Journal articles: 'Mathematical and symbolic'

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Wolfram, Stephen. "Symbolic mathematical computation." Communications of the ACM 28, no. 4 (April 1985): 390–94. http://dx.doi.org/10.1145/3341.3347.

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Bing, Thomas J., and Edward F. Redish. "Symbolic manipulators affect mathematical mindsets." American Journal of Physics 76, no. 4 (April 2008): 418–24. http://dx.doi.org/10.1119/1.2835053.

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Lutovac, Miroslav, and Dejan Tosic. "Symbolic signal processing and system analysis." Facta universitatis - series: Electronics and Energetics 16, no. 3 (2003): 423–31. http://dx.doi.org/10.2298/fuee0303423l.

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We present new software in MATLAB and Mathematica for symbolic signal processing and system analysis. Our mission is to encapsulate high-tech engineering and sophisticated mathematical knowledge into easy-to-use software that effectively solves practical problems.

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Vasileva, Natalia, Vladimir Grigorev-Golubev, and Irina Evgrafova. "Mathematical programming in Mathcad and Mathematica." E3S Web of Conferences 419 (2023): 02007. http://dx.doi.org/10.1051/e3sconf/202341902007.

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An article generalizes the long-term work of authors with packages of applied mathematical programs. It discusses and demonstrates the features and methods of solution of mathematical tasks in mathematical package Mathcad and Mathematica: from the simplest ones, included in the set of typical problems of mathematical disciplines for training specialists for shipbuilding, to complex computational tasks and applied problems of professional orientation, which require the construction of a mathematical model and analysis of the results obtained. The examples show the solution of mathematical problems in symbolic form, mathematical studies in the Mathcad and Mathematica environment, and mathematical programming with these packages.

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Behmanesh-Fard, Navid, Hossein Yazdanjouei, Mohammad Shokouhifar, and Frank Werner. "Mathematical Circuit Root Simplification Using an Ensemble Heuristic–Metaheuristic Algorithm." Mathematics 11, no. 6 (March 19, 2023): 1498. http://dx.doi.org/10.3390/math11061498.

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Symbolic pole/zero analysis is a crucial step in designing an analog operational amplifier. Generally, a simplified symbolic analysis of analog circuits suffers from NP-hardness, i.e., an exponential growth of the number of symbolic terms of the transfer function with the circuit size. This study presents a mathematical model combined with a heuristic–metaheuristic solution method for symbolic pole/zero simplification in operational transconductance amplifiers. First, the circuit is symbolically solved and an improved root splitting method is applied to extract symbolic poles/zeroes from the exact expanded transfer function. Then, a hybrid algorithm based on heuristic information and a metaheuristic technique using simulated annealing is used for the simplification of the derived symbolic roots. The developed method is tested on three operational transconductance amplifiers. The obtained results show the effectiveness of the proposed method in achieving accurate simplified symbolic pole/zero expressions with the least complexity.

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Zhanatauov, S. U. "VERBAL, SYMBOLIC, MATHEMATICAL, SEMANTIC, BEHAVIORAL, COGNITIVE MODELS." Theoretical & Applied Science 113, no. 09 (September 30, 2022): 169–74. http://dx.doi.org/10.15863/tas.2022.09.113.32.

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Diez, F., and R. Moriyon. "Solving mathematical exercises that involve symbolic computations." Computing in Science & Engineering 6, no. 1 (January 2004): 81–84. http://dx.doi.org/10.1109/mcise.2004.1255826.

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Torresi, Sandra. "Interaction between domain-specific and domain-general abilities in math´s competence." Journal of Applied Cognitive Neuroscience 1, no. 1 (December 7, 2020): 43–51. http://dx.doi.org/10.17981/jacn.1.1.2020.08.

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This article is an approach to some viewpoints about interactions between domain-specific and general cognitive tools involved in the development of mathematical competence. Many studies report positive correlations between the acuity of the numerical approximation system and formal mathematical performance, while another important group of investigations have found no evidence of a direct connection between non-symbolic and symbolic numerical representations. The challenge for future research will be to focus on correlations and possible causalities between non-symbolic and symbolic arithmetic skills and general domain cognitive skills in order to identify stable precursors of mathematical competence.

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Xu, Chang, Feng Gu, Katherine Newman, and Jo-Anne LeFevre. "The hierarchical symbol integration model of individual differences in mathematical skill." Journal of Numerical Cognition 5, no. 3 (December 20, 2019): 262–82. http://dx.doi.org/10.5964/jnc.v5i3.140.

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Symbolic number knowledge is strongly related to mathematical performance for both children and adults. We present a model of symbolic number relations in which increasing skill is a function of hierarchical integration of symbolic associations. We tested the model by contrasting the performance of two groups of adults. One group was educated in China (n = 71) and had substantially higher levels of mathematical skill compared to the other group who was educated in Canada (n = 68). Both groups completed a variety of symbolic number tasks, including measures of cardinal number knowledge (number comparisons), ordinal number knowledge (ordinal judgments) and arithmetic fluency, as well as other mathematical measures, including number line estimation, fraction/algebra arithmetic and word problem solving. We hypothesized that Chinese-educated individuals, whose mathematical experiences include a strong emphasis on acquiring fluent access to symbolic associations among numbers, would show more integrated number symbol knowledge compared to Canadian-educated individuals. Multi-group path analysis supported the hierarchical symbol integration hypothesis. We discuss the implications of these results for understanding why performance on simple number processing tasks is persistently related to measures of mathematical performance that also involve more complex and varied numerical skills.

