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Journal articles on the topic 'Quantitative Algebra'

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Published: 5 October 2024

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1

Perrucci, Daniel, and Marie-Françoise Roy. "Quantitative fundamental theorem of algebra." Quarterly Journal of Mathematics 70, no. 3 (May 15, 2019): 1009–37. http://dx.doi.org/10.1093/qmath/haz008.

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Abstract Using subresultants, we modify a real-algebraic proof due to Eisermann of the fundamental theorem of Algebra (FTA) to obtain the following quantitative information: in order to prove the FTA for polynomials of degree d, the intermediate value theorem (IVT) is required to hold only for real polynomials of degree at most d2. We also explain that the classical proof due to Laplace requires IVT for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs.

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Burch, Lori, Erik S. Tillema, and Andrew M. Gatza. "“Counting” on Quantitative Reasoning for Algebra." Mathematics Teacher: Learning and Teaching PK-12 114, no. 6 (June 2021): 452–62. http://dx.doi.org/10.5951/mtlt.2020.0183.

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Use this approach to developing algebraic identities as a generalization of combinatorial and quantitative reasoning. Secondary school students reason about important ideas in the instructional sequence, and teachers consider newfound implications for and extensions of this generalization in secondary algebra curricula.

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McIver, A. K., C. C. Morgan, and T. Rabehaja. "Program algebra for quantitative information flow." Journal of Logical and Algebraic Methods in Programming 106 (August 2019): 55–77. http://dx.doi.org/10.1016/j.jlamp.2019.04.002.

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4

Holgate, Philip. "Biometric and chromosome algebras." Journal of Applied Probability 29, no. 2 (June 1992): 247–54. http://dx.doi.org/10.2307/3214563.

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This note continues the development of the infinite-dimensional genetic algebra approach to problems of population genetics. Two algebras are studied. One describes the familiar problem of a quantitative characteristic, and the other provides a way of treating the whole chromosome as an entity.

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Holgate, Philip. "Biometric and chromosome algebras." Journal of Applied Probability 29, no. 02 (June 1992): 247–54. http://dx.doi.org/10.1017/s0021900200043011.

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This note continues the development of the infinite-dimensional genetic algebra approach to problems of population genetics. Two algebras are studied. One describes the familiar problem of a quantitative characteristic, and the other provides a way of treating the whole chromosome as an entity.

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6

Sari, Puspita, and Swee Fong Ng. "Exploring quantitative relationship through area conservation activity." Journal on Mathematics Education 13, no. 1 (February 11, 2022): 31–50. http://dx.doi.org/10.22342/jme.v13i1.pp31-50.

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Algebra as a study of quantitative relationship is one of four conceptions of school algebra which serves as a foundation for the concept of function. However, there is still a lack of attention to this particular relationship, especially in early algebraic reasoning. This study aims to investigate how the aspect of quantitative relationship in early algebra can be explored through area conservation activities. Understanding area conservation is said to be fundamental in developing the concept of area measurement. In this study, a ten-year old pupil was observed during her involvement while comparing area of two polygons that can be decomposed into equivalent triangles. Data for this study include the pupil’s written artefacts, and video recordings of the activities and interviews. Findings from this study show that the area conservation activity has the potential to build the notion of quantitative relationships in early algebra. The quantitative relationship between the unit of measurement and the result of measurement of a shape can also be explored, that is, the smaller the unit of measurement, the larger the result of measurement. Hence, this study can provide a groundwork for further studies in the relation between quantitative relationship in algebra and area conservation in geometry at the elementary school level.

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Thompson, Robert C. "High, low, and quantitative roads in linear algebra." Linear Algebra and its Applications 162-164 (February 1992): 23–64. http://dx.doi.org/10.1016/0024-3795(92)90371-g.

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Arendasy, Martin, Markus Sommer, Georg Gittler, and Andreas Hergovich. "Automatic Generation of Quantitative Reasoning Items." Journal of Individual Differences 27, no. 1 (January 2006): 2–14. http://dx.doi.org/10.1027/1614-0001.27.1.2.

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This paper deals with three studies on the computer-based, automatic generation of algebra word problems. The cognitive psychology based generative/quality control frameworks of the item generator are presented. In Study I the quality control framework is empirically tested using a first set of automatically generated items. Study II replicates the findings of Study I using a larger set of automatically generated algebra word problems. Study III deals with the generative framework of the item generator by testing construct validity aspects of the item generator produced items. Using nine Rasch-homogeneous subscales of the new intelligence structure battery (INSBAT, Hornke et al., 2004 ), a hierarchical confirmatory factor analysis is reported, which provides first evidence of convergent as well as divergent validity of the automatically generated items. The end of the paper discusses possible advantages of automatic item generation in general ranging from test security issues and the possibility of a more precise psychological assessment to mass testing and economical questions of test construction.

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MCIVER, ANNABELLE, LARISSA MEINICKE, and CARROLL MORGAN. "Hidden-Markov program algebra with iteration." Mathematical Structures in Computer Science 25, no. 2 (November 10, 2014): 320–60. http://dx.doi.org/10.1017/s0960129513000625.

