Relevant bibliographies by topics / Mathematics education – Arithmetic, number theory – Natural numbers

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  2. Dissertations / Theses
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Academic literature on the topic 'Mathematics education – Arithmetic, number theory – Natural numbers'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Mathematics education – Arithmetic, number theory – Natural numbers"

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Nesher, Pearla, and Tamar Katriel. "Learning Numbers: A Linguistic Perspective." Journal for Research in Mathematics Education 17, no. 2 (1986): 100–111. http://dx.doi.org/10.5951/jresematheduc.17.2.0100.

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The difference in the status of numbers—as predicates in natural language and as objects in the formal language of mathematics—is argued to have consequences for children's learning of numbers and for the construction of arithmetic texts in the primary grades. This distinction is exemplified by the findings of an empirical study that utilized particular morphological properties of Hebrew relating to gender inflections for number words. The findings indicate that there is a crossing of the two language systems in children's oral reading of a mixed arithmetic text (words and numerals).
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Björklund, Camilla, Ference Marton, and Angelika Kullberg. "What is to be learnt? Critical aspects of elementary arithmetic skills." Educational Studies in Mathematics 107, no. 2 (2021): 261–84. http://dx.doi.org/10.1007/s10649-021-10045-0.

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AbstractIn this paper, we present a way of describing variation in young children’s learning of elementary arithmetic within the number range 1–10. Our aim is to reveal what is to be learnt and how it might be learnt by means of discerning particular aspects of numbers. The Variation theory of learning informs the analysis of 2184 observations of 4- to 7-year-olds solving arithmetic tasks, placing the focus on what constitutes the ways of experiencing numbers that were observed among these children. The aspects found to be necessary to discern in order to develop powerful arithmetic skills wer
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Brown, P. G. "Some comments on inverse arithmetic functions." Mathematical Gazette 89, no. 516 (2004): 403–8. http://dx.doi.org/10.1017/s0025557200178246.

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In many of the basic courses in Number Theory, Finite Mathematics and Cryptography we come across the so-called arithmetic functions such as ϕn), σ(n), τ(n), μ(n), etc, whose domain is the set of natural numbers. These functions are well known and evaluated through the prime factor decomposition of n. It is less well known that these functions possess inverses (with respect to Dirichlet multiplication) which have interesting properties and applications.
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4

Zazkis, Rina, and Stephen Campbell. "Divisibility and Multiplicative Structure of Natural Numbers: Preservice Teachers' Understanding." Journal for Research in Mathematics Education 27, no. 5 (1996): 540–63. http://dx.doi.org/10.5951/jresematheduc.27.5.0540.

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This study contributes to a growing body of research on teachers' content knowledge in mathematics. The domain under investigation was elementary number theory. Our main focus concerned the concept of divisibility and its relation to division, multiplication, prime and composite numbers, factorization, divisibility rules, and prime decomposition. We used a constructivist-oriented theoretical framework for analyzing and interpreting data acquired in clinical interviews with preservice teachers. Participants' responses to questions and tasks indicated pervasive dispositions toward procedural att
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Furuya, Isamu, and Takuya Kida. "Compaction of Church Numerals." Algorithms 12, no. 8 (2019): 159. http://dx.doi.org/10.3390/a12080159.

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In this study, we address the problem of compaction of Church numerals. Church numerals are unary representations of natural numbers on the scheme of lambda terms. We propose a novel decomposition scheme from a given natural number into an arithmetic expression using tetration, which enables us to obtain a compact representation of lambda terms that leads to the Church numeral of the natural number. For natural number n, we prove that the size of the lambda term obtained by the proposed method is O ( ( slog 2 n ) ( log n / log log n ) ) . Moreover, we experimentally confirmed that the proposed
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Jupri, Al, Dian Usdiyana, and Ririn Sispiyati. "Realistic Mathematics Education Principles for Designing a Learning Sequence on Number Patterns." Jurnal Kiprah 8, no. 2 (2020): 105–12. http://dx.doi.org/10.31629/kiprah.v8i2.2358.

