Basic Mathematical Concepts and Methods

Understanding the correct concepts can avoid misconceptions in basic mathematical material. There is still a mathematical misconception among PGSD students due to the low understanding of the concept. Lecturing the basic mathematical concepts as a subject that must be taken by PGSD students can be done by internalizing Islamic values in it. The concepts in mathematics are full of the values they contain including Islamic values. Therefore, it is necessary to have teaching materials on the basic concepts of mathematics based on the internalization of Islamic values. This study aims at 1) to determine the characteristics of teaching materials on the basic concepts of mathematics based on the internalization of Islamic values, 2) to improve understanding of mathematical concepts through learning with teaching materials on the basic concepts of mathematics based on the internalization of Islamic values. This research is a development research. Analysis of the data used included the validity analysis of teaching materials, analysis of practicality of teaching materials, analysis of the effectiveness of teaching materials, descriptive statistics, and Gain normalization tests. Improving the understanding of student mathematical concepts can be seen in the average score of 61.54 pretest and the post-test average score of 85.41. From the normalized gain test calculation shows an increase of 0.62 in the medium category. From the results of the study it is expected that the teaching materials of the basic concepts of mathematics based on the internalization of Islamic values can be applied in learning through various learning innovations with student centered. Keywords: Teaching materials of mathematics basic concepts in Elementary, Internalization of Islamic values, concept understanding Ability.

Back to table of contents Previous article Next article Book ReviewNo AccessThe Growth of Basic Mathematical and Scientific Concepts in ChildrenRichard Trautman, M.D.Richard TrautmanNew York, N.Y.Search for more papers by this author, M.D.Published Online:30 Apr 2018https://doi.org/10.1176/appi.psychotherapy.1963.17.2.332aAboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail PDFThis content is only available as a PDF. Access content To read the fulltext, please use one of the options below to sign in or purchase access. Personal login Institutional Login Sign in via OpenAthens Purchase Save for later Item saved, go to cart PPV Articles - APT - American Journal of Psychotherapy $35.00 Add to cart PPV Articles - APT - American Journal of Psychotherapy Checkout Please login/register if you wish to pair your device and check access availability. Not a subscriber? Subscribe Now / Learn More PsychiatryOnline subscription options offer access to the DSM-5 library, books, journals, CME, and patient resources. This all-in-one virtual library provides psychiatrists and mental health professionals with key resources for diagnosis, treatment, research, and professional development. Need more help? PsychiatryOnline Customer Service may be reached by emailing [email protected] or by calling 800-368-5777 (in the U.S.) or 703-907-7322 (outside the U.S.). FiguresReferencesCited byDetailsCited byNone Volume 17Issue 2 1963, pp. 169–362Pages 332-334 Metrics PDF download History Published online 30 April 2018 Published in print 1 April 1963

The aim of this study is to discuss the conceptual dimensions of pre-service mathematics teachers' approaches to the basic concepts and operations of mathematics. 25 pre-service mathematics teachers in the first semester of the 2022-2023 academic year, who were educated at a state university, participated in the research. Four open-ended questions about the basic concepts of mathematics were asked to pre-service mathematics teachers and their written opinions were received. Content and descriptive analysis were applied to the responses. As a result of the analyzes, pre-service teachers did not approach these questions in the context of conceptual knowledge, but generally gave the answers in the context of procedural knowledge. Pre-service mathematics teachers used reflective thinking, which they used to compare the procedural knowledge processes they gained in the formal education process with the previous solutions, in these question solutions as well.

In this paper, some counter-examples are given to analyze deeply several common easily confused basic concepts and theories in unary function calculus. Through the examples, it can seen that we must truly understand the basic concepts of advanced mathematics. In order to learn higher mathematics better; it needs us to have a deep understanding about the concept in unary function calculus. In this paper, a number of counter-examples are given to intensify these basic concepts and theories, and the authors gives some explanations for the concept of several common mistakes.

