Juan Luis Prieto, Rafael Luque and a few other enthusiastic math professors decided to form the TEM Group in November 2011 because they realized their students needed more up-to-date knowledge and skills in addition to their regular curriculum. Initially, their main aim simply was to offer them space for reflection on mathematical concepts and the methods to teach them.

Soon enough they identified technology in math education as a major topic that is really necessary for their students. Similarly to other Latin American countries, in Venezuela the Bolivarian Government has decided to distribute computers to schools and children in order to provide the conditions for the integration of technology into education. They have given out about 3 million laptops to primary students. However, it remained necessary for teachers to develop skills and knowledge to apply them in their teaching practice.

Juan Luis claims that GeoGebra was a pretty obvious choice for them because of it being open source, accessible to everyone and easy to use. This is how it all started.
By today they have developed five scopes of action “Líneas de acción” as they call them and they structure their work along these lines:

1. Professional development for teachers and educators. They develop and organize GeoGebra workshops where teachers get an opportunity to re-think the way they teach mathematics and integrate modern technologies as tools to make their practice more effective. In 2012 they had 160 participants, among them there were primary school teachers, secondary school teachers of math, physics and technical drawing, pedagogical coordinators and students of math education.
2. Developing resources for teachers. They create GG activities and theoretical guidelines as well as technological resources for the workshops to hand out for teachers. These tool-kits help teachers see the mathematical content they need to teach in their classes in a new light.
3. Continuous self-study. The members of the TEM Group keep asking themselves: what do they need to learn themselves in order to better help their students? Towards that end they hold self-study groups led by TEM members and they invite national and international experts to assist them as “critical friends”.
4. Investigation- They build their projects of investigation- aiming at understanding better the processes that work in the improvement of math education – on the results of and conclusions from their workshops. Their university students, students of math education are integrated members of their group. The students are working on their own research projects, currently there are five in progress. Last year they presented for example at the Latin American GeoGebra Congress in Montevideo, Uruguay and in early 2013 at the International Pedagogical Conference in La Habana, Cuba. They are going to publish their results in their university’s journal as well as the GeoGebra Journal of the GeoGebra Institute in Sao Paulo, Brazil.
5. Social action- In addition to the narrowly science-related work the TEM Group also organizes awareness campaigns for making students more sensitive to social issues and problems of the education system. The explicit aim is to get their students more deeply committed so that they can apply the knowledge and skills they get from TEM  for the improvement of education in underdeveloped regions.

If you are interested in learning more about the TEM group or if you would like to cooperate with them you can reach them through their facebook page or e-mail: grupotem11@gmail.com

Photos:

In countries like India educational software technologies seem still out of reach due to internet access problems in schools and the high cost of most educational softwares. Since GeoGebra can be downloaded for free on a single laptop, then uploaded to many computers, and can be run without any internet access, it creates a favourable learning environment.

Other than Internet access, another critical factor is the IT knowledge of teachers working in a digital environment. A “higher aim” set in the Indian National Curriculum Framework now is to the develop the children’s inner resources to think and reason mathematically, to be able to come to logical conclusions and handle abstraction. This requires teachers to fundamentally change their teaching methods. That is also why professional development related to GeoGebra is not only about learning how to enter a digital environment, but also about discovering its new, pedagogical potential in everyday teaching.

Other than one-time workshops, regular follow-up activities and an easy-to-reach mentoring system are necessary, too, so that teachers feel more confident about the use of the software in their classes.

GeoGebra Institutes in India provide high quality, children focused trainings and support teachers while overcoming these problems.

After a successful GeoGebra workshop in Bhilai, another one was held also in India, 9 10th February, 2013 at the Delhi Public School in Patna, Bihar State. The workshop was organized by Delhi Public School in Patna in order to get the participating teachers acquainted with the use of the software and discuss how to integrate it into everyday teaching. Dr. Praveen Kumar Chaurasia (Assistant Professor, GI National Council of Educational Research and Training (NCERT), see http://pkchaurasia.iitiancollege.info/) was the resource person for the workshop, and focused his training on the possibility of using GeoGebra in child-centered learning, highlighting the pedagogical aspects of the software rather than technical ones. Dr. P.K. Chaurasia also talked about the National Curriculum Framework in India and its recommendation for child-centered learning which can be fulfilled using Geogebra. His experience tells us that children use GG as a cognitive tool that helps them to construct meaning based on their prior knowledge and conceptual framework. He showed the participants how to design applets using the software. Right after this session everybody created their own applets.