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The number pattern is one of mathematics topics taught for junior high school students that relate between arithmetic and algebra domain. This topic bridges arithmetical and algebraic thinking. Therefore, the learning for this topic should be designed meaningfully. This research aims to design a learning sequence on the number patterns using principles of Realistic Mathematics Education (RME). To do this, we used design research method, particularly the preliminary design phase, with the following three steps. First, literature study was conducted to collect student difficulties in the learnin
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MANCOSU, PAOLO. "MEASURING THE SIZE OF INFINITE COLLECTIONS OF NATURAL NUMBERS: WAS CANTOR’S THEORY OF INFINITE NUMBER INEVITABLE?" Review of Symbolic Logic 2, no. 4 (2009): 612–46. http://dx.doi.org/10.1017/s1755020309990128.

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Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collection A is properly included in a collection B then the ‘size’ of A should be less than the ‘size’ of B (part–whole principle). This second intuition was not developed mat
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Simpson, Stephen G. "Ordinal numbers and the Hilbert basis theorem." Journal of Symbolic Logic 53, no. 3 (1988): 961–74. http://dx.doi.org/10.2307/2274585.

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In [5] and [21] we studied countable algebra in the context of “reverse mathematics”. We considered set existence axioms formulated in the language of second order arithmetic. We showed that many well-known theorems about countable fields, countable rings, countable abelian groups, etc. are equivalent to the respective set existence axioms which are needed to prove them.One classical algebraic theorem which we did not consider in [5] and [21] is the Hilbert basis theorem. Let K be a field. For any natural number m, let K[x1,…,xm] be the ring of polynomials over K in m commuting indeterminates
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9

Et. al., B. Mahaboob,. "AN INNOVATIVE STUDY ON SUM OF POWERS OF INTEGERS." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 4 (2021): 1260–66. http://dx.doi.org/10.17762/turcomat.v12i4.1186.

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The generalization of sum of integral powers of first n-natural numbers has been an interesting problem among the researchers in Analytical Number Theory for decades. This research article mainly focuses on the derivation of generalized result of this sum. More explicit formula has been derived in order to get the sum of any arbitrary integral powers of first n-natural numbers. Furthermore by using the fundamental principles of Combinatorics and Linear Algebra an attempt has been made to answer an interesting question namely: Is the sum of integral powers of natural numbers a unique polynomial
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Sivaraman, Dr R. "Expressing Numbers in terms of Golden, Silver and Bronze Ratios." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (2021): 2876–80. http://dx.doi.org/10.17762/turcomat.v12i2.2321.

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The idea of expressing certain kind of numbers as linear combination of special class of numbers has always been an interesting exercise in mathematics. In this paper, I present an interesting way to write a given natural number as sum or difference of integral powers of golden ratio, silver ratio and bronze ratio. Suitable illustrations enabling the process are briefed in the paper.
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Dissertations / Theses on the topic "Mathematics education – Arithmetic, number theory – Natural numbers"

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Schwartzkopff, Robert. "The numbers of the marketplace : commitment to numbers in natural language." Thesis, University of Oxford, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.711821.

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Fonseca, Rubens Vilhena. "Números primos e o Teorema Fundamental da Aritmética: uma investigação entre estudantes de licenciatura em Matemática." Pontifícia Universidade Católica de São Paulo, 2015. https://tede2.pucsp.br/handle/handle/11036.

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Made available in DSpace on 2016-04-27T16:57:37Z (GMT). No. of bitstreams: 1 Rubens Vilhena Fonseca.pdf: 1601945 bytes, checksum: 9bd5a69dcacb920b758afcd188c86010 (MD5) Previous issue date: 2015-04-22<br>This work aims to analyze a didactic sequence directly linked to the research question, which sought to provide students an investigative route in order to find solutions to the problems raised, which are in the field of number theory, and are related to prime numbers and Fundamental Theorem of Arithmetic, objects of this research, developed with students of the degree course in mathematics
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Books on the topic "Mathematics education – Arithmetic, number theory – Natural numbers"

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Bussi, Maria G. Bartolini. Building the Foundation : Whole Numbers in the Primary Grades: The 23rd ICMI Study. Springer Nature, 2018.

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Ovchinnikov, Sergei. Number Systems: An Introduction to Algebra and Analysis. American Mathematical Society, 2015.

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Bussi, Maria G. Bartolini, and Xu Hua Sun. Building the Foundation : Whole Numbers in the Primary Grades: The 23rd ICMI Study. Springer, 2019.

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Bussi, Maria G. Bartolini, and Xu Hua Sun. Building the Foundation : Whole Numbers in the Primary Grades: The 23rd ICMI Study. Springer, 2018.

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