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II INTERNATIONAL CONFERENCE ON MATHEMATICS TEXTBOOK UNIVERSIDADE FEDERAL DO EST ADO DO RIO DE JANEIRO/ UNIVERSIDADE FEDERAL DO RIO DE JANEIRO
11MAY2017
MAKING DIGITAL MANIPULATIVES FOR MATHE-TEXTBOOKS: AN OVERVIEW OF THE NOWADAYS MAJOR USER-FRIENDLY SYSTEMS
Humberto Jose Bortolossi
http://www.professores.uff.br/hjbortol/
Universidade Federal Fluminense
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CONTEXT
Portable devices like smartphones, tablets, and notebooks are increasingly cheap and, in consequence, increasingly popular.
More than just a substitute vehicle for access to traditional paper textbooks contents, literature has pointed to how the use of etextbooks through this type of technology can potentially transform teaching and learning of mathematics (Pepin et al., 2016).
The Brazilian government's largest program of free distribution of Basic School textbooks (the PNLD program) requires competing publishers to deliver a digital version of the textbook with interactive resources.
PISA now includes computer-based assessments to measure digital proficiency to solve mathematical problems.
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CONTEXT
If you are in a project to write an e-textbook ( or even a paper textbook) of Mathematics and you want to create digital manipulatives for it, how to make them? Who will make them?
2013
SOCIEDADE BRASILEIRA DE MATEMATICA
Motivation: the free distribution of Android tablets for students in Public Schools.
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CONTEXT
If you are in a project to write an e-textbook (or even a regular textbook) of Mathematics and you want to create digital manipulatives for it, how to make them? Who will make them?
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Motivation: to produce collaboratively textbooks of Mathematics with academic excellence and open license!
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CONTEXT
Your textbook project could hire a specialized team of programmers. But ...
• This is very expansive ...
• Quite often, what you have asked them to do is not what you get (the same problem occurs with diagrams and pictures) ... Corrective interactions take a lot of time and patience.
• Who will update the digital manipulatives after the end of the contract?
• The programmers may be using a user-friendly system that you could be using too!
So, the focus of this talk is about user-friendly systems to make digital manipulatives.
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USER-FRIENDLY SYSTEMS
If you wish your digital manipulatives run across different platforms, then your user-fi-iendly system should expo11 to HTML5 + JavaScript + WebGL (for 3D).
Big advantage: math notation using MathJax/KaTeX (with LaTeX syntax)!
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DESCARTES
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License: LGPL (GNU Lesser General Public License)
Expression power: 2D and 3D diagrams, functions, bitmap images, sounds, videos, scripting, buttons, input fields, dropdown menus, etc.
Number of developers: 4.
Library size: 800 Kb (very robust and light).
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CINDERELLA
Geometry. Moth in Motion.
https ://www .cinderella.de http:/ /cindyjs.org
License: Apache 2. 0
Expression power: 2D and 3D diagrams, functions, bitmap images, scripting, buttons, sliders. It has a powerful math engine based on projective geometry.
Number of developers: 4.
Library size: ~400 Kb (very robust and light).
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GEOMETRY EXPRESSIONS
http://www.geometryexpressions.com http://euclidsmuse.com/
http:// geo metryexpressions. com/ gxwe b/
License: US$ 249.00 (but JavaScript files are free even for commercial use)
Expression power: 2D diagrams, functions, bitmap images, buttons, sliders. Powerful engine: constraint-based symbolic geometry!
Number of developers: 3 (?)
Library size: ~100 Kb (very robust and very very fast).
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GEOMETRY EXPRESSIONS
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GEOMETRY EXPRESSIONS
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GEOGEBRA
GeoGebra Dynamic Mathematics for Everyone
http://www.geogebra.org
License: free for non-commercial use. For commercial use (2015): $2.50
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10 000 books: US$ 5 000,00 by year
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GEOGEBRA
Ge Gebra Dynamic Mathematics for Everyone
http://www.geogebra.org
Expression power: 2D and 3D diagrams, functions, bitmap images, sounds, scripting, spreadsheet, statistical functions, buttons, sliders, checkboxes, dropdown menus.
Number of developers: 12 (GeoGebra has a large user community!)
Library size: ,..._,80000 Kb (very slow when the construction becomes a little bit complex; 3D: only simple shapes).
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GeoGebra Graphing Calculator
GEOGEBRA APPS
GeoGebra 3D
Very robust and fast!
Native Apps for Smartphones and Tablets
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JA V ASCRIPT PROGRAMMING
There are JavaScript libraries for almost every topic in Mathematics!
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Aten~ao: como o programa faz uso dos numeros harmonicas, que demoram a divergir, se a fra <;ao for maior do que 3, o programa pode demorar ou ate mesmo travar. Este aplicativo funciona tambem em tablets e smartphones.
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Decomposing fractions as sum of Egyptian fractions
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CONCLUDING REMARKS
There are good (and free) user-friendly options to develop digital manipulatives to be used withe-textbooks and regular textbooks!
Such user-friendly software allow teachers (and even students) to modify and adapt the produced digital manipulatives accordingly their needs.
Even if you project has a dedicated programming team, user-friendly systems may be used to test ideas and, also, to give a better notion about what is expected.
Technology by itself does nothing. It is important to think about how to integrate it properly in textbooks to enhance learning. The best software in textbook publishing is, by far, the mind of a good author!
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THANK YOU!