Explore the vast range of titles available.

We introduce the Math4Speed (M4S), a paper-and-pencil measure incorporating the four arithmetic operations with items of varying complexity. M4S consists of 50 addition, 50 subtraction, 50 multiplication, and 50 division problems, limited to 2 min per operation. The psychometric evaluation was conducted by combining convenience samples of young adults (N = 1,165), who were mainly university students (77.2%), from six European countries (the United Kingdom, Belgium, Germany, Poland, Greece, and Spain). Reliability and validity were satisfactory. Construct validity was reflected in the largest associations between inverse operations (e.g., multiplication and division). Convergent and divergent validity were reflected in higher associations of the M4S with other arithmetic measures than with a spelling test. As a freely available measure, M4S will be widely accessible and will in this first step allow cross-study comparison for typical experimental samples. In the next step, we invite all researchers to contribute to further development of M4S by providing more culturally diverse, minority, or representative samples to broaden the use cases of this screening of arithmetic fluency and enable more generalizability. Interested contributors can get in contact via email (math4speed@psychologie.uni-tuebingen.de). Nous présentons l'instrument de mesure Math4Speed (M4S), un test papier-crayon combinant les quatre opérations arithmétiques avec des items de complexité variable. Le test M4S comprend 50 problèmes d'addition, 50 problèmes de soustraction, 50 problèmes de multiplication et 50 problèmes de division, limités à 2 minutes par opération. L'évaluation psychométrique a été réalisée en combinant des échantillons de commodité de jeunes adultes (N = 1 165), principalement des étudiants universitaires (77,2 %), provenant de six pays européens (Royaume-Uni, Belgique, Allemagne, Pologne, Grèce et Espagne). La fiabilité et la validité sont satisfaisantes. La validité de construction se reflète dans les associations les plus importantes entre les opérations inverses (par exemple, la multiplication et la division). La validité convergente et divergente se reflète par des associations plus fortes entre l'instrument de mesure M4S et d'autres mesures arithmétiques qu'avec un test d'orthographe. En tant qu'instrument de mesure gratuit, M4S sera largement accessible et permettra, dans un premier temps, d'effectuer des comparaisons entre études pour des échantillons expérimentaux typiques. Dans la prochaine étape, nous invitons tous les chercheurs à contribuer à la poursuite du développement du M4S en fournissant des échantillons culturellement plus diversifiés, minoritaires ou représentatifs pour élargir les cas d'utilisation de ce dépistage de la fluidité arithmétique et permettre une généralisation accrue. Les contributeurs intéressés peuvent envoyer un courriel à (math4speed@psychologie.uni-tuebingen.de). Public Significance Statement Speeded tests of arithmetic fluency are often used to quickly gain knowledge about a person's level of mathematical competence. Many different tests are available measuring different types of arithmetic skills, but these tests might not be highly correlated, as they are based on the use of different strategies and solving procedures. Thus, scientific conclusions might be not specific to design and sample used but rather to diagnostic instruments chosen or available. The current article introduces an easy-to-use paper-and-pencil measure that can be freely administered to young adults typically tested in psychological experiments in different countries.

Research on immigrant children's education highlights the need for effective teaching strategies, particularly in mathematics, which often acts as a gatekeeper for academic advancement. This study implemented an eight-week arithmetic intervention in a preschool class, targeting low-performing immigrant children. The intervention group was taught using a direct instruction teaching model, while the control group received teaching as usual. Using a quasi-experimental design, trained teachers conducted 24 sessions of 30 min each, with small groups of students. The intervention helped children transition from informal to formal mathematics concepts, focusing on number relations and operations. Immigrant pupils particularly benefited, showing improved understanding through the targeted instruction compared to the control group receiving regular lessons. The result suggest that basic arithmetic progress can be improved by immigrant pupils through intensive practice in preschool class.

