emblem

Applied Mathematics Digital Explorations (Spring 2010)

Contact:John Flynt

email: john.flynt@colorado.edu

Page Contents

Hours

Open Individual hours to be listed.
  • Joshua Aragon
  • Anne Byrne
  • Adrian Flynt
  • Toby Jones
  • Paul Kunz
  • Tyler Manteuffel
  • Troy Owens
  • Hayley Schneider
  • Tanvi Shah
  • Brian Stanton
  • Ross Woodworth

Rational and Description of Labs

The rational and description of a Digital Explorations is difficult for many people to understand. On the one hand, when it is said that students will be introduced to labs involving games, simulations, animations, or interactive application, it is easy for the impression to arise that a tradition computer science course is being taught. Accordingly, students will be engaged in long hours of learning programming and then applying it in the development of one of these artifacts.

Nothing could be farther from the actual practice, which has been thoroughly established over the past two years in a number of context involving hundreds of students. In practice, the applications are developed from labs. A lab is a written document published as a PDF file. The document provides step-by-step procedures for constructing the artifact. Included with the lab are the art and code for the artifact. The art and code are broken down into components that the student can gradually incorporate into the construction process, repeatedly compiling and testing as he or she goes to see how the artifact emerges with his or her labors.

Each lab is designed to require approximately an hour and a half to three hours of the student’s time. It is designed to be worked by anyone, with little stress, and it is composed to provide a complete, rewarding experience involving active learning. Mathematics and science are shown to lead to a complete, attractive, interesting game, simulation, animation, or interactive application that the student can sit back in the end and recognize as his or her own creation. She or he will know the creation because he or she has constructed it in a step-by-step way, learning along the way a number of valuable skills: programming, composition of digital art, mathematics, science, use of Flash, and so on.

The design and use of the Digital Explorations lab is based on M. Csikszentmihalyi’s model of autotelic learning and flow. As shaped through the activities of the Digital Explorations workshops, Csikszentmihalyi’s model involves the following stages: [1, 2]:

  1. The coach opens the session by sitting among a group of students. He or she uses a laptop or workstation, and his or her monitor screen is projected onto a large screen that the whole group can see. The coach guides the group to the Digital Explorations website. Within the website, students in the workshop access the website and operate or play the artifact the workshop features to see how it works. By operating or playing it, they establish in their minds a clear idea of a mathematically or scientifically oriented artifact that they can build.
  2. After operating or playing the artifact, the students are then guided by the coach to access a lab. The lab is a PDF file. It contains step-by-step procedures for constructing the artifact. It also contains, if relevant, artistic and other resources that the student uses to in their construction of the artifact. In the lab, a scenario of how to build the artifact (the set of goals for the workshop) is clearly defined.
  3. The coach guides the students through the lab. Using the PDF file, they are able to work along with the example Actions taken toward the goals elicit immediate feedback. Each change the student make as the artifact is being constructed leads immediately to changes in the behavior of the application, and these are shown through testing.
  4. The goals that are sought are matched by skills that the student acquires as he or she constructs the artifact. To make this possible, the construction activity always begins with few assumptions, and all activities center, not on learning background knowledge but on constructing the foreground artifact.
  5. Within the context provided by the construction project, one goal leads to another, and each successive goal involve an equal or incrementally greater challenge. The challenge centers on the artifact, but is also leads to understanding how an artifact encapsulating mathematical and scientific work is constructed.
  6. Along the way, as the student encounters successive challenges, learning takes place, skills increase, and further goals are found.
  7. Along the way, actions take place in the context of a sense of a whole and attainable outcome, something that is perceived as being realizable.
  8. As a key outcome, those working on the artifact in a group create a common understand which engenders common interests that can be communicated.
  9. The effort ends with artifacts that all participants can display. Csikszentmihalyi describes such activity as looking backward over a completed effort.

[1] Csikszentmihalyi, M. (1996). Creativity: Flow and the Psychology of Discovery and Invention New York: Harper Perennial.

[1] Csikszentmihalyi, M. (1997). Finding Flow: The Psychology of Engagement with Everyday Life. New York: Basic Books.

Resource Documents and Links

Flash Courses

  • APPM 1720.  This course provides an introduction to Flash development.

Projects in Progress

This link provides alpha vesions of projects under construction or being tested the Digial Explorations group.

Starter and Demo Labs

These projects represent but a few of over a hundred developed over the past two years. Starter projects are very important since they can be morphed into other projects. An attempt will be made to provide a master list of links to as many projects as possible. The construction time for these projects ranges from around half an hour to three hours.

Conceptual Topics

Flash Introductory Topics 1

Flash Introductory Topics 2

Show Me Application

          The Show Me Demo.

v

Object-Oriented Programming - Document Classes

          View the Document (Walker) application.

Publishing a Flash Project to the Web

This lab allows you to create an HTML page for your application. It can be used with any project.

          Sample of Published SWF.

Data Types and Components

This lab is designed to provide those with a little programming background with an overview of the ActionScript programming language.

Timer Explorations

This lab deals extensively with collision detection, use of a timer, and different approaches to manipulating Sprites and MovieClips. It begins with code in the Actions Panel and then moves it to an document file. An algorithm to detect isolated collisions is detected using Boolean values generated from individual pixel readings.

          Try the application.

Drag and Drop

This lab allows you to explore simple ways of picking up and dropping objects onto targets.

          Try the application.

XML Hanging Words Game

This lab allows to you load XML data to be used in a game scenario.

          Try the Hanging Words game.

Monty Hall

This lab allows you to explore probability.

          Try the application.

Baskets and Bitmaps

          Try the application.

Timer Explorations

This lab includes several projects that explore different ways of implementing timing controls. It is the first of two labs that explore the Timer class.

          Try the application.

Balloon Flight

This lab provides a context in which to explore how to add collision detection and other features to a previously developed application. The balloon now shows a flame as it rises, the tower blinks, and balloon navigation can be put on autopilot.

          Try the application.

Sending Messages Between SWF Files

This lab explores how it is possible to send messages between different SWF's in a given page.

          Try the application.

Using the Date Class

This application explores use of the Date class to investigate how change can be shown as successions of activities.

          Try the application.

Database Connections

Supplemental Material: XML, Sound, and Video

This lab provides you with opportunities to explore use of sound and video in your projects. It also provides you with an introduction to XML, which you can employ to load complex sets of of information into your projects.