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Multiple Representations (mathematics Education)
In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal (e.g., mental construct) and external (e.g., graph). Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties. Multiple representations include graphs and diagrams, tables and grids, formulas, symbols, words, gestures, software code, videos, concrete models, physical and virtual manipulatives, pictures, and sounds. Representations are thinking tools for doing mathematics. Higher-order thinking The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills.S. Ainsworth, P. Bibby, and D. Wood, "Information technology and multiple representations: New opportunities – new problems, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagram
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word ''graph'' is sometimes used as a synonym for diagram. Overview The term "diagram" in its commonly used sense can have a general or specific meaning: * ''visual information device'' : Like the term " illustration", "diagram" is used as a collective term standing for the whole class of technical genres, including graphs, technical drawings and tables. * ''specific kind of visual display'' : This is the genre that shows qualitative data with shapes that are connected by lines, arrows, or other visual links. In science the term is used in both ways. For example, Anderson (1997) stated more generally: "diagrams are pictorial, yet abstract, represen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Math Symbol
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics. The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing point (geometry), points in geometry, and lower-case letters were used for variable (mathematics), variables and constant (mathematics), constants. Letters are used for representing many other sorts of mathematical objects. As the number of these sorts has remarkably increased in modern mathematics, the Greek alphabet and some Hebrew alphabet, Hebre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
YouTube
YouTube is a global online video platform, online video sharing and social media, social media platform headquartered in San Bruno, California. It was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by Google, and is the List of most visited websites, second most visited website, after Google Search. YouTube has more than 2.5 billion monthly users who collectively watch more than one billion hours of videos each day. , videos were being uploaded at a rate of more than 500 hours of content per minute. In October 2006, YouTube was bought by Google for $1.65 billion. Google's ownership of YouTube expanded the site's business model, expanding from generating revenue from advertisements alone, to offering paid content such as movies and exclusive content produced by YouTube. It also offers YouTube Premium, a paid subscription option for watching content without ads. YouTube also approved creators to participate in Google's Google AdSens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
WebQuest
A WebQuest is an inquiry-oriented lesson format in which most or all the information that learners work with comes from the web. These can be created using various programs, including a simple word processing document that includes links to websites. Distinguishing characteristics A WebQuest is distinguished from other Internet-based research by four characteristics. First, it is classroom-based. Second, it emphasizes higher-order thinking (such as analysis, creativity, or criticism) rather than just acquiring information. And third, the teacher preselects the sources, emphasizing information use rather than information gathering. Finally, though solo WebQuests are not unknown, most WebQuests are group work with the task frequently being split into roles. Structure A WebQuest has 5 essential parts: introduction, task, process, resources, evaluation, and conclusion. The original paper on WebQuests had a component called guidance instead of evaluation. Task The task is the f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Learning Styles
Learning styles refer to a range of theories that aim to account for differences in individuals' learning. Although there is ample evidence that individuals express personal preferences for how they prefer to receive information, few studies have found any validity in using learning styles in education. Many theories share the proposition that humans can be classified according to their "style" of learning, but differ in how the proposed styles should be defined, categorized and assessed. A common concept is that individuals differ in how they learn. The idea of individualized learning styles became popular in the 1970s, and has greatly influenced education despite the criticism that the idea has received from some researchers. Proponents recommend that teachers have to run a needs analysis to assess the learning styles of their students and adapt their classroom methods to best fit each student's learning style. Critics say there is no consistent evidence that identifying an indivi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manipulative (mathematics Education)
In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through developmentally appropriate hands-on experience. The use of manipulatives in mathematics classrooms throughout the world grew considerably in popularity throughout the second half of the 20th century. Mathematical manipulatives are frequently used in the first step of teaching mathematical concepts, that of concrete representation. The second and third steps are representational and abstract, respectively. Mathematical manipulatives can be purchased or constructed by the teacher. Examples of common manipulatives include number lines, Cuisenaire rods; fraction strips, blocks, or stacks; base ten blocks (also known as Dienes or multibase blocks); interlocking linking cubes (such as Unifix); construction sets (such as Polydron and Zome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuisenaire Rods
