I had been looking several years for good classroom mathematical modeling software; when I discovered GeoGebra, it was an memorable day. I sat with a laptop in my recliner and didn’t get up for three hours, just playing and exploring. Whatever I asked GeoGebra to do, it did with ease and precision. Since then I’ve used GeoGebra in all my classes, given several conference presentations and workshops for districts, and become a Resource Manager and Trainer for the California GeoGebra Institute.

GeoGebra is well suited to promote equity in the math classroom:

• It is free, open-source software

• No internet connection is necessary

• No programming experience is needed

• It is intuitive, user-friendly, and easy to use

• GeoGebra has been translated into 52 languages

• It can run on all platforms since it is written in Java

• There is a version for new/younger learners and users

• There is a worldwide network of support from a user forum

• It creates multiple representations as equations, graphs, tables

• It can be used from primary grades through college level courses

In spite of affordability (FREE) of this software, implementation of GeoGebra is still not widely seen. When a teacher uses a software tool, it is much more likely that students will use it. Here’s my story about introducing GeoGebra in my classroom: I started the program and let students view it using my LCD projector; then I asked a student to come up and sit at my desk. I instructed her to press certain icons to create a diagram, and within two minutes she had stopped listening to me and was running the program on her own – it’s that easy! After giving a basic introduction to the program, all my classes were then able to visit the campus computer lab and create, explore, learn, and play with the mathematics in multiple representations.

Students easily use calculators because they are familiar with the mathematics underlying the keys they press, and so I’ve been able to teach graphing calculator skills and mathematics concepts at the same time. It’s possible to do the same with GeoGebra, since there are few barriers to entry. Teachers accept and promote the use of calculators in learning many concepts in mathematics; we need to promote GeoGebra as well in a similar, but stronger fashion, since the potential for learning is much greater.

GeoGebra was designed specifically for teaching mathematics, and its rich multiple representation environment invites exploring and creating virtual models and simulations. There is a large international support system of educators and an increasing number of articles, videos, books, and ready-made materials for classroom use. Those interested in the growing STEM education and collaboration movement will find this technology to be a welcome breath of fresh educational air. To give you an idea of the popularity of this software, there were more than 7 million visits to the main GeoGebra website, www.geogebra.org, in 2011; the visitors came from 226 countries and territories. 

We need to provide free and open access to powerful mathematical modeling tools and strong mathematics curricula to all students and educators without regard to age or background. My verdict: GeoGebra is a sure winner, and I strongly encourage all teachers to get comfortable with this software so their students will be better able to develop mathematical minds with this easily accessible and friendly tool. Enjoy!

KenKen 6x6 Number Sense

KenKen is a self-motivating puzzle that builds number sense. As an added bonus, using this teaching and learning tool builds creative logical thinking and patterns of self-reliance. It also develops strong focus for an extended period of time, a necessary skill in mathematical problem solving. This article spotlights some of the prime factorization, number trees, and number combinations found in KenKen.

KenKen and Sudoku share two of the same rules, which makes an easy transition for teachers and students: numbers in each row and column must not repeat. The third rule sets KenKen apart as being more mathematical than Sudoku. In KenKen there are Cages, which are heavily outlined areas with specific numerical properties.

The most commonly used puzzles for classroom use are 4×4, 5×5, and 6×6. As with Sudoku, KenKen comes in several levels of difficulty. This allows the instructor to introduce the puzzle at the elementary level, and then gradually ramp up the challenge level as students are ready.

Here is a 6×6 KenKen from the 3-7-12 issue of the NY Times at the Medium difficulty level:

What I suggest solvers do is write the possible numbers at the top or bottom as on a number line. This gives a sense of number magnitude and provides a great help when solving.

A. Look at the 9+ cage: How many different sets of three numbers add up to nine? Hint: there is more than one way.

B. Check out the 4+ cage: How many different sets of three numbers multiply to 4? Again, there is more than one way.

C. Now let your eyes rest on a similar region, the 24+ cage, with even more possibilities. Hint: what is the prime factorization of 24, and how many ways can you make a factor tree for 24?

By looking at numerical possibilities, along with other clues from rows and columns, it’s possible to solve this KenKen by logic and reasoning alone, with no guesswork. This is the hallmark of great mathematical thinking!

Every teacher that has talked/emailed me after using KenKen with students is enthusiastic in support of this methodology. Students always look forward to doing KenKens, and it’s always a great addition to a Friday workday, or useful as extra credit. Give it a try, and you will be a hero with your students!

KenKen puzzles can be found for free on several websites. Here are my two favorites, which publish six new puzzles daily: www.nytimes.com/ref/crosswords/kenken  and  www.kenken.com

The second site also has allows participants to receive regularly via email a nine page PDF file with KenKen puzzles in sizes from 3×3 through 6×6, including answers – something for everybody!

http://www.youtube.com/watch?v=oJcZMO6Uh1o

GeoGebra first steps advanced customizing

GeoGebra Video First Steps-Advanced Customizing demonstrates five areas to modify the graphing area in GeoGebra to suit your graphing style. Learn how to:

• Control the x-y Settings, grid and axes and the size of the graphing window
• Set Bold, color attributes for grid
• For the x-y axes, set positive direction, distance, tick marks
• Choose from the 3 different types of graphs
• Set x:y scale ratio to suit various types of graphs 

After you view this video, you will have the graphing area in GeoGebra set up exactly the way you want it so that you will be more productive and comfortable.

http://www.youtube.com/watch?v=HYG-75nDeGg

This is the first of a four-part series in getting started with GeoGebra. Here are links to the other parts:

Video-GeoGebra-First Steps-Downloading

GeoGebra Video First Steps-Basic Customizing

GeoGebra First Steps-Intermediate Customization

http://www.youtube.com/watch?v=kqEb7A8YjAk

This is the first of a four-part series in getting started with GeoGebra. Here are links to the other parts:

Video-GeoGebra-First Steps-Downloading

GeoGebra Video First Steps-Basic Customizing

GeoGebra First Steps-Advanced Customizing

GeoGebra logo

There were more than 7 Million visits to www.geogebra.org in 2011; this compares to 5 million in 2010. The visitors came from 226 countries and territories. 