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Lestari, Nurcholif Diah Sri, Wasilatul Murtafiah, Marheny Lukitasari, Suwarno Suwarno, and Inge Wiliandani Setya Putri. "IDENTIFIKASI RAGAM DAN LEVEL KEMAMPUAN REPRESENTASI PADA DESAIN MASALAH LITERASI MATEMATIS DARI MAHASISWA CALON GURU." KadikmA 13, no. 1 (April 30, 2022): 11. http://dx.doi.org/10.19184/kdma.v13i1.31538.

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Representation is one of the fundamental abilities of mathematics reflected by students understanding of mathematics concepts, principles, or procedures, so it becomes crucial for teachers to develop students' mathematical representation skills. This research was time to describe the representation used in the problem and the level of mathematical representation ability needed to solve mathematical literacy problems. The data was collected through the assignment to design mathematical literacy problems between 3-10 pieces and interview as triangulation on 35 prospective elementary school teacher students. The data are grouped based on various representations and analyzed quantitatively and descriptively. Then one problem is chosen randomly for each type of representation to describe the level of representation ability needed to solve the problem qualitatively. The results show that the mathematical representations used in designed mathematical literacy problems are pictorial-verbal, pictorial-symbolic, verbal-symbolic, pictorial, verbal, symbolic, and pictorial-verbal-symbolic representations. The level of representational ability that tends to be needed to solve problems is levels 0 and 1. This study suggests that prospective teacher students should develop mathematical representation knowledge to improve the quality of their learning in the future

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Klepikov, P. N. "Mathematical Modeling in Problems of Homogeneous (Pseudo)Riemaimian Geometry." Izvestiya of Altai State University, no. 1(111) (March 6, 2020): 95–98. http://dx.doi.org/10.14258/izvasu(2020)1-15.

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Currently, mathematical and computer modeling, as well as systems of symbolic calculations, are actively used in many areas of mathematics. Popular computer math systems as Maple, Mathematica, MathCad, MatLab allow not only to perform calculations using symbolic expressions but also solve algebraic and differential equations (numerically and analytically) and visualize the results. Differential geometry, like other areas of modern mathematics, uses new computer technologies to solve its own problems. The applying is not limited only to numerical calculations; more and more often, computer mathematics systems are used for analytical calculations. At the moment, there are many examples that prove the effectiveness of systems of analytical calculations in the proof of theorems of differential geometry.This paper demonstrates how symbolic computation packages can be used to classify neither conformally flat nor Ricci parallel four-dimensional Lie groups with leftinvariant (pseudo)Riemannian metric of the algebraic Ricci soliton with the zero Schouten-Weyl tensor.

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Valverde, Jose C., Fernando L. Pelayo, Juan A. Martinez, and Juan J. Miralles. "Symbolic mathematical computing of bifurcations in dynamical systems." Journal of Computational Methods in Sciences and Engineering 4, no. 1-2 (October 13, 2004): 115–23. http://dx.doi.org/10.3233/jcm-2004-41-214.

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Hettle, Cyrus. "The Symbolic and Mathematical Influence of Diophantus's Arithmetica." Journal of Humanistic Mathematics 5, no. 1 (January 2015): 139–66. http://dx.doi.org/10.5642/jhummath.201501.08.

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Lambe, Larry, and Richard Luczak. "Object-oriented mathematical programming and symbolic/numeric interface." Mathematics and Computers in Simulation 36, no. 4-6 (October 1994): 493–503. http://dx.doi.org/10.1016/0378-4754(94)90081-7.

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Shabel, Lisa. "Kant on the `symbolic construction' of mathematical concepts." Studies in History and Philosophy of Science Part A 29, no. 4 (December 1998): 589–621. http://dx.doi.org/10.1016/s0039-3681(98)00023-5.

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Nizaruddin, Nizaruddin, Muhtarom Muhtarom, and Yanuar Hery Murtianto. "EXPLORING OF MULTI MATHEMATICAL REPRESENTATION CAPABILITY IN PROBLEM SOLVING ON SENIOR HIGH SCHOOL STUDENTS." Problems of Education in the 21st Century 75, no. 6 (December 15, 2017): 591–98. http://dx.doi.org/10.33225/pec/17.75.591.

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The students’ multi-mathematical representation capability in problem solving is very important and interesting to discuss, specifically for problems in the two-variable linear equation system. Data was collected from 48 students using written tests and in-depth interviews with selected participants. The research findings showed that few students are using three representations namely symbolic - verbal - table representation, and symbolic representation, however most of the students are using three representations namely symbolic - verbal - images representation, and two representations namely symbolic – verbal representations, and the rest used symbolic representation. In the use of verbal representation, some students had difficulty composing words and all students encountered difficulties in the translational process from symbolic representation and verbal representation to other types of representation. The ability to understand concepts and relationships between mathematical concepts was found to be a necessary condition for the achievement of multi-mathematical representation capability. It is therefore recommended that teachers use a variety of different types of representation, such as verbal, tables and images, to enhance students' understanding of the material. Keywords: multiple representations, problem solving, two-variable linear equation system.

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Nizaruddin, Nizaruddin, Muhtarom Muhtarom, and Yanuar Hery Murtianto. "EXPLORING OF MULTI MATHEMATICAL REPRESENTATION CAPABILITY IN PROBLEM SOLVING ON SENIOR HIGH SCHOOL STUDENTS." Problems of Education in the 21st Century 75, no. 6 (December 15, 2017): 591–98. http://dx.doi.org/10.33225/17.75.591.

