Graphical Representation
Graphical representation in mathematics refers to the visual depiction of data or mathematical functions using graphs, charts, or diagrams. It provides a clear and intuitive way to understand and analyze mathematical relationships, trends, and patterns. By representing mathematical concepts visually, graphical representation helps in making complex information more accessible and understandable.
7 Key excerpts on "Graphical Representation"
- Nicoleta Gaciu(Author)
- 2020(Publication Date)
- SAGE Publications Ltd(Publisher)
...3 Graphical Representation of data Chapter Objectives In this chapter, we will: introduce the concept of Graphical Representation of educational data present key principles for the Graphical Representation of data consider the essential features of different methods to visualise quantitative data understand how to create and work with tables and graphs in R correctly demonstrate examples from educational research to illustrate the use of graphs and tables for different types of variables and scales of measurement. The Graphical Representation of data is the process of transformation of data into information through a wide range of graphical displays, including graphs, maps, pictograms and tables in a symbolic representation. This process is a vital part of data analysis that facilitates the process of identifying, interpreting and understanding patterns or trends, which may not be visible in the raw data. It is also a useful and accurate communication tool for a range of educational stakeholders. A proper understanding of graphical display is one of the most important aspects of data analysis for students, teachers and researchers, helping them to avoid mistakes when summarising large data sets and analysing relevant patterns in quantitative data. For anyone engaged in educational research, it is very helpful to find relevant patterns in the Graphical Representation of data before performing any statistical tests or transforming statistical values into more meaningful concepts. The Graphical Representation of data depends on the type of quantitative data. For example, to organise and summarise categorical data, a bar graph can be used. For a time series, a line graph is recommended. Small data sets are usually easier to interpret if data is displayed in tabular form...
eBook - ePubStatistics for Psychologists
An Intermediate Course
- Brian S. Everitt(Author)
- 2001(Publication Date)
- Psychology Press(Publisher)
...For this reason researchers who collect data are constantly encouraged by their statistical colleagues to make both a preliminary graphical examination of their data and to use a variety of plots and diagrams to aid in the interpretation of the results from more formal analyses. The prime objective of this approach is to communicate both to ourselves and to others. But just what is a graphical display? A concise description is given by Tufte (1983). Data graphics visually display measured quantities by means of the combined use of points, lines, a coordinate system, numbers, symbols, words, shading and colour. Tufte estimates that between 900 billion (9 × 10 11) and 2 trillion (2 × 10 12) images of statistical graphics are printed each year. Some of the advantages of graphical methods have been listed by Schmid (1954). In comparison with other types of presentation, well-designed charts are more effective in creating interest and in appealing to the attention of the reader. Visual relationships as portrayed by charts and graphs are more easily grasped and more easily remembered. The use of charts and graphs saves time, because the essential meaning of large measures of statistical data can be visualized at a glance (like Chambers and his colleagues, Schmid may perhaps be accused of being prone to a little exaggeration here). Charts and graphs provide a comprehensive picture of a problem that makes for a more complete and better balanced understanding than could be derived from tabular or textual forms of presentation. Charts and graphs can bring out hidden facts and relationships and can stimulate, as well as aid, analytical thinking and investigation. Schmid’s last point is reiterated by the late John Tukey in his observation that “the greatest value of a picture is when it forces us to notice what we never expected to...
eBook - ePubStatistical Literacy at School
Growth and Goals
- Jane M. Watson(Author)
- 2013(Publication Date)
- Routledge(Publisher)
...Some aspects of the cognitive demands of coordinate graphing are common to the needs of plotting algebraic functions as well as statistical representations, whereas other demands are different for the fields of algebra and statistics. Gaea Leinhardt and her colleagues provided an excellent summary in the general field in 1990, 7 whereas Fran Curcio set the stage for graphing of data 8 and continued updating valuable background information with Susan Friel and George Bright. 9 More specific research on statistical representations has focused very much on the purpose for which graphs are required to be created or interpreted. Sometimes the research has overlapped with the interests of science educators 10 and sometimes more generally with those of psychologists. 11 Lionel Pereira-Mendoza and his colleagues contributed to the understanding of how young children work with pictographs and bar graphs, 12 whereas John Ross and Bradley Cousins studied high school students struggling with graphing association and correlation. 13 Little research has focused on students’ interpretation of graphs in the media but Cliff Konold and his team have considered students’ work with stacked dot plots and how these representations assist in the discussion of variation in data sets. 14 Setting aside distinctions of terminology and details of particular graph types, the important links contributing to an understanding of data representation are shown in Fig. 3.1. Usually several types of representations could be used to illustrate a connection or connections. Keeping in mind the curriculum model suggested in Chapter 1 (cf. Fig. 1.1), data representation is often seen, as it is here, as the link between data collection, often through sampling, and data summary, often through analysis of central tendency and spread. The initial question that led to the data collection, however, may still impinge on the type of data representation selected, and hence the connection is featured...
