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In this research paper, we solved the chemical kinetic system of nonlinear ordinary differential equations by the Modified Adomian i.e. Rach Adomian Decomposition Method (RADM). Rach Adomian Decomposition Method relies on the initial values of the unknowns in two different cases and provides approximate solutions of the problem in the series form. To check the accuracy of the Rach Adomian Decomposition Method, We have compared the outcomes of this approach with those of the IM method. The RADM method is shown to give good results. [ABSTRACT FROM AUTHOR]

This review aims to identify whether TDIC's have been used in the teaching-learning process of mathematics at the school level. In order to achieve this goal, the methodology used is an integrative literature review, via the CAPES Portal, in which the Scopus, Web of Science and Scielo databases were consulted. The search for published materials was restricted to a period of ten years, from 2008 to 2018. After collection, the data were organized through the reference manager Mendeley. Based on the results, it can be concluded that the use of TDIC's for the teaching-learning process has been gradually increasing and has been identified as positive. Furthermore, it has been proven that use occurs at different educational levels - pre-school, elementary and high school; there is the use of different methodologies, devices and applications - Ipad, tablet, inverted classroom and games. Although the initial integrative review resulted in 836 publications, when applying the inclusion and exclusion filters, only 14 studies corresponded to the objective proposed in this study, thus proving the existence of a scientific niche to be explored. [ABSTRACT FROM AUTHOR]

In this article we present a mapping, in the conception of Biembengut, regarding the methodologies adopted in the studies by the authors of the articles regarding the teaching and learning of Algebra in Higher Education published in the journal Mathematical Education Research (EMP) between the years 2010 and 2020. Based on a corpus of work composed by 14 investigations, we intended to identify the objectives, the methodological approach adopted aiming to reach them, the procedures used to collect and analyze the data, the types of sources used, and in case it applies, the subjects. Regarding the methodological perspectives, all 14 articles are of qualitative nature, with a predominance of studies which are purely field works (11), compared to those which are purely documental (two) and those which combine bibliographic research and field work (one). The use of a Study and Research Path, in the framework of the Anthropological Theory of the Didactic, present in two studies, constitutes itself as an innovative methodological approach. In the field works we observe that the themes of the investigations were worked by means of: semi-structured interviews carried out with students of the Mathematics undergraduate programs and with research teachers; interventions with teachers in training, undergraduate Mathematics students, undergraduate Engineering students, students without having their graduation specified and the analysis of participation of subjects (without specifying which) in a forum of Mathematics. Based on the corpus of work analyzed, we are not able to state that there are signs of reconfigurations or reorganizations caused by digital technologies in terms of methodologies of studies in Mathematical Education. [ABSTRACT FROM AUTHOR]

The aim of this essay is to map subsidized studies in the theoretical-methodological perspective of meta-analysis within the field of Mathematical Education, available at the Biblioteca Digital Brasileira de Teses e Dissertações (Brazilian Digital Library of Thesis and Dissertations, BDTD), with an emphasis on institutional, procedural and thematic aspects, as well as to analyze two meta-analysis investigations that address concepts perimeter and area. Therefore, this research is characterizes as qualitative of the mapping type. The results show an increase in the number of productions developed by researchers from several higher education institutions in the country and the increase of discussions about this methodological procedure, in view of the diversity of methodological and theoretical references used. Variation in the type and quantity of studies analyzed is verified, with the most frequent theme is related to the processes of teaching and learning Mathematics regarding the study of concepts of school math (12 out of 26 studies), for example, area and perimeter, identified as the object of investigation of the two researches assessed. [ABSTRACT FROM AUTHOR]

Considering the importance of interviews with children to investigate mathematical knowledge, here we have an essay to discuss and analyze the relationships between epistemology and methodology in the process of production of data for research. In this article, our goal is to highlight the relationships between epistemological foundations and ways to elaborate questions, asking and interpreting children's answers. We discuss about nuances, mishaps and particularities of the interviews with children and presented as a qualified approach the clinical interview and the Piagetian clinical method. The syntheses indicate the importance of using appropriate tools to investigate the mathematical object, as well as considering the particularities of the children's universe and the epistemic-methodological coherence adopted by the researcher. [ABSTRACT FROM AUTHOR]

