# 6 Graphing Tools for Teaching and Learning Mathematics

Technology is an essential tool for learning mathematics.  Given the right tool, the student can  maximize problem solving that cannot be solved easily using pencil and paper. For example, using a graphing tool, an activity may be designed that will let students explore the effects of the $a, h$ and $k$ in the quadratic function$f(x)=a(x-h)^2+k$, where  $a, h$ and $k$ are real numbers.

The list below contains several excellent graphing tools that can be used to teach and learn mathematics. All of these tools are free; some of them are available online, and some are downloadable.

1. GeoGebra (Online/Download) – GeoGebra is a free dynamic mathematics software that integrates algebra, geometry, calculus and statistics. It is capable of graphing  polynomial, trigonometric, exponential, and logarithmic functions. It can also be used to create bar graphs and histograms. In addition, it is a dynamic geometry software that can be used to explore properties of geometric objects.

2. Wolfram Alpha (Online) – Wolfram Alpha is a computational search engine.  A computational search engine is a search engine that generates mathematical results such as graphs, tables, and properties of functions.  It can also perform numerical computations, simplify algebraic expressions, solve equations, and many others.

3. Microsoft Mathematics (Download) – Microsoft Mathematics is a free graphing software and calculator developed by Microsoft Corporation.  It can be used to graph both 2d and 3d polynomial and  trigonometric functions. Further, it has the capability of recognizing ink handwriting and can be used as add-in to Microsoft Word.

4. Desmos (Online) – Desmos is one the most powerful graphing calculators available online. It is capable of plotting polynomial, trigonometric, and polar graphs. Desmos plots the graph in color code, which means that you don’t have to change the colors of multiple graphs. Desmos is in HTML 5 format, so it runs on iPads.

5. Graph.tk (Online) – Graph.tk is an easy-to-use  HTML5 graphing tool. It’s one of the simplest and user-friendly online calculators.  To plot a function, all you have to do is to press the + button located at the upper right portion of the page, type your equation, and press the ENTER key.

6. Fooplot (Online) – Fooplot is another online grapher calculator that is capable of graphing 2d and 3d functions. It can plot graphs of polynomial, trigonometric, and hyerbolic trigonometric functions.  It is also supports graphing of piecewise functions. Fooplot graphs can be exported in PNG, SVG, and PDF formats.

### Guillermo Bautista

I am interested in integrating technology in teaching mathematics particularly on the use of GeoGebra. You can contact me at gpbautista1@gmail.com.