Please visit and share these pages to discover the best GeoGebra materials and coolest math-loving people!

• GeoGebra Institutes

• GeoGebra User Forum

• GeoGebraTube

• GeoGebra Facebook Page

• GeoGebra Twitter Page

• GeoGebra on LinkedIn

• GeoGebra on Google+

This information comes from the GeoGebra Year 2011 Report. You may read the entire report online there.

• view grid and axes

• Get to the Home Position easily

• Set your font size for you and for classroom/large audience viewing

• Set your text defaults for on-screen writing

• Set your default drawing options for point, lines, and other shapes

After you view this video at my Math Video University site, you will be off and running towards setting up GeoGebra exactly the way you want it. Enjoy!

This is the first of a four-part series in getting started with GeoGebra. Here are links to the other parts:

Video-GeoGebra-First Steps-Downloading

GeoGebra First Steps-Intermediate Customization

GeoGebra First Steps-Advanced Customizing

GeoGebra Video

GeoGebra – First Steps – Downloading

is a tutorial showing the viewer how to navigate to the GeoGebra website and download this free open-source dynamic software package. Users will be introduced to the main GeoGebra site and the several ways to interact with this powerful mathematics software package.

Download and join the math playground for the mind!

Note: I’ve begun hosting all my videos at my Math Video University site. You can find the video here.

This is the first of a four-part series in getting started with GeoGebra. Here are links to the other parts:

GeoGebra Video First Steps-Basic Customizing

GeoGebra First Steps-Intermediate Customization

GeoGebra First Steps-Advanced Customizing

Centre for Learning & Performance Technologies

From the Centre for Learning & Performance Technologies, here are the Top 100 Tools for Learning 2011.

This, the 5th Annual Survey of Learning Tools, was finalised on 13 November 2011. This year’s list was compiled from the Top 10 Tools lists of 531 learning professionals worldwide – from education, training and workplace learning.

What is a “learning tool”? This could be a tool you use to create or deliver learning content/solutions for others, or a tool you use for your own personal learning.

GeoGebra ranked #6 on the New entrants on the list.

BigBlueButton ranked #74 overall. For those who aren’t familiar with BigBlueButton, it’s used for web conferencing and distance learning – the future of much of education, and the future is now.

For complete statistics and more information, please visit:

http://c4lpt.co.uk/top-100-tools-for-learning-2011/ 

GeoGebra logo

My favorite math teaching software, GeoGebra, just got a nice boost. The GeoGebra Institute of California has a new website.
The mission of the International GeoGebra Institute (IGI) is to empower students and teachers at all levels to learn and teach mathematics with our easy-to-use and freely available software and interactive materials. The IGI is a rapidly growing network of non-profit organizations around the world. Our California GeoGebra Institute will support local users in the following activities:

• face-to-face workshops for teachers
• online support for GeoGebra users
• presentations at California conferences
• publications in California journals

GeoGebra supports free learning materials (applets) which have interactive graphics, algebra, and spreadsheet components. These materials are available from elementary school levels through university levels.
We wish to show California teachers and students how to use GeoGebra so that it can be used as a major curriculum force in the classroom.  GeoGebra is very easy to use, with a point and click interface. You can quickly create interactive applets that illustrate concepts in all of the major school mathematics curriculum areas. GeoGebra is a free program that can perform geometric constructions, graph functions, create sliders that can be used to define functions, find derivatives and integrals and change everything dynamically. It is also straightforward to create html files that will be available online to anyone with a browser. Since GeoGebra is a java program, Mac or PC computers both work fine. Come join us in celebrating this terrific software!

A big thanks goes to Andy Hammons, our website creator/guru, who made this possible. Andy is the 2011 Hesperia USD District Teacher of the Year.

Michael Borcherds, lead developer of GeoGebra, asked why GeoGebra is successful in the GeoGebra Forum;  I summarized the responses and came up with 15 reasons.  Here are the reasons why GeoGebra has been so successful all these years.

1. It is FREE.
2. It is open source – meaning, it is developed collaboratively by us:programmers, teachers, mathematicians, and users not just a few people.
3. It runs in multiple operating systems (Windows, Mac, Linux, etc.).
4. It runs in different devices (computers, mobile phones, tablets).
5. It promotes mathematical connections (algebra, geometry, calculus, statistics, etc.).
6. It highlights  multiple representations (equations, graphs, tables).
7. It is intuitive, user-friendly, and easy to use.
8. Its files can be easily uploaded to the web as applets.
9. It can be exported to different file formats (png, pdf, eps, etc.).
10. It supports Latex typesetting.
11. It supports spreadsheet, CAS, and 3D (GeoGebra 5.0).
12. It has an elegant appearance and dynamic colors.
13. It has excellent support community.
14. It can be used by elementary school students up to graduate schoolstudents.
15. It is updated frequently.