The aim of the current study is to analyze the relationships between qualitative and quantitative approaches, or macro and micro relationships, in research about Mathematics Education developed in postgraduate programs in the last ten years. The discussion was based on a search carried out in Capes' collection in order to better understand articulations between these research spaces. The search carried out in the Bank of theses and dissertations was based on keywords and resulted in five dissertations and two theses produced between 2010 and 2019. Analysis has shown weak articulation between macro and micro research spaces in five of the seven texts, whose quantitative approach was linked to the idea of frequency counting and used to describe the analyzed data. In two, the analyzes showed a strong articulation between macro and micro research approaches, in which a dialogue between what was observed in one and another space is evident, developing a process of hybridization in methodological approaches. [ABSTRACT FROM AUTHOR]

Noninteractive zero-knowledge (NIZK) proof systems are fundamental primitives used in many cryptographic constructions, including public-key encryption secure against chosen ciphertext attack, digital signatures, and various other cryptographic protocols. We introduce new techniques for constructing NIZK proofs based on groups with a bilinear map. Compared to previous constructions of NIZK proofs, our techniques yield dramatic reduction in the length of the common reference string (proportional to security parameter) and the size of the proofs (proportional to security parameter times the circuit size). Our novel techniques allow us to answer several long-standing open questions in the theory of noninteractive proofs. - We construct the first perfect NIZK argument system for all NP. - We construct the first universally composable NIZK argument for all NP in the presence of an adaptive adversary. - We construct a non-interactive zap for all NP, which is the first that is based on a standard cryptographic security assumption. [ABSTRACT FROM AUTHOR]

No abstract is available for this article. [ABSTRACT FROM AUTHOR]

A set A ⊆ ω is cototal under enumeration reducibility if A ≤e A, that is, if the complement of A is total. We show that the e-degrees of cototal sets characterize the e-degrees of maximal anti-chain complements, the e-degrees of enumeration-pointed trees on 2<ω, and the e-degrees of languages of minimal subshifts on 2ω. As a consequence, we obtain a characterization of the Turing degree spectra of nontrivial minimal subshifts: they are the enumeration cones of cototal sets. From the perspective of the Turing degrees, this provides a complete understanding of the computational power of minimal subshifts. We also obtain an application to computable structure theory, showing that the enumeration cones of cototal sets characterize those structure spectra which are Turingupward closures of Fσ sets of reals. [ABSTRACT FROM AUTHOR]

This paper presents a novel binary bat algorithm (NBBA) to solve 0–1 knapsack problems. The proposed algorithm combines two important phases: binary bat algorithm (BBA) and local search scheme (LSS). The bat algorithm enables the bats to enhance the exploration capability while LSS aims to boost the exploitation tendencies and, therefore, it can prevent the BBA–LSS from the entrapment in the local optima. Moreover, the LSS starts its search from BBA found so far. By this methodology, the BBA–LSS enhances the diversity of bats and improves the convergence performance. The proposed algorithm is tested on different size instances from the literature. Computational experiments show that the BBA–LSS can be promise alternative for solving large-scale 0–1 knapsack problems. [ABSTRACT FROM AUTHOR]

Cancer stem cells are responsible for tumor survival and resurgence and are thus essential in developing novel therapeutic strategies against cancer. Mathematical models can help understand cancer stem and differentiated cell interaction in tumor growth, thus having the potential to help in designing experiments to develop novel therapeutic strategies against cancer. In this paper, by using theory of functional and ordinary differential equations, we study the existence and stability of nonlinear growth kinetics of breast cancer stem cells. First, we provide a sufficient condition for the existence and uniqueness of the solution for nonlinear growth kinetics of breast cancer stem cells. Then we study the uniform asymptotic stability of the zero solution. By using linearization techniques, we also provide a criteria for uniform asymptotic stability of a nontrivial steady-state solution with and without time delays. We present a theorem from complex analysis that gives certain conditions that allow for this criteria to be satisfied. Next, we apply these theorems to a special case of the system of functional differential equations that has been used to model nonlinear growth kinetics of breast cancer stem cells. The theoretical results are further justified by numerical testing examples. Consistent with the theories, our numerical examples show that the time delays can disrupt the stability. All the results can be easily extended to study more general cell lineage models. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

