Concept Of Subtraction Research Articles

Early Numerical Competencies and Students with Mathematics Difficulty

Children start elementary school with variable mathematics ski11s. Some childrenunderstand the fundamentals of numbers and mathematics, while others struggle with basic counting, number recognition, understanding of symbols, quantity discrimination, and concepts of addition and subtraction. Often, this set of early numerical competencies is referred to as number sense or early numeracy competencies. Students need to establish and understand these competencies before moving on to more complex mathematical tasks. This article describes important early num erical competencies and provides a description of how these competencies can be taught to students who struggle with mathematics.

The Indonesian’s Road Transportations as The Contexts to Support Primary School Students Learning Number Operation

This paper highlights the Indonesian's road transportation contexts, namely, angkot, that used in learning and teaching of addition and subtraction in first grade and second grade MIN-2 Palembang. PMRI approach that adopt from RME was used in this design research. From teaching experiment was founded that the student used many strategies when teaching and learning process conducted. In situational level they used their knowledge of experience-base activity, in referential level they use manik-manik (string of beads), and in general level they used number line to solve the problem. From the research was known that the Indonesian's road transportation context helps student to understand basic concept of addition and subtraction. The suggestion to further research this context can be used in design research of multiplication.

A comparison of curricula related to the teaching of addition and subtraction concepts

In this paper, we are interested in curricula contents related to the addition and subtraction concepts. A comparative study between Turkey, France and United Kingdom is carried out in order to identify different learning methods adopted and to evaluate these methods according to the educational system of each country. The results show that main differences between three countries curricula are due to the structures of pre-school systems and to the use of technology.

Solving the fuzzy earliness and tardiness in scheduling problems by using genetic algorithms

The scheduling problems with fuzzy processing times and fuzzy due dates are concerned in this paper. The fuzzy earliness and fuzzy tardiness are proposed based on the concepts of subtraction and maximum of any two fuzzy numbers, which are defined by using the well-known “Extension Principle” in fuzzy sets theory. The objective function is taken as the weighted sum of fuzzy earliness and fuzzy tardiness through the concept of addition among fuzzy numbers. In this case, the objective function turns into a fuzzy-valued function. The purpose of this paper is to obtain an optimal schedule that minimizes this fuzzy-valued objective function. The genetic algorithm will be invoked to solve this problem. Two numerical examples are also provided to clarify the discussions in this paper by using the commercial software MATLAB.

Characterization of unknown genetic modifications using high throughput sequencing and computational subtraction.

BackgroundWhen generating a genetically modified organism (GMO), the primary goal is to give a target organism one or several novel traits by using biotechnology techniques. A GMO will differ from its parental strain in that its pool of transcripts will be altered. Currently, there are no methods that are reliably able to determine if an organism has been genetically altered if the nature of the modification is unknown.ResultsWe show that the concept of computational subtraction can be used to identify transgenic cDNA sequences from genetically modified plants. Our datasets include 454-type sequences from a transgenic line of Arabidopsis thaliana and published EST datasets from commercially relevant species (rice and papaya).ConclusionWe believe that computational subtraction represents a powerful new strategy for determining if an organism has been genetically modified as well as to define the nature of the modification. Fewer assumptions have to be made compared to methods currently in use and this is an advantage particularly when working with unknown GMOs.

Children’s understanding of addition and subtraction concepts

After the onset of formal schooling, little is known about the development of children’s understanding of the arithmetic concepts of inversion and associativity. On problems of the form a + b − b (e.g., 3 + 26 − 26), if children understand the inversion concept (i.e., that addition and subtraction are inverse operations), then no calculations are needed to solve the problem. On problems of the form a + b − c (e.g., 3 + 27 − 23), if children understand the associativity concept (i.e., that the addition and subtraction can be solved in any order), then the second part of the problem can be solved first. Children in Grades 2, 3, and 4 solved both types of problems and then were given a demonstration of how to apply both concepts. Approval of each concept and preference of a conceptual approach versus an algorithmic approach were measured. Few grade differences were found on either task. Conceptual understanding was greater for inversion than for associativity on both tasks. Clusters of participants in all grades showed that some had strong understanding of both concepts, some had strong understanding of the inversion concept only, and others had weak understanding of both concepts. The findings highlight the lack of developmental increases and the large individual differences in conceptual understanding on two arithmetic concepts during the early school years.