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The students’ multi-mathematical representation capability in problem solving is very important and interesting to discuss, specifically for problems in the two-variable linear equation system. Data was collected from 48 students using written tests and in-depth interviews with selected participants. The research findings showed that few students are using three representations namely symbolic - verbal - table representation, and symbolic representation, however most of the students are using three representations namely symbolic - verbal - images representation, and two representations namely symbolic – verbal representations, and the rest used symbolic representation. In the use of verbal representation, some students had difficulty composing words and all students encountered difficulties in the translational process from symbolic representation and verbal representation to other types of representation. The ability to understand concepts and relationships between mathematical concepts was found to be a necessary condition for the achievement of multi-mathematical representation capability. It is therefore recommended that teachers use a variety of different types of representation, such as verbal, tables and images, to enhance students' understanding of the material. Keywords: multiple representations, problem solving, two-variable linear equation system.

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Karolina, Rosfita, Laila Hayati, Junaidi Junaidi, and Arjudin Arjudin. "Analisis Kemampuan Representasi Matematis Ditinjau Dari Tingkat Kemampuan Siswa Dalam Penyelesaian Masalah Bentuk Aljabar Di SMPN 4 TanjungTahun Ajaran 2021/2022." Griya Journal of Mathematics Education and Application 2, no. 4 (December 28, 2022): 1085–98. http://dx.doi.org/10.29303/griya.v2i4.255.

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This study aims to describe the ability of mathematical representation in solving algebraic problems in terms of the ability level of students at SMPN 4 Tanjung, the Academic Year 2021/2022. The type of research used is descriptive qualitative. The sample used was 27 students with the sampling technique used was purposive random sampling. Data collection techniques were carried out through tests and interviews. Based on the results of student test analysis, it was found that (1) the number of subjects in the high category was 6 students, indicating that the visual, symbolic, and verbal indicators were able to solve problems correctly and completely (2) the number of subjects in the medium category was 9 students. , shows that the visual, symbolic, and verbal indicators can state the problem but are incomplete (3) Furthermore, the number of subjects in the low category is 12 students, indicating that students have not been able to achieve the indicators of symbolic and verbal mathematical representation ability. The results of the research on students' mathematical representation abilities are 44.65%, the percentage value obtained from students' mathematical representation abilities on visual indicators is 18.31% in the high category, students' mathematical representation abilities on symbolic indicators are 15.43% in the medium category, then the ability students' mathematical representation of verbal indicators obtained 10.90% in the low category. This research on the ability of mathematical representation uses 3 indicators, namely visual or image representation, symbolic or expression, and verbal or written text words for further development by looking at other representational abilities.

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Císaro, Sandra Elizabeth González, and Héctor Oscar Nigro. "Symbolic Data Analysis." International Journal of Signs and Semiotic Systems 3, no. 1 (January 2014): 1–9. http://dx.doi.org/10.4018/ijsss.2014010101.

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Standard data mining techniques no longer adequately represent the complexity of the world. So, a new paradigm is necessary. Symbolic Data Analysis is a new type of data analysis that allows us to represent the complexity of reality, maintaining the internal variation and structure developed by Diday (2003). This new paradigm is based on the concept of symbolic object, which is a mathematical model of a concept. In this article the authors are going to present the fundamentals of the symbolic data analysis paradigm and the symbolic object concept. Theoretical aspects and examples allow the authors to understand the SDA paradigm as a tool for mining complex data.

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Tikhomirova, Tatiana, Yulia Kuzmina, and Sergey Malykh. "Does symbolic and non-symbolic estimation ability predict mathematical achievement across primary school years?" ITM Web of Conferences 18 (2018): 04006. http://dx.doi.org/10.1051/itmconf/20181804006.

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The article presents the results of a longitudinal study of the association between number sense and success in learning mathematics in primary school. We analysed the data of 133 schoolchildren on two aspects of number sense related to the symbolic and non-symbolic magnitude estimation abilities and academic success in mathematics in third and fourth grade. The average age of schoolchildren during the first assessment was 9.82 ± 0.30; during the second assessment – 10.82 ± 0.30. For the analysis of interrelations, the cross-lagged method was used. It was shown that the reciprocal model best describes the data suggesting cross-lagged associations between number sense and the success in learning mathematics at primary school age. The results of the longitudinal analysis revealed differences in the relationship between the success in learning mathematics with the two aspects of number sense: academic success in third grade only predicted the indicator of number sense associated with the symbolic magnitude estimation ability in fourth grade. The differences in the age dynamics of the two aspects of number sense in primary school are also revealed: the indicator of number sense associated with the non-symbolic magnitude estimation ability was the most stable over time.

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T, Ahmad Yani, and Lucius Chih Huang Chang. "Presentation of Mathematics Object in Verbal and Symbolic Forms to Increase Conceptual Understanding in Category Statistics Math." JETL (Journal Of Education, Teaching and Learning) 2, no. 2 (October 1, 2017): 253. http://dx.doi.org/10.26737/jetl.v2i2.303.

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Abstract. This study aims to obtain objective information about the presentation of mathematical objects in the form of verbal and symbolic to improve the conceptual understanding and interest in student learning after being given a lesson with the presentation of mathematical objects in the form of verbal and symbolic in the Mathematical Statistics Course Semester VI Mathematics Education Study Program PMIPA FKIP University of Tanjungpura Pontianak The sample of this research is the fourth semester students who follow the Basic Mathematics course of Mathematics Education program of PMIPA FKIP for the academic year 2016-2017. Data collection is done by giving test result of learning after given treatment. The essay-like test is 10 questions. The result of the research shows that there is an increase of students' learning result through presentation of mathematical object in verbal and symbolic form to improve conceptual understanding in Mathematics Statistics Semester VI Mathematics Education Study Program and there is an increase of learning interest after given learning by presentation of mathematical object in verbal and symbolic form.