No abstract is available for this article. [ABSTRACT FROM AUTHOR]

We comment on the Friedmann and Hagen's quantum mechanical derivation of the Wallis formula for π . In particular, we demonstrate that not only the Gaussian trial function, used by Friedmann and Hagen, but also the Lorentz trial function can be used to get the Wallis formula. The anatomy of the integrals leading to the appearance of the Wallis ratio is carefully revealed. [ABSTRACT FROM AUTHOR]

On the odd day, a mathematician might wonder what constructive mathematics is all about. They may have heard arguments in favor of constructivism but are not at all convinced by them, and in any case they may care little about philosophy. A typical introductory text about constructivism spends a great deal of time explaining the principles and contains only trivial mathematics, while advanced constructive texts are impenetrable, like all unfamiliar mathematics. How then can a mathematician find out what constructive mathematics feels like? What new and relevant ideas does constructive mathematics have to offer, if any? I shall attempt to answer these questions. [ABSTRACT FROM AUTHOR]

The traditional National mathematical Olympiad for University students took place in Pamporovo resort from 18 to 21 May 2017. The event was hosted by the Plovdiv University “P. Hilendarski”. More than 100 students participated in the Olympiad representing 14 Universities from Bulgaria and 2 Universities from abroad. The competition was organized in 3 groups depending on the mathematical curriculum in different Universities. The paper discusses the problems of the third group, in which students from Economics Universities study Mathematics with small number of classes. Methodological solutions are proposed. [ABSTRACT FROM AUTHOR]

This classroom-based investigation sought to document how, in real time, STEM teachers and students attempt to locate the invariant mathematical relations that are threaded through the range of activities and representations in these classes, and how highlighting this common thread influences student participation and learning. The authors conducted multimodal discourse analyses of teacher–student interactions during multiday observations in 3 urban high school STEM classes. The focal lessons were in electrical engineering and mechanical engineering (within Project Lead the Way), and precollege geometry. Across 3 cases, teachers and students actively built and maintained cohesion of invariant mathematical relations across activities and representations. Pre- and postlesson interviews revealed that teachers intentionally managed cohesion to provide the continuity across the curricular activities that teachers believed would promote student understanding. The findings contribute to ways of fostering STEM integration and ways of grounding abstractions to promote meaning making and transfer. [ABSTRACT FROM PUBLISHER]

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier–Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. [ABSTRACT FROM AUTHOR]

The object of study of this research is how the Theory of Semiotics Representation Registers is evident in Brazilian scientific research therefore aims to reveal the level of coverage, mathematical object, methodological procedures and aspects of Duval most prevalent theory in these research. In this way, it is a bibliographical research design with state of the art. The results show the predominance of Basic Education; the variety of mathematical objects; the highlight of both sequences as Teaching of Mathematics activities as methodological procedures used and the treatment and conversion transformations as aspects of the more obvious Duval theory most evident in the mapped research. [ABSTRACT FROM AUTHOR]

This paper presents reflections on the teaching and learning of Differential and Integral Calculus notions. By relevant theoretical contributions, we propose activities to address calculation notions as limits and derivatives, taking as a guiding principle an active methodology in the case, the Problem-Based Learning (Problem Based Learning - PBL). Expected to integrate mathematical content and concepts with the university of professional practices, promoting meaningful learning. We believe that by inserting motivators, real or realistic problems, certain obstacles observed in teaching and learning calculus, can be softened as well as contribute to the construction of disciplinary knowledge. [ABSTRACT FROM AUTHOR]

The development of topics of Statistics from the accomplishment of a practical activity of collection and real data analysis, propitiates to the people to qualify their critical thinking, self-organization, collective and collaborative work. The aim of this study was to do a qualitative research in a High School class to evaluate the effects of a teaching practice in the learning of topics of Statistics. As a group, everyone planned and did field research focusing on themes that had been suggested by the students themselves. This activity stands out because the data collected was based on a random sample of the residents of the town. The qualitative analysis of students' answers to specific questions, based on the Collective Subject Discourse methodology, revealed proper understanding of statistical concepts, and also showed the satisfaction of students to be part of the process. [ABSTRACT FROM AUTHOR]