Early Number Competencies of Children at the Start of Formal Education

In Ghana, like many other countries, mathematics is compulsory throughout the preuniversity period of education. However, a good proportion of pupils and students at basic secondary levels of education find the subject very difficult, while at the same time, those who profess not to be good in it take pleasure in doing so. The teaching and learning of mathematics have therefore been the concern of mathematics educators, teachers, parents and indeed all those who manage education. Addition and subtraction occupy a central position in the Primary Mathematics Curriculum in Ghana. The question then is: do pupils come to formal school without sufficient knowledge in counting and strategies for solving addition and subtraction problems? The focus of this study was to investigate pupils' counting strategies and how these influenced their procedures for solving addition and subtraction tasks at the start of formal school. A qualitative case study approach was adopted for the collection of data form BS1 pupils of two primary schools in Winneba. These pupils were just beginning their formal basic education in September. Findings from the two-site case study evidence were analysed for their significance. The results of the study suggest that pupils possess varied abilities and competencies in counting when they start formal school. The findings also revealed that pupils have and demonstrate a fair knowledge of addition and subtraction concepts. Another issue that came to light was the impact the socio-economic background of the home has on pupils' early number competence. Summary and conclusions of the study were based on the evidence of these findings.African Journal of Educational Studies in Mathematics and Sciences Vol. 3 2005: pp. 21-29

Number words in young children’s conceptual and procedural knowledge of addition, subtraction and inversion

Three studies addressed children’s arithmetic. First, 50 3- to 5-year-olds judged physical demonstrations of addition, subtraction and inversion, with and without number words. Second, 20 3- to 4-year-olds made equivalence judgments of additions and subtractions. Third, 60 4- to 6-year-olds solved addition, subtraction and inversion problems that varied according to the inclusion of concrete referents and number words. The results indicate that number words play a different role in conceptual and procedural development. Children have strong addition and subtraction concepts before they can translate the physical effects of these operations into number words. However, using number words does not detract from their calculation procedures. Moreover, consistent with iterative relations between conceptual and procedural development, the results suggest that inversion acquisition depends on children’s calculation procedures and that inversion understanding influences these procedures.

Teaching Raman Spectroscopy in Both the Undergraduate Classroom and the Laboratory with a Portable Raman Instrument

We have evaluated a small portable Raman instrument on loan from B&W Tek, Inc., and have determined that it can successfully be used in the classroom both as a visual aid for teaching the fundamentals of Raman spectroscopy and for a variety of undergraduate experiments as a normal component of an instrumental analysis class. Having portable Raman instrumentation would allow the instructor to demonstrate the principles of Raman spectroscopy, as well as the concepts of calibration curves, blank subtraction, detection limits, and regression analysis. Both qualitative and quantitative types of experiments were done for solid Tylenol tablets, aqueous solutions of isopropyl alcohol, dimethyl sulfoxide, methanol, and ethanol, and gaseous CO2 and N2O4. Additionally, surface‐enhanced resonance Raman spectra of Rhodamine 6G were obtained using a chloride ion–activated silver colloid. Spectra from the B&W Tek, Inc., instrument were comparable to literature Raman spectra.

Pre-Service Early Childhood Educators' Perceptions of Math-Mediated Language

This study argues that maximizing early childhood educators' abilities to create social opportunities for co-construction of knowledge rests on two understudied assumptions, one theoretical and one empirical. Theoretically this study rejects the notion of language as an impartial conveyor of knowledge in favor of one in which math and language interact. This alternative framework is termed Math- Mediated Language (MML) and argues that the perception of common terms that adults possess is an important part of the knowledge that practitioners possess about linking conceptually related linguistic and mathematical knowledge. Empirical findings from a survey recording participants' reactions to seven categories of terms with mathematical meanings and three categories of distracter terms were analyzed. The data indicated that when asked to think about math, practitioners more readily accessed words for operation terms than relational terms. Additionally, participants demonstrated stronger tendencies toward additive terms conveying addition or subtraction concepts over multiplicative ones conveying multiplication or division concepts. The findings point to patterns in the ways that participants view mathematical language demonstrating that language interacts with even simple interpretations of basic mathematical terminology. The implications of this are that practitioners interpretations of everyday language may influence their ability to see opportunities for teaching mathematical concepts not only in the context of an explicit math lesson but throughout the broader early childhood curriculum.

