Written Proofs and Dynamic Geometry

The question has been asked, "If we have software like Geogebra, is there a need to have formal proofs in Geometry class when I can simply construct a figure in Geogebra that maintains its properties under the 'drag test?"

The first thing that I did was go to Wolfram Alpha and look up the mathematical definition of "Proof" and it said 

The definition of mathematical proof does not specify written or otherwise.  

I think that written proofs go hand in hand with a dynamic sketch in a program like Geogebra.  In order to construct an appropriate figure, a few things must first happen: 

1-You must have an understanding of the mathematics.  You can not just guess to draw a perpendicular bisector, circle, or parallel line.  Most students would not go to those constructions without some indication as to why we would need them.  

2-By using the elements of a construction, you are also using the reasoning that goes with the written theorems that have already been established. 

By using the Dynamic Geometry Software (DGS), we allow our students to have a visual as well as a written proof. Many students learn visually and allowing them to use DGS to construct formal proofs, we help them through the reasoning process by seeing the theorems at work.  

I am currently working on a project for a mathematical technology class at Auburn, and in this class, we are to show different properties of a problem using DGS.  DGS has properties that allow you to show "step-by-step" processes.  So students could use the advanced features of DGS to illustrate their formal proofs in class.  

In NCTM's Principles to Actions(2014), they talk about Mathematical Action Technology (like DGS) and how it allows students to see the same information in a variety of ways.  "The ability to shift between different representations of a problem (e.g. visual/graphical, symbolic, numerical) can help students develop a deeper understanding of mathematical concepts. Further research suggests that the effect of working with virtual manipulatives on a computer screen is equivalent to using physical materials (Sarama and Clements, 2009)" (NCTM, 2014, p. 84). 

So, is there a need for formal proofs, YES! It is another way of representing the geometric sketch.  I think that both forms of the proof are necessary and allows students to reason through and see the written proof in action.  

References:

National Council of Teachers of Mathematics. (2014). Principles ot Actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.

Sarama, J., & Clements, D. H. (2009). 'Concrete' Computer Manipulatives in Mathematics Education. Child Development Perspectives , 3 (3), 145-150.