Cuisenaire rods are mathematics learning aids for students that provide an interactive, hands-on way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisors. In the early 1950s, Caleb Gattegno popularised this set of coloured number rods created by Georges Cuisenaire (1891–1975), a Belgan primary school teacher, who called the rods ''réglettes''. According to Gattegno, "Georges Cuisenaire showed in the early 1950s that students who had been taught traditionally, and were rated 'weak', took huge strides when they shifted to using the material. They became 'very good' at traditional arithmetic when they were allowed to manipulate the rods." History The educationalists Maria Montessori and Friedrich Fröbel had used rods to represent numbers, but it was Georges Cuisenaire who introduced the rods that were to be used across the world from the 1950s onwards. In 1952 he published ''Les nombres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spreadsheet
A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form. Spreadsheets were developed as computerized analogs of paper accounting worksheets. The program operates on data entered in cells of a table. Each cell may contain either numeric or text data, or the results of formulas that automatically calculate and display a value based on the contents of other cells. The term ''spreadsheet'' may also refer to one such electronic document. Spreadsheet users can adjust any stored value and observe the effects on calculated values. This makes the spreadsheet useful for "what-if" analysis since many cases can be rapidly investigated without manual recalculation. Modern spreadsheet software can have multiple interacting sheets and can display data either as text and numerals or in graphical form. Besides performing basic arithmetic and mathematical functions, modern spreadsheets provide built-in functions for common financial a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft Excel
Microsoft Excel is a spreadsheet developed by Microsoft for Microsoft Windows, Windows, macOS, Android (operating system), Android and iOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro (computer science), macro programming language called Visual Basic for Applications (VBA). Excel forms part of the Microsoft Office suite of software. Features Basic operation Microsoft Excel has the basic features of all spreadsheets, using a grid of ''cells'' arranged in numbered ''rows'' and letter-named ''columns'' to organize data manipulations like arithmetic operations. It has a battery of supplied functions to answer statistical, engineering, and financial needs. In addition, it can display data as line graphs, histograms and charts, and with a very limited three-dimensional graphical display. It allows sectioning of data to view its dependencies on various factors for different perspectives (using ''pivot tables'' and the ''sce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LibreOffice Calc
LibreOffice Calc is the spreadsheet component of the LibreOffice software package. After forking from OpenOffice.org in 2010, LibreOffice Calc underwent a massive re-work of external reference handling to fix many defects in formula calculations involving external references, and to boost data caching performance, especially when referencing large data ranges. Calc is capable of opening and saving most spreadsheets in Microsoft Excel file format. Calc is also capable of saving spreadsheets as PDF files. As with the entire LibreOffice suite, Calc is available for a variety of platforms, including Linux, macOS, Microsoft Windows, and FreeBSD. Available under the Mozilla Public License, Calc is free and open-source software. There is now a closed beta of LibreOffice on AmigaOS 4.1. Features Capabilities of Calc include: * Ability to read/write OpenDocument (ODF), Excel (XLS), CSV, and several other formats. * Support for many functions, including those for imaginary numbers, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Sheets
Google Sheets is a spreadsheet program included as part of the free, web-based Google Docs Editors suite offered by Google. The service also includes: Google Docs, Google Slides, Google Drawings, Google Forms, Google Sites and Google Keep. Google Sheets is available as a web application, mobile app for: Android, iOS, Microsoft Windows, BlackBerry OS and as a desktop application on Google's ChromeOS. The app is compatible with Microsoft Excel file formats. The app allows users to create and edit files online while collaborating with other users in real-time. Edits are tracked by a user with a revision history presenting changes. An editor's position is highlighted with an editor-specific color and cursor and a permissions system regulates what users can do. Updates have introduced features using machine learning, including "Explore", offering answers based on natural language questions in a spreadsheet. History Google Sheets originated from XL2Web, a web-based spreadsheet appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GeoGebra
GeoGebra (a portmanteau of ''geometry'' and ''algebra'') is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is available on multiple platforms, with apps for desktops (Windows, macOS and Linux), tablets ( Android, iPad and Windows) and web. History GeoGebra's creator, Markus Hohenwarter, started the project in 2001 as part of his master's thesis at the University of Salzburg. After a successful Kickstarter campaign, GeoGebra expanded its offering to include an iPad, an Android and a Windows Store app version. 2013 GeoGebra incorporated Bernard Parisse's Xcas into its CAS view. The project is now freeware (with open-source portions) and multi-lingual, and Hohenwarter continues to lead its development at the University of Linz. GeoGebra includes both commercial and not-for-profit entities that work together from the head office in Linz, Austria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
