Video Based Hypermedia for Communicating Mathematics Tom Apostol, Teresa Chambel, José F. Rodrigues, and Lara Santos CalTech - California Institute of Technology, USA University of Lisbon and CMAF, Portugal

1.Introduction 2.The Use of Video in Mathematics 3.What is Video Based Hypermedia ? 4.Learning with Video Based Hypermedia 5.Hypervideo Technologies 6.Case Studies 7.Conclusions Table of Contents

1. Introduction Mathematics is important ! But, people often find it unengaging and frightening Raise public understanding and appreciation for math Important challenge and concern in recent years Through Associations, programs and campaigns Websites, conferences, exhibits, competitions, videos

2. The Use of Video in Mathematics Why To show students that learning math can be exciting and intellectually rewarding, understandable, exciting, worthwhile To provide an entertaining and informative look into current research To initiate discussions, stimulate further research,... Who School, University or General public What Geometry, topology, visualization of classical ideas History of math, topics in high school math, Applications in real world

2. The Use of Video in Mathematics Main Benefits Video treats math in ways not possible in text and chalkboard Live action, music, special effects, computer animation Stimulates Interaction with teachers and colleagues Possible to transmit large amount of info in a short time Video can be complemented with other materials

2. The Use of Video in Mathematics However Learning requires more flexible mechanisms to manipulate multiple resources of the media at hand

3. What is Video Based Hypermedia ? Spatio-temporal link from Video to Video Navigation History

3. What is Video Based Hypermedia ? Spatio-temporal link from Video to Text

3. What is Video Based Hypermedia ? Different Video Indexes Text centered and Video centered pages

3. What is Video Based Hypermedia ? Exercises: Index, video and text

4. Learning with Video Based Hypermedia Experiential Cognition Leads to a state in which we percieve and react to events efficiently and effortlessly Its enjoyement is also its danger Reflective Cognition Is that of comparison and contrast, of thought and decision making. Requires some structure and organization Modes of Cognition Don Norman Both essential, Require different technological support

4. Learning with Video Based Hypermedia Different media and the way they are used and integrated, can support different modes of cognition

4. Learning with Video Based Hypermedia To support reflection: Compositional representation Time to reflect Examples Text, Television, Communication tools, Web Different media can transmit the same information … but, the medium is not a neutral carrier Each technological medium has affordances … that make it easier to do some things better than others

4. Learning with Video Based Hypermedia Television and video, when properly constructed, can be a powerful tool for reflection If the user can : select what is to be seen, control the pace of the material, it is easy to go back and forth, stop, make annotations, compare and relate to other materials; Integration with video Allowing “natural” experiential cognitive attitude Inducing and supporting reflection processes

5. Hypervideo Technologies Effective reflection requires structure and organization The main issue in Hypermedia Hypermedia Powerful way to structure and interact with information Truly hypermedia? Illustration versus participate in links Video Rich, Interesting, more complex Hypervideo A more powerful model : Spatial and temporal dimensions Truly integrate different media New concepts of navigation

5. Hypervideo Technologies We developed / are developing: HTIMEL: model and tools for hypervideo support on the Web New forms of integration and navigation of video in hypermedia, with a special emphasis on learning support. Video annotation tools Course material, following these concepts and using these tools. Using video processing techniques (CutViewer…) … Related Work A review … SMIL is one of the most relevant for Web environments.

6. Case Studies The Story of π Part of a series of modules To introduce basic concepts in high school Grab attention, and motivate to learn more Historical documents and applications to real world Live action, music, special effects, computer animation Videotape (≈30 min) + Workbook

6. Case Studies Touching Soap Films Educational film about Minimal Surfaces Kalle, the main actor, explores the palace of soap films For pupils and popular scientifically interested people Computer animations Video + Website

7. Conclusions Visual representations Essential aid to communicate math concepts Increase efficacy of the math message Improve learning processes Effective reflection and learning Require more flexible mechanisms to manipulate the multiple resources of different media

7. Conclusions Hypervideo provides mechanisms to structure, navigate and interact with rich media information spaces open and flexible integration of multiple media, adaptable to learning styles and situations

Acknowledgements Prof. Nuno Guimarães Prof. Konrad Poltier Maria Haydée Morales YOU for listening