The socialization of Visual Basic 6.0 based applications for calculating prime, odd and even numbers aims to introduce efficient tools for studying and implementing basic mathematical concepts interactively. This application is designed with a user-friendly interface to support mathematics teaching, both at secondary school level and in basic programming training activities. The app's key features include: Prime Number Check: Allows users to identify whether a number is a prime number. Odd and Even Classification: Provides a feature that automatically determines whether a certain number is odd or even. Calculations in a Specific Range: Provides calculation results for numbers within a specified range, supporting the exploration of mathematical patterns. The socialization process is carried out through training and interactive demos for potential users, such as teachers, students and the technology community. Evaluation shows that this application is able to improve understanding of basic mathematical concepts and speed up the manual calculation process. By utilizing Visual Basic 6.0 as a development platform, this application offers flexibility and compatibility with older operating systems, making it accessible to users with limited hardware. It is hoped that this application can be a useful educational tool in studying mathematics practically.

In this review, the theoretical studies are presented for the microcavitation bubble dynamics problems, which mainly depend on the microcavitation models, such as the Rayleigh-Plesset model, the Church model, the diffusion-concentration model, and the Keller-Miksis model in biological systems. The various solutions to these models, which were formulated based on basic mathematical and physical concepts, are schematically presented. Moreover, these models are employed in many different physical problems, such as the treatment of cancerous tumours via a technique known as histotripsy and lipid shells of membrane cells, that employ focused ultrasonic therapy as a non-invasive tissue ablation method. Using the mechanical action of bubble clouds, historic triumph destroys tissue differently than the thermally ablative techniques of therapeutic ultrasonography. Also, lipid-coated microbubbles are used in different therapeutic applications. Besides, the effect of different physical coefficients on Newtonian, non-Newtonian fluids, and viscoelastic media studied by numerical and analytical methods with external fields is examined for incompressible fluid states, and the Navier-Stokes hydrodynamic equations are investigated. It is anticipated that this work will serve as a valuable guide for the use of microcavitations in many medicinal applications, such as histotripsy, lipid shells in membrane cells and diver's tissue.

Different kinds of computer arithmetic follow an abstract mathematical pattern and are just special realizations of it. The basic mathematical concepts are sketched here. The concepts of rounding, of a screen, and of rounded arithmetic operations are defined in an axiomatic manner fully independent of special data formats and encodings. These abstract concepts are then applied and illustrated by the two elementary models of computer arithmetic for real numbers and for real intervals. In the latter case definition of the arithmetic operations as set operations does not suffice. Executable formulas have to be derived. We also demonstrate how this can be achieved. In an appendix we sketch a hardware realization of interval arithmetic and show that most of what is needed for it is already available on current x86-processors.

The Pseudo Keynesians (Joan Robinson, Austin Robinson, Richard Kahn) Against J. M. Keynes on the Liquidity Preference Theory of the Rate of Interest: The Reliance of Joan Robinson on A. Robinson and R. Kahn

Solomon Feferman has expressed skepticism or reserve about set theory, especially higher set theory, in many writings, and in his mathematical work he has largely stayed away from set theory. The paper undertakes to describe and diagnose Feferman’s attitude toward set theory, especially higher set theory. Section 1 discusses his opposition to Platonism in relation to some understandings of what Platonism is. Section 2 discusses his interest in predicativity, his analysis of predicative provability, and his sympathy for “predicativism,” although he denies being an adherent and has used impredicative methods in his own metamathematical work. It also notes his reconstruction of Hermann Weyl’s attempt to construct the elements of analysis on a predicative basis. Section 3 concerns his attitude toward proof theory. Section 4 turns more to philosophy. His anti-platonism is compared with the well known platonism of Godel. Unlike Godel, Feferman views concepts as human creations. He notes that basic mathematical concepts can differ in clarity and argues that less clear concepts, in particular those of set theory, can give rise to questions that do not have definite answers. It is questioned whether Feferman’s conceptual structuralism gives mathematics the degree of objectivity that its application in science requires. In Sect. 5 remarks are made about Hilary Putnam’s criticism of Feferman’s claim that a predicative system conservative over PA is adequate for the mathematics applied in science. The difference is seen to turn on Putnam’s scientific realism.

This chapter describes the ability of a pharmacist and pharmacy technician to undertake accurate calculations relating to concentrations and dilutions of pharmaceutical preparations, which is a key part of good pharmaceutical practice. It analyzes the consideration of calculations relating to percentages and ratios, concentrated and diluted solutions, and alligation. It also explains the terms ‘percentage’ and ‘ratio’, which is shows, are basic mathematical concepts. The chapter looks at how percentages are used in pharmacy to express the amount of liquid or solid in a defined amount of liquid or solid. It covers the conversion of concentrated liquid solutions into more dilute solutions.