Copyright of Basrah Journal of Science / Magallat Al-Barat Li-L-ulum is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study aims to investigate the nature of different mathematics teaching modes (prescriptions) that guide prospective teachers during their instruction. The participants were 24 junior prospective middle school mathematics teachers (19 females and 5 males) who were attending a mathematics methods course at a private university in central Turkey. Each participant was tasked with applying an innovative prescribed curriculum about equivalent fractions to a single elementary or middle school student; he/she is required to videotape the teaching session. We collected these teaching videos and analyzed them through a phenomenographic approach. Results suggest that the participants select and operate with certain teaching prescriptions while teaching. The mathematical knowledge of the teacher is not the only factor that affects his/her teaching; ingrained prescriptions influence and guide their teaching as well. All these teaching prescriptions are selected according to the teachers' strongly held beliefs about teaching and learning based on their prior schooling experiences and not on their experiences in their coursework. We also found that having prospective teachers operate with an innovative curriculum does not improve their teaching in the presence of these prescriptions. [ABSTRACT FROM AUTHOR]

Chain rule plays an important role in fractional calculus. There are many definitions of fractional derivative, and this paper shows that the chain rule is invalid for Jumarie's modification of Riemann-Liouville definition. [ABSTRACT FROM AUTHOR]

An investigation of compressible Rayleigh–Taylor instability (RTI) using Direct Numerical Simulations (DNS) requires efficient numerical methods, advanced boundary conditions, and consistent initialization in order to capture the wide range of scales and vortex dynamics present in the system, while reducing the computational impact associated with acoustic wave generation and the subsequent interaction with the flow. An advanced computational framework is presented that handles the challenges introduced by considering the compressive nature of RTI systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification dependent vorticity production. The foundation of the numerical methodology described here is the wavelet-based grid adaptivity of the Parallel Adaptive Wavelet Collocation Method (PAWCM) that maintains symmetry in single-mode RTI systems to extreme late-times. PAWCM is combined with a consistent initialization, which reduces the generation of acoustic disturbances, and effective boundary treatments, which prevent acoustic reflections. A dynamic time integration scheme that can handle highly nonlinear and potentially stiff systems, such as compressible RTI, completes the computational framework. The numerical methodology is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis. [ABSTRACT FROM AUTHOR]

The Leray–Hopf solutions to the Navier–Stokes equation are known to be unique on R 2 . In our previous work, we showed the breakdown of uniqueness in a hyperbolic setting. In this article, we show how to formulate the problem in order so the uniqueness can be restored. [ABSTRACT FROM AUTHOR]

This paper presents an optimal performance analysis for an isothermal model which performs work at a steady state via the energy transfer from a chemical reaction, using the methodology of the so-called Finite Time Thermodynamics (FTT). Furthermore, three optimal operation modes namely, Maximum Power, Maximum Omega function and Efficient Power are presented for the model. Results show analogies in the optimal performance between thermal and isothermal engine models. [ABSTRACT FROM AUTHOR]

The lack of updating and training of teachers in the use of information technology and communications (ICT) as a teaching and learning of mathematics, have limited its methodological work, causing poor performance in the integral learning students and ability to solve practical problems they face in society. That is why this paper aims to consider the more specific contradictions that occur in the teaching and learning of mathematics based on the use of ICT. In this context, it is concluded that recognizes the mathematical task computerized (TMI) as a means to contribute to the improvement of student learning, taking into account the contradiction occurs between the comprehensive nature of the student's education to society and the diverse nature of the ownership of the contents taught in the course. [ABSTRACT FROM AUTHOR]

