Technology

The use of technology was pervasive in this course. It was used for classroom management, problem solving, communication, representation and reasoning and proof.

Classroom Management

We used a smart board or computer with a projector to take attendance daily. All class materials were accessible through Sakai or other Internet sources. Most assignments were submitted and returned electronically through Sakai, as well. The one exception was our blog, where we posted summaries and reflections on various subjects, the present post being one example. 

As future teachers, it will be advantageous to make use of any technology that can simplify our regularly occurring classroom procedures. 

Problem Solving

Virtually every assignment in ETE 339 allowed for multiple means of completion. As such, we needed access to a variety of Internet-based resources for up-to-date information. We also made use of calculators to perform fast, accurate calculations. This allowed us to focus on looking for numerical patterns instead of wasting precious time on labor-intensive, hand-written algorithms. While we didn't use it for problem-solving in class, the Geometers Sketch Pad might also be used by students in a problem-solving fashion. 

Our future students must be able to use technology in problem-solving, too. They must be fluent in the use of calculators, Internet browsers, and various types of software (word processing, spreadsheet, graphing, geometry) such that they can use these resources to solve real-life mathematical problems. Technology can also assist in achieving the necessary precision in mathematical calculations. 

Communication

The main way in which we used technology this semester was for communication. We used an online blog to post our summaries of readings and reflections. Classmates and our professor followed our blog were able to leave comments. We also used a wiki and google docs to complete group papers. Both allowed us to leave comments for other authors or to receive emails when changes or comments were made. Email was also heavily used between class members and the instructor to ask questions or offer support. Communicating in writing enabled us to become adept at mathematical discourse in a way that simply talking in class would not achieve. It also allowed us to work on the same project at different times and from different places. In our upcoming Curriculum plan, we will add video and PowerPoint presentations to our technology repertoire. We have already had opportunity to see how video can be used to augment mathematical communication through three separate video analyses. 

By allowing our future students to make use of technology to augment or facilitate mathematical communication, it will enable them to better construct arguments and criticize those created by others.

Representation
During the process of creating our activity file, we discovered many technological tools in the form of online applets. These permitted us to create virtual representations. Some were simple virtual manipulatives. Others, like the Geometers' Sketch Pad, had more sophisticated capabilities that allowed us to see patterns in numbers and repeated reasoning. We also used spreadsheet software when a physical model  of open-topped boxes was inadequate to answer our question as to which box dimensions would give us the greatest volume.
Technology offers students an additional tool at their disposal to make sense of and solve mathematical problems. 

Reasoning and Proof
Throughout this course we have used technology to express mathematical reasoning. Through blogs, the wiki, and other computer-based collaborative efforts, we have needed to express our understanding of mathematical concepts and effective pedagogy. In our future classroom, students will use technology to aid them in identifying patterns, explaining them and proving how they know their thought processes are correct.