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The study focuses on improving higher-order thinking skills (HOTS) in mathematics students using a Desmos-assisted planar analytic geometry course. Analytic geometry, which is essential for understanding geometric properties using analytic methods, requires students to develop problem-solving, analysis, assessment, and creativity abilities. However, current educational practices fall short of acquiring these abilities due to insufficient instructional techniques, textbooks, and a lack of integration with information and communication technologies. To address these shortcomings, the study proposes a Desmos-assisted textbook meant to increase students' HOTS through the use of interactive Desmos platform tools such as graphic depiction, experimentation, simulation, and collaborative learning. The textbook development followed the PLOMP model, which included preliminary research, prototyping, and assessment phases, ensuring the textbook's validity and practicality through reiterated evaluations. The findings show that the textbook is highly valid and practical for instructional purposes, improving students' knowledge of mathematical concepts and ability to engage in HOTS processes. Despite some difficulties with HOTS-related practice questions, generally student feedback was positive, emphasizing the textbook's function in supporting a deeper understanding of analytic geometry and encouraging problem-solving skills. The study indicates that integrating technology such as Desmos into mathematics education can greatly contribute to the development of students' HOTS, and recommends its use in teaching techniques as well as additional research on its implementation in educational contexts.

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

Strategi memecahkan suatu permasalahan terjadi ketika identifikasi solusi untuk masalah sulit dirumuskan. Siswa jarang memanfaatkan kemampuan berpikir reflektif dalam menyelesaikan suatu permasalahan. Oleh karena itu, penelitian ini membantu mengkategorikan pemikiran reflektif siswa dalam memecahkan masalah. Subjek penelitian adalah 3 dari 38 mahasiswa di salah satu universitas di Jawa Tengah. Teknik pengumpulan data adalah tes, angket, rekaman video, wawancara, dan catatan lapangan. Keabsahan data dilaksanakan dengan teknik triangulasi. Data dianalisis dengan cara teknik reduksi data, penyajian, dan verifikasi. Hasil penelitian menunjukkan bahwa setiap subjek penelitian mempunyai jenis pemikiran reflektif berbeda. Pertama, pemikiran reflektif klarifikatif adalah proses pemecahan masalah dimulai dengan kesulitan, kemudian memfilter informasi dengan pengetahuan yang dipelajari berdasarkan pengalaman. Kedua, pemikiran reflektif konektif adalah proses memecahkan masalah ketika mengalami kesulitan dan kemudian mengatasinya dengan menghubungkan konsep dalam menemukan solusi permasalahan. Sementara itu, pemikiran reflektif produktif adalah proses berpikir dalam memecahkan masalah ketika mereka mengalami kesulitan dengan proses pemecahan masalah solusi berbeda. Penelitian ini dapat dijadikan evaluasi oleh calon guru dalam memaksimalkan kemampuan berpikir reflektif dan mempermudah mahasiswa dalam menyelesaikan masalah geometri analitik.

Self-Efficacy is one of the factors that support the success of students in participating in the lecture process, but this is not paid much attention to, causing students to experience low grades and have not been able to develop themselves. This study was conducted to see the achievement self-efficacy of students who offer space analytic geometry courses and the achievement of the dimensions self-efficacy of students who offer space analytic geometry courses. The purpose of this study was to determine the achievement self-efficacy dimensions self-efficacy in learning space analytic geometry. The type of research used is descriptive quantitative and qualitative research. The subjects of this study consisted of 62 students for the 2020/2021 academic year who were selected from high, medium, and low ability levels. From the results of data analysis, it was found that: (1) the achievement of self-efficacy in learning space analytic geometry was included in the medium category, and (2) the achievement of each dimension of self-efficacy in learning space analytic geometry was also included in the medium category.