Noise subtraction in antiferromagnetically coupled magnetic recording media

We have investigated, both experimentally and theoretically, the media noise of antiferromagnetically coupled (AFC) recording media. In particular, we have studied how the lower-layer magnetic properties affect the media noise of the composite system. We find that AFC media perform well even for intrinsically noisy lower layers, such as soft-magnetic Co or CoCr layers with high intergranular exchange coupling. To understand the experimentally observed behavior, we propose a new concept of noise subtraction in AFC magnetic systems, in which the noise of the lower layer is anticorrelated to and subtracts from the noise in the upper layers and acts as a low-pass magnetic filter of the magnetization state in the upper layer.

A conductance-controlled variable transformer turns ratio regulator for a zero-voltage-zero-current power switching converter

This paper describes the application of the conductance control to a very high-efficiency parallel-regulated converter. Conductance control is one of the best ways of providing simplicity of design while preserving fast dynamic response and high reliability in power converters. The parallel regulator was conceived for space applications, to regulate a zero-voltage and zero-current power switching topology that works at constant frequency and constant duty cycle, but its range of applicability can be extended to any kind of power converter or inverter that utilizes a transformer to produce an isolated output. By using the concept of addition or subtraction of AC voltages, a fully regulated output voltage is achieved. The resultant effect of this regulation scheme is that the main transformer of the converter or inverter appears to have a variable turns ratio. This turns constant can be changed dynamically by means of a conductance control scheme and in almost a lossless way to maintain the converter (or inverter) outputs.

O livro didático na educação infantil: reflexão versus repetição na resolução de problemas matemáticos

O artigo analisa livros didáticos de matemática utilizados em salas de educação infantil, especificamente o tópico de resolução de problemas de estrutura aditiva. Foram examinadas doze coleções de livros, a partir de quatro eixos: a forma de introdução aos conceitos de adição e subtração; os tipos de problemas propostos; a utilização das ilustrações nos enunciados dos problemas; e o tipo de registro solicitado às crianças. Constatou-se que os livros didáticos analisados apresentam uma pequena variedade em relação à estrutura dos problemas. Assim, problemas envolvendo adição se limitam às estruturas de combinação e transformação e a maioria dos problemas de subtração restringe-se à estrutura de transformação. Em relação às ilustrações, observou-se que este recurso é bastante utilizado para fornecer os dados no enunciado do problema. Notaram-se, ainda, vários casos em que a própria ilustração fornece a resposta. Quanto ao tipo de registro, evidenciou-se que este se limita, geralmente, à solicitação da escrita dos dados e da resposta do problema em espaços previamente determinados. Freqüentemente é indicado o sinal da operação esperada para a solução do problema. Conclui-se que os livros didáticos de pré-escola analisados pretendem trabalhar com resolução de problemas, no entanto, as situações propostas são repetitivas e não estimulam o desenvolvimento e o confronto de estratégias diversas por parte das crianças.

A high-efficiency regulation technique for a zero-voltage zero-current power switching converter

This paper describes the application of a new regulation technique to a resonant converter that features zero-voltage (ZV) and zero-current (ZC) switching and works at constant frequency and duty cycle. The regulator utilizes the concept of regulating only a percentage of the total power in a bidirectional manner, thus allowing the converter to be optimized for both mass and efficiency. The proposed regulation technique has a wide range of applicability to almost all types of power converters or inverters that utilize a transformer to produce an isolated output. By using the concept of addition or subtraction of AC voltages, a fully regulated output voltage is achieved. The resultant effect of this regulation technique is that the main transformer of the converter or inverter appears to have a variable turns ratio. This turns ratio can be changed dynamically and in almost a lossless way to maintain the converter (or inverter) regulation. This technique can be used most effectively when input-voltage variation is limited to a reasonable tolerance range (e.g., + or -25%).

A Longitudinal Study of Invention and Understanding in Children's Multidigit Addition and Subtraction

This 3-year longitudinal study investigated the development of 82 children's understanding of multidigit number concepts and operations in Grades 1-3. Students were individually interviewed 5 times on a variety of tasks involving base-ten number concepts and addition and subtraction problems. The study provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords and the role that different concepts may play in that invention. About 90% of the students used invented strategies. Students who used invented strategies before they learned standard algorithms demonstrated better knowledge of base-ten number concepts and were more successful in extending their knowledge to new situations than were students who initially learned standard algorithms. An understanding of most fundamental mathematics concepts and skills develops over an extended period of time. Although cross-sectional studies can provide snapshots of the development of these concepts at particular points in time, longitudinal studies provide a more complete perspective; however, relatively few studies have traced the development of fundamental mathematics concepts in children over more than a single year. In this paper we report the results of a 3-year longitudinal study of the growth of children's understanding of addition and subtraction involving multidigit numbers. We focus particularly on children's construction of invented strategies for adding and subtracting multidigit numbers. The overarching goal of the study was to investigate the role that invented strategies may play in developing an understanding of multidigit addition and subtraction concepts and procedures. We trace the development and use of invented addition and subtraction strategies and examine the relation of these strategies to the development of fundamental knowledge of base-ten number concepts and the use of standard addition and subtraction algorithms. Finally, we consider what the use of invented strategies affords by way of avoiding systematic errors and extending knowledge of basic multidigit operations to new problem situations.