The finite element method (FEM) is currently one of the most efficient and universal methods of numerical calculation for solving partial differential equations from engineering and scientific fields. The basic mathematical concepts are based on the work of Ritz, Galerkin, Trefftz and others at the beginning of the twentieth century. With the advance of modern computer science in the 1960s, these approaches of numerical solution could be successfully implemented with FEM. This development was motivated to an enormous extent by tasks of structural analyses in aviation, construction and mechanical engineering. The formulation of the finite element method in its current standard was developed thanks to the pioneer work of (among others) Argyris, Zienkiewicz, Turner, and Wilson. Therein, the system of differential equations is converted into an equivalent variational problem (weak formulation), mostly utilizing mechanical principles or weighted residual methods.KeywordsHybrid Stress ModelHybrid Variational PrincipleField QuantitiesVirtual DisplacementHyperelastic Material BehaviorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper presents a novel and comprehensive canonical quantization of the quaternionic scalar field within Minkowski spacetime, addressing challenges and inconsistencies observed in the quaternionic scalar field quantization, particularly regarding micro-causality. Using basic mathematical concepts, we develop a rigorous framework for a scalar field that preserves its quaternionic nature throughout the quantization process. This paper derives the full Lagrangian density, field equations and, crucially, obtains the explicit expressions for the Hamiltonian and momentum operators for the quaternionic scalar field. While quaternionic formalisms can offer alternative perspectives on known physical models, this study focuses on establishing a consistent quantization procedure for a quaternionic field as an entity, thereby rectifying the theoretical discrepancies and laying groundwork for further exploration into models where the noncommutative structure of quaternions may lead to novel physical insights or more compact descriptions of fundamental quaternionic fields.

We explore an approach to merging simulation and natural language in which conceptual structures are used which can repre sent the structure and meaning of sentences as well as basic mathematical concepts. Sentences can be transformed to these structures, and, via language generation, the structures can be transformed into mathematical equations. The process is illustrated using a text description of a plankton respiration model. The ap proach shows how qualitative natural language statements can be merged with both qualitative and quantitative modeling and simulation.

Yu, M. and Du, H., 2019. Numerical analysis of long period wave characteristics in sea area based on mathematical probability and statistics. In: Guido-Aldana, P.A. and Mulahasan, S. (eds.), Advances in Water Resources and Exploration. Journal of Coastal Research, Special Issue No. 93, pp. 119–124. Coconut Creek (Florida), ISSN 0749-0208.In order to improve the numerical analysis ability of long period wave characteristics in sea area, a numerical analysis method of long period wave feature in sea area based on mathematical probability statistics is proposed. The big data statistical analysis model of long period wave feature analysis in sea area is constructed, and the feature modeling and probability density feature analysis of long period wave data in sea area are carried out by using fuzzy association rule feature mining method. Combined with the mathematical probability statistical method, the fuzzy regional clustering processing of the long period wave data in the sea area is realized, and the feature quantity of the association rules of the long period wave in the sea area is extracted. The fuzzy clustering of the long period wave in the sea area is carried out by using the fuzzy C means clustering fusion method, and the random probability density distribution characteristic quantity of the long period wave in the sea area is excavated in the data clustering center. Combined with the feature space distributed structure reorganization method, the long period wave data is reorganized in the sea area, and the transmission control and feature numerical analysis optimization of the long period wave data in the sea area are realized. The simulation results show that the numerical analysis of long period wave characteristics in sea area is accurate and the data clustering performance is better, which improves the evaluation ability of long period wave dynamic evolution in sea area.

Brain atlases have a wide range of use from education to research to clinical applications. Mathematical methods as well as computational methods and tools play a major role in the process of brain atlas building and developing atlas-based applications. Computational methods and tools cover three areas: dedicated editors for brain model creation, brain navigators supporting multiple platforms, and atlas-assisted specific applications. Mathematical methods in atlas building and developing atlas-aided applications deal with problems in image segmentation, geometric body modelling, physical modelling, atlas-to-scan registration, visualisation, interaction and virtual reality. Here I overview computational and mathematical methods in atlas building and developing atlas-assisted applications, and share my contribution to and experience in this field.