The SAS Problem is here!

Enter the lengths of two sides of a triangle and the measures of the angle those two angles form, and this will give you a sketch and the opportunity to show the missing measures.

It was designed with the goal of giving students/teachers and inexhaustible supply of practice. Students can create and solve their own problems, and be able to check their results. The twofold gain is allowing students to discover when they have errors all by themselves, and saving the teacher from the role of answer-checker.

File available at http://tube.geogebra.org/m/1517789

Motivate students and hold them accountable..

John Metallo has a short article in the Albany Times Union of Saturday. August 15, 2015. The entire article can be found here. In under 20 sentences, he pretty much nails the issue regarding student success in school.

The victory of Jason Day in the PGA Championship has reminded me that the road to success has three major parts: decent opportunities, good guidance (instruction), and the will to succeed. Far too often the latter is ignored when it comes to education "reform". I suspect that is because the powers-that-be feel they have no power to change the students' "will", but see an easy route via changing the "guidance" and "opportunities". You know the old theory of "change what you can."

Our New York governor seems to be all over "accountability" for teachers and schools, yet somehow absolves students of any responsibility in the matter.  I fully believe that students have the ultimate responsibility, but I also feel that the adults in their world can do much much more to help them get motivated.

The famous quote (prayer, call it what you wish) goes like this:

God, grant me the serenity to accept the things I cannot change,

The courage to change the things I can,

And the wisdom to know the difference.

This, as a code for life, might seem self-evident, but it is anything but. Taken literally, it can lead to a feeling of complacency. It presumes wisdom, but how do we measure our own wisdom? What if we sense, incorrectly, that there is something that we cannot change? Unless we acknowledge our lack of wisdom, we would be falsely serene.

I believe that, as a culture, we have underestimated our powers to improve student motivation. We have become complacent in that regard, passing the buck to causes we perceive as beyond our control.

Perhaps it is time to address the issue of focusing on student failure over and above school failure. Successfully eliminating student failure would, in essence, eliminate failing schools. Yet, doing such is impossible without addressing student motivation (the "will to succeed").

I hope that I am doing a small part with my work in GeoGebra and my inclusion of some of them in my blog postings. What I do know is that I would make sure that students spent whatever time they could working with GeoGebra, not because it is a panacea for mathematics instruction, but because it could be one of the best motivating factors we have.

ASA is Here!!

Last week I posted a GeoGebra file for the SSS problem in trigonometry. Here is a companion for the ASA setting. Another example of how dynamic geometry can be a powerful aid in school.
 
File available at http://tube.geogebra.org/m/1489891

Make sure you know all sides of it and see it from all angles!

This was created with the specific goal of supplying self-practice for students in which they can check their own results. It might also be adapted for classroom use.

It continues my quest to see dynamic geometry (such as GeoGebra used here) become an integral part of school mathematics.

Math is Art is Math is Art

Just another example of the interface between artistic design and mathematics.
Are schools connecting the two disciplines yet?
math is fun!!!
 

What Strength!!

Here is a picture of a pair of sneakers hanging from power (or telephone) lines on a road just outside of Valatie, NY. These sneakers have been hanging there for years. At least 5 years if not ten or more. 

During these years we have had storms blow through that have knocked down tree limbs and even entire trees. Ice storms that have made birch trees bend over to touch the ground. We have had snow falls of two feet or more, driving rains that have sent water around closed windows into rooms of houses. In addition, we have had summer heat waves well into the 90's, and thunderstorms that have sent lightning to the ground with a vengeance.

Despite all these weather extremes, these sneakers have stood their ground (or wire, if you wish).

All I want to know is: What kind of laces do they have? 

Birth of a Hexagon

The first image shown here was initially created in Geogebra, and then saved as an animated gif, and edited a bit for size on screen  (and to keep file size down.) The second is an embedding of the actual Geogebra file (available here)

My main point in creating it was twofold: 1) another example of how dynamic geometry can be used with students at younger and younger ages, and 2) a bit of practice for me in using a single slider as a time line for an animation.