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Lafay, Anne, Joël Macoir, and Marie-Catherine St-Pierre. "Impairment of Arabic- and spoken-number processing in children with mathematical learning disability." Journal of Numerical Cognition 3, no. 3 (January 30, 2018): 620–41. http://dx.doi.org/10.5964/jnc.v3i3.123.

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The performance of 24 French-Quebec 8‒9-year-old children with Mathematical Learning Disability (MLD) in Arabic and spoken number recognition, comprehension and production tasks designed to assess symbolic number processing was compared to that of 37 typically developing children (TD). Children with MLD were less successful than TD children in every symbolic numerical task, including recognition of Arabic and spoken numbers. These results thus suggested that this deficit of symbolic number recognition could compromise symbolic number comprehension and production. Children with MLD also presented with general cognitive difficulties as reading difficulties. Taken together, our results clearly showed that children with MLD presented with a symbolic numerical processing deficit that could be largely attributed to their poorer written language skills.

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Bodea, Marcel Smilihon. "Mathematical Language / Scientific Interpretation / Theological Interpretation." DIALOGO 1, no. 1 (November 30, 2014): 47–51. http://dx.doi.org/10.51917/dialogo.2014.1.1.6.

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The specific languages referred to in this presentation are: scientific language, mathematical language, theological language and philosophical language. Cosmological, scientific or theological models understood as distinct interpretations of a common symbolic language do not ensure, by such a common basis, a possible or legitimate correspondence of certain units of meaning. Mathematics understood as a symbolic language used in scientific and theological interpretation does not bridge between science and theology. Instead, it only allows the assertion of a rational-mathematical unity in expression. In this perspective, theology is nothing less rational than science. The activity of interpretation has an interdisciplinary character, it is a necessary condition of dialogue. We cannot speak about dialogue without communication between various fields, without passing from one specialized language to another specialized language. The present paper proposes to suggest this aspect.

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Sowa, Marcin. "SPECIALIZED SYMBOLIC COMPUTATION FOR STEADY STATE PROBLEMS." Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska 3, no. 1 (February 14, 2013): 5–8. http://dx.doi.org/10.35784/iapgos.1429.

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An implementation of symbolic computation for steady state problems is proposed in the paper. A mathematical basis is derived in order to specify the quantities that the implementation will concern. An analysis is performed so that an optimal algorithm can be chosen in terms of the two chosen criteria – the operation time and memory needed to store symbolic expressions. The implementation scheme of the specialized class for symbolic computation is presented with the use of a general figure and by an example. The implementation is made in C++ but the presented idea can also be applied in other programming languages that share similar properties. A program using the proposed algorithm was studied for its efficiency in terms of calculation time and memory used by symbolic expressions. This is made by comparing the calculations made by the author’s program with those made by a script written in Mathematica.

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Steffe, Leslie P., and John Olive. "Symbolizing as a Constructive Activity in a Computer Microworld." Journal of Educational Computing Research 14, no. 2 (March 1996): 113–38. http://dx.doi.org/10.2190/58t5-v1gf-ugel-7exw.

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In the design of computer microworlds as media for children's mathematical action, our basic and guiding principle was to create possible actions children could use to enact their mental operations. These possible actions open pathways for children's mathematical activity that coemerge in the activity. We illustrate this coemergence through a constructivist teaching episode with two children working with the computer microworld TIMA: Bars. During this episode, in which the children took turns to partition a bar into fourths and thirds recursively, the symbolic nature of their partitioning operations became apparent. The children developed their own drawings and numeral systems to further symbolize their symbolic mental operations. The symbolic nature of the children's partitioning operations was crucial in their establishment of more conventional mathematical symbols.

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Heid, M. Katheleen, and Rose Mary Zbiek. "A Technology-Intensive Approach to Algebra." Mathematics Teacher 88, no. 8 (November 1995): 650–56. http://dx.doi.org/10.5951/mt.88.8.0650.

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Computer-lntensive Algebra (CIA) focuses on the use of technology to help develop a rich understanding of fundamental algebraic concepts in real-world settings. CIA students learn about functions, variables, systems, equivalent expressions, and equivalent equations in the context of developing, critiquing, and exploring mathematical models of real-life situations. Students use computing tools in their mathematical explorations for easy access to numerical, graphical, and symbolic representations of mathematical ideas. CIA is a fundamentally reformulated beginning-algebra curriculum whose concepts and techniques differ essentially from those of traditional algebra courses. CIA focuses on mathematical modeling instead of classic word problems; it centers on algebraic concepts, such as function and variable, instead of on pencil-and paper algebraic routines; it replaces symbolic manipulation with symbolic reasoning; and it encourages using multiple representations and strategies in algebraic problem solving instead of mastering and using one representation or strategy at a time.

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Schneider, Michael, Kassandra Beeres, Leyla Coban, Simon Merz, S. Susan Schmidt, Johannes Stricker, and Bert De Smedt. "Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: a meta-analysis." Developmental Science 20, no. 3 (January 14, 2016): e12372. http://dx.doi.org/10.1111/desc.12372.

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Krämer, Walter. "Computer-Assisted Proofs and Symbolic Computations." Serdica Journal of Computing 4, no. 1 (March 31, 2010): 73–84. http://dx.doi.org/10.55630/sjc.2010.4.73-84.

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We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

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Nunes, Terezinha. "Cognitive Invariants and Cultural Variation in Mathematical Concepts." International Journal of Behavioral Development 15, no. 4 (December 1992): 433–53. http://dx.doi.org/10.1177/016502549201500401.