[LANGUAGE=”English”] Background and PurposeThe main purpose of teaching number sense to young children is to establish a core knowledge framework for number concepts, thereby enabling young children to understand a wide range of number problems and providing a basis for children to learn more complex number concepts in the future. Number sense is also fundamental for learning formal mathematics later in life. Studies have associated a lack of number sense in early childhood with a subsequent decline and difficulty in mathematical learning. Therefore, cultivating number sense in early childhood is essential for future mathematics achievement.The development of young children’s numerical cognition and mathematical skills is closely linked to the establishment of a mental number line. Additionally, studies have discovered a strong correlation between an individual’s innate perception of the mental number line and their proficiency in a range of mathematical abilities, including understanding number concepts, estimating quantities, and performing arithmetic.With the goal of developing young children’s number sense and basic arithmetic skills, this study designed a set of targeted intervention tools in the form of digital number line games. These tools were designed to help young children develop an understanding of mental number lines, thereby improving their number sense and basic arithmetic skills. This study also compared the improvement effects of the number line game and a non-number line game on the aforementioned learning objectives to determine which game was more effective at improving the relevant learning outcomes.Literature ReviewThe meaning of number senseNumber sense can be described as an individual’s ability to understand, relate, and connect numbers. Children with number sense can understand the relevant concepts and principles of numbers. Number sense includes several mathematical aspects, such as the ability for estimating small quantities, counting and cardinality, comparing numbers, recognizing number patterns, and transforming numbers. The concept of number sense in early childhood refers not to a single mathematical ability but rather encompasses a set of essential cognitive components that aid in comprehending numbers and abstract numerical symbols. These components include a conceptual understanding and the ability to perform practical numerical operations.Development of a mental number line and the relationship between a mental number line and number sense in childrenThe ability to place numbers on a mental number line is associated with the development of number sense, which is the ability to understand, relate, and connect numbers. Relevant studies have suggested that an individual’s perception of the mental number line influences their development of several number sense components (e.g., estimating, counting, and transforming numbers). Therefore, as soon as young children are capable of counting, connecting, and estimating the size of numbers and have learnt the numeral system and the spatial arrangement of numbers, they may acquire the ability to perceive a mental number line. Through educational activities, children can learn how to spatially arrange numbers (i.e., visualize a mental number line) and effectively develop a complete understanding of advance number concepts, including number transformation.Relationship between the construction of a mental number line and basic arithmeticThe construction of a mental number line involves spatially arranging numbers by size in the mind. Numbers are arranged in a continuous, quantity-based analogical format in ascending order (from left to right). When constructing a mental number line, basic arithmetic is performed. For example, the number after 6 is 7. To arrive at 7, addition arithmetic (6 + 1) must be performed. Therefore, the construction of a mental number line plays an important role in the development of basic arithmetic skills.MethodsThis study employed an experimental research design. A total of 105 preschool children from rural areas in eastern Taiwan were enrolled into this study. Participants were randomly divided into three groups: two experimental groups and a control group. A pretest-posttest analysis was performed to explore the influence of number line games on number sense and basic arithmetic skills. One-way analysis of covariance was performed to determine whether significant differences were present between the pretest and posttest results and between the three groups to eliminate the influence of confounding variables.ResultsResults for the number senseCovariate analysis revealed significant differences in posttest scores between the three groups (F(2,101) = 64.47, p < .05, eta squared η2 = .56). Furthermore, the improvement in number sense in the two experimental groups was significant. Both interventions (a number line game and a non-number line game) significantly improved the number sense to a similar extent.Results for basic arithmetic skillsSignificant differences were observed in the improvement of addition and subtraction skills between the two experimental groups and the control group. Basic arithmetic skills were better in the two experimental groups than in the control group. Additionally, the group that played the number line game performed significantly better than the group that played the non-number line game.ConclusionThis research is one of the few studies that has explored the development of number sense among young children by using a number line game. The findings indicate that the number line game, which was designed in accordance with the mental number line concept, can effectively enhance number sense among young children. However, in terms of improving number sense, similar learning outcomes can also be achieved by using non-number line games. In terms of improving basic arithmetic skills (addition and subtraction), the number line game was more effective than the non-number line game (traditional number decomposition and synthesis game). Furthermore, the non-number line game was more effective than the intervention in the control group. Overall, the digital game intervention aimed at improving mathematical learning among young children (whether it involves a number line game or a traditional non-number line game) had a positive effect on improving numerical ability, including number sense and basic arithmetic. The number line game was more effective than the non-number line game and the intervention in the control group. These findings are expected to advance the theoretical literature of mathematics education in early childhood and the teaching practices of mathematics for young children.[LANGUAGE=”Chinese”] 本研究以幼兒階段數感與基本算術能力的發展為目標，設計以心理數線為理論背景的數位數線遊戲，探究心理數線遊戲對幼兒數感與基本算術能力的學習成效，並進行心理數線遊戲及非心理數線遊戲的成效差異比較。本研究採前、後測實驗研究設計，實際研究參與對象為臺灣東部地區的幼兒共105位，將研究對象分為三組（心理數線遊戲組、非心理數線遊戲組與控制組）。結果顯示，以心理數線概念所建構的數位數線遊戲，在數感能力的提升上確實能獲得顯著的學習成效，且傳統的非心理數線概念所設計的數字概念學習遊戲亦同樣能提升幼兒的數感能力。然而，在基本算術能力（加減法）的學習成效上，心理數線遊戲的學習成果明顯比非數線遊戲來得好。研究結果建議，幼教相關教學人員在建構幼兒的數感能力與基礎算術能力時，使用心理數線遊戲是一個很好的教學工具選項。

