As a former engineer, of the electrical / electronics type (BSEE), and an MBA grad (finance and marketing), I have an affinity for diagrams, especially those with boxes, circles, arrows, and cogent text conveying nearly the “1,000 words” equivalent of a picture, maybe even more. So when my C&I (curriculum and instruction) prof led a recent class on concept maps, I was engrossed in the activity, and sold on the possibilities to use them in classrooms as tools with which students could relate the multitude of concepts tossed at them within a course.
A quick google of “concept map” took me to Wikipedia’s site which works fine for me as general background, and tutorial. So for further details, check out their site. Here’s a brief excerpt from that site.A concept map is a diagram showing the relationships among concepts. They are graphical tools for organizing and representing knowledge. Concepts, usually represented as boxes or circles, are connected with labeled arrows in a downward-branching hierarchical structure. The relationship between concepts can be articulated in linking phrases such as “gives rise to”, “results in”, “is required by,” or “contributes to”. The technique for visualizing these relationships among different concepts is called “Concept mapping”.
Our prof also mentioned the availability of “freeware” that helped generate concept maps. While I have not used the software, it is available from a company called ihmc: the Institute for Human and Machine Cognition. A fascinating technical report prepared by ihmc delves into the psychological, physiological, and epistemological bases for concept maps.
Here is an example of a concept map from their software, explaining concept maps. What a wonderful recursive way to illustrate the concept.
And finally, here is the work product from my C&I group of four mathematics teacher candidates. While we were just exposed to concept maps, we, like our future students, dove in and unleashed our creativity upon our poster paper. I spent my entire time detailing applications of Systems of Equations embodied in matrix form highlighting how math lives within the products we use everyday such as a cell phone, GPS navigation device, ABS brakes, and investment portfolios. For each product, I named a common field of research associated with the product within which all the matrix algebra of the form [A][X]=[Y] takes place, running on a microprocessor or DSP, as well as a famous innovator in that field, not necessarily directly related to the product, itself.
I enjoyed my time, although I ended up being banished to the corner of the poster since my contributions were not deemed to be central to the mathematical concept under discussion. It was all good as my math cohort companions eagerly elicited elaborate explanatory elements entailing equations of linear systems. Note: I did not allow myself to be constrained to linear equations, so nth order equations will fit just fine. Also, I couldn’t help myself so I displayed my concepts in 4×3 matrix form, too.