Arithmetic Research Papers - Academia.edu (original) (raw)

The systematic implications of irrational numbers, for those interested.

Calculia is considered to be the ability of performing arithmetic operations, the preconditions for the development of mathematical skills in the complex functioning of psychological functions represented in neuro-anatomical systems, as... more

Calculia is considered to be the ability of performing arithmetic operations, the preconditions for the development of mathematical skills in the complex functioning of psychological functions represented in neuro-anatomical systems, as well in the interaction with the environment. Problems in acquiring arithmetic skills can be described as difficulties in counting as well as developmental dyscalculia. Reported prevalence rate for this problem in general population is 6%-10%. The most common difficulties in counting are: difficulties in logic, difficulties in planning, perseverance of inappropriate (responses) procedures and poor understanding of arithmetic operations. This paper aims to identify the influence of assessed arithmetic skills and to clarify to what extent the assessed cognitive skills affect each other in children with difficulties in counting. The relations between the level of working memory and acquiring of arithmetic skills, between the attention and the conceptual...

In this paper, a methodology for the development of fault-tolerant adders based on the radix 2 signed digit (SD) representation is presented. The use of a number representation characterized by a carry propagation confined to neighbor... more

In this paper, a methodology for the development of fault-tolerant adders based on the radix 2 signed digit (SD) representation is presented. The use of a number representation characterized by a carry propagation confined to neighbor digits implies interesting advantages in terms of error detection, fault localization, and repair. Errors caused by faults belonging to a considered stuck-at fault set can be detected by a parity-based technique. In fact, a carry-free adder preserving the parity of the augends can be implemented allowing fault detection by using a parity checker. Regarding fault localization, the "carry-free" property of the adder ensures the confinement of the error due to a permanent fault to only few digits. The detection of the faulty digit has been obtained by using a recomputation with shifted operands method. Finally, after the fault localization, graceful degradation of the system intended as the reduction of the performances versus a correct output computation can be obtained by using two different procedures. The first one allows obtaining the correct output by recomputing the result performing two different shift operations and using the intersection of the obtained results to recover the correct output, while the second one is based on a reduced dynamic range approach, which allows us to obtain the result in only one step, but with fewer output digits.

Mathematics Short-cut Techniques with Formulas

Binary image compression is desirable for a wide range of applications, such as digital libraries, map archives, fingerprint databases, facsimile, etc. In this paper, we present a new highly efficient algorithm for lossless binary image... more

Binary image compression is desirable for a wide range of applications, such as digital libraries, map archives, fingerprint databases, facsimile, etc. In this paper, we present a new highly efficient algorithm for lossless binary image compression. The proposed algorithm introduces a new method, direct redundancy elimination, to efficiently exploit the two-dimensional redundancy of an image, as well as a novel

This paper presents new, fast hardware for computing the exponential function, sine, and cosine. The main new idea is to use low-precision arithmetic components to approximate high precision computations, and then to correct very quickly... more

This paper presents new, fast hardware for computing the exponential function, sine, and cosine. The main new idea is to use low-precision arithmetic components to approximate high precision computations, and then to correct very quickly the approximation error periodically so that the effect is to get high precision computation at near low-precision speed. The algorithm used in the paper is a nontrivial modification of the well-known CORDIC algorithm, and might be applicable to the computation of other functions than the ...

Nunes and Bryant (Children doing mathematics, Blackwell, Oxford, 1996) proposed that an understanding of the additive composition of number could be a precursor to an understanding of the decimal structure. If this is so, children should... more

Nunes and Bryant (Children doing mathematics, Blackwell, Oxford, 1996) proposed that an understanding of the additive composition of number could be a precursor to an understanding of the decimal structure. If this is so, children should achieve an understanding of additive composition before they can handle the decimal structure. The aim of our study was to determine the developmental timing

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities... more

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing collections (i.e., non-symbolic number magnitude). Moreover, they automatically processed number magnitude when comparing the physical size of Arabic digits in an Stroop paradigm adapted for processing speed differences. Finally, no evidence was found for differential patterns of performance between MD and MD/RD children in these tasks. These findings suggest that children with mathematics learning disabilities have difficulty in accessing number magnitude from symbols rather than in processing numerosity per se.

Abstract-We describe a sequential universal data compression procedure for binary tree sources that performs the “double mixture.” Using a context tree, this method weights in an ef-ficient recursive way the coding distributions... more

Abstract-We describe a sequential universal data compression procedure for binary tree sources that performs the “double mixture.” Using a context tree, this method weights in an ef-ficient recursive way the coding distributions corresponding to all bounded memory tree sources, and ...

This is the ultimate proof that the Prime Numbers are not Random Numbers as famous Mathematicians believe and claim publicly through presentations you can find on U Tube Any pupil around the world and a wide public will understand the... more

This is the ultimate proof that the Prime Numbers are not Random Numbers as famous Mathematicians believe and claim publicly through presentations you can find on U Tube
Any pupil around the world and a wide public will understand the first 2 pages of the paper below. Feel free to ask questions by emailing me constantine.adraktas@mit-partners.eu

A r q. R o b e r t o S a l d i v a r O l a g u e. G r a d u a d o e n I C S , E s c u e l a d e A r q u i t e c t u r a , S c r a n t o n P. a. , U S A. Titulado en Arquitectura en el Instituto Tecnológico de Zacatecas, México M a y o d e... more

A r q. R o b e r t o S a l d i v a r O l a g u e. G r a d u a d o e n I C S , E s c u e l a d e A r q u i t e c t u r a , S c r a n t o n P. a. , U S A. Titulado en Arquitectura en el Instituto Tecnológico de Zacatecas, México M a y o d e l 2 0 1 3

This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students’ construction of fraction composition schemes. A fraction composition scheme... more

This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students’ construction of fraction composition schemes. A fraction composition scheme consists of the operations and concepts used to determine, for example, the size of 1/3 of 1/5 of a whole in relation to the whole. Students’ whole number multiplicative concepts were found to be critical constructive resources for students’ fraction composition schemes. Specifically, the interiorization of two levels of units, a particular multiplicative concept, was found to be necessary for the construction of a unit fraction composition scheme, while the interiorization of three levels of units was necessary for the construction of a general fraction composition scheme. These findings contribute to previous research on students’ construction of fraction multiplication that has emphasized partitioning and conceptualizing quantitative units. Implications of the findings for teaching are considered.

Recent studies have shown that the use of educational games during learning process is dramatically increased. Furthermore, researchers suggest the attachment of adaptive features in order to motivate students and assess their knowledge... more

Recent studies have shown that the use of educational games during learning process is dramatically increased. Furthermore, researchers suggest the attachment of adaptive features in order to motivate students and assess their knowledge level on a specific educational subject. In this paper, we present an educational browser-based game with coins that contributes to understanding better the addition process in elementary education. The game encompasses user modeling and adaptive techniques. It determines students’ knowledge level and helps them outcome difficulties and obtain fluency in arithmetic addition skills.

""Sharing a field into plots of equal area is one of the oldest known mathematical problems. Some of these sharing problems lead to wonderful arithmetic problems that seem to have excited the curiosity of Mesopotamian mathematicians. This... more