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3 (B): De Winne Ivan GeoGebra and Moodle integration

Abstract. How to improve the GeoGebra filter to integrate GeoGebra applets in the Moodle VLE ?

The Moodle VLE is used to offer online training courses for math teachers on the didactical use of GeoGebra.

Mathelo offers also homework help for students.

http://www.mathelo.be 

 

My proposal ...The GeoGebra filter allows users (teachers) to embed GeoGebra files in Moodle webpages, forums, quizzes by creating a link to the .ggb file using (as usual) the link symbol in the editor bar. It should be possible to use a GeoGebra plugin for Moodle to insert GeoGebra applets directly in Moodle’s html editor.

• The users clicks on a new GeoGebra icon in the Moodle html editor
• This starts the GeoGebra web-application in a popup window
• The user creates a GeoGebra file and saves it.
• The result is stored in the Moodle system.

Because this html editor is available in the forum it can enrich the forum for students as a kind of studyhelp. Students post there questions and GeoGebra applets inside the system.

This extended hml editor can also be a great help for teachers to create quizzes, lesson plans with interactive elements.

 

4 (A): Walther Neuper. On analogies between geometry and algebra on computers

Abstract. ((this talk also concerns (F) "research ideas/topics", "international research projects"))

One reason for GeoGebra's success in education is the strength in two domains at once, in geometry and in algebra. GeoGebra is able to handle two different representations of one and the same mathematical concept in parallel --- and thus supports the learner in filtering out the essence, and in developing abstractions of the mathematical concept.

This talk will try a gedankenexperiment: Let us replace GeoGebra's algebra system by an experimental single-stepping algebra system under development at TU Graz, www.ist.tugraz.at/projects/isac, --- what would be the consequences and what questions would be raised ? Being aware of their sketchy nature, we mention three points.

(1) The algebraic objects become concern of stepwise construction: a formula (i.e. a function, an equation) is being rewritten by a step applying a rule which results in another formula, and so forth until the stepwise construction reaches some final result.

Thus algebraic objects become more analogous to geometric objects, since GeoGebra supports stepwise construction of those objects already --- analogies are an important prerequisite for abstracting to the respective mathematical concept!

(2) The single-stepping system is a logic-based system: all rules used for transforming formulas can be inspected in the context where they are profen, and in the context where they are applied. In principle the system allows to trace down any rule to the respective axioms and definitions.

What an analogy between algebra and geometry could mean in this point, is still an open question to the author.

(3) If both kinds of objects, the algebraic and the geometric ones, can be stepwise constructed --- how relate steps on the both kinds?

This question also is an open one for the author at the time being.

Tackling such questions is the aim of a special track at CADGME under the title "Convergence on Mathematics Assistants".

 

5 (A): Dani Novak. Ideas for enhancing GeoGebra

My actual updated presentation is in and includes a video

http://docs.google.com/View?id=dhgj3bkq_1410cmx8grf8

 

Abstract. Currently GeoGebra appeals to teachers because it is such an easy and intuitive tool to teach mathematics.  However it is hard to imagine most students using it on their own without a reason.  In my presentation I would like to share ideas from a language that I designed with a colleague and hopefully inspire the developers of GeoGebra to add features that motivate a wider audience.

In my 5 minute presentation to the group I would like to present a language that I designed with David Rosenthal who programmed in java (one can get it from http://familymath.org/seelogo).  I would like to share ideas with the developers of GeoGebra and see if some of these ideas can be integrated with GeoGebra.  One very simple idea is the ability to allow various input modes (like percent and fraction to exist).

I would like to explore with the group possibility of adding more "game like" features to GeoGebra (The SeeLogo language has a game mode that kinds love to use since they can use their imagination.   (Scratch also has similar feature)  Currently GeoGebra is primarily designed for teachers who want to teach math concepts but it may be possible to extend this to allow situations (like the micro worlds Seymour Papert was taking about in his book "Mind Storms")  where students could play and discover on their own.

See http://docs.google.com/Doc?id=dhgj3bkq_1102hpq99mj5

 

12: Michael Gage. WeBWorK -- GeoGebra applet interface

Abstract. A brief description of the applet API deployed by the online homework system WeBWorK and how it might interact with GeoGebra.  Here is a brief description of the WeBWorK applet API from

http://webwork.maa.org/wiki/Applets . There are specific examples of applets in WeBWorK at

http://hosted2.webwork.rochester.edu/webwork2/applet_dev

and PointAndGraph_AppletDemos

You can use the guest login to view the examples.