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Vygotsky and Luria suggested that the higher forms of conscious activity are accomplished with the support of culturally elaborated systems of signs. These systems of signs are viewed as symbolic tools, by analogy with technical tools, and like the latter shape human activity. The aim of this paper is to explore two alternative hypotheses about the nature of the effect of symbolic systems on psychological functions. The first hypothesis maintains that culturally elaborated systems of signs affect psychological functioning in a general way. It leads, for example, to the prediction of a "great divide" between literates and nonliterates. The second hypothesis holds that systems of signs have specific effects on the organisation of human activity when these systems are used to support skilled action but no generalised effect is predicted. This second hypothesis leads to the prediction of withinindividual differences as a function of the use of different symbolic systems, a prediction inconsistent with the first hypothesis. Some examples of research carried out to investigate these hypotheses are described in this paper. Empirical support for the second but not the first hypothesis is found in the research reviewed here.

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Malykh, Mikhail D., Anton L. Sevastianov, and Leonid A. Sevastianov. "About Symbolic Integration in the Course of Mathematical Analysis." Computer tools in education, no. 4 (December 28, 2019): 94–106. http://dx.doi.org/10.32603/2071-2340-2019-4-94-106.

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The work of transforming a database from one format periodically appears in different organizations for various reasons. Today, the mechanism for changing the format of relational databases is well developed. But with the advent of new types of database such as NoSQL, this problem was exacerbated due to the radical difference in the way data was organized. This article discusses a formalized method based on set theory, at the choice of the number and composition of collections for a key-value type database. The initial data are the properties of the objects, information about which is stored in the database, and the set of queries that are most frequently executed or the speed of which should be maximized. The considered method can be applied not only when creating a new key-value database, but also when transforming an existing one, when moving from relational databases to NoSQL, when consolidating databases.

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Jemmer, Patrick. "Symbolic algebra in mathematical analysis of chemical-kinetic systems." Journal of Computational Chemistry 18, no. 15 (November 30, 1997): 1903–17. http://dx.doi.org/10.1002/(sici)1096-987x(19971130)18:15<1903::aid-jcc6>3.0.co;2-s.

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Mashuri, Anwas, Arum Dwi Rahmawati, and Heri Cahyono. "KEMAMPUAN REPRESENTASI MATEMATIS SISWA DALAM PEMECAHAN MASALAH TRIGONOMETRI DITINJAU DARI KOMPETENSI PENGETAHUAN." Jurnal Karya Pendidikan Matematika 6, no. 2 (October 11, 2019): 59. http://dx.doi.org/10.26714/jkpm.6.2.2019.59-65.

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This study aims to determine the ability of verbal, visual, and symbolic mathematical representations in solving trigonometric problems. The subjects of this study were students of class XII IPA 1 Ngawi High School. This study uses a qualitative method. The data validation used in this study uses the time triangulation method. Analysis of the data used uses the stages of Huberman and Miles. The results of this study indicate that participants answered not only based on the numbers given, but also used the definition of trigonometric ratios on verbal representation. On the other hand, the subject is able to determine the position of the object to be observed. However, the subject failed to determine the direction of the depression angle in the sketch made on the visual representation. Failure to determine the direction of the angle of depression causes errors in using mathematical equations correctly. Finally, participants did not succeed in using mathematical equations correctly in symbolic representations. Based on some of the explanations above, we can recommend the importance of translation between mathematical representations and mathematical problems, as well as translations between mathematical representations (verbal, visual, and symbolic) in learning mathematics in class

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Martinez-Gil, Jorge, Shaoyi Yin, Josef Kung, and Franck Morvan. "Matching Large Biomedical Ontologies Using Symbolic Regression Using Symbolic Regression." Journal of Data Intelligence 3, no. 3 (August 2022): 316–32. http://dx.doi.org/10.26421/jdi3.3-2.

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The problem of ontology matching consists of finding the semantic correspondences between two ontologies that, although belonging to the same domain, have been developed separately. Ontology matching methods are of great importance today since they allow us to find the pivot points from which an automatic data integration process can be established. Unlike the most recent developments based on deep learning, this study presents our research efforts on the development of novel methods for ontology matching that are accurate and interpretable at the same time. For this purpose, we rely on a symbolic regression model (implemented via genetic programming) that has been specifically trained to find the mathematical expression that can solve the ground truth provided by experts accurately. Moreover, our approach offers the possibility of being understood by a human operator and helping the processor to consume as little energy as possible. The experimental evaluation results that we have achieved using several benchmark datasets seem to show that our approach could be promising.

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Burgin, Mark, and Rao Mikkililineni. "Seven Layers of Computation: Methodological Analysis and Mathematical Modeling." Filozofia i Nauka Zeszyt specjalny, no. 10 (May 10, 2022): 11–32. http://dx.doi.org/10.37240/fin.2022.10.zs.1.

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We live in an information society where the usage, creation, distribution, manipulation, and integration of information is a significant activity. Computations allow us to process information from various sources in various forms and use the derived knowledge in improving efficiency and resilience in our interactions with each other and with our environment. The general theory of information tells us that information to knowledge is as energy is to matter. Energy has the potential to create or modify material structures and information has the potential to create or modify knowledge structures. In this paper, we analyze computations as a vital technological phenomenon of contemporary society which allows us to process and use information. This analysis allows building classifications of computations based on their characteristics and explication of new types of computations. As a result, we extend the existing typologies of computations by delineating novel forms of information representations. While the traditional approach deals only with two dimensions of computation—symbolic and sub-symbolic, here we describe additional dimensions, namely, super-symbolic computation, hybrid computation, fused computation, blended computation, and symbiotic computation.

