Falling Dominos: Math and Visualization Beget Art
This week's resource perhaps should be viewed as a "required" precursor or primer for a previous resource on Math and Art. That is, you might want to first read this week's text to be sure you understand most of the previous week's resource.
Claudia Alsina and Roger Nelson's Math Made Visual: Creating Images for Understanding Mathematics is another great resource to explore...and learn from. It does not focus on art, but rather explores the process of creating mathematical drawings that help students understand important mathematical ideas and proofs.
Both authors began with the process of creating "proofs without words." This led them to collaborate in their further explorations of the creative use of visuals to deepen understanding of any idea in mathematics.
The book is organized into two parts. The twenty brief chapters in Part I present methods for visualizing a mathematical idea, then offers related challenges for the reader to try. Part II focuses on the pedagogical aspects of developing visual thinking and the role of hands-on experiences in the learning process. Some of the topics In Part I are:
The authors include some hints and solutions for the challenge exercises. Also, an extensive list of references is included.
- Representing Number by Graphical Elements, Segments, Areas, and Volumes
- Identifying Key Elements Involving Geometry
- Employing Isometry, Similarity, and Area-Preserving Transformations
- Tiling and Dissections
- 3-D Models
One concern is the authors' intential avoidance of the use of technology. In fact, they claim that "many, if not most, of the ideas presented here are independent of technology." My guess is that all readers/users of the text will use technology in some form when trying to create concrete visuals for their students (or even for themselves).