My teaching career began in the fall of 1997 when a faculty member experienced a heartache about a week before the semester began. During the intervening years between then and today, my peers, colleagues, and even those in business & industry, have noticed a tremendous decline in people's ability to write.
College Writing Tip Six: Check for consistency and congruence errors.
Some exams, quiz, short answer and essay questions can be validated within an exam, if one is paying attention. Some questions are deliberately written to see if students are paying attention. An early question, for instance, may