Month: March 2010

Happened to stumble across Mango Languages last night. It seems to be a nicely constructed site for language instruction. Once upon a time I worked for a firm headquartered in Germany, and had taken some company-sponsored language lessons, so I poked around in the first-level German module. One of the things I noticed right away was that translation was required in both directions. First, I was asked to translate from English to German. Then, after practicing a phrase, I was asked to translate from German back to English. This was easy for the first couple of phrases, but became increasingly difficult as I had to juggle more and more words in my head. I gave up halfway through the lesson as it was getting late, and my head was starting to hurt. However, someone fluent in both languages has obviously mastered the translation going in either direction.

All engineers deal at some level with the language of their particular engineering specialty, as well as the language of mathematics. Fluency in math provides magnificent tools for creating and analyzing new engineering methods. However, my recent experience as a graduate student (as well as two decades as a design engineer) leads me to believe that the emphasis is too heavily focused on the making the translation from physical reality into the language of mathematics. Once the math domain has been entered, there is little effort to move back into the physical domain. This seems to me a great oversight, as I consider engineers to be those who function primarily in the physical realm, rather than the mathematical domain. I love the beauty of mathematics, but I fear that the current generation of engineers may lack much substantive understanding of how to convert mathematical results into an enhanced understanding of physical realities. Many of my classmates fail to “see” how a problem solution relates to any real-world situation.

On the other hand, I frequently find myself struggling for hours trying to make the connection between a solution and its physical meaning. Often times the available textbooks and reference materials made it sound as though this connection should be immediately clear to the reader. It drives me crazy when technical material makes no concession for those of us who are not yet be completely fluent in the “language.” Since learning is a lifelong process, all of us should be constantly entering domains to which we have not been previously exposed. While the use of a particular method or technique may be plain-as-day to its creator, it’s often not nearly so obvious to those of us struggling to acquire an understanding of the new concept. So I suppose this post should serve as a reminder for myself to keep looking for better ways to describe technical concepts in a manner that novices can comprehend, and that experts will still find insightful. I’m not sure that it can be done at the same time, or via the same communication method, but surely there has to be a better way.

While skimming through a year-old post over at edtechpost, I noticed the following reflection:

So I will forgive you if you ignore me from here on out as a perennial dimwit when I tell you that it took me this long to ‘get’ how crucial narrative and storytelling are to everything we are doing, be it learning online, connecting, weaving one’s online presence, blogging…

What really caught my eye was the phrase “narrative and storytelling.” Why are these factors not more frequently incorporated into the teaching of technical issues? While sitting through long lectures that cover intricate mathematical development, I often long to hear more about the context in which the methodology was developed.

• What problem drove the development of a new approach? These equations don’t just drop out of the heavens! Aspiring engineers need to understand that effective problem solving is within their grasp; that “correct” solutions are not just found in dusty old reference texts. Novel methods are driven by persistence and hard work—this reality is rarely emphasized.
• How long did it take to create, prove, and document the approach? It’s easy to get frustrated when the development of a new method hits repeated roadblocks. There needs to be some understanding of the hundreds (or thousands) of hours that are often spent in developing a new solution. Even though a proof can be sketched out in two minutes, the path from problem statement to solution is usually not intuitively obvious.
• Finally, a pet peeve of mine: All contributions are made by real people with real lives, not mystical figures existing beyond the earthly realm. Even if there is no time for biographical sketches of these individuals, what is the correct pronunciation of their names? Most engineers finally figure out that “Euler” is “oy-ler,” not “you-ler.” However, I’ve sat through many lectures where a theorem author is identified on the overhead slide, but their name is never mentioned aloud. And rarely have I heard any emphasis on correct pronunciation. This small detail seems central to allowing engineers to properly communicate with others in the language of mathematics, as well as providing some sense of human involvement. By the way, I often refer to the Mathematics Pronunciation Guide. How else would I learn that “Stieltjes” is pronounced “steel-tyuhs?”

Having taught college courses many moons ago, I am well aware that trying to incorporate contextual material into lectures means even more work for already overstretched professors or lecturers. However, I’ve come to the decision that it’s better to master a few topics than to be aware of many. A good story makes any topic easier to remember, and also promotes a richer understanding of the material.