This exploratory qualitative article with an inductive approach aims to analyze the needs of students of the mathematics education study program at one of the leading universities in Surakarta City regarding learning media that can facilitate the implementation of distance learning during the Coronavirus pandemic. Data were obtained through distributing questionnaires using Google Form to 63 students who had taken the analytic geometry course at the beginning of the Coronavirus pandemic, interviews with 2 lecturers, and 3 students selected through snowball sampling technique. The results of the analysis showed that students need interactive audio-visual teaching materials that can be accessed easily without any internet network constraints. It is evidenced by the results of the survey which show that 70% of students need audio-video-based learning media. The results of this study become the basis for developing learning media that supports the implementation of distance learning

The main objective of this research is to analyze the effect of learning using Geogebra software on student learning outcomes in analytic geometry courses. The type of research used in this study is a quasi-experimental and data obtained by using test instrument testing, both pretest and posttest. The pretest that was first distributed was used to determine the students' initial abilities, while the posttest was given to determine the level of understanding (learning outcomes) of students. The population in this study were students in the fifth semester who took the Analytical Geometry Course at the Tadris Mathematics Study Program FTIK (Faculty of Tarbiyah and Teacher Training) IAIN Pekalongan. Respondents in this study consisted of two classes, namely the control class (class B) and the experimental class (class C). Analysis of the data used in this study is using the free sample t test. The results obtained concluded that there was no difference in learning outcomes between students who were given the Geogebra learning model and students who were given the conventional (conventional) learning model. This can be seen from the results of the t test, with a significance value of 0.126 0.05.

In this paper, 168 researches on Linear Algebra (LA) and Analytic Geometry (AG) at the university are analyzed, with the objective of knowing if these researches deal with the phenomenon of the split between this knowledge and to investigate about the main topics that guide the research on these subjects. An analysis is made using qualitative techniques obtaining a categorization in an inductive way. The results allow us to conclude that the split between LA and AG that operates in the study programs is not addressed by the researchers. Most focus on describing and analyzing students' difficulties with this knowledge, and among the proposals for teaching, the incorporation of software stands out. Only a minority consider, from an epistemological point of view, the benefits of a hybrid teaching between LA and AG

Abstract: Symbolic representation is a dominating ability in geometry. The purpose of this study was to determine the written responses of students when representing geometric objects in mathematical equations. The research used a qualitative descriptive method which was carried out on IAIN Metro students. The test instrument used is in the form of questions to measure the ability of students' symbolic representation with indicators presenting visual representations to mathematical equations or expressions representation. The test instrument is in the form of a circle image along with tangents and polar lines which then must be described by students based on what they see in the picture. Based on the research results, it was obtained three types of student symbolic representation mistakes when solving analytic geometry problems Abstrak: Representasi simbolik merupakan kemampuan yang penting dikuasai dalam geometri. Tujuan penelitian ini adalah untuk mengetahui kesalahan mahasiswa ketika merepresentasi objek geometri ke dalam persamaan matematika. Penelitian menggunakan metode deskriptif kualitatif yang dilakukan pada mahasiswa IAIN Metro. Instrumen yang digunakan berupa soal untuk mengukur kemampuan representasi simbolik mahasiswa dengan indikator menyajikan representasi visual ke representasi persamaan atau ekspresi matematis. Instrumen tes berupa gambar lingkaran beserta garis singgung dan garis kutubnya yang kemudian harus dideskripsikan oleh mahasiswa berdasarkan apa yang mereka lihat pada gambar tersebut. Hasil penelitian menunjukkan tiga jenis kesalahan mahasiswa yang sering terjadi dalam melakukan representasi simbolik objek geometri, yaitu tidak memahami konsep, kesalahan dalam membaca data yang terdapat pada gambar, serta kesalahan melakukan operasi matematika.

The purpose of this study is to analyse the independence of students learning on the flat analytic geometry of the Covid-19. This research was conducted on students in the second semester with 72 resopondents consisting of 15 males and 52 females. Data retrieval is carried out using a self-sufficiency study poll as many as 20 items of statements that have been compiled based on learning independence indicators. The scale used in this study was the Likert scale. Data analysis to know the independence of learning students used descriptive analytical techniques with the ideal criteria namely the ideal mean and the ideal deviation standard. Based on data analysis obtained by the results of independence of learning with indicators: a self- confident is good enough (31.75%), the activeness is quite good (37.50%), discipline is good (52.10%), and responsibility is good (64.57%).