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We use hidden Markov models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or ‘implements’ relation that compares two programs with respect to their information leakage; and we propose a program algebra for source-level reasoning about such programs, in particular as a means of establishing that an ‘implementation’ program leaks no more than its ‘specification’ program.This joins two themes: we extend our earlier work, having iteration but only qualitative (Morgan 2009), by making it quantitative; and we extend our earlier quantitative work (McIver et al. 2010) by including iteration.We advocate stepwise refinement and source-level program algebra – both as conceptual reasoning tools and as targets for automated assistance. A selection of algebraic laws is given to support this view in the case of quantitative noninterference; and it is demonstrated on a simple iterated password-guessing attack.

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Wang, Yingxu, Mehrdad Valipour, and Omar A. Zatarain. "Quantitative Semantic Analysis and Comprehension by Cognitive Machine Learning." International Journal of Cognitive Informatics and Natural Intelligence 10, no. 3 (July 2016): 13–28. http://dx.doi.org/10.4018/ijcini.2016070102.

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Knowledge learning is the sixth and the most fundamental category of machine learning mimicking the brain. It is recognized that the semantic space of machine knowledge is a hierarchical concept network (HCN), which can be rigorously represented by formal concepts in concept algebra and semantic algebra. This paper presents theories and algorithms of hierarchical concept classification by quantitative semantic analysis based on machine learning. Semantic equivalence between formal concepts is rigorously measured by an Algorithm of Concept Equivalence Analysis (ACEA). The semantic hierarchy among formal concepts is quantitatively determined by an Algorithm of Relational Semantic Classification (ARSC). Experiments applying Algorithms ACEA and ARSC on a set of formal concepts have been successfully conducted, which demonstrate a deep machine understanding of formal concepts and quantitative relations in the hierarchical semantic space by machine learning beyond human empirical perspectives.

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Brown, Jennifer L., Glennelle Halpin, and Gerald Halpin. "Relationship between High School Mathematical Achievement and Quantitative GPA." Higher Education Studies 5, no. 6 (October 28, 2015): 1. http://dx.doi.org/10.5539/hes.v5n6p1.

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<p>The demand for STEM graduates has increased, but the number of incoming freshmen who declare a STEM major has remained stagnant. High school courses, such as calculus, can open or close the gate for students interested in careers in STEM. The purpose of this study was to determine if high school mathematics preparation was a significant prerequisite for success in the pre-engineering curriculum at the post-secondary level. The College Freshman Survey was administered to a sample of 2,328 incoming freshman students, then their survey responses were matched with the grades and standardized test scores provided by the university’s institutional research office. A multiple regression analysis was conducted to predict quantitative pre-engineering GPA. The most significant predictor of quantitative GPA was adjusted ACT math score. Other significant contributors to the models were calculus, algebra II, trigonometry, and algebra I grades. The results suggest that high school preparation in specific mathematics subjects does have a positive impact on success in pre-engineering education.</p>

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Langham, Belinda, Sue Sundberg, and Terry Goodman. "Developing Algebraic Thinking: An Academy Model for Professional Development." Mathematics Teaching in the Middle School 11, no. 7 (March 2006): 318–23. http://dx.doi.org/10.5951/mtms.11.7.0318.

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To think algebraically, one must be able to understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; and analyze change in various contexts, according to Navigating through Algebra (NCTM 2001). Many teachers, however, often view algebra as a set of isolated skills and procedures.

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Gasim, Abdul Sattar. "Eighth Grade Students' Attitude Toward Algebra in Maldivian Schools." International Journal of Social Research and Innovation 1, no. 1 (March 20, 2018): 51–66. http://dx.doi.org/10.55712/ijsri.v1i1.7.

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Students’ attitude towards algebra is important in deciding the factors that influence students’ achievement in algebra as well as mathematics learning. This is a quantitative study which has explored the algebra attitudes of eighth grade students. The study population included students from two main schools in Male’ who were selected using stratified random sampling. One component of the Fennema Sherman Mathematics Attitudes Scale and three components of the Attitude Towards Mathematics Inventory (ATMI) by Tapia and Marsh were used to survey the algebra attitudes of 39 boys and 45 girls in grades eight. The results show that the learners have a neutral attitude for the components of the attitude towards algebra as well as for the total attitude and that there is no gender difference in their attitude.

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Xiao, Yuan, Qing Song Jiang, Ruo Meng Chen, and Jian Ping Ye. "Research on Risk Assessment of Amusement Ride Based on FTA." Advanced Materials Research 740 (August 2013): 315–18. http://dx.doi.org/10.4028/www.scientific.net/amr.740.315.

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According to the failure features of amusement rides, the Fault Tree Analysis model of risk assessment for amusement rides was built based on technology risk, operation risk and management risk. Using Boolean algebra, the minimum cut set of fault tree and 24 kinds of accident way from top to bottom were obtained. In the fault tree, the failure probability of the bottom event was obtained according to triangular fuzzy probability. The failure probability and risk of amusement ride subsystem were obtained according to Boolean algebra method. The weights of the risk of each subsystem were obtained with successive analysis method, and the quantitative risk of amusement ride was obtained with the weight and risk of subsystems. According to the quantitative risk assessment model of fault tree, the quantitative risk assessment steps were introduced.