Using a Base-Ten Blocks Learning/Teaching Approach for First- and Second-Grade Place-Value and Multidigit Addition and Subtraction

A learning/teaching approach used base-ten blocks to embody the English named-value system of number words and digit cards to embody the positional base-ten system of numeration. Steps in addition and subtraction of four-digit numbers were motivated by the size of the blocks and then were carried out with the blocks; each step was immediately recorded with base-ten numerals. Children practiced multidigit problems of from five to eight places after they could successfully add or subtract smaller problems without using the blocks. In Study 1 six of the eight classes of first and second graders (N=169) demonstrated meaningful multidigit addition and place-value concepts up to at least four-digit numbers; average-achieving first graders showed more limited understanding. Three classes of second graders (N=75) completed the initial subtraction learning and demonstrated meaningful subtraction concepts. In Study 2 most second graders in 42 participating classes (N=783) in a large urban school district learned at least four-digit addition, and many children in the 35 classes (N=707) completing subtraction work learned at least four-digit subtraction.

Using a Base-Ten Blocks Learning/Teaching Approach for First- and Second-Grade Place-Value and Multidigit Addition and Subtraction

A learning/teaching approach used base-ten blocks to embody the English named-value system of number words and digit cards to embody the positional base-ten system of numeration. Steps in addition and subtraction of four-digit numbers were motivated by the size of the blocks and then were carried out with the blocks; each step was immediately recorded with base-ten numerals. Children practiced multidigit problems of from to eight places after they could successfully add or subtract smaller problems without using the blocks. In Study 1 six of the eight classes of first and second graders (N = 169) demonstrated meaningful multidigit addition and place-value concepts up to at least four-digit numbers; average-achieving first graders showed more limited understanding. Three classes of second graders (N = 75) completed the initial subtraction learning and demonstrated meaningful subtraction concepts. In Study 2 most second graders in 42 participating classes (N = 783) in a large urban school district learned at least four-digit addition, and many children in the 35 classes (N = 707) completing subtraction work learned at least four-digit subtraction. The English spoken system of number words is a named-value system for the values of hundred, thousand, and higher; a number word is said and then the value of that number word is named. For example, with seven hundred twelve, the thousand names the value of the five to clarify that it is not ones (= five) but is thousands. In contrast, the system of written multidigit number marks is a positional base-ten system in which the values are implicit and are indicated only by the relative positions of the number marks. In order to understand these systems of English words and written number marks for large multidigit numbers, children must construct named-value and positional base-ten conceptual structures for the words and the marks and relate these conceptual

From the concrete to the abstract: mathematics for deaf children.

An overview of the status, trends and methodology of teaching mathematics to deaf students showed that teachers are ill-prepared for the job at hand. They rely too heavily on textbooks and pencil and paper tasks while ignoring the hands-on exploration of objects that will allow children to better conceptualize basic mathematic principles. The authors offer an effective strategy for accomplishing a shift in instructional strategy. Incorporating characteristics from Piaget's theory of child development, the strategy supports the notion of using non-graded, 10-minute activity sessions to help hearing-impaired learners comprehend the concepts of addition, subtraction, multiplication and division.

A 3-D beam subtraction method for inhomogeneity correction in high energy X-ray radiotherapy

Most methods of inhomogeneity correction in high energy X-ray beams, assume an infinite lateral extent of the heterogeneous volumes ("slab models") or require sophisticated time-consuming computer algorithms. We present here a method, developed for parallelepiped inhomogeneities based on a beam subtraction concept combined with a conventional "slab model". Provided that the conventional model is appropriately chosen, this method gives agreement with experimental results better than 1% in most cases. It accounts properly for the scatter modification according to the size and position of the inhomogeneous volume. One example of a computer application is also presented.

The Acquisition of Addition and Subtraction Concepts in Grades One through Three

Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problemsolving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.