses case examples from two instructors from a Mathematics and Computational Sciences department who are using open educational resources and instructional technology as part of an inclusive active learning pedagogy. The first case study is from an integral calculus course and the second case study is from a discrete mathematics course. The article highlights the role of the educational developer in providing pedagogical and technological support to the faculty. The support the educational developer provides is framed by an inclusive pedagogy that foregrounds access and accessibility. Future considerations provided in the article highlight the need for connections and collaborations supported through a Teaching and Learning Collaboration with an emphasis on active learning, classroom training, and open educational resources to create more pedagogically comprehensive and inclusive learning environments.

Mathematical Models and Comparative Analysis for Rice and Soya Bean Irrigation Crop Water Needs: A Case Study of Bida Basin Niger State, Nigeria

In this manuscript, mathematical models for cropping water need (C.W.N) and the size of land for irrigation (S.L.I) were formulated. The solutions of the models for Crop water need for Soya beans and Rice, and the size of land for irrigation (S.L.I) of the two crops was obtained. We fill the gap by considering the size of the irrigation land which is not considered by the Food and Agriculture Organization (F.A.O). The computational Method of solutions is carried out to get effective results. The climatic data of the study area (Bida Basin) under which our research is based includes: Rainfall, Humidity, Sunshine hours, minimum and maximum temperature, evapotranspiration were secondary data collected from Nigeria Metrological Society (NIMET). We compared the results of CROPWAT 8.0 software developed by the Food and Agriculture Organization (F.A. O) and our computational method so that we can arrive at a new finding and better results. The results for the computational method with the size of Land for irrigation shows that there is an increase in crop water need for the crops than the results of CROPWAT 8.0 software developed by the Food and Agriculture Organization (F.A. O) in which the size for the land is not considered. We therefore, recommended that the integral calculus can be used to estimate the irregular shape of the size of the land if the land shape is not in rectangular form before solutions are given for accuracy and effective results.

Curiosity Matematis Mahasiswa dalam Pembelajaran Daring Ditinjau Berdasarkan Level Kemampuan Akademik dan Gender (Studi Kasus dalam Pembelajaran Kalkulus Integral)

The possession of mathematical curiosity (curiosity) in learning Integral calculus is very important. Moreover, learning is carried out online due to the covid-19 pandemic. The level of academic ability and gender, which is a social behavior inherent in individuals, will indirectly contribute to mathematical curiosity (curiosity). Therefore, this study was conducted with the aim of describing students' mathematical curiosity in online learning in terms of academic ability level and gender. The Mathematics Education Study Program FKIP UIR is the place where this research is carried out. The implementation time is the odd semester of the 2020/2021 academic year with a sample of 50 people obtained with consideration. This research was conducted using quantitative research. The research instrument was a mathematical curiosity questionnaire which was given to students on a non-test basis with the help of google classroom. Descriptive analysis was used to analyze the data obtained in this study. The results of the analysis of research data inform that Overall, students' curiosity in bold learning is included in the criteria with a percentage of 78.88%. The mathematical Curiosity of students with a high level of academic ability is included in the criteria with a percentage of 79.79%, 78.19%, and the mathematical Curiosity of students with a low level of academic ability is included in the very strong criteria with a percentage of 83, 13% . The mathematical curiosity of male and female students is included in the criteria with a percentage of 75.89% and 78.74%