The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite second-order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochastic quantity ξ, hence acting as a kind of random basis. The PCE methodology has been developed as a mathematically rigorous Uncertainty Quantification (UQ) method which aims at providing reliable numerical estimates for some uncertain physical quantities defining the dynamic of certain engineering models and their related simulations. In the present paper, we use the PCE approach in order to analyze some equity and interest rate models. In particular, we take into consideration those models which are based on, for example, the Geometric Brownian Motion, the Vasicek model, and the CIR model. We present theoretical as well as related concrete numerical approximation results considering, without loss of generality, the one-dimensional case. We also provide both an efficiency study and an accuracy study of our approach by comparing its outputs with the ones obtained adopting the Monte Carlo approach, both in its standard and its enhanced version. [ABSTRACT FROM AUTHOR]

The article discusses the purported solving of the abc conjecture in arithmetic geometry by mathematician Shinichi Mochizuki. Topics include the implications of the abc conjecture for whole numbers and prime numbers, the length of Mochizuki's proof in relation to his development of the notion of inter-universal geometry, and the opinions of mathematicians including Ivan Fesenko, Jordan Ellenberg, and Gerd Faltings on Mochizuki's work.

Research has established that executive functions, the skills required to monitor and control thought and action, are related to achievement in mathematics. Until recently research has focused on working memory, but studies are beginning to show that inhibition skills-the ability to suppress distracting information and unwanted responses-are also important for mathematics. However, these studies employed general mathematics tests and therefore are unable to pinpoint how inhibition skills relate to specific components of mathematics. We explored how inhibition skills are related to overall achievement as well as factual, procedural and conceptual knowledge in 209 participants aged 11-12, 13-14 and adults. General mathematics achievement was more strongly related to inhibition measured in numerical compared with non-numerical contexts. Inhibition skills were related to conceptual knowledge in older participants, but procedural skills in younger participants. These differing relationships can shed light on the mechanisms by which inhibition is involved in mathematics. [ABSTRACT FROM AUTHOR]

This study used participant observation to explore students' thinking when learning the concept of factorial functions. First-year university students undertaking a mathematics methodology course were asked to find the number of ways in which five people could sit around a circular table with five seats. Using grounded theory as a qualitative research strategy, we analysed student responses and written reflections according to the sequence of their experiential realities: practical and textual experiences. This was followed by an analysis of their reflections on both experiences in a pedagogical context. We found that the way basic mathematics operations are learned impacts on the student's ability to experience components of new problems as familiar. Consequently, they encounter these problems as new and unfamiliar. At the same time we found that engagement with practical experience does allow for the emergence of representations that have the potential to be used as foundations for learning new and unfamiliar concepts. The blending of practical, textual and teaching experiences provoked students' thinking and ultimately their understanding of a given new and unfamiliar mathematics concept. [ABSTRACT FROM AUTHOR]

This mathematical article explains in complete detail the "Not-on-the-line transformation" phenomenon used regarding lines. U.S President Barack Obama quote precedes this article. He says "My credibility is not on the line". Topics also include about how the transformation of lines can be explained by mapping the lines.

The article offers information on mathematical solutions and operations created by students of St Ursula's College in New South Wales at the two amusement rides Tower of Terror and Giant Drop.

Copyright of Tecnura is the property of Tecnura and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

BACKGROUND: Many models of assessing radiopharmaceutical kinetics for dosimetry have been developed, starting from the formula of Marinelli. They are either inaccurate or require taking multiple patient uptake measurements. MATERIAL AND METHODS: Radiotracer behavior is approached to a modified Bateman equation ("biphasic model"). The calculated effective half time, maximum uptake and the cumulated uptake according to the biphasic model is compared to the values obtained with the most popular Marinelli's method ("simplified model"). The calculations can be performed by free online-accessible software on the site: www.nuk.bieganski.org ("Calculator"). RESULTS: Using of the software allows a direct comparison of the obtained effective half times according to both, the simplified and the biphasic, models. Further errors can come from imprecise measure of the maximum uptake value (especially, when the time of the measurement differs from the true point of the maximum uptake) and from neglecting of the ascending branch of the time-uptake curve. It is possible to compare the cumulated uptake values according to both models ("correction factor"). The results can be combined with the widely known formula of Marinelli. The operations require only one additional uptake measurement, which could be performed shortly after the i.v. administration of the radiotracer, i.e., during the same visit of the patient. CONCLUSION: The proposed theoretic model could be verified practically for some i.v.-administered radiopharmaceuticals. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new existence, uniqueness and Ulam-Hyers stability theorems for coincidence problems for two single-valued mappings. The main results of this paper extend the results presented in O. Mlesņitę: Existence and Ulam-Hyers stability results for coincidence problems, J. Nonlinear Sci. Appl., 6 (2013), 108-116. In the last section two examples of application of these results are also given. [ABSTRACT FROM AUTHOR]