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Permatasari, Besse Intan. "KREATIVITAS DAN HASIL BELAJAR." De Fermat : Jurnal Pendidikan Matematika 1, no. 1 (June 29, 2018): 46–54. http://dx.doi.org/10.36277/defermat.v1i1.15.

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This study aims to determine whether there is an influence of creativity on mathematics learning outcomes of students of Mathematics Education in University of Balikpapan Study Program on Linear Algebra Courses. The approach used is a quantitative approach with ex post facto research type. The population of this research is all students of Mathematics Education Study Program Linear Algebra Course in the School Year 2017/2018, which are 49 students. Samples were chosen randomly are 25 students. The results showed that there is a positive and significant effect on student learning outcomes in Linear Algebra Subject

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Steinerberger, Stefan. "Localized quantitative criteria for equidistribution." Acta Arithmetica 180, no. 2 (2017): 183–99. http://dx.doi.org/10.4064/aa170410-22-5.

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17

Dubhashi, Devdatt P. "On decidable varieties of Heyting algebras." Journal of Symbolic Logic 57, no. 3 (September 1992): 988–91. http://dx.doi.org/10.2307/2275444.

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In this paper we present a new proof of a decidability result for the firstorder theories of certain subvarieties of Heyting algebras. By a famous result of Grzegorczyk, the full first-order theory of Heyting algebras is undecidable. In contrast, the first-order theory of Boolean algebras and of many interesting subvarieties of Boolean algebras is decidable by a result of Tarski [8]. In fact, Kozen [6] gives a comprehensive quantitative classification of the complexities of the first-order theories of various subclasses of Boolean algebras (including the full variety).This stark contrast may be reconciled from the standpoint of universal algebra as arising out of the byplay between structure and decidability: A good structure theory entails positive decidability results. Boolean algebras have a well-developed structure theory [5], while the corresponding theory for Heyting algebras is quite meagre. Viewed in this way, we may hope to obtain decidability results if we focus attention on subclasses of Heyting algebras with good structural properties.K. Idziak and P. M. Idziak [4] have considered an interesting subvariety of Heyting algebras, , which is the variety generated by all linearly-ordered Heyting algebras. This variety is shown to be the largest subvariety of Heyting algebras with a decidable theory of its finite members. However their proof is rather indirect, proceeding via semantic interpretation into the monadic second order theory of trees. The latter is a powerful theory—it interprets many other theories—but is computationally highly infeasible. In fact, by a celebrated theorem of Rabin, its complexity is not bounded by any elementary recursive function. Consequently, the proof of [4], besides being indirect, also gives no information on the quantitative computational complexity of the theory of .Here we pursue the theme of structure and decidability. We isolate the indecomposable algebras in and use this to prove a theorem on the structure of if -algebras. This theorem relates the -algebras structurally to Boolean algebras. This enables us to bootstrap the known decidability results for Boolean algebras to the variety if .

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Guerrero, Shannon M. "The Value of Guess and Check." Mathematics Teaching in the Middle School 15, no. 7 (March 2010): 392–98. http://dx.doi.org/10.5951/mtms.15.7.0392.

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OLIVEIRA, JOSÉ N. "WEIGHTED AUTOMATA AS COALGEBRAS IN CATEGORIES OF MATRICES." International Journal of Foundations of Computer Science 24, no. 06 (September 2013): 709–28. http://dx.doi.org/10.1142/s0129054113400145.

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The evolution from non-deterministic to weighted automata represents a shift from qualitative to quantitative methods in computer science. The trend calls for a language able to reconcile quantitative reasoning with formal logic and set theory, which have for so many years supported qualitative reasoning. Such a lingua franca should be typed, polymorphic, diagrammatic, calculational and easy to blend with conventional notation. This paper puts forward typed linear algebra as a candidate notation for such a unifying role. This notation, which emerges from regarding matrices as morphisms of suitable categories, is put at work in describing weighted automata as coalgebras in such categories. Some attention is paid to the interface between the index-free (categorial) language of matrix algebra and the corresponding index-wise, set-theoretic notation.

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Ehlke, N. J., and R. R. Hill Jr. "Quantitative genetics of allotetraploid and autotetraploid populations." Genome 30, no. 1 (February 1, 1988): 63–69. http://dx.doi.org/10.1139/g88-012.