本研究以幼兒階段數感與基本算術能力的發展為目標，設計以心理數線為理論背景的數位數線遊戲，探究心理數線遊戲對幼兒數感與基本算術能力的學習成效，並進行心理數線遊戲及非心理數線遊戲的成效差異比較。本研究採前、後測實驗研究設計，實際研究參與對象為臺灣東部地區的幼兒共105位，將研究對象分為三組（心理數線遊戲組、非心理數線遊戲組與控制組）。結果顯示，以心理數線概念所建構的數位數線遊戲，在數感能力的提升上確實能獲得顯著的學習成效，且傳統的非心理數線概念所設計的數字概念學習遊戲亦同樣能提升幼兒的數感能力。然而，在基本算術能力（加減法）的學習成效上，心理數線遊戲的學習成果明顯比非數線遊戲來得好。研究結果建議，幼教相關教學人員在建構幼兒的數感能力與基礎算術能力時，使用心理數線遊戲是一個很好的教學工具選項。 Background and Purpose The main purpose of teaching number sense to young children is to establish a core knowledge framework for number concepts, thereby enabling young children to understand a wide range of number problems and providing a basis for children to learn more complex number concepts in the future. Number sense is also fundamental for learning formal mathematics later in life. Studies have associated a lack of number sense in early childhood with a subsequent decline and difficulty in mathematical learning. Therefore, cultivating number sense in early childhood is essential for future mathematics achievement. The development of young children’s numerical cognition and mathematical skills is closely linked to the establishment of a mental number line. Additionally, studies have discovered a strong correlation between an individual’s innate perception of the mental number line and their proficiency in a range of mathematical abilities, including understanding number concepts, estimating quantities, and performing arithmetic. With the goal of developing young children’s number sense and basic arithmetic skills, this study designed a set of targeted intervention tools in the form of digital number line games. These tools were designed to help young children develop an understanding of mental number lines, thereby improving their number sense and basic arithmetic skills. This study also compared the improvement effects of the number line game and a non-number line game on the aforementioned learning objectives to determine which game was more effective at improving the relevant learning outcomes. Literature Review The meaning of number sense Number sense can be described as an individual’s ability to understand, relate, and connect numbers. Children with number sense can understand the relevant concepts and principles of numbers. Number sense includes several mathematical aspects, such as the ability for estimating small quantities, counting and cardinality, comparing numbers, recognizing number patterns, and transforming numbers. The concept of number sense in early childhood refers not to a single mathematical ability but rather encompasses a set of essential cognitive components that aid in comprehending numbers and abstract numerical symbols. These components include a conceptual understanding and the ability to perform practical numerical operations. Development of a mental number line and the relationship between a mental number line and number sense in children The ability to place numbers on a mental number line is associated with the development of number sense, which is the ability to understand, relate, and connect numbers. Relevant studies have suggested that an individual’s perception of the mental number line influences their development of several number sense components (e.g., estimating, counting, and transforming numbers). Therefore, as soon as young children are capable of counting, connecting, and estimating the size of numbers and have learnt the numeral system and the spatial arrangement of numbers, they may acquire the ability to perceive a mental number line. Through educational activities, children can learn how to spatially arrange numbers (i.e., visualize a mental number line) and effectively develop a complete understanding of advance number concepts, including number transformation. Relationship between the construction of a mental number line and basic arithmetic The construction of a mental number line involves spatially arranging numbers by size in the mind. Numbers are arranged in a continuous, quantity-based analogical format in ascending order (from left to right). When constructing a mental number line, basic arithmetic is performed. For example, the number after 6 is 7. To arrive at 7, addition arithmetic (6 + 1) must be performed. Therefore, the construction of a mental number line plays an important role in the development of basic arithmetic skills. Methods This study employed an experimental research design. A total of 105 preschool children from rural areas in eastern Taiwan were enrolled into this study. Participants were randomly divided into three groups: two experimental groups and a control group. A pretest-posttest analysis was performed to explore the influence of number line games on number sense and basic arithmetic skills. One-way analysis of covariance was performed to determine whether significant differences were present between the pretest and posttest results and between the three groups to eliminate the influence of confounding variables. Results Results for the number sense Covariate analysis revealed significant differences in posttest scores between the three groups (F(2,101) = 64.47, p < .05, eta squared η 2 = .56). Furthermore, the improvement in number sense in the two experimental groups was significant. Both interventions (a number line game and a non-number line game) significantly improved the number sense to a similar extent. Results for basic arithmetic skills Significant differences were observed in the improvement of addition and subtraction skills between the two experimental groups and the control group. Basic arithmetic skills were better in the two experimental groups than in the control group. Additionally, the group that played the number line game performed significantly better than the group that played the non-number line game. Conclusion This research is one of the few studies that has explored the development of number sense among young children by using a number line game. The findings indicate that the number line game, which was designed in accordance with the mental number line concept, can effectively enhance number sense among young children. However, in terms of improving number sense, similar learning outcomes can also be achieved by using non-number line games. In terms of improving basic arithmetic skills (addition and subtraction), the number line game was more effective than the non-number line game (traditional number decomposition and synthesis game). Furthermore, the non-number line game was more effective than the intervention in the control group. Overall, the digital game intervention aimed at improving mathematical learning among young children (whether it involves a number line game or a traditional non-number line game) had a positive effect on improving numerical ability, including number sense and basic arithmetic. The number line game was more effective than the non-number line game and the intervention in the control group. These findings are expected to advance the theoretical literature of mathematics education in early childhood and the teaching practices of mathematics for young children.