Reviews are offered for several articles which appeared in 2012 and 2013 in different periodicals including "Euler's Musical Mathematics" in "The Mathematical Intelligencer", "Killer Problems" in "American Mathematical Monthly" and "A Result Concerning Fibonacci Primes" in "Mathematical Spectrum".

The article focuses on the mathematical calculations and techniques required to play American Roulette, a casino game named after a French diminutive for little wheel, which uses standard numbers from one to 36 and special numbers like '0' (zero) and '00' (double zero). It notes the different kinds of bets that can be made, where each type having a probability of win is denoted by the ratio of the number of winning numbers to 38.

cThe article aims at providing the condition when there is no solution, a unique solution or infinitely many solutions to a linear, second-order and homogeneous recurrence with constants, real coefficients and real initial conditions in second-order recurrence relations. It mentions the use of quasi-periodic integer sequences to make a first order recurrence assumption in geometric sequence.

The article focuses on the ways of defining the sine function in trigonometry, which finds applications in mathematics and physics. It notes the geometrical and differential forms in which sine and cosine functions appear as solutions of harmonic differential equations. It puts forth the use of variables to represent arc's length in a unit circle by considering movement of object around the circle having constant speed.

The article discusses the interesting formulations in divisibility of large numbers by two, three, five and nine. It mentions a method to find the divisibility of the number 12,313,515 by three, which states the adding of its component numbers which give 21 as a result which is divisible by 3, and the method concludes that 12,313,515 is also divisible by 3. It notes the number theory formulated by Russian mathematician A. K. Zbikowski, to find divisibility of numbers by 7, 11, and 13.

The article focuses on the different mathematical ways of writing any number greater than three, as the sum of consecutive positive integers, by finding the number of ways to create that same integer. It mentions the importance of thinking about a good problem, a good test data and an odd factor for extreme problems. It notes that any number 'n' having two or more odd prime factors are partitionable by three and five.

In teaching, representations are used as ways to illustrate the concepts underlying a specific topic. For example, use symbols (e.g., 1 + 2 = 3) to express the concept of addition. To compare students’ abilities to interpret different representations in mathematics, the symbolic representation (SR) test and the pictorial representation (PR) test were designed, and then administered to 681 sixth graders in Taipei, Taiwan. This study adopts two different modeling perspectives, the testlet perspective and the multi-ability perspective, to analyze this SR and PR test data in the context of item response theory. The main results show that: 1. Students scored on average significantly higher on the SR test than the PR test. 2. The effects of the item stem testlets could be large, but they are statistically non-significant; however, the influence of the number of items in the testlet should also be considered. 3. The nature of the option representations, SR and PR, represents two different mathematics abilities. 4. The main factor that influences students’ item responses is students’ abilities to interpret SR and PR, and the testlet effects generated from the shared item stem can be ignored. 5. Regarding the parameter estimates of the best-fitting model: (a) the person ability variance estimates show that the ability distributions on the SR and PR dimension may not be the same, (b) the correlation estimate between the SR and PR dimension indicates that these two abilities are moderately correlated, and (c) the item difficulty estimates for different models are similar. Suggestions for teaching practice and future studies are provided in the Conclusion. [ABSTRACT FROM AUTHOR]

