Mathematica


 * Description **

Mathematica is a computer application that is used by students and teachers all over the world as a tool for solving various computations, as well organizing and graphing data. It is used in many different fields of study such as engineering, business, finance, science, medicine, arts, mathematics and many more (1). In the educational field, it is used to give students an interactive approach at learning how various elements of their studies work and interact. A license to purchase the application is based on who intends to purchase it and how it will be used. Those who do not have the application but wish to open documents created with Mathematica can download the free Wolfram CDF Player onto their computers. This will allow them to view and print these types of files.


 * History **

Mathematica was created by Wolfram Research, a company founded by Stephen Wolfram in 1987 (2). Wolfram was born in London in 1959 (3). He spent his educational career studying physics and received a PhD in theoretical physics by the time he turned twenty (3). In 1973 he implemented the use of computers in his studies. He released the first computer algebra system in 1981(3). He spent the next several years using the computer to run various experiments (3). In 1986, Wolfram founded the first research center (3). After conducting researching in various fields, along with teaching in various subject, Wolfram created Wolfram Research Inc (3).

Mathematica’s first version was released on June 23, 1988 (3). This program proved to be ahead of others like it, putting Wolfram Research as the leader in its industry (3). It became an important tool based on its advancements in computation, technology and business (3). Mathematica was developed further and Wolfram was able to use it as a tool in his personal studies (3). He was able to use his newly created tool to make discoveries in several fields. Wolfram Research has grown, but Wolfram is still responsible for his creation, Mathematica. Realizing how useful Mathematica became, he created a free online version, Wolfram Alpha. While it does not do all that Mathematica can do, it does give everyone the opportunity to take part in some of Wolfram’s greatest work.


 * Impact on Teaching and Learning **

In K-12 classrooms, as well as in higher education classrooms, Mathematica has served as an interactive tool to help in the mathematics classroom. After students grasp basic concepts while studying graphs and functions, they are able to go into Mathematica and instantly view more complex problems and images. They can rotate the graphs in a way that give them several points of view. This allows students to understand all aspect of the graph and how it is created.

Mathematica also allows students to move past basic the basic algebraic or computational concepts and make more meaningful connections. They are able to make connections and applications to real life situations while avoiding basic computational errors (4).

There are also features on Mathematica that are beneficial for teachers. Instructors are able to create quizzes and tests through Mathematica, as well as create interactive slide show lectures. There are tools that allow them to create drop down menus to show details examples and solutions.

If students require extra assistance while using the program, there are several [|demonstrations] available online. This allows teachers to spend less time in the classroom instructing students on how to use the application and more time on the more important material that should be taught in the course.


 * Practical Applications, Examples and Demonstrations **



This is an example of a basic integration problem as well as a graphing problem using Mathematica. The first line In[4] is where the student is able to go in and input what they wish to solve. The "Integrate" refers to the operation that is to be performed. The following line shows the answer. The next time In[5] shows another problem that is asking to be solved. The "Plot 3D" refers to a three-dimensional graph for the function sin(y+sin(3x)). The following pieces of information help the computer to understand the domain and range for the given graph.

More complex plots and graphs can be computer with Mathematica such as the image above.

The image above shows an example of a lecture that would be given to students. The box on the left shows the computations that are being done where the orange and yellow box shows the lecture and directions.

The Mathematica website also gives great examples through a video showing applications of Mathematica in Secondary Education and in Community Colleges.


 * References **

(1) @http://www.wolfram.com/solutions/

(2) @http://www.wolfram.com/company/background.html

(3) @http://www.stephenwolfram.com/about-sw/

(4) http://www.wolfram.com/broadcast/screencasts/k12andcceducation/


 * External Links **

Mathematica Review by Tech Powered Math @http://www.techpoweredmath.com/mathematica-review/

Mathematica Documentation Center, Mathematica Guide and Examples http://reference.wolfram.com/mathematica/guide/Mathematica.html

Mathematica For Students: Help for Math, Science, Engineering Classes []


 * About the Author **

Yasmin Saban is a current graduate student in Educational Technology at the University of Hawaii at Manoa. She is a Pre-Algebra and Algebra 1 teacher at St. Andrew's Priory. Her undergraduate studies at Concordia University forced her to use Mathematica in the classroom. This page was created as a project for ETEC 602. Yasmin Saban can be reached at ysaban@hawaii.edu.