Mbth: GeoGebra Type: Mathematical Software Founder: Markus Hohenwarter Version Language: English Software Introduction, Software Introduction, Software Features, Function Introduction, Geometry Window, Algebra Window, Worksheet Window, Research Institute, International Situation, China Situation, User Authentication, Beginners, Expert Users, Training Experts, Software Introduction GeoGebra is a dynamic mathematical software integrating geometry, algebra and calculus. It was designed by Marcus Hornwater, a professor of mathematics at Atlanta University in Florida. On the one hand, GeoGebra is a dynamic geometry software. You can draw points, vectors, line segments, lines, polygons, conic curves and even functions on them, and you can change their properties later. On the other hand, you can also directly input equations and point coordinates. Therefore, GeoGebra also has the ability to handle variables (these variables can be a number, angle, vector or point coordinates), and it can also differentiate and integrate functions, find out the roots of equations or calculate the minimax of functions. So GeoGebra has the function of dealing with algebra and geometry at the same time, so the left side of GeoGebra window is the algebra area, and the right side is the geometry area (also called drawing area), as shown in the following figure. Software features * can be used for learning, teaching and evaluation free of charge. * Powerful, easy to use and interactive. * Support for multiple languages. * Really observe and experience mathematics and science in interesting ways. * Can be applied to various courses or projects. * Millions of people around the world are using it. Function introduction The following briefly introduces several windows: Quadratic function geometry window can use the drawing tools provided in the toolbar to draw geometric figures in the geometric area with the mouse. Select a drawing tool from the toolbar, and you can know how to use the selected tool through the tool use tips (behind the toolbar). Any object generated in the geometric region has an algebraic feature in the algebraic region. Note: You can drag the objects in the geometric area with the mouse, and the algebraic features in the algebraic area will be dynamically updated at the same time. Each icon in the toolbar represents a toolbox, which contains some drawing tools with similar functions. You can use the left mouse button to press the small arrow in the lower right corner of the icon to open the toolbox. Tip: Drawing tools are classified according to the properties of generated objects. For example, you can generate different types of points in the Point Toolbox (default display) and the Geometric Transformation Toolbox (default display). In the algebra window, you can directly enter the algebraic expression in the Geogebrar command area, and then press Enter, and the entered algebraic expression will appear in the algebra area, and the corresponding graph will appear in the geometry area. In the field of algebra, mathematical objects are divided into free objects and derived objects. An object is classified as a free object if it is generated without using any existing objects. A newly generated object is classified as a derived object if it is generated by using other existing objects. Tip: If you want to hide the features in the Algebra area, you can designate the object as an auxiliary object, as shown below: in the Algebra area, right-click the object and select Auxiliary Object in the right-click menu, or select Properties in the pop-up menu, select the label Basic in the Properties dialog box, and then check the box before the Auxiliary Object option. By default, the "auxiliary object" will not appear in the algebra area, but you can select "auxiliary object" in the view menu, and then you can see it in the algebra area. You can modify the object in the algebra area: first, confirm that the moving tool has been selected, then double-click the object in the algebra area, you can edit the algebraic feature data of the object directly in the text box, and then press Enter, and the graphic feature of the object will change accordingly. If you double-click the derived object in the algebra area, you can "redefine" the object in the dialog box that appears. Geogebra also provides many commands. You can press the' command' button on the right side of the command area to open the command window table, select a command from the menu (or directly enter the command in the command input box), and then press the F 1 key to get the syntax structure and required parameters of the command. Worksheet window In the worksheet area of Geogebra, each cell has a specified name, which is used to specify the location of the cell. This is similar to an OFFICE worksheet. For example, the cell name in column A, row 1, is A 1. Note: When cell names are used in expressions or commands, the cell names represent the content data in the cells. This process is called cell data reference. In the worksheet, you can enter not only numerical values, but also all mathematical objects supported by Geogebra, such as coordinates of points, functions, commands, etc. Geogebra will immediately display the graphic features of the mathematical objects entered in the worksheet in the geometric area, and the names of the objects will correspond to the positions in the worksheet, such as A5 and C3. Note: By default, the objects in the worksheet are classified as auxiliary objects in the algebra area. GeoGebra also set up a special organization to support teacher training, teaching experience sharing and scientific research. Its headquarters, International GeoGebra Research Institute, is located in Europe, and there are 159 GeoGebra research institutes in the world. China 2011On May 25th, under the leadership of Professor Cao Yiming from the School of Mathematical Sciences of Beijing Normal University, China GeoGebra Research Institute was established. As the chief research institute of GeoGebra in China, GeoGebra China Research Institute will lead and assist the construction and development of other research institutes in China. Committed to the research work of GeoGebra-related mathematics teaching and learning, awarded China GeoGebra user-level certification, provided professional