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Rosyidin, Muhammad Ali, and Abdul Haris Rosyidi. "Translation Failure from Verbal to Symbolic Representations on Contextual Mathematics Problems: Female vs Male." Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika (JRPIPM) 5, no. 2 (April 29, 2022): 117–41. http://dx.doi.org/10.26740/jrpipm.v5n2.p117-141.

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Representation translation is the ability to change one form of representation to another. This research aims to describe the failure of the translation of verbal to symbolic representations in solving contextual problems in male and female students. The research partisipant were eight students of class VII an Islamic public school at Gresik. The data collection technique is through task-based interviews. The data on the translation of verbal to symbolic representations were analyzed by unpacking the source, preliminary coordinator, constructing the target, and determining equivalence. The results showed that at the stage of unpacking the source, both male and female students experienced the same failure, namely not understanding more complex contextual problems. In the preliminary coordinator stage, male students failed to understand the requested symbolic representation, understand the meaning of mathematical symbols, and determine keywords, while female students only failed due to their mistakes in the previous stage. In the constructing the target stage, male students failed to construct a symbolic representation of the plans made and translate into mathematical symbols, while female students failed to translate verbal words into mathematical symbols and mathematical operations. At the determining equivalence stage, male and female students have not been able to do it.

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Kim, S. H., and N. P. Suh. "Mathematical Foundations for Manufacturing." Journal of Engineering for Industry 109, no. 3 (August 1, 1987): 213–18. http://dx.doi.org/10.1115/1.3187121.

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For the field of manufacturing to become a science, it is necessary to develop general mathematical descriptions for the analysis and synthesis of manufacturing systems. Standard analytic models, as used extensively in the past, are ineffective for describing the general manufacturing situation due to their inability to deal with discontinuous and nonlinear phenomena. These limitations are transcended by algebraic models based on set structures. Set-theoretic and algebraic structures may be used to (1) express with precision a variety of important qualitative concepts such as hierarchies, (2) provide a uniform framework for more specialized theories such as automata theory and control theory, and (3) provide the groundwork for quantitative theories. By building on the results of other fields such as automata theory and computability theory, algebraic structures may be used as a general mathematical tool for studying the nature and limits of manufacturing systems. This paper shows how manufacturing systems may be modeled as automatons, and demonstrates the utility of this approach by discussing a number of theorems concerning the nature of manufacturing systems. In addition symbolic logic is used to formalize the Design Axioms, a set of generalized decision rules for design. The application of symbolic logic allows for the precise formulation of the Axioms and facilitates their interpretation in a logical programming language such as Prolog. Consequently, it is now possible to develop a consultive expert system for axiomatic design.

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Marinov, Marin, and Petya Asenova. "Teaching the Notion Conic Section with Computer." Mathematics and Informatics LXIV, no. 4 (August 30, 2021): 395–409. http://dx.doi.org/10.53656/math2021-4-5-pred.

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The article discusses the problem of introducing and constructing mathematical concepts using a computer. The Wolfram Mathematica 12 symbolic calculation system is used at each stage of the complex spiral process to form the notion of conic section and the related concepts of focus, directrix and eccentricity. The nature of these notions implies the use of appropriate animations, 3D graphics and symbolic calculations. Our vision of the process of formation of mathematical concepts is presented. The notions ellipse, parabola and hyperbola are defined as the intersection of a conical surface with a plane not containing the vertex of the conical surface. The conical section is represented as a geometric location of points on the plane for which the ratio of the distance to the focus to the distance to the directrix is a constant value. The lines of hyperbola and ellipse are determined by their foci. The equivalence of different definitions for conical sections is commented.

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Motazedi, Niloufar, Matthew P. Cartmell, and Jem A. Rongong. "Extending the functionality of a symbolic computational dynamic solver by using a novel term-tracking method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 19 (November 5, 2017): 3439–52. http://dx.doi.org/10.1177/0954406217737104.

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Symbolic computational dynamic solvers are currently under development in order to provide new and powerful tools for modelling nonlinear dynamical systems. Such solvers consist of two parts; the core solver, which comprises an approximate analytical method based on perturbation, averaging, or harmonic balance, and a specialised term-tracker. A term-tracking approach has been introduced to provide a powerful new feature into computational approximate analytical solutions by highlighting the many mathematical connections that exist, but which are invariably lost through processing, between the physical model of the system, the solution procedure itself, and the final result which is usually expressed in equation form. This is achieved by a highly robust process of term-tracking, recording, and identification of all the symbolic mathematical information within the problem. In this paper, the novel source and evolution encoding method is introduced for the first time and an implementation in Mathematica is described through the development of a specialised algorithm.

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Welleck, Sean, Peter West, Jize Cao, and Yejin Choi. "Symbolic Brittleness in Sequence Models: On Systematic Generalization in Symbolic Mathematics." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (June 28, 2022): 8629–37. http://dx.doi.org/10.1609/aaai.v36i8.20841.

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Neural sequence models trained with maximum likelihood estimation have led to breakthroughs in many tasks, where success is defined by the gap between training and test performance. However, their ability to achieve stronger forms of generalization remains unclear. We consider the problem of symbolic mathematical integration, as it requires generalizing systematically beyond the training set. We develop a methodology for evaluating generalization that takes advantage of the problem domain's structure and access to a verifier. Despite promising in-distribution performance of sequence-to-sequence models in this domain, we demonstrate challenges in achieving robustness, compositionality, and out-of-distribution generalization, through both carefully constructed manual test suites and a genetic algorithm that automatically finds large collections of failures in a controllable manner. Our investigation highlights the difficulty of generalizing well with the predominant modeling and learning approach, and the importance of evaluating beyond the test set, across different aspects of generalization.