In the humanoid competition field, identifying landmarks for localizing robots in a dynamic environment is of crucial importance. By convention, state-of-the-art humanoid vision systems rely on poles located outside the middle of the field as an indicator for generating landmarks. However, in compliance with the recent rules of Robocup, the middle pole has been discarded to deliberately provide less prior information for the humanoid vision system to strategize its winning tactics on the field. Previous localization method used middle poles as a landmark. Therefore, robot localization tasks should apply accurate corner and distance detection simultaneously to locate the positions of goalposts. State-of-the-art corner detection algorithms such as the Harris corner and mean projection transformation are excessively sensitive to image noise and suffer from high processing times. Moreover, despite their prevalence in robot motor log and fish-eye lens calibration for humanoid localization, current distance estimation techniques nonetheless remain highly dependent on multiple poles as vision landmarks, apart from being prone to huge localization errors. Thus, we propose a novel localization method consisting of a proposed corner extraction algorithm, namely, the contour intersection algorithm (CIA), and a distance estimation algorithm, namely, analytic geometric estimation (AGE), for efficiently identifying salient goalposts. At first, the proposed CIA algorithm, which is based on linear contour intersection using a projection matrix, is utilized to extract corners of a goalpost after performing an adaptive binarization process. Then, these extracted corner features are fed into our proposed AGE algorithm to estimate the real-word distance using analytic geometry methods. As a result, the proposed localization vision system and the state-of-the-art method obtained approximately 3-4 and 7-23 centimeter estimation errors, respectively. This demonstrates the capability of the proposed localization algorithm to outperform other methods, which renders it more effective in indoor task localization for further actions such as attack or defense strategies.

Rapid development of technology for the past two decades has greatly influenced mathematic learning system. Mathematica software is one of the most advanced technology that helps learn math especially in Geometry. Therefore this research aims at investigating the effectiveness of analytic geometry learning by using Mathematica software on the mathematical abstraction ability, motivation, and independence of students. This research is a quantitative research with quasi-experimental method. The independent variable is learning media, meanwhile the dependent variables are students’ mathematical abstraction ability, motivation, and independence in learning. The population in this research was the third semester students of mathematics education program and the sample was selected using cluster random sampling. The samples of this research consisted of two distinct classes, with one class as the experimental class was treated using Mathematica software and the other is the control class was treated without using it. Data analyzed using multivariate, particularly Hotelling’s T2 test. The research findings indicated that learning using Mathematica software resulted in better mathematical abstraction ability, motivation, and independence of students, than that conventional learning in analytic geometry subject.

Turk dilinde yazilmis devrin en iyi analitik geometri kitabi sayilabilecek Hendese-i Tahliliyye (Cild-i evvel, Istanbul, 1331/1915) adli eserinin sonuna Sukru Sayan, (?-1943) “Kemmiyyat-i mevhumenin suret-i iraesine dair yeni bir nazariyye” adli bir makale eklemistir. Sukru Sayan makalesinin basliginda “yeni bir nazariyye” ifadesini kullanmakla birlikte, bu calismasinda yeni bir fikir ortaya atmadigi gibi yeni bir cebirsel hesaplama kolayligi da getirmemistir. Esas fikri bir gosterim degisIkliginden ibaret kalan bu makale, ozgun bir katkidan ziyade Osmanli matematikcileri arasinda o devirde yayginlik kazanan ortaya yeni bir sey koyabilmek arzusunun verimsiz bir urunu olarak gorulebilir. Sukru Sayan’in makalesi, soz konusu arzuya dikkat cekmek amaciyla burada incelenmistir.

