Reflection: Learning by Drawing in Stem
The "constructive use" idea of using drawing as a means of inventing a novel form of visualization is a really good idea for a math classroom because of the way it allows students to connect with the topic they are learning, but also possibly find understanding for themselves and a way of visualization that could benefit their classmates as well. Further to this point is the "interactive use" of drawing that the authors explore. Drawings can be used to exchange ideas, construct arguments or even tell stories, all of which are tools that could be used in a math classroom to enhance learning and create a sense of ownership among students of the knowledge they are exploring.
I would use drawing in my math classroom as a means of creating visualizations (novel or not) so that students can discover more about the topic and have a better understanding of it. Drawings take time, especially drawings that are meant to be mathematical in nature. If you are trying to be accurate to a pattern, function, or set of data, care must be taken to ensure correctness. This helps students by giving them time to process what they learning and also to help each other to figure out this different kind of "problem".
Natural and Unnatural Drawings
Drawing Reflection
Drawing natural objects and comparing them to natural objects is an interesting process because of the differences in structure, form and purpose. Straight lines and right angles typify these characteristics in human made objects because it makes manufacturing easier, they are built for one purpose, and it is easier to arrange or organize objects of a regular and confined shape. For instance, a box or rectangular container is built to hold things, the construction of such a box can be done by machine because a rectangular prism is a relatively simple object, and the arrangement of multiple boxes is easy because they can be conveniently placed next to each other or stacked. Right angles and straight lines also exist in nature in places like certain rock formations, the path that light travels is always a straight line, certain plants grow in very straight lines (bamboo) and will sometimes have branches that occur at right angles by chance because of optimization towards resources.
Fractal geometry: a pattern that can be defined by some process or mathematical relation which identify subsequent iterations of the pattern.
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