Submission #12

 

18: Peter Richert and Jan Becker. Vom eLearning zum iLearning

Abstract. Die Zeit ist gekommen für den Übergang vom eLearning --- dem electronic learning --- zum iLearning --- dem interactive learning --- das zum einen auf dem klassischen eLearning aufbaut, zum anderen aber durch die Interaktion mit dem Lernenden einen völlig neuen Ansatz enthält.

Mit dem Tool GeoGebra ist es möglich, den Lösungsfortschritt bei einer Aufgabe zu überprüfen, ohne die Lösung zu verraten. Leider bekommt man die Lösung dann auch nicht gezeigt, wenn man nicht mehr weiter weiss, kann dann aber im eLearning Script die Theorie nachlesen...

Durch die Verbindung von Netzwerkberechnungen der Elektrotechnik und derdynamischen Mathematik-Software GeoGebra im neu geschaffenen iLearning-Tool konnte auf Basis von javascript und klassischem html / php dieser völlig neue Ansatz realisiert werden.

Submission #18

 

38: Katja Prnaver, Stanislav Šenveter, Vesna Zmazek and Jernej Regvat. Including Sound in GeoGebra Applets

Abstract. GeoGebra helps us creating interactive e-material. We consider dynamic, interactive mathematics as using Drag&Drop principle for moving mathematical objects and learning the relation between them. For mathematics in early years of school, it is important to have a possibility to add audio elements to evaluation or presentation of instructions, questions and results. This gives a child in early years of primary school, especially to those with troubles reading or with special needs, very effective and didactically welcomed audio instructions. Depending on their behavior and/or solution, given by the movement of elements in applet, a sound is played to the child, depending on the correctness of their answer. Moreover, an additional explanation of terms or instructions to new exercise are provided.

We have used GeoGebra's support of communication using JavaScript in HTML environment, making it possible to control the applet on the website. Consequently, we have decided to implement sound in our applets. First of all, a simple example of interaction has been created in HTML, and linked to one of our applets, which was ready for sound communication, and used JavaScript functions and sound manager. The sound is turned on/off at certain state of applet or at a predefined value of a variable in applet. This variable is either controlled within applet or is given values that accordingly turn the sound off or on in JavaScript/HTML environment. Since this procedure requires quite some programming knowledge, we have developed an e-learning unit within Exe Eum program. A teacher with good knowledge of GeoGebra and Exe Eum, but with lesser knowledge of programming, has now an option to link the applet with sound using the graphical interface implemented in Exe Eum. This makes creation of applets, which are to be linked with the sound, possible for authors with no programming knowledge.

Procedure of creating e-material/didactic game: First of all, a scenario of learning situation or didactic game needs to be designed. Based on the design, an applet is created. In this applet, we need to plan the sounds to be run at certain moment. Finally, the Exe Eum tool is used to link appropriate sounds to the predicted applet variable values.

To give a better idea on what is possible to create with the described procedure, a simple applet is shown. The applet presents dynamic presentation of number comparison, resulting in an interactive game - a tool to learn number comparison through a game.

 

42 (A): Tatsuyoshi Hamada. The harmony of mathematical software and free documents on KNOPPIX/Math

Abstract. KNOPPIX/Math offers many documents and mathematical software packages. Once you run the live system, you can enjoy a wonderful world of mathematical software without needing to install anything yourself. The KNOPPIX/Math project began in February 2003. Project members included many mathematicians, mathematical software designers, and writers of free documents. Once a year, we released the newer edition of KNOPPIX/Math, the current version KNOPPIX/Math/2009 was presented at the MSJ (The Mathematical Society of Japan) annual meeting (March 25--29, 2009) at Tokyo University.

We can try several dynamical geometry software on one DVD, for example, C.a.R., DrGeo, GeoGebra, GEONExT, KSEG, KidsCindy, Kig, PyGeo, and GeoProof. We also include some documents, examples and flash movies of these systems. For the usability of open source software systems, in some universities and high schools, KNOPPIX/Math is already used as an educational tool. Mathematicians and researchers in related areas are using KNOPPIX/Math as their desktop environment, and are using it for education, research and demonstration of various topics.