[English]: This case study aimed to describe the metacognition of male students in solving analytical geometry problems referring to cognitive style. The subjects were mathematics students who enrolled in Analytic Geometry course and selected by purposive sampling technique. The instrument of this research was the researcher as the main instrument and a problem-solving test as the supporting instrument. Data were collected using a think-aloud method and analyzed through three steps: reducing data, presenting data, and drawing conclusions. The results of this study show that at the stage of understanding the problem, FI and FD male students read questions silently and did not write what is known and asked in the problem. At the planning stage, FD male student drew elements that are fully known, while male FI students did not do so. At the stage of implementing the plan, FI male student was aware of less effective strategy, while FD male students did not. In re-checking phase, FI male student used a variety of strategies and checked whether or not the results meet the criteria of solving the problem, while FD male students used a variety of strategies but are assisted with a prompt. This study shows that FI and FD male students have similar metacognition profile at the stage of understanding the problem, but they are different in planning, doing the plan and re-checking the result of problem-solving. Keywords : Metacognition, Gender, Analytic geometry, Cognitive style, Problem-solving [Bahasa]: Peneltian studi kasus ini bertujuan untuk mendiskripsikan metakognisi mahasiswa laki-laki dalam memecahkan masalah geometri analitik ditinjau dari gaya kognitif. Subjek penelitianadalah mahasiswa matematika yang mengambil mata kuliah Geometri Analitik dipilih dengan teknik purposive sampling. Instrumen penelitian meliputi instrumen utama (peneliti) dan instrumen bantu (soal pemecahan masalah geometri analitik). Data dikumpulkan dengan menggunakan metode think aloud. Analisis data dilakukan dengan cara reduksi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan pada tahap memahami masalah, mahasiswa laki-laki FI dan FD membaca soal dalam hati serta tidak menuliskan yang diketahui dan ditanyakan. Pada tahap menyusun rencana, mahasiswa laki-laki FD menggambar unsur-unsur yang diketahui secara lengkap, sedangkan mahasiswa laki-laki FI tidak melakukannya. Pada tahap melaksanakan rencana, mahasiswa laki-laki FI menyadari terdapat strategi yang kurang efektif, sedangkan mahasiswa laki-laki FD tidak melakukannya. Pada tahap mengecek kembali, mahasiswa laki-laki FI menggunakan strategi bervariasi dan mengecek apakah hasil yang diperoleh memenuhi kriteria yang digunakan untuk memecahkan masalah, sedangkan mahasiswa laki-laki FD menggunakan strategi yang bervariasi tetapi dibantu dengan pertanyaan. Penelitian ini menunjukkan bahwa mahasiswa laki-laki FI dan FD memiliki profil metakognisi yang sama pada tahap memahami masalah namun berbeda pada menyusun rencana, melaksanakan rencana dan mengecek kembali hasil pemecahan masalah. Kata kunci: Metakognisi, Gender, Geometri analitik, Gaya kognitif, Pemecahan masalah

As a result of literature analysis the expediency of free access of bachelors majoring in Computer Sciences and Information Technologies to modern information educational resources, in particular, e-learning courses in the process of studying mathematical disciplines is substantiated. It was established that the e-learning course is a complex of teaching materials and educational services created for the organization of individual and group training using information and communication technologies. Based on the outlined possibilities of applying the e-learning course, as well as its didactic functions, the structure of the certified e-learning course “Analytic Geometry” based on the Moodle platform was developed and described. Features of application of cloud-oriented resources are considered: Desmos, Geogebra, Wolfram|Alpha, Sage in the study of the discipline “Analytic Geometry”. The results of the pedagogical experiment on the basis of Borys Grinchenko Kyiv University and A. S. Makarenko Sumy State Pedagogical University are presented. The experiment was conducted to verify the effectiveness of the implementation of the e-learning course “Analytic Geometry”. Using the Pearson criterion it is proved that there are significant differences in the level of mathematical preparation of experimental and control group of students. The prospect of further scientific research is outlined through the effectiveness of the use of e-learning courses for the improvement of additional professional competences of students majoring in Computer Sciences and Information Technologies (specialization “Programming”, “Internet of Things”).

This paper proposes an experimental path aimed at guiding upper secondary school students to overcome that discontinuity, often perceived by them, between learning geometry and learning algebra. This path contributes to making students aware of how the algebraic language, formalized in the most powerful form by Descartes, grafts itself onto the geometric language. This is realized by introducing a problem included in a text written by Abū Kāmil before the year 870. This awareness acquired by the students, when accompanied by some semiotic considerations, allows the translation of the problem from “spoken” algebra to “symbolic” algebra, and it represents the background for a possible use of the same problem within the framework of analytic geometry. This proposition manifests a didactic and popular efficacy that supports and favors the recognition of the object it is talking about in different contexts, helping to create a unitary vision of mathematics.

This paper presents a new approach for watermarking by using geometric analytic and mathematical model providing robustness to embed the watermarking in postage stamp (ps) image, using the angle between two lines to insert the embedded information in blue component for pixels. Analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and analysis. The modern and advanced meaning refers to the geometry of analytic varieties, to develop a data-hiding method that has a good performance in color images. Furthermore, the watermark must be either robust or fragile; depending on the application. The expression "robust" in this paper refers to the capability of the watermark to resist manipulations of the media. Two types of watermarked attack was used; the JEPQ compression as lossy compression (where compressing and decompressing data retrieve hidden information that may be close enough to the original image), and the enhancement filter (mean filter). This proposed watermarking system refers to the watermark objective evaluation test or (WOET).

This study is part of an investigation that analyzes an innovative approach for the teaching of Analytic Geometry in the first year of postcompulsory education in Catalonia (Spain). The didactic approach consists of a sequence that begins with activities that induce mathematization, and is completed with a further formalization of the contents. The analysis of the mathematization made by the students has a central role in this research. The study also examines the students’ subjective assessments on the implementation of activities with GeoGebra. These analysis show that, compared to the traditional methodology, there is an improved performance in mathematization, as well as an increased self-awareness, motivation and involvement of students in the learning process.

Neste trabalho foram conduzidos testes preliminares sobre o uso do método altura relativa, desenvolvido originalmente por Andrade & Leite (1997), para condução de inventário florestal. O método proposto foi comparado com um dos métodos usuais, que consiste em medir o diâmetro de todas as árvores, a altura de cerca de 15 árvores e a altura de cerca de cinco árvores dominantes por parcela. Para processamento desses dados são utilizadas equações hipsométricas e volumétricas, sendo estas últimas geradas com dados de cubagem de árvores no povoamento. No método da altura relativa são utilizados apenas dados obtidos nas parcelas, não sendo necessário cubar árvores no povoamento. Os dados de quatro parcelas e de 277 árvores-amostra foram utilizados para comparação das duas metodologias (usual e altura relativa). Os volumes estimados pelos dois métodos foram iguais (156,21 e 156,19 m³/ha). Portanto, pode-se concluir que o método alternativo é promissor, resultando ainda em algumas vantagens, como: redução do número de alturas medidas nas parcelas e eliminação das atividades de cubagem de árvores-amostra e de ajuste de modelos volumétricos e, ou, de taper.Preliminary tests were conducted of on the use of the Relative Height Method, developed originally by Andrade and Leite (1997), to corry out a forest inventory. The proposed method was compared with one of the conventional methods, that consists of measuring the diameter of all the trees, the height of about 15 trees and the height of about five dominant trees per plot. For processing these data, hipsometric and volumetric equations are used, with the latter being generated from tree scaling data in the stand. The relative height method includes only data obtained in the portions, without the need to scale trees in the stand. Data of four plots and 277 tree samples were used to compare the two methodologies (conventional and relative height). The volumes for the two methods were similar (156,21 and 156,19 m³/ha). Thus, it can be concluded that the alternative method is promising, even resulting in some advantages, such as: reduction of the number of heights measured in the plots, elimination of the activities of tree sample scaling and adjustment of volumetric and, or, taper models.

Juozas Stoukus (1886–1946) was an educator, a mathematician, the author of the textbooks. He wrote the following books: “Analizinės geometrijos pagrindai” (Basics of Analytic Geometry), “Begalinių mažybių analizio pagrindai” (Basics of Infinitesimal Variable Analysis), “Aritmetikos uždavinynas” (Book of Problems in Arithmetic), 1, 2 parts, “Geometrijos uždavinynas” (Book of Problems in Geometry), 1, 2 parts.