In the next blog post we will share the latest news about the work of GeoGebra Institute, Kerala, which is now linking GeoGebra with its empowering social business activities.

Guest post by Réka Berkes

• in Chrome (works best): http://www.geogebra.org/chrome
• or in other browsers: http://app.geogebra.org

Today we are announcing the new Spreadsheet view in GeoGebraWeb. You now have the Algebra, Graphics and Spreadsheet view available in your web browser, all based on HTML5 without the need for any plugins. It is now also working in 44 languages (with Hindi as a new language) and variants.

Our development team is continuously working to make GeoGebraWeb better, faster and add more and more functionality of our desktop application. It would be great if you could give us feedback and suggestions in our GeoGebraWeb User Forum.

What is working now:

• Graphics, algebra, and spreadsheet view
• Tools and style bar of the graphics view
• Input bar
• Open and save ggb files, also with Google Drive

What is coming next in GeoGebraWeb:

• Right-click menus
• Properties dialogs
• CAS view
• …

A similar kind of workshop is going to take place on Saturday, 19th January 2013 at Maitri College. Again the students will be from department of education (B.Ed. and D.Ed.) with mathematics background. I will share some of the photographs of the event also.

Guest post by Sanjay Gulati, GeoGebra Ambassador

Speed & Stability

As well as the usual bug-fixing and adding features, while developing version 4.2 we have rewritten large parts of GeoGebra so that it will be much more stable and also faster (much faster in some cases) than previous versions.

In particular, the following will be much faster:

• anything using the Sequence command
• the following commands when used on polynomials: Derivative/Integral/Tangent/Degree/Coefficients/Expand

Here is an example of a file using Derivative[ ] that is much faster in GeoGebra 4.2.

Here is a very nice demonstration of volume of revolution by Daniel Mentrard running in GeoGebra 4 and here is the same file in GeoGebra 4.2. Drag the red point marked “View3D” to see how much faster it is.

CAS View

The long awaited view for symbolic calculations is here. It allows you to symbolically factor, expand, differentiate or integrate expressions that may include parameters, and it is dynamically connected to all the other views. The documentation is available at http://wiki.geogebra.org/en/CAS_View.

Here is an example showing how the CAS View interacts with the Graphics View. Drag the points A, B, C to see the exact calculation of the coordinates change.

Features

The feature that’s taken the most programming time in this release is that worksheets can now be viewed on devices without Java (eg iPads, Android Tablets, Chromebooks). The best way to make use of this is to upload your applets to GeoGebraTube (File -> Share) and then the conversion will be done automatically. At the moment only the Graphics View is supported. You can test how worksheets will look and behave on tablets by adding ?mobile=true on the end of the URL in GeoGebraTube, eg
http://www.geogebratube.org/student/m20510?mobile=true

The Pen Tool has been enhanced so that it now creates a PolyLine rather than drawing to a bitmap. Together with new Delete Tool (drag a “rubber” to delete) it’s now much easier & better to use.

You can now drag a parabola, but keep its vertex fixed. Just hold down <Alt> when dragging!

The Rigid Polygon Tool has been enhanced with a small but useful feature: simply click on a polygon to make a “rigid” copy of it (ie the copy can be rotated and translated by dragging)

Neel Shah, as part of Google Summer of Code, has programmed some shape recognition algorithms for the Freehand Shape Tool, which will recognize circles, lines, line segments, triangles and quadrilaterals. It works very well on an interactive whiteboard (IWB).

You may also check a nice overview of new  features by Guillermo Bautista
and there are brief details of the hundreds of other changes in the Official Release Notes.

Power

Kai Chung Tam has programmed the PSLQ algorithm for us in Java which allows a Surd to be numerically reconstructed from a decimal. So for example SurdText[2.414213562373095] returns a nice FormulaText ie [latex]\sqrt{2}+1[/latex]. See here for an example.

We have made it much easier to make worksheets with slopefields and the particular integral like this.

All you need to type is:

f(x,y)=x/y
SlopeField[f]
A=(1,1)
Locus[A,f]

If you need more control over the spacing, there are some options, see the online manual.

Sergio Arbeo, as part of Google Summer of Code, has added a new command LocusEquation. This will calculate the equation of a (geometrical) locus using Gröbner bases.

For example here is the (numerical) locus of a parabola with the calculated (exact) locus overlaid.