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Wege, Theresa Elise, Sophie Batchelor, Matthew Inglis, Honali Mistry, and Dirk Schlimm. "Iconicity in mathematical notation: Commutativity and symmetry." Journal of Numerical Cognition 6, no. 3 (December 3, 2020): 378–92. http://dx.doi.org/10.5964/jnc.v6i3.314.

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Mathematical notation includes a vast array of signs. Most mathematical signs appear to be symbolic, in the sense that their meaning is arbitrarily related to their visual appearance. We explored the hypothesis that mathematical signs with iconic aspects – those which visually resemble in some way the concepts they represent – offer a cognitive advantage over those which are purely symbolic. An early formulation of this hypothesis was made by Christine Ladd in 1883 who suggested that symmetrical signs should be used to convey commutative relations, because they visually resemble the mathematical concept they represent. Two controlled experiments provide the first empirical test of, and evidence for, Ladd’s hypothesis. In Experiment 1 we find that participants are more likely to attribute commutativity to operations denoted by symmetric signs. In Experiment 2 we further show that using symmetric signs as notation for commutative operations can increase mathematical performance.

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Li, Chengfeng. "The Core Literacy of Mathematics-The Cultivation of Mathematical Operation Ability." Lifelong Education 9, no. 7 (December 8, 2020): 1. http://dx.doi.org/10.18282/le.v9i7.1451.

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The core literacy of mathematics can be divided into the following aspects: mathematical abstraction, mathematical thinking, mathematical application, mathematical operation, logical reasoning, data analysis, mathematical modeling, intuitive imagination, number-shape connection, rigorous verification, mathematical emotion, reasonable guessing, Mathematical culture, careful thinking, use of mathematical tools, mathematical language or symbolic language. Mathematical ability is the most basic and main ability, and it is the foundation of other mathematical literacy. Cultivation of Mathematical Ability

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Becker, Nicole, Courtney Stanford, Marcy Towns, and Renee Cole. "Translating across macroscopic, submicroscopic, and symbolic levels: the role of instructor facilitation in an inquiry-oriented physical chemistry class." Chemistry Education Research and Practice 16, no. 4 (2015): 769–85. http://dx.doi.org/10.1039/c5rp00064e.

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In physical chemistry classrooms, mathematical and graphical representations are critical tools for reasoning about chemical phenomena. However, there is abundant evidence that to be successful in understanding complex thermodynamics topics, students must go beyond rote mathematical problem solving in order to connect their understanding of mathematical and graphical representations to the macroscopic and submicroscopic phenomena they represent. Though traditional curricular materials such as textbooks may provide little support for coordinating information across macroscopic, submicroscopic, and symbolic levels, instructor facilitation of classroom discussions offers a promising route towards supporting students' reasoning. Here, we report a case study of classroom reasoning in a POGIL (process-oriented guided inquiry learning) instructional context that examines how the class coordinated macroscopic, submicroscopic, and symbolic ideas through classroom discourse. Using an analytical approach based on Toulmin's model of argumentation and the inquiry-oriented discursive moves framework, we discuss the prevalence of macroscopic, submicroscopic and symbolic-level ideas in classroom reasoning and we discuss how instructor facilitation strategies promoted reasoning with macroscopic, submicroscopic, and symbolic levels of representation. We describe one sequence of instructor facilitation moves that we believe promoted translation across levels in whole class discussion.

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Aleksander, Veraksa. "SYMBOLIC REPRESENTATION IN THE COGNITIVE ACTIVITY OF YOUNG SCHOOLCHILDREN ON THE EXAMPLE OF MATHEMATICS." Poiésis - Revista do Programa de Pós-Graduação em Educação 8 (March 21, 2014): 64. http://dx.doi.org/10.19177/prppge.v8e0201464-82.

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In the paper, differences between sign-oriented representation and symbolic representation are discussed. The study explored perspectives of using symbolization to teach young schoolchildren the mathematical concept. The author recognizes relevant (that allows the proceeding to sign representation) and irrelevant symbolization. The three groups of young schoolchildren (N=49) were taught the mathematical concept of a function using different programs: traditional, employing sign representation and two experimental – based on relevant and irrelevant symbolizations. The experiment demonstrated that symbolic representation can facilitate mastering of the mathematical concept of a function if the content of symbol possesses structural interrelations that could be converted into sign form.

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D., Jansirani, and Manickavasagan T. "Construction and Validation of Symbolic Retention Ability Test." RESEARCH REVIEW International Journal of Multidisciplinary 8, no. 7 (July 15, 2023): 181–87. http://dx.doi.org/10.31305/rrijm.2023.v08.n07.025.

