Technology Tips: Constructing and Exploring Pascal's Triangle in TinkerPlots
| Autor: | Shannon O. Driskell, Dan MacKinnon, Kathleen Lynch-Davis |
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| Rok vydání: | 2009 |
| Předmět: |
Programming language
business.industry Pascal (programming language) Pascal's triangle computer.software_genre Binomial theorem Constructivist teaching methods symbols.namesake Software symbols Calculus Probability distribution Fathom business computer Pencil (mathematics) Mathematics computer.programming_language |
| Zdroj: | The Mathematics Teacher. 102:628-632 |
| ISSN: | 2330-0582 0025-5769 |
| DOI: | 10.5951/mt.102.8.0628 |
| Popis: | Shannon Driskell Shannon.driskell@notes.udayton.edu University of Dayton Dayton, OH 45469 TinkerPlots software allows users to engage in data analy sis through the construction of graphical representations of data that can be shifted and changed dynamically. Based on its sister program, Fathom , TinkerPlots takes a constructivist approach to displaying data?that is, users construct, rather than select, types of graphs?thus allowing the creation of a surprising range of charts, tables, graphs, and other mathematical visu alizations that fall outside traditional categories. An example of the unusual visualiza tions easily constructed in TinkerPlots is a dynamic version of Pascal's triangle (see fig. 1). Pascal's triangle is encoun tered in many contexts in school math ematics: Elementary school students are often encouraged to explore its patterns, while secondary school students deal with it when discussing the binomial theorem, recursion, combinations, and probability distributions. Constructing Pascal's triangle within TinkerPlots is a good way to gain a deeper understanding of its mathemati cal structure while learning how the software can be used to generate and display data. In addition, TinkerPlots presents a vehicle for exploring Pascal's triangle far beyond what can be accom plished through pencil and paper alone. In this environment, the triangle can be extended over and above what can be calculated manually, and the many pat terns within the triangle can be explored dynamically by shifting between views and by transforming the data. For most uses of TinkerPlots involv ing data analysis, the values of attributes are typed in directly or imported from an external source. The TinkerPlots construction of Pascal's triangle is an example of generated, or programmed, data?that is, the software has been instructed to generate the data directly rather than by using measurements or other observed data. The activity described in this article uses the soft ware's built-in functions, which allow attribute values to be created from formulas. A user with an understanding of the basic structure of Pascal's triangle |
| Databáze: | OpenAIRE |
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