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Theoretical studies were conducted to compare quantitative genetic parameters in hypothetical allotetraploid and autotetraploid populations with the same genetic information. Concepts of factorial experiments and methods of direct product matrix algebra were used to express genetic effect contrasts in similar forms for each ploidy type. Quantitative genetic effects could be expressed as follows: (i) the population mean; (ii) four linear contrasts that could be equated to additive effects with either ploidy type; (iii) six contrasts resulting from interactions between two alleles, two of these equated to dominance effects and four to additive × additive effects in the allotetraploid and all six equated to digenic effects in the autotetraploid; (iv) four contrasts from interactions between three alleles, which equated to additive × dominance effects in the allotetraploid and to trigenic effects in the autotetraploid; and (v) one contrast that resulted from interactions between four alleles, which equated to the dominance × dominance effect in the allotetraploid and the quadrigenic effect in the autotetraploid. In hypothetical populations for which gene functions were the same and gene frequencies were equal, contrasts involving similar numbers of genes were identical for each ploidy type. The mean and total variance of the hypothetical populations would be identical. The parent–offspring covariance, variance among half-sib families, and the variance among full-sib families would be slightly larger in allotetraploid than in autotetraploid populations for traits affected by genes with nonadditive effects. We concluded that response to recurrent selection, general combining ability in diallel crosses, and the probability of finding a superior single cross hybrid would be larger in the allotetraploid than in the autotetraploid populations when nonadditive genetic effects are present. The relationship between ploidy types for specific combining ability in diallel crosses depended on the importance of digenic effects. Plant breeders working on species with autotetraploid inheritance should consider looking for allotetraploid forms before embarking on programs to produce hybrid cultivars.Key words: genetic variance; covariance, parent–offspring; breeding behavior; matrix algebra.

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Sebrechts, Marc, Mary Enright, Randy Elliot Bennett, and Kathleen Martin. "Using Algebra Word Problems to Assess Quantitative Ability: Attributes, Strategies, and Errors." Cognition and Instruction 14, no. 3 (September 1996): 285–343. http://dx.doi.org/10.1207/s1532690xci1403_2.

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Alam, Mahbub, Anish Ghosh, and Shucheng Yu. "Quantitative Diophantine approximation with congruence conditions." Journal de Théorie des Nombres de Bordeaux 33, no. 1 (May 21, 2021): 261–71. http://dx.doi.org/10.5802/jtnb.1161.

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He, Yan Mary, and Hongming Nie. "Quantitative equidistribution of angles of multipliers." Fundamenta Mathematicae 257, no. 1 (2022): 95–113. http://dx.doi.org/10.4064/fm63-7-2021.

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Maybee, John S., and Gerry M. Wiener. "From qualitative matrices to quantitative restrictions." Linear and Multilinear Algebra 22, no. 3 (February 1988): 229–48. http://dx.doi.org/10.1080/03081088808817837.

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Septiani, Indah Tri, and Abd Qohar. "Kerjasama Mahasiswa dalam Pembelajaran Kooperatif Tipe Jigsaw pada Mata Kuliah Pengantar Aljabar." Jurnal Didaktik Matematika 7, no. 1 (April 30, 2020): 60–71. http://dx.doi.org/10.24815/jdm.v7i1.15365.

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The lecture on algebra has not involved students in working together. Thus, one effort that can be done is implementing the jigsaw cooperative learning model. This study aims to describe the student collaboration activities in the introduction to algebra course using the jigsaw cooperative learning. This research is a quantitative descriptive study. The subjects were 32 first semester students of 2019 who were enrolled in the introduction to algebra course in the Mathematics Education Study Program, FMIPA, Universitas Negeri Malang. The instrument in this study was an observation sheet of student activities, and the supporting data were the results of individual exercises. Data were analyzed descriptively. The results showed that student collaboration activities in the jigsaw cooperative learning in the introduction to algebra course were very good, as indicated by the average score of students in completing individual exercise problems was 90. Thus, it can be concluded that the selection of an appropriate learning model can enhance student collaboration in learning abstract mathematical concepts.

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Pons, D. J., and J. K. Raine. "Relative effectiveness of mechanisms for simulating uncertainty in quantitative systems." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 217, no. 4 (April 1, 2003): 531–40. http://dx.doi.org/10.1243/095440503321628198.

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Simulation of engineering systems may involve high uncertainty, especially at the early stage of design. It is often necessary to explore the performance of systems under the influence of random events or when probabilistic rather than deterministic input data are known. This paper introduces a probabilistic computational tool that exists within a general methodology called design for system integrity (DSI). DSI supports engineers in design and manufacture by providing an assessment mechanism to analyse system design at all stages including early conceptual design. DSI is compared with the algebra of random variables, the Monte Carlo method and fuzzy theory.

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Sutherland, Scot McRobert, and Tobin F. White. "Constraint-Referenced Analytics of Algebra Learning." Journal of Learning Analytics 3, no. 3 (December 19, 2016): 143–69. http://dx.doi.org/10.18608/jla.2016.33.8.

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The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on procedural understanding. Procedural skill was analyzed by modeling the complexity of attempts to make equivalent transformations of algebraic expressions. The constraint-referenced analytics system uses log files of student inputs on a classroom network of handheld devices to measure success rate as students make attempts to replace one algebraic expression with another equivalent expression. The analytics engine produced psychometrically verifiable results. Moving averages of student performance revealed that when students experienced a period of struggle and persisted in attempting similar transformations, an apparent conceptual shift led to subsequent success. Students also responded to periods of struggle by switching to familiar tasks or choosing non-participation.