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Education is a method or process of transmitting or learning universal mental processes, developing the abilities of thought and assessment, and, in general, intellectually modifying oneself or others for mature life. The ability to compare number and symbols, such as digits, efficiently is linked to mathematical competence across the life span. The teacher's use of symbolic representations becomes second nature, as they are deeply integrated with conceptual understanding and subject knowledge. Such representations, however, may place significant additional demands on learners who are already challenged by the abstract nature of concepts as well as the variety of unfamiliar substances to which these concepts are applied in the curriculum. Taking a broadly constructivist approach to learning, While the majority of students are conceptual thinkers who communicate verbally, some students have a different learning style, that the students are more interested to solve the mathematical problems by using formula and symbols. Thus, the Symbolic Retention Ability help the student to understand the mathematical problems in a meaningful way and solving them in a systematic way. This paper is an attempt to construct and validate a tool for assessing the symbolic retention ability among higher secondary students. For this purpose, a collection of 60 mathematical statements with related symbols from the content of XI standard mathematics text-book covering six dimensions viz. geometry, statistics, probability, number theory, calculus and set theory. These gathered 60 statements were undergone pilot study with 100 higher secondary students in Puducherry region and on the basis of index of difficulty and index of discrimination values 37 statements have been selected. The reliability and validness have also been found for this test. Hence, a complete and full-fledged Symbolic Retention Ability Test has been constructed and validated through this study and it will be an enough tool to measure the Symbolic Retention Ability of the higher secondary students.

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Wikantari, Ni Nyoman Yustini, Laila Hayati, Wahidaturrahmi Wahidaturrahmi, and Baidowi Baidowi. "Analysis of mathematical representation ability on pythagoras theorem reviewed from learning style of junior high school students." Jurnal Pijar Mipa 17, no. 6 (November 30, 2022): 775–81. http://dx.doi.org/10.29303/jpm.v17i6.3311.

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This study aims to determine the mathematical representation ability of class IX students with visual, auditory, and kinesthetic learning styles on the Pythagoras Theorem material at SMPN 1 (public junior high school) Gunungsari Indonesia in the 2021/2022 academic year. This type of research is descriptive with a quantitative approach. The populations in this study were all students of class IX SMPN 1 Gunungsari. The research sampling technique used purposive sampling, and the sample was class IX-H. The instruments used are learning style questionnaires, mathematical representation ability tests, and interview guidelines. The results of this study indicate that the mathematical representation ability of students with visual learning styles is 35.56% in the low category, or students have yet to be able to meet the overall visual, symbolic, and verbal representation indicators. Furthermore, the mathematical representation ability of students with auditory and kinesthetic learning styles is 49.86% and 41.87% in the medium category. Respectively, students have been able to meet the indicators of visual and symbolic representation quite well but have yet to be able to fulfill the visual and symbolic representation and verbal representation indicators.

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Mala, Firdous. "Alice’s Adventures in Wonderland: Carroll’s Symbolic Attack on Mathematical Symbolism." Journal of Humanistic Mathematics 12, no. 1 (January 2022): 348–51. http://dx.doi.org/10.5642/jhummath.202201.26.

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Kathleen Heid, M. "How Symbolic Mathematical Systems Could and Should Affect Precollege Mathematics." Mathematics Teacher 82, no. 6 (September 1989): 410–19. http://dx.doi.org/10.5951/mt.82.6.0410.

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Computer programs are now available that perform most of the algebraic and numerical-manipulation procedures on which school mathematics now concentrates. The defining characteristic of these symbolic mathematical systems is that, unlike many of the popular computer languages, they can manipulate variables as well as numbers. They can perform rationalnumber arithmetic, solve equations, produce equivalent expressions of a variety of types, apply trigonometric identities, evaluate limits and sums, compute the algebraic form of derivatives and integrals, perform matrix manipulations, and produce accurate numerical answers-with hundreds of digits if appropriate. In short, they can perform with more dependable accuracy and greater speed most of the algebraic and numerical procedures on which students now spend most of their mathematical careers.

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Limongelli, C., and M. Temperini. "Abstract specification of structures and methods in symbolic mathematical computation." Theoretical Computer Science 104, no. 1 (October 1992): 89–107. http://dx.doi.org/10.1016/0304-3975(92)90167-e.

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Lingefjärd, Thomas, and Djamshid Farahani. "The symbolic world of mathematics." Journal of Research in Mathematics Education 6, no. 2 (June 24, 2017): 118. http://dx.doi.org/10.17583/redimat.2017.2391.

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In understanding upper secondary school students’ interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in symbolic representations of different phenomena. Two theoretical perspectives have been used to conduct the analysis: Tall and Vinner's theoretical perspectives on learning and Gray’s & Talls’s theory of three mathematical worlds. The findings provide evidence that a detailed analyse of student’s utterances show difference in quality related to student’s interpretations of a distance-time relation. The qualities were related to student’s concept images of functions and derivatives.

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Salsabila, Nais Qonita, Sri Subanti, and Budi Usodo. "Mathematical Literacy of Auditory Learner: Study on Junior High School Students." International Journal of Progressive Sciences and Technologies 38, no. 2 (May 13, 2023): 110. http://dx.doi.org/10.52155/ijpsat.v38.2.5285.

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Mathematical literacy refers to a person's ability to use mathematics in different situations, such as applying and interpreting mathematical concepts and using facts and procedures to explain or predict events. There are seven fundamental abilities involved in mathematical literacy, including: (a) communication, (b) mathematising, (c) representation, (d) reasoning and argument, (e) devising problem-solving strategies, (f) using symbolic, formal, and technical language and operations, and (g) using mathematical tools. This study is a descriptive research with a qualitative approach that aims to describe and explain the mathematical literacy abilities of junior high school students with an auditory learning style. The research subjects were eighth-grade students from Islamic Junior High School (MTsN) 1 Surakarta. Based on the results and discussions, it can be concluded that students with an auditory learning style possess the following mathematical literacy abilities: (a) communication, (b) mathematising, (c) representation, (d) reasoning and argument, (e) devising problem-solving strategies, (f) using symbolic, formal, and technical language and operations, and (g) using mathematical tools. Each of these abilities will be explained in detail in the following discussion.

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Journal articles on the topic 'Mathematical and symbolic'

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