本研究以幼兒階段數感與基本算術能力的發展為目標，設計以心理數線為理論背景的數位數線遊戲，探究心理數線遊戲對幼兒數感與基本算術能力的學習成效，並進行心理數線遊戲及非心理數線遊戲的成效差異比較。本研究採前、後測實驗研究設計，實際研究參與對象為臺灣東部地區的幼兒共105位，將研究對象分為三組（心理數線遊戲組、非心理數線遊戲組與控制組）。結果顯示，以心理數線概念所建構的數位數線遊戲，在數感能力的提升上確實能獲得顯著的學習成效，且傳統的非心理數線概念所設計的數字概念學習遊戲亦同樣能提升幼兒的數感能力。然而，在基本算術能力（加減法）的學習成效上，心理數線遊戲的學習成果明顯比非數線遊戲來得好。研究結果建議，幼教相關教學人員在建構幼兒的數感能力與基礎算術能力時，使用心理數線遊戲是一個很好的教學工具選項

Purpose. This study aims to develop a new teaching module to illustrate the arithmetic systems of Elliptic Curve Cryptography, a powerful yet simple algorithm for information security, by exploring the capability of the Visual Basic Applications of Microsoft Excel in user friendly way. Methodology. The research is performed using research and development approach, which is divided into five steps utilizing VBA features of Microsoft Excel. It starts with modeling arithmetic in Microsoft Excel spreadsheet, then testing the validity through calculation and setup of the actual arithmetic of Elliptic Curve Cryptography using VBA Excel, before performing the test of the VBA application and finally visualizes the results in graphical mode. Findings. Novel teaching software based on of Microsoft Excel Visual Basic Applications is produced that is able to simulate arithmetic system behind Elliptic Curve Cryptography in an easy way for students. Originality. To the best of the authors’ knowledge, this is the first simulation based on Excel VBA to illustrate the arithmetic systems of Elliptic Curve Cryptography for teaching purposes. Practical value. In general, mastering cryptography will need a steep learning curve; however, using Microsoft Excel as a simulation platform will accelerate learning. The main practical value is the ease of Microsoft Excel, which will turn cryptography learning which was commonly very difficult for student to become easier and user friendly.

The Muskingum method is one of hydrological approaches that has been used for flood routing for many years thanks to its simplicity and reasonable accuracy over other methods. In engineering works, the calculation of the Peak section of a flood hydrograph is crucially important. In the present study, using the particle swarm optimization (PSO) algorithm, instead of using a single basic flood, the parameters of the linear Muskingum method (X, K, Δt) are calculated by computed arithmetic and geometric means relevant to two basic floods in the form of eight different models for calculating the downstream hydrograph. The results indicate that if the numerical values of the calculated flood inflow are placed in the interval of the inflow and the basic flood which the parameters X, K, Δt are from, the computation accuracy in approximating the outflow flood related to the peak section of the inflow hydrograph increases for all the mentioned models. In other words, if the arithmetic mean of X, K and the geometric mean of Δt, relevant to the two basic floods, are used instead of using values of X, K, Δt of a single basic flood, the computational accuracy in estimating the flood peak section of the hydrograph in downstream has the highest increase among all the eight models. Thus, the Mean Relative Error (MRE) relevant to the peak section of the inflow hydrograph of the third flood (observational flood) obtained by the first and second basic floods was equal to 4.89% and 2.91%, respectively, while in case of using the arithmetic mean of X and K and the geometric mean of Δt, related to the first and second basic floods (the best models presented in this study), this value is equal to 1.66%.