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Latifah, Nur, and Nur Baiti Nasution. "PENGARUH MODEL PEMBELAJARAN AIR BERBANTU MEDIA LAGU MATERI ALJABAR TERHADAP KEMAMPUAN PEMAHAMAN KONSEP." Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 5, no. 1 (April 30, 2024): 553–60. http://dx.doi.org/10.46306/lb.v5i1.445.

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The purpose of this study was to analyze and improve the concept understanding abilities of class VII students using the AIR learning model assisted by algebra song. This research uses a type of experimental research with a one group pretest-posttest design. This type of experimental research is included in quantitative research methods. The sampling technique uses cluster random sampling technique. The instrument for collecting data in this research is a test instrument in the form of pretest and posttest questions. All students in class VII F were given pretest questions on real numbers and their operations. At the next 2 meetings, treatment was given in the form of learning algebra material using the AIR learning model assisted by algebra song. After the treatment was carried out, posttest questions on algebra material were given to students. Next, analysis of all data is carried out using the following steps: analysis of initial and final data, data presentation stage, and conclusions. The results of the research show that there is an increase in students' ability to understand concepts by using the AIR learning model assisted by algebra song media. The use of the AIR learning model assisted by algebra song is said to be significant in improving the ability to understand concepts because the proportion of students after being given the AIR learning model assisted by algebra song who completed it exceeded the KKM score (>70) of more than 75% of the total number of students

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ÇALIK UZUN, Selcen, and Sedef ÇELİK DEMİRCİ. "Collaborative Testing as an Alternative Assessment Technique in Algebra Education." International e-Journal of Educational Studies 7, no. 14 (May 25, 2023): 287–309. http://dx.doi.org/10.31458/iejes.1240193.

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This study aims to analyze the impact of collaborative testing of students’ cognitive and affective learning outcomes in learning algebra in mathematics education. The sample of the study was 33 students of 6th grade. The mixed method approach was employed, using both quantitative and qualitative data collection techniques. Data collection instruments included (a) exams consisting of open-ended questions developed by the researchers to test student attainments in algebra (Algebra Attainment Test), (b) Mathematical Attitudes Scale aiming to determine student attitudes towards math lessons, (c) Exam Anxiety Inventory aiming to determine student exam anxiety levels, and (d) interviews aiming to determine students’ opinions on collaborative testing. According to the analysis of the quantitative data, it was determined that the experimental group's mean score on the algebra attainment test was higher than the control group. But it was not statistically significant. Furthermore in the total mean score of the exam anxiety was found a decrease in the experimental group but it was not significant. However, it was determined that there was a significant difference between the attitudes of the students in the experimental group towards mathematics. The analysis of the qualitative study data revealed that students’ views were both positive and negative on the “cognitive”, “affective”, “social” and “suggestions” themes about collaborative testing. As a result of the research, we evaluated the effectiveness of collaborative testing in the form of group work based on assessment activities. At the same time, we presented the advantages and disadvantages of the technique and discussed its usability as an alternative assessment technique.

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Lebedev, Vladimir V. "Quantitative estimates in Beurling-Helson type theorems." Sbornik: Mathematics 201, no. 12 (February 11, 2011): 1811–36. http://dx.doi.org/10.1070/sm2010v201n12abeh004133.

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PETSCHE, CLAYTON. "A QUANTITATIVE VERSION OF BILU'S EQUIDISTRIBUTION THEOREM." International Journal of Number Theory 01, no. 02 (June 2005): 281–91. http://dx.doi.org/10.1142/s1793042105000145.

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We use Fourier-analytic methods to give a new proof of Bilu's theorem on the complex equidistribution of small points on the one-dimensional algebraic torus. Our approach yields a quantitative bound on the error term in terms of the height and the degree.

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Listiawati, Enny. "Penggunaan Video Screencast O-Matic Pada Mata Kuliah Aljabar Abstrak." Jurnal Matematika 8, no. 2 (February 7, 2019): 114. http://dx.doi.org/10.24843/jmat.2018.v08.i02.p103.

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In the millennial era an innovative and creative learning media is needed by utilizing technology that can improve the quality of student learning in abstract algebra lectures. One of them is by using Screencast O-Matic (SOM) software application. SOM is software that is generally used for making tutorial videos to explain or explain learning material.The purpose of this study was to determine the effectiveness of the use of SOM in abstract algebra learning in terms of student activity and completeness of student learning outcomes. The subjects of this study were the 5th semester students of the 5th semester Mathematics education program at STKIP Bangkalan PGRI who were participating in the Abstract Algebra course. 35 students. This type of research is quantitative descriptive, with the research instruments being the observation sheet of student activities and learning outcomes test questions. The results of this study are the use of Screencast O-matic software media in learning abstract algebra courses said to be effective based on indicators of effectiveness consisting of effective student activities and student learning outcomes completed in a classical manner.