eBook - ePub- Wayne A. Wickelgren(Author)
- 2012(Publication Date)
- Dover Publications(Publisher)
...10 Topics in Mathematical Representation As stated in Chapter 2, problems contain information concerning givens, actions, and goals. The first and most basic step in problem solving is to represent this information in either symbolic or diagrammatic form. Symbolic form refers to the expression of information in words, letters, numbers, mathematical symbols, symbolic logic notation, and so on. Diagrammatic form refers to the expression of information by a collection of points, lines, angles, figures, directed lines (vectors), matrices, plots of functions, graphs, and the like. Often the same information should be represented using a variety of symbolic or diagrammatic notations. In fact, diagrammatic representation is generally labeled; for example, points, lines, and cells in a matrix have symbols attached to them in the diagram. Of course, problems are stated originally in some form, often relying heavily upon verbal language. The first step in solving such a problem is to translate from the representation given explicitly or implicitly in the original statement of the problem to a more adequate representation. This chapter is concerned with selected topics in the mathematical or precise representation of information in problems. Although precise representation of the information in a problem is the first step to take in trying to solve a problem, I deferred discussing this important topic to this late chapter of the book for two reasons. First, although some general statements can be made about the representation of information in a large variety of problems, most of the principles of representation are specific to particular problem areas. Effective representation for problems from some area of mathematics, science, or engineering depends upon knowing centuries of conceptual development in the relevant areas of mathematics, science, and engineering...
- Joan M. Kenney, Euthecia Hancewicz(Authors)
- 2005(Publication Date)
- ASCD(Publisher)
...It is also a pictorial language that uses visual models to communicate. How teachers use the language of pictures and diagrams to communicate with students and check for understanding is the subject of this chapter. The following scenarios involve students using or creating graphic representations in their mathematics classrooms. The first section, Reading Graphics, shows students dealing with technical usage as they read graphs, charts, and diagrams. What definitions do they assign the mathematical terms that their teachers use? What visual model does the word conjure up for them? How can working with graphic representations provide the teacher with insight into a student's thought processes so that what Pimm (1987) calls "semantic contamination" can be identified and addressed? The second section, Artful Listening in Mathematics, confronts the issue of mathematics' technical syntax. Here, students are drawing to learn. They are not copying exemplars into their notebooks for later reference but rather creating personal images of what they understand. How does syntactical subtlety lead them astray? How can the drawings that they create be a window on their thinking, especially for students who cannot adequately articulate where their confusion lies? Regardless of whether students are reading graphic models or creating them, the teacher's questions play a key role. In addition to providing feedback about student understanding, questions also serve a mediating function, helping students discover what they know (or don't know) as they attempt to construct mathematical meaning. In my role as a classroom-based staff developer, I observe middle school students and collect data for their teachers. After each of the lessons described in this chapter, I met with the teacher to reflect collaboratively on what I had noticed. The major reflection questions that we discussed are included at the end of each case...
eBook - ePub- Hugh Coolican(Author)
- 2018(Publication Date)
- Routledge(Publisher)
...Chapter 14 Graphical Representation of data This chapter deals with the representation of data sets in charts or graphs. In a bar chart frequencies of data in discrete categories are presented for comparison and this must be done fairly, without visual distortion. Line charts are useful for demonstrating a time series – changes over time in a measure of a person or group. Interval data points, grouped into continuous categories, can be represented graphically as a histogram or as a frequency polygon. Tukey (1977) promoted techniques of exploratory data analysis with an emphasis on thorough examination of patterns before submitting data sets to tests of statistical significance. Two methods are included here: stem and leaf diagrams, and box-plots. SPSS procedures are included for common types of chart. Graphs in general People who dislike statistics nevertheless tend to like drawing graphs. However they are also prone to putting far too many of them into a report to make it look more interesting. It’s worth stopping to think, just what is a graph or chart for? It is not to make your report look more scientific or credible. Basically it transmits useful information to your reader. It should be a way of summing up at a glance the main features of your data or some important aspect of them. If it doesn’t do that, if it isn’t easy to understand completely (without referring to the text in your report) or if it presents the absolutely obvious, then it isn’t a good or useful chart. Before you rush to produce what many students find to be the most artistic part of a psychological research report, do take note of some cautionary advice. Over-production and decoration – don’t scatter charts around your report showing every conceivable arrangement of data and in a profusion of pretty colours and patterns. You should be very parsimonious and only produce what will be helpful, not distracting, to your reader...
eBook - ePubThe Learning and Teaching of Geometry in Secondary Schools
A Modeling Perspective
- Pat Herbst, Taro Fujita, Stefan Halverscheid, Michael Weiss(Authors)
- 2017(Publication Date)
- Routledge(Publisher)
...Diagrams and Other Representations, and the Conceptions of Figure If the last section can be summarized, our discussion of the role of diagrams (and, we add, other concrete representations of figures) in geometry seems thus to leave us with the following observations: p.68 (1) Diagrams have played a crucial role in the historical construction of geometric knowledge, scaffolding this construction. Diagrams have made some properties transparent while others were being investigated, and have then supported the bringing of such transparency to question before retreating to the back to become mere illustrations of abstract concepts. (2) The use of diagrams in communication can be plagued by problems: not only can they lose information, but they can also add unintended information, and they can support multiple meanings with single signs. (3) A continuity between the elementary and secondary geometry, the latter building on earlier geometric knowledge, may require not the doing away with concrete representations of figure but rather the management of the use of those concrete representations so as to encourage mathematization. (4) Such management of concrete representations might be part of mathematization itself, as when the more incidental drawings that accompany thinking (Roth & Maheux, 2015) are turned into ready-made diagrams that can be used as models (Azzouni, 2013). 2.5. A Modeling Perspective in the Study of Figures We are proposing to conceptualize the study of geometry in secondary schools as a process of coming to know geometric figures as mathematical models of the experiential world...