The current text provides a comprehensive introduction to essential oils, their biosynthesis, naming, analysis, and chemistry. Importantly, this text quickly brings the reader up to a level of competence in the authentication of essential oils and their components. It gives detailed descriptions of enantiomers and other forms of stereoisomers relevant to the study of natural volatiles and essential oils. The text also describes GC-MS work and provides tips on rapid calculation of arithmetic indices, how to interpret suggested names from the NIST mass spectral library, and what additional efforts are required to validate essential oils and defeat sophisticated adulteration tactics. In brief, essential oils are mixtures of volatile organic compounds that were driven out of the raw plant material in distillation, condensed into an oil that is strongly aroma emitting, and collected in a vessel as the top layer (uncommonly bottom layer) of two phase separated liquids: oil and water. Essential oils commonly include components derived from two biosynthetic groups, being terpenes (monoterpenes, sesquiterpenes and their derivatives) and phenylpropanoids (aromatic ring with a propene tail). The current text provides details of how terpenes and phenylpropanoids are further categorised according to their parent skeleton, then recognised by the character of oxidation, which may be from oxygen, nitrogen, or sulphur, or the presence/absence of a double bond. The essential oil’s science niche is an epicentre of individuals from diverse backgrounds, such as aromatherapy, pharmacy, synthetic and analytical chemistry, or the hobbyist. To make the science more accessible to the curious student or researcher, it was necessary to write this fundamentals-level introduction to the chemistry of essential oils (i.e., organic chemistry in the context of essential oils), which is herein presented as a comprehensive and accessible overview. Lastly, the current review constitutes the only resource that highlights common errors and explains in simplistic detail how to correctly interpret GC-MS data then accurately present the respective chemical information to the wider scientific audience. Therefore, detailed study of the contents herein will equip the individual with prerequisite knowledge necessary to effectively analyse an essential oil and make qualified judgement on its authenticity.

In prior work, we fit the mixture Rasch model to item responses from a fractions survey administered to a nationwide sample of middle grades mathematics teachers in the United States. The mixture Rasch model located teachers on a continuous, unidimensional scale and fit best with 3 latent classes. We used item response data to generate initial interpretations of the reasoning characteristic of each latent class. Our results suggested increasing facility reasoning about fraction arithmetic from one class to the next. The present study contributes two further arguments for the validity of our initial interpretations. First, we administered the same survey to a new sample of future middle grades mathematics teachers before and after 20 weeks of instruction on multiplication, division, and fractions, and we found that from pretest to posttest future teachers transitioned from one latent class to another in ways consistent with increased proficiency in fraction arithmetic. Second, we interviewed 8 of the future teachers before and after the instruction and found that future teachers’ reasoning during interviews was largely consistent with our original interpretation of the 3 latent classes. These results provide further support for our original interpretation of the mixture Rasch analysis, demonstrate the utility of our approach for capturing growth and change in future teachers’ reasoning during teacher education coursework, and contribute innovative applications of psychometric models for surveying teachers’ reasoning at scale.

This paper presents a new design method of the reverse (residue-to-binary) converter for the flexible 3-moduli residue number system (RNS) set {2k,2n-1,2n+1}, where k and n are a pair of arbitrary integers ≥2. The basic equation of the reverse converter is formulated in two alternative forms, each of which consists of two separate parts: one depending on input variables of the converter, and the other being a single constant. The constant can be either added inside the reverse converter or shifted out to the residue datapath channels, in most cases at no hardware cost or extra delay. From the set of basic functions, which are essentially different than those of the only two known general converters proposed for this moduli set, four versions of a converter can be designed for any pair of k and n. Experimental results obtained using the commercial 65-nm low-power design kit and industrial synthesis tools for all dynamic ranges from 8 to 40 bits suggest that, compared to the state-of-the-art designs, at least one version of the newly proposed converters is superior w.r.t. delay, power consumption, and area, for all dynamic ranges considered. The savings for the best versions (these with constants moved to the datapath channels) are up to 12.7% for the area and from 2.5% to 14% (5.8 % on average) for the delay, while the power consumption is reduced up to 23.2% (5.6% on average).