training for normal students and front-line teachers, shared successful cases and advanced experiences in mathematics teaching and learning, and promoted cooperation among local research institutions in GeoGebra, China. Subsequently, with the efforts of Tianjin Normal University and Nanjing Normal University, Tianjin GeoGebra Research Institute and Nanjing GeoGebra Research Institute were established one after another, and Beijing GeoGebra Research Institute is under construction. User authentication This certification instruction is based on the GeoGebra certification guide provided by GeoGebra International Research Institute, and revised by GeoGebra China Research Institute in combination with the user certification requirements of GeoGebra China. The certified users of China GeoGebra Research Institute are divided into three levels: primary users: GeoGebra users (primary users), intermediate users: GeoGebra experts (advanced users) and GeoGebra trainers (training experts). Applicants can apply for primary or intermediate users according to their own level and the following specific requirements. Advanced users are training experts certified by GeoGebra Research Institute of China. Applicants need to be proficient in the use of software and have rich experience in using it, so they can only apply for advanced user certification after applying for intermediate user certification for one year. Applicants should send the application materials to the application mailbox according to the requirements of "application materials" applied by users at all levels. After being certified by China Institute of Geographical Sciences, the certificate will be issued. Novice user GeoGebra users (novice users) must meet the following conditions when applying for GeoGebra user authentication: 1. Operation requirements (1) Be familiar with various functional areas of GeoGebra, skillfully use drawing tools and be able to use basic commands. (2) Dynamic objects can be used to make attractive teaching courseware. (3) GeoGebra can be used to make ggb files, statistical charts, etc. And apply them to documents or web pages. (4) Have a certain understanding of GeoGebra's help function, and get help information in time when encountering unfamiliar tools or commands. 2. Teaching requirements (1) Understand the dynamic function of GeoGebra. (2) With self-made teaching materials, GeoGebra is used as a demonstration and display tool. (3) You can choose to use the existing GeoGebra courseware resources on GeoGebra website or other channels. (4) Have enough ability for students to participate in making courseware with GeoGebra. 3. The role requirement (1) is to be able to ask questions and seek answers in the GeoGebra forum, thus expanding the understanding of the software. 4. Application materials (1) Resume (2) Proof of using GeoGebra in teaching. Expert users (such as classroom videos, photos, etc. GeoGebra experts (expert users) applying for GeoGebra expert certification must meet the following conditions: 1. Operation requirements (1) Proficient in the use of algebraic expressions and commands. (2) Skillfully use advanced functions of GeoGebra, such as animation, list, dynamic text, conditional display, etc. (3) Be able to analyze the existing GeoGebra synthetic drawing method by using the drawing navigation function or other methods. (4) Ability to build customized tools and customized user interfaces. (5) Familiar with the advanced functions of dynamic worksheets. 2. Teaching requirements (1) Use GeoGebra as a teaching tool, and design the curriculum structure according to classroom needs. (2) Be able to modify and adjust the existing ggb files and dynamic worksheets according to local courses and students' needs. (3) Introduce students' use of GeoGebra and instruct them to use GeoGebra independently, so as to help them with discovery learning and mathematics experiments. 3. Role requirements (1) can answer questions raised by other users of GeoGebra User Forum. (2) Be able to produce and share creative teaching materials. (3) Actively contact other educators, promote cooperation and exchange, and share the experience of using GeoGebra. (4) To hold seminars to introduce the basic operation of GeoGebra to other colleagues, so that they can understand the methods of improving mathematics teaching by using educational technology. 4. application materials (1) resume (2) courseware made by GeoGebra. (ggb documents should be included, and specific courses should be indicated) (3) Teaching cases and schemes to improve teaching by using GeoGebra. (GeoGebra seminar minutes, results presentation and future activity plan. (such as activity videos, photos or conference papers, etc. Note: Normal students can obtain intermediate user certification by attending GeoGebra training courses in their universities and meeting the course requirements. However, applicants for GeoGebra trainers must submit the above materials. Training expert GeoGebra trainer (training expert) must meet the following conditions when applying for GeoGebra expert certification: 1. Operational requirements (1) Those who have applied for GeoGebra expert certification for one year. (2) Know how to get extra information and help when there is a problem in using GeoGebra. (3) Understand the different installation methods of GeoGebra and the differences between them. (4) Be able to write interactive exercises using JavaScript, and use the management system or. 2. Teaching requirements (1) Cooperate with local GeoGebra College to compile teaching materials and hold seminars. (2) hold seminars to provide opportunities for beginners and advanced users and those who intend to apply for GeoGebra users and GeoGebra experts certification. 3. Role requirements (1) participate in the construction of GeoGebraWiki, so as to promote the communication and cooperation among members in the user group. (2) Ability to independently research and publish papers. (3) Be able to report cases of using GeoGebra to improve teaching at teachers' exchange meetings or teachers' meetings. 4. Application materials (1) resume (2) electronic version 2)GeoGebra expert certification certificate. (3) Using GeoGebra to improve teaching cases and schemes. (Related papers on GeoGebra research. (pdf version or provide database link)