Subtraction problems of the type M − S = ? can be solved with various mental calculation strategies. We investigated fourth- to sixth-graders' use of the subtraction by addition strategy, first by fitting regression models to the reaction times of 32 two-digit subtractions. These models represented three different strategy use patterns: the use of direct subtraction, subtraction by addition, and switching between the two strategies based on the magnitude of the subtrahend. Additionally, we compared performance on problems presented in two presentation formats, i.e., a subtraction format (81 − 37 = .) and an addition format (37 + . = 81). Both methods converged to the conclusion that children of all three grades switched between direct subtraction and subtraction by addition based on the combination of two features of the subtrahend: If the subtrahend was smaller than the difference, direct subtraction was the dominant strategy; if the subtrahend was larger than the difference, subtraction by addition was mainly used. However, this performance pattern was only observed when the numerical distance between subtrahend and difference was large. These findings indicate that theoretical models of children's strategy choices in subtraction should include the nature of the subtrahend as an important factor in strategy selection. [ABSTRACT FROM AUTHOR]

The article focuses on the prospect of pedagogical content knowledge in planning efficient mathematical knowledge for framework of teaching curriculum. It notes the student's ability to react and respond with mathematical integrity is significant prospect for teaching practice improvement. It mentions some vignettes as impetus for teachers' instructional plans which were lost in pedagogical purposes.

This paper fits the area of Mathematics Education at Higher Education, especially the area of studies concerning the teaching and learning of Differential Calculus. We present, in this study, theoretical elements and teaching approaches concerning the concept of Calculus proposed by David Tall and others, gathered from the development of a panorama including papers written by these researchers. In an introductory way, we present elements about the constitution of this area of Mathematics Education, as well as questions which enhance it. With this paper, the authors hope to have contributed to the consolidation of the area of Mathematics Education at Higher Education in general, and to the GT -- No. 04, because not only do they broaden the diffusion of one theorist but also try to summarize the results of researches. [ABSTRACT FROM AUTHOR]

The majority of recent studies conclude that children’s private speech development (private speech internalization) is related to and important for mathematical development and disabilities. It is far from clear, however, whether private speech internalization itself plays any causal role in the development of mathematical competence. The main concerns of the present study were whether phonological awareness skills relate to private speech internalization, and whether the answer to this question changes with children’s age and mathematical achievement levels. Comparisons were made between 67 children diagnosed with math difficulties and 67 children without math difficulties from Grade 2 to Grade 7 in primary schools. Two separate laboratory investigations were performed to explore children’s developmental levels of private speech and phonological awareness, respectively. Analysis was based on private speech differences, phonological awareness differences, and differences in occurrence of private-speech/phonological-awareness category combinations. Children without math difficulties showed a grade-determined shift from less to more internalized private speech and from lower to higher levels of phonological awareness. In contrast, the development of children with math difficulties seemed almost to stop at the inaudible private speech/low level of phonological awareness combinations. Silence/high phonological level was the primary alternative for typical math achievers. Results are discussed in terms of directions for future research. [ABSTRACT FROM PUBLISHER]

In one of the first attempts at providing a mathematical framework for the Hirsch index, Egghe and Rousseau (2006) assumed the standard Lotka model for an author's citation distribution to derive a delightfully simple closed formula for his/her h-index. More recently, the same authors ( Egghe & Rousseau, 2012b) have presented a new (implicit) formula based on the so-called shifted Lotka function to allow for the objection that the original model makes no allowance for papers receiving zero citations. Here it is shown, through a small empirical study, that the formulae actually give very similar results whether or not the uncited papers are included. However, and more important, it is found that they both seriously underestimate the true h-index, and we suggest that the reason for this is that this is a context-the citation distribution of an author-in which straightforward Lotkaian informetrics is inappropriate. Indeed, the analysis suggests that even if we restrict attention to the upper tail of the citation distribution, a simple Lotka/ Pareto-like model can give misleading results. [ABSTRACT FROM AUTHOR]

Modern nuclear medicine frequently needs to be supported by software for calculations. A self-designed free-accessible online tool named "Calculator" is presented. It can be used from the web-site www.nuk.bieganski.org, option "Calculator". The programs offer: calculations of quantity of a radionuclide after a time (equation of simple radioactive decay), quantity of the second and third nuclide in the decay chain (successive radioactive decay, computation with Bateman equations and their limits), converting of activity units as well as of activity of a radioactive substance into its mass and vice versa, and calculations related to radionuclide therapy (radionuclide uptake, effective half time and activity needed for therapy). Mathematical and historical backgrounds of the algorithms used are shortly discussed in this work. [ABSTRACT FROM AUTHOR]