Oct 142014
 
GGB logo Programming with GeoGebra

GeoGebra logo

Here’s a nice post by Riley Eynon-Lynch from the Point of Inflection website –  PROGRAMMING WITH GEOGEBRA
Some of his main points:

This post is about some of the virtues of programming computers in math class. I include a long anecdote and a quick geogebra tutorial. The punchline: teaching kids to program introduces them to an environment that gives instantaneous, continuous, 100% correct, 0% helpful feedback without judgement. The computer doesn’t say, “you’ve made a mistake here,” it just shows you a result, and it’s up to you to interpret it, decide if it’s a correct result, and find the problem if it’s not.
. . . the best reason to teach them to program geogebra is that geogebra programs only work if they are mathematically sound. I can see in an instant whether a student has created the program correctly or not. When they go on to create other geogebra programs, I can assess whether they understand the concept or not, and more importantly, they can assess their own knowledge. Geogebra will show students if they understand or not, but won’t give suggestions or hints. It also doesn’t mind if they are wrong 400 times in a row.

I agree with Riley wholeheartedly and have noticed the same things with my students; I especially like the fact that the learning is almost entirely dependent on the effort that students put forth, and that one item learned inevitably leads to another, and another, . . .
Thanks, Riley, for calling attention to this great aspect of GeoGebra.

Oct 052014
 
GGb Schools and Students 300x43 GeoGebra Loved by Students Teachers Schools

GeoGebra-a Powerful Tool for Students

GeoGebra.org has had a facelift and is worth visiting/revisiting. The new interface suits computers and mobile devices well, and has something for everyone. Its strength is ease of use paired with great power to visualize mathematics. The following was taken directly from the newly configured site:

GeoGebra is a multi-platform mathematics software that gives everyone the chance to experience the extraordinary insights that math makes possible.
Students love it because… it makes math tangible – GeoGebra makes a link between Geometry and Algebra in an entirely new, visual way – students can finally see, touch, and experience math.
It makes math dynamic, interactive, and fun – GeoGebra teaches students math in a new and exciting way that goes beyond the blackboard and leverages new media.
It makes math accessible and available – GeoGebra allows students to connect with math anywhere and at any time – in school, at home, on-the-go.
It makes math easier to learn – it creates the interactions that students need in order to “absorb” mathematical concepts.
Teachers love it because… it allows teachers to continue teaching – GeoGebra doesn’t replace teachers. It helps teachers do what they do best – teaching.
It allows teachers to plan and deliver better lessons. GeoGebra gives teachers the freedom to be themselves, creating lessons they know their students will find interesting.
It allows teachers to connect with other teachers. GeoGebra teachers are part of a global math community.
Schools love it because… Students who use GeoGebra = Students who are more motivated = Students who get better results.

Sep 262014
 
Visual Patterns no 115 300x78 Visual Pattern Site by Fawn Nguyen

pattern no. 155 from Fawn Nguyen’s site visualpatterns.org

When I taught 7th grade for six years visual patterns were used to start the school year because they did so many great things for students. They were engaging to the students, visually stimulating, allowed all students easy entry to the math involved, worked great for student projects, and addressed many math standards. Here’s a site with a lot of patterns you can use in your classroom, along with commentary for teacher use.

As of the date of this post (Sept 2014) there are 145 patterns, along with the Equation Key. Fawn Nguyen is the host of the site, and teachers/others are encouraged to submit patterns for others to use. She has another site, Finding Ways, that in her words: “is where I tell stories that are mainly about teaching and learning mathematics in the classroom.”

Take a look and be prepared to find some nice patterns to use when teaching linear functions.

Sep 252014
 

Malin Christersson Digital Math Malin Christersson Digital Math for GeoGebra EnthusiastsMalin Christersson’s site, Digital Mathematics, is a great place to spend some time for GeoGebra enthusiasts. It has some of the best tutorials on the web, organized into seven clusters. Malin provides clear and detailed explanations, some with embedded videos, that help the new as well as experienced user to get more out of GeoGebra. Malin also has provided further work in the areas of Non-Euclidean Geometry, Latex/LyX, Geometry, Functions, Trigonometry, Calculus, Statistics, Linear Algebra, and Fractals.

From the site:
“This is a collection of material that I have used when teaching or giving workshops about GeoGebra. All pages are written in HTML5 and styled using CSS3. They are fully functional only if viewed from a modern browser, e.g. Google Chrome or Firefox. The GeoGebra worksheets on this site can be found at MalinC’s GeoGebra-book. When GeoGebraTune is down, the worksheets on this site will not work. Since this web site relies heavily on lengthy Javascript calculations, it may be worth pointing out that Google Chrome is faster than the other browsers when it comes to Javascript (no, I don’t work for Google, and I personally prefer Firefox, but I have made several tests to check out browsers when it comes to Javascript, and Chrome is best).”

I’ve learned a lot from reading Malin’s work and suggest the site for all those who are serious about GeoGebra. It makes me want to delve deeper into the mechanics of this great educational software, and points out one of its open-source strengths: that of people all over the globe sharing what they know and love.

Sep 242014
 

Dissect the circle into four parts of equal area by drawing three curved lines of equal length.
– idea from Arithmetrics, by Jerome S. Meyer, pg 88
Move slider halfway to reveal a hint if you’re stuck.

Questions for you or your students:
1- Why are the 3 curved lines of equal length?
2- How do you show that the 3 curved lines make equal areas?

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

here.

Sep 232014
 

Van Aubel’s Theorem describes a relationship between squares constructed on the sides of a quadrilateral. In Martin Gardner’s “Mathematical Circus,” pg 179, he shows generalizations of this theorem. This one is for triangles. Starting with a triangle, construct a square on each side. In this case Van Aubel’s Theorem says that the line segment between the centers of two of the squares and the line segment between a vertex of the triangle and the center of its opposite square are of equal lengths and are at right angles to one another.

Draggable points are colored red.

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Yin and Yang Extended

 GeoGebra  Comments Off
Sep 232014
 

Here’s the familiar yin-yang figure in a circle of radius 1. If you continue subdividing the diameter of the large circle into semicircles, this wavy line approaches the diameter as a limit. It’s tempting to say that this wavy line then has a length of 2, but of course, its length is still π. Starting at the top and moving downward, any path (mix and match) also has length π.
– idea from “Wheels, Life and other Mathematical Amusements“, by Martin Gardner, pg 54

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Sep 232014
 

How many rows with 4 plants per row can be made with different numbers of trees?
Interesting questions to pose about graph theory for classroom exploration -from Time Travel and other Mathematical Bewilderments, by Martin Gardner, pgs 280-290

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Sep 232014
 

Here’s an interesting problem to pose for classroom discussion and exploration: How many rows with 3 plants per row can be made with different numbers of trees?

-from Time Travel and other Mathematical Bewilderments, by Martin Gardner, pgs 280-290

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Sep 212014
 

Each row begins with the number 1 at the left. Skip counting by 2, 3, 4, 5, and so on gives the rest of each row. The diagram can be continued as far as desired.
Adding the numbers in each L-shaped region forms a well known mathematical sequence; what pattern shows up?
Another mathematical pattern is formed by the numbers along the diagonal? What pattern is this?

– idea from Math Puzzles & Games, by Michael Holt, pg 27

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.