 

49 (B): Peter Tierney-Fife. Work of Peter Tierney-Fife of Education Development Center, Inc. with GeoGebra and Online Systems

Abstract. I work on and support multiple teacher professional development and exploratory research projects that incorporate GeoGebra and other mathematics technology resources.  Much of the recent teacher professional development work of Education Development Center (EDC) in Maine, USA, targets mathematics teachers of middle grades and high school (ages 12-17) students. A common thread across projects is the use of technology tools to enhance mathematics learning and teaching. We train teachers to use GeoGebra and we also design GeoGebra tools for and in collaboration with teachers, and host these tools on our Moodle site (http://maine.edc.org - the GeoGebra tool lists are at the bottom of the page). Many of our uses of GeoGebra are as an authoring application to create applets for student exploration of key concepts and to remediate common misconceptions or areas of difficulty. Most of our recent projects also have a project-specific Moodle course/site that is used during professional development, acts as a repository of professional development resources,  and allows for an online community space for participants (for an example site without participant information, see http://maineoer.edc.org -  click on GeoGebra in Algebra I).

I would personally love to see a comprehensive and searchable tutorial site with topics and examples that are explained in small, detailed steps for teachers, with screencasts and sample GeoGebra files to download.

We would love to see expanded capability within GeoGebra and in connection with Web-based resources for data capture (such as saving tool state and number values) and, ideally, some kind of classroom-level data analysis tool and interface.

For short presentation outline see: http://maine.edc.org/file.php/1/Tierney-FifeGGBConf.html

Submission #49

 

50 (A): Eno Tonisson. Some Remarks on Integration of CAS in GeoGebra

Abstract. The remarks are based on a comparative study of different computer algebra systems, an impression of GeoGebra and a brief testing of the GeoGebra CAS (GeoGebra 3.3.10.0 March 29, 2009). The first part of the text is focused on the CAS in GeoGebra. The second part of the text includes some aspects that are gleaned from different CASs with relation to school mathematics. Hopefully, the aspects could be taken into consideration in development of the GeoGebra CAS.

Submission #50

 

57 (A): Francisco Botana, Jose Valcarce, Jesus Escribano and Miguel Abanades. Adding symbolic proving and discovering capabilities to GeoGebra

Abstract. While GeoGebra can work wonders illustrating geometric properties, these can seldom be justified and become no more than visual proofs. Adding symbolic capabilities to GeoGebra would allow not only to prove known results, but also to discover new properties in a mathematically sound way.

The modification proposed is the implementation of these capabilities in GeoGebra together with the reported ongoing CAS integration.

• GDI (videos)
• Prove and discover geometric properties: LAD, LADucation.
• Connecting CAS and DGS: GeoGebra and SAGE.

Submission #57 

 

60 (B): Bernát Kalló. Ideas to improve the GeoGebra wiki

Abstract. Trying to face the roots of the problems with GeoGebraWiki.

To be honest, GeoGebraWiki is not very comfortable. I was thinking about the reasons and found out the following:

Firstly, it's not very well organized. We do not use features like categories, redirections, namespaces and templates. Instead, we only use topic pages, which make the whole thing very hierarchical. Secondly, it's rather black-and-white (and blue, of course :-). Usually, what makes a wiki look more colorful is templates. Another huge problem is that all languages are in the same wiki. This makes features like random page and lists of pages useless, may cause name collisions, and it's difficult for non-English users to use the English interface. However, as I see it, the root of most problems is the lack of a working wiki community. All discussion is carried out on the forum, and, consequently, there's no discussion about the wiki. Wiki discussion should normally happen on talk pages. People with many languages being in the same wiki also makes communication difficult.

So what I suggest is:

* Put different languages in separate wikis.

* Start a community.

* Start using organizational features.

I'll detail these a bit deeper in my presentation.

Submission #60

 

63 (A): Kurt Söser. Touchscreen and GeoGebra

Abstract. On October 22nd, Windows 7 comes to life for public users. One of the main new features is a (Multi)Touchscreen supported interface. Let's imagine to use GeoGebra with your fingers and/or stylus and use all the helping sort of things we probably know from the IPhone (Zoom,...). Maybe there is a way to use a ruler and a stylus for input in GeoGebra.