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Zhang, Zhidong. "Designing Cognitively Diagnostic Assessment for Algebraic Content Knowledge and Thinking Skills." International Education Studies 11, no. 2 (January 26, 2018): 106. http://dx.doi.org/10.5539/ies.v11n2p106.

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This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory model and the quantitative assessment structure. Simulated data was applied to the model to illustrate the purpose. The diagnostic assessment model was represented by a Bayesian network model. Four explanatory variables and nine evidential variables were identified. These were developed to describe the content domain and cognitive structure in an algebra learning process. The diagnostic assessment model both exhibited learning progresses and provided diagnostic feedback. Through students’ performance examples model-based achievement scores were reported at three levels: 1) evidential variable level, 2) explanatory variable lower level, and 3) explanatory variable higher level. This study revealed that the diagnostic assessment model can effectively report learners’ progress in algebra learning in both content knowledge and thinking skills.

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Maimuna, Leni. "Mutu Hasil Belajar Aljabar Linear melalui Pembelajaran Daring di Palcomtech Palembang." WACANA AKADEMIKA: Majalah Ilmiah Kependidikan 4, no. 2 (November 21, 2020): 130. http://dx.doi.org/10.30738/wa.v4i2.8491.

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This research is a quantitative study which aims to determine the quality of college student learning outcomes during online learning in Linear Algebra courses. The subjects of this research were 50 college students of Informatics Engineering and Information Systems, STMIK and Polytechnic at Palcomtech Palembang. Data regarding college students' abilities and difficulties were obtained from test methods, documentation and observation during online learning. Online learning that is done through the zoom application and group whatsapp. Data were analyzed to determine the quality of Linear Algebra learning outcomes through online learning. Based on the data obtained from college student scores, namely 8 independent assignments, 2 quizzes, Mid-Semester Exams and Final Semester Exams during online learning in Linear Algebra courses, the average college student grade was 76.67. The value category is in a high range, which is good.

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Domina, Thurston, Andrew M. Penner, Emily K. Penner, and Annemarie Conley. "Algebra for All: California's Eighth-Grade Algebra Initiative as Constrained Curricula." Teachers College Record: The Voice of Scholarship in Education 116, no. 8 (August 2014): 1–32. http://dx.doi.org/10.1177/016146811411600801.

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Background/Context Across the United States, secondary school curricula are intensifying as a growing proportion of students enroll in high-level academic math courses. In many districts, this intensification process occurs as early as eighth grade, where schools are effectively constraining their mathematics curricula by restricting course offerings and placing more students into Algebra I. This paper provides a quantitative single-case research study of policy-driven curricular intensification in one California school district. Research Questions (1a) What effect did 8th eighth grade curricular intensification have on mathematics course enrollment patterns in Towering Pines Unified schools? (2b) How did the distribution of prior achievement in Towering Pines math classrooms change as the district constrained the curriculum by universalizing 8th eighth grade Algebra? (3c) Did 8th eighth grade curricular intensification improve students’ mathematics achievement? Setting Towering Pines is an immigrant enclave in the inner-ring suburbs of a major metropolitan area. The district's 10 middle schools together enroll approximately 4,000 eighth graders each year. The districts’ students are ethnically diverse and largely economically disadvantaged. The study draws upon administrative data describing 8th eighth graders in the district in the 2004–20-05 through 2007–20-08 school years. Intervention/Program/Practice During the study period, Towering Pines dramatically intensified middle school students’ math curricula: In the 2004–20-05 school year 32% of the district's 8th eighth graders enrolled in Algebra or a higher- level mathematics course; by the 2007–20-08 school year that proportion had increased to 84%. Research Design We use an interrupted time-series design, comparing students’ 8th eighth grade math course enrollments, 10th grade math course enrollments, and 10th grade math test scores across the four cohorts, controlling for demographics and prior achievement. Findings/Results We find that students’ odds of taking higher level mathematics courses increased as this district implemented the state's Algebra mandate. However, even as the district implemented a constrained curriculum strategy, mathematics achievement growth between 6th sixth and 10th grade slowed and the achievement advantages associated with 8th eighth grade Algebra declined. Conclusions/Recommendations Our analyses suggest that curricular intensification increased the inclusiveness and decreased the selectivity of the mathematics tracking regime in Towering Pines middle schools. However, the findings suggest that this constrained curriculum strategy may have may have unintended negative consequences for student achievement.

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Clarke, Kevin A. "Logical Constraints: The Limitations of QCA in Social Science Research." Political Analysis 28, no. 4 (April 20, 2020): 552–68. http://dx.doi.org/10.1017/pan.2020.7.

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Researchers employing qualitative comparative analysis (QCA) and its variants use two-element Boolean algebra to compare cases and identify putative causal conditions. I show that the two-element Boolean algebra constrains research in three important ways: it restricts what we can say about sets and the interactions between sets, it embodies a logical language that is too weak to capture modern social science theories, and it restricts our analysis of causation to necessity and sufficiency accounts and does not allow for counterfactuals. Modern quantitative analysis suffers none of these restrictions and provides a much richer way to understand the social world.