Photo by Robin Smidsrød

The summit took place at the Google Headquarters in Mountain View. About 300 mentors worldwide came together to have an unconference about participant-driven topics including student selection process, events, financial questions of open source development, free software in education, and more. Lots of important FOSS took part in the sessions like LibreOffice, The GNU Project, KDE, Gnome, PHPBB, Joomla, Mediawiki, Inkscape and Xapian. GeoGebra was represented by Balázs Koren and Zoltán Kovács from Hungary and Austria.

Mentors from other mathematics related free software were also participating, namely Virgilio Gomez Rubio from the R project and Burcin Erocal from Sage. GeoGebra already has some kind of direct connections to both software, and this meeting was a good time to plan further developments between us.

As usual, Google offered a great hospitality to all participants. California was sunny during these days and it was a perfect time to make excursions to important places of the Silicon Valley and San Francisco as well.

San Francisco and the Golden Gate bridge from North

Ivan Petrović, PhD student at University of Belgrade

The EACA conference has just ended, but the hard development in theorem proving did not stop. Our Serbian contributor Ivan Petrović did very nice improvements on GeoGebra by working hard on the OpenGeoProver (OGP) prototype during the last week. Now the desktop version of GeoGebra has 5 possible ways to prove a statement, and OGP, the latest one, does a really good job.

Predrag Janičić, associate professor at University of Belgrade

Now the recent benchmarks show that Ivan’s prover (based on Predrag Janičić‘s GCLC, but fully rewritten in Java) gives the correct answer in 40 out of the 44 test cases, and beats the other provers in the most difficult computations, namely the Desargues’s theorem and the Simson line. In general, it has the second best average in computation time (Recio: 89, OGP: 315, Botana: 540, PureSymbolic: 2091 ms), and the best standard deviation (OGP: 250, Recio: 399, Botana: 2226, PureSymbolic: 9467 ms), which means OGP is the most stable prover engine for GeoGebra at the moment. (The 5th prover is the Auto method: it tries to find the best prover engine by using some heuristics. This is the default in GeoGebra.)

The official announcement of our joint work will be on 22 June at the CADGME conference in Novi Sad, Serbia.

Both of my kids are also GeoGebra fans, but they are too young to really understand the difference between proof and verification yet. A proof is a theoretical confirmation that a statement (for example, “the bisector lines of a triangle are concurrent”) is always true. A verification is usually an experiment, that the statement is indeed true, by choosing a large set of examples.

GeoGebra is not the first software which provides proving. The first pieces of software were written back in the 1980’s. But oddly enough, many of the first scientific papers were also written by researchers of University of Linz, lead by Professor Bruno Buchberger, founder of the Gröbner basis theory.

Now GeoGebra has several built-in methods to decide if a statement is true in general or not, and one of the used methods is based on Gröbner bases. To avoid heavy computations on a single workstation, we can outsource them to another software, namely Singular, which runs as a web service remotely. On the other hand, we also use a sophisticated method to avoid symbolic computations completely. Professor Tomas Recio, a Spanish expert of algebraic geometry, developed this idea, and Simon Weitzhofer (mentioned in my first post) implemented it in Java recently.

Luckily enough, even other colleagues joined us from different countries. Professor Francisco Botana, a pioneer in open source based mathematics, also from Spain, and Professor Predrag Janicic from University of Belgrade, lead developer of GCLC, offered their help in extending GeoGebra with state-of-the-art methods to provide fast computations. Also Ivan Petrovic, a PhD student of Predrag, works on the open sourced, Java based OpenGeoProver, to enhance it to be an optional prover engine for GeoGebra. We also have a Google Summer of Code 2012 student, Damien Desfontaines from Paris, France, in our group, who helps Ivan to implement the area method, to extend the set of applicable statements for proving. One day maybe we will have readable proofs as well, since the fast algorithms usually don’t give acceptable output for a human. But currently we are really satisfied with some yes/no/unknown result, which should also be used in both experimenting and teaching mathematics.

The basics are working already good, fast and intuitively enough. See this table for an overview: Botana’s method is the Singular based Gröbner basis calculation, pure symbolic method is just dealing with parametric polynomials in Java internally, the OpenGeoProver backend is not listed yet. (The numbers mean milliseconds.) One can also try Recio’s method (and as fallback, the pure symbolic method) in the web version of GeoGebra, or wait for the desktop version (4.1.81.0 should be stable enough, but it is not released yet at the moment), or just watch this YouTube video. For those who are interested in the details, the documentation of the Prove and ProveDetails commands will also help.