With new tablet computers coming out later this year it could be a fascinating way to do mathematics on a pc, especially for pupils. Of course there has to be some changes in the user interface, but this could be easily done by custom tools.

By the way: another thing in Windows 7 is the new mathematics input, which can change handwritten math symbols into computer text. This would be a great addendum to the normal LaTeX input abilities of GeoGebra.

Another thing I would like to show the participants: I figured out a whiteboard-like system with the Wii-Mote an a Infra-red pen. (http://johnnylee.net/projects/wii/)

 

65 (A): Ilya Serbis. Authoring utility for dynamic worksheets with solution checking creation

Abstract. GeoGebra is very convenient tool for creating and manipulating geometry constructions. But when you want to check whether the problem has been solved and all objects were constructed as it should be GeoGebra is almost inappropriate.

Consider a problem: “Construct a point equally distant from a 3 given straight lines”.

To implement check for such a problem you should communicate with reach GeoGebra's JavaScript interface. You need to write program on JavaScript to check whether bisectors and cross point were constructed.

So I propose to create an independent utility which will have a high level interface and to be aimed to generate such a programs (or complete html pages). Using it everyone who have no JavaScript knowledge could create dynamic worksheets with check.

The simplest way to set up check rule is to construct required object and tell the utility that the same object should be constructed by students. Also it may be a set of rules (for example length(a) > length(b); the point which is cross of triangle EFG bisectors lays inside polygon BCD; number of lines on drawing <= 3 and so on).

The utility can also have an ability to add buttons and labels to show some tips. Scripts will enable them by special conditions (may be after some student’s right construction steps)

 

70 (A): Ilya Serbis. Some handy interface features

Abstract. Propose to add keyboard shortcut for every essential tool and visual "mouse tips" to guide user throw the process of constructing. For example, mouse cursor for perpendicular line tool could look like at the begining  and like after that. (see Submission #70)

I have seen this in Russian DGS MathConstructor

 

71 (B): Peter Kortesi and Pellumb Kllogjeri. Extended help files for GeoGebra

Abstract. We plan to develop an extended help for GeoGebra, which contains beside the

detailed description of the commands, some examples of the use of it, and some cross links to related commands well.

The aim of the examples is to make it more easy to handle the commands, as it can be used in a copy+paste form, and check the result.

Sample for the command LowerSum

Command: LowerSum[f,a,b,n]

f : function

a: left limit of the sequence (left bound)

b: right limit of the sequence (right bound)

n: the number of subdivions of the sequence [a,b]

Description: The command will return the lower sum for the area of the lower approximating rectangles of the area limited by the curve  y=f(x), the lines:x=a, x=b and y=0.

Examples:

1. f(x)=cos(x)+sin(x)

   LowerSum[f(x),0,sqrt(10),10]

2. f(x)=cos(x)+sin(x)

   LowerSum[f(x),0,22/7,n]  (Remark: Put n as a slider taking values n=1,2,…50)

3. f(x)=2*x^2-5*x+2

   LowerSum[f(x),a,a+b,n] 

   (Remark: Put a as a slider taking values between -4,4, b a slider taking values between 0,5, and n as a slider taking values n=1,2,…100)

See as well: UpperSum,  Integral.

 

79 (A): Josef Böhm. Some Ideas

Abstract. I have been a CAS and DGS user for many years as a teacher in secondary school and in pre- and in-service courses for teachers as well. I also have been in connection and communication with the respective software developers. My main interest is bringing all the benefit of CAS and DGS (and spreadsheet features) together to have a more or less all-purpose tool for modern technology supported math education.

The main issue will be how to link the dynamic geometry, the spreadsheet and the future CAS (& the future 3D-geometry?) in such a way that it can easily be used not only by experts and highly motivated teachers but also by the average teacher and pupil.

There is a unique chance to design a real “pedagogical” CAS from the very beginning. A lot of very experienced teachers who have worked with various CA-sytems can bring in their expertise and can help avoiding errors and “pedagogical gaps” appearing in other systems.

The strength of GeoGebra as it is its intuitive use and the developers must take care that this highly appreciated property might not get lost by overloading the wholes system. (Sometimes less might be more!)

It might make sense to create a rough time table for significant steps in developing the CAS (and 3D?) functionalities.

Besides that I am very much impressed by the CAS-features implemented in the background of GeometryExpressions and I wonder if something similar could be possible in a future – future – version of GeoGebra.