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Veith, Joaquin M., Philipp Bitzenbauer, and Boris Girnat. "Exploring Learning Difficulties in Abstract Algebra: The Case of Group Theory." Education Sciences 12, no. 8 (July 28, 2022): 516. http://dx.doi.org/10.3390/educsci12080516.

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In an earlier contribution to Education Sciences we presented a new concept inventory to assess students’ conceptual understanding of introductory group theory—the CI2GT. This concept inventory is now leveraged in a pretest-post-test design with N=143 pre-service teachers to enrich this body of work with quantitative results. On the one hand, our findings indicate three recurring learning difficulties which will be discussed in detail. On the other hand, we provide a summative evaluation of the Hildesheim Teaching Concept and discuss students’ learning gain in different sub-domains of group theory. Together, the results allow for an empirical perspective on educational aspects of group theory and thus bridge the gap between qualitative and quantitative research in this field which constitutes a desideratum to date.

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Liang, Su, and Tina Vega. "A Preliminary Report on Students’ Reflections about Their Learning in an Active Learning Classroom." International Journal of Contemporary Education 6, no. 2 (September 14, 2023): 49. http://dx.doi.org/10.11114/ijce.v6i2.6393.

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In the past decades, College Algebra has become a big hurdle for students to graduate or further pursue STEM or related careers. For most of the student population, College Algebra is a terminal course and only a small portion of students take it for further mathematics courses. The traditional content of College Algebra does not serve either group of students well (Mathematical Association of America, 2004; Mathematical Association of America & National Council of Teachers of Mathematics, 2012). In recent years, at a large Hispanic-serving university, the course design for liberal arts students has been changed. An active-learning curriculum has been implemented, namely Quantitative Reasoning. This curriculum engages students with opportunities to learn math concepts from relevant everyday sources and even their own personally collected data. Students build their own understanding of mathematics by relevant data-based situations experienced through preview activities designed to prepare students for class, collaboration in class discussion and discovery through relevant problem situations, and practice activities extending learning after each lesson. The purpose of this study was to investigate student perceptions of their learning outcomes from an active-learning structured course. That is, what impact does a course design with pre-assignment tasks, authentic problem solving through collaboration in class, and practice assignments after lessons have on diverse student populations in a quantitative reasoning course?

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Ghorbel, Fatma, Fayçal Hamdi, and Elisabeth Métais. "Dealing with Precise and Imprecise Temporal Data in Crisp Ontology." International Journal of Information Technology and Web Engineering 15, no. 2 (April 2020): 30–49. http://dx.doi.org/10.4018/ijitwe.2020040102.

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This article proposes a crisp-based approach for representing and reasoning about concepts evolving in time and of their properties in terms of qualitative relations (e.g., “before”) in addition to quantitative ones, time intervals and points. It is not only suitable to handle precise time intervals and points, but also imprecise ones. It extends the 4D-fluents approach with crisp components to represent handed data. It also extends the Allen's interval algebra. This extension allows reasoning about imprecise time intervals. Compared to related work, it is based on crisp set theory. These relations preserve many properties of the original algebra. Their definitions are adapted to allow relating a time interval and a time point, and two time points. All relations can be used for temporal reasoning by means of transitivity tables. Finally, it proposes a crisp ontology that based on the extended Allen's algebra instantiates the 4D-fluents-based representation.

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Burger, Edward B., Amanda Folsom, Alexander Pekker, Rungporn Roengpitya, and Julia Snyder. "On a quantitative refinement of the Lagrange spectrum." Acta Arithmetica 102, no. 1 (2002): 55–82. http://dx.doi.org/10.4064/aa102-1-5.

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Takeuchi, Mamoru. "Quantitative results of algebraic independence and Baker's method." Acta Arithmetica 119, no. 3 (2005): 211–41. http://dx.doi.org/10.4064/aa119-3-1.

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Bugeaud, Yann. "Quantitative versions of the Subspace Theorem and applications." Journal de Théorie des Nombres de Bordeaux 23, no. 1 (2011): 35–57. http://dx.doi.org/10.5802/jtnb.749.

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Bilu, Yuri F., and Marco Strambi. "Quantitative Riemann existence theorem over a number field." Acta Arithmetica 145, no. 4 (2010): 319–39. http://dx.doi.org/10.4064/aa145-4-2.

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Ramaré, O. "Quantitative steps in the Axer–Landau equivalence theorem." Acta Arithmetica 187, no. 4 (2019): 345–55. http://dx.doi.org/10.4064/aa170424-13-5.

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van Ittersum, Jan-Willem M. "Quantitative results on Diophantine equations in many variables." Acta Arithmetica 194, no. 3 (2020): 219–40. http://dx.doi.org/10.4064/aa171212-24-9.

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Shusterman, Mark. "The tamely ramified geometric quantitative minimal ramification problem." Compositio Mathematica 160, no. 1 (November 9, 2023): 21–51. http://dx.doi.org/10.1112/s0010437x23007510.

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We prove a large finite field version of the Boston–Markin conjecture on counting Galois extensions of the rational function field with a given Galois group and the smallest possible number of ramified primes. Our proof involves a study of structure groups of (direct products of) racks.

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Niess, Margaret L., Pejmon Sadri, and Kwangho Lee. "Mathematical Explorations: Variables and Spreadsheets Connect with Real-World Problems." Mathematics Teaching in the Middle School 13, no. 7 (March 2008): 423–31. http://dx.doi.org/10.5951/mtms.13.7.0423.

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Spreadsheet software is generally available in schools and is in wide-spread use in business. The use of spreadsheets can help students make mathematical connections with problems in the world around them. Many real-life quantitative problems require algebra for decision making. Examples include the impact of rising gas prices on family budgets; the amount of gasoline left in the tank of a car and the distance to the nearest gas station; and the level of monthly income versus money needed to pay for food, rent, utilities, and clothing. Although these issues do not require complex mathematics, they do require knowledge of basic algebra involving variables and equations.

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Merrydian, Siska, Yumiati Yumiati, and Mery Noviyanti. "Factors Influencing Madrasah E-Learning Satisfaction on Mathematics Teachers of Madrasah Tsanawiyah in Jakarta." JTAM (Jurnal Teori dan Aplikasi Matematika) 6, no. 4 (October 7, 2022): 976. http://dx.doi.org/10.31764/jtam.v6i4.9883.

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This study analyzes the effect of attitude, quality, and flexibility on satisfaction and the implications for the desire to continue using madrasah e-learning for mathematics teachers in seventh grade for algebra material. The research includes non-experimental quantitative research. The population of this research is a mathematics teacher at the seventh-grade Madrasah Tsanawiyah in DKI Jakarta Province who teaches algebra material using madrasah e-learning. Sampling by convenience sampling and obtaining a sample of 225 teachers. The method of data collection is using a questionnaire. A Likert scale 1-5 questionnaire to collect data, data analysis method using PLS-SEM. Interviews with nine teachers were conducted to explore the causes of teachers agreeing and disagreeing with using e-learning madrasah in algebra learning. The results showed that teacher attitudes, e-learning quality, and e-learning flexibility significantly and positively affected e-learning satisfaction. E-learning satisfaction significantly and positively affects the desire to continue using e-learning. The interviews showed that teachers agreed because e-learning madrasah could help and facilitate teachers and students, and teachers did not agree because they encountered some difficulties in learning algebra.

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Wahyuniar, Lilia Sinta, Umi Mahdiyah, Siti Rochana, and Dwi Harini. "The Influence of Mathematical Logical Intelligence on Student Learning Outcomes in Linear Algebra Courses." Journal of Instructional Mathematics 4, no. 2 (November 29, 2023): 88–97. http://dx.doi.org/10.37640/jim.v4i2.1871.

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The purpose of this study was to determine the effect of mathematical logical intelligence on student learning outcomes in Linear Algebra courses. The research method used is quantitative. The sampling technique used in this study was simple random sampling. Data collection in this study used a mathematical logical intelligence test of 20 multiple choice questions and a test of student learning outcomes in linear algebra courses of 5 description questions. The variables in this study consisted of independent variables and dependent variables. The independent variable in this study is mathematical logical intelligence (X), while the dependent variable in this study is student learning outcomes in Linear Algebra courses (Y). The instrument test in this study consisted of validity test, distinguishing power, difficulty level and reliability test. The classical assumption test in this study consists of normality test and linearity test. The data analysis technique used simple linear regression. The result of this study is that there is an influence between mathematical logical intelligence on student learning outcomes in linear algebra courses of 0.527 or 53%. While the other 47% is influenced by other variables outside this study.

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Igcasama, Raymund Medrano, Dexter T. Ramirez, and Naome P. Salanap. "Evaluation of Photo Math in Teaching Elementary Algebra." Journal of Education Research and Evaluation 4, no. 4 (November 17, 2020): 408. http://dx.doi.org/10.23887/jere.v4i4.29749.

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This study aims to evaluate “Photo Math” in teaching Elementary Algebra. Specifically, it aimed to identify the effect of teaching Elementary Algebra with the use of “Photo Math”. To achieved these objectives, the researchers used qualitative, quantitative and experimental design. This was conducted through a separate teaching demo in Elementary Algebra of the two Grade 7 sections. Pre-test was administered before the conduct of the demo and post-test after the teaching demo. The study showed that there was a significant difference between the pre-test and post-test results of the section with “Photo Math” as intervention. Moreover, there was also a significant difference between the pre-test and post-test results of the section without the said application as intervention. However, it showed that there was no significant difference between the two section. The first section showed that there was an effect to the performance of the students when “Photo Math” was applied as teaching tool but it was not fully claimed when compared with the traditional method of teaching. This was because the sample size of the study is small so it was recommended to have a larger number of sample size to see the effect of “Photo Math” in teaching Elementary Algebra. The study implied that Photo math as a teaching tool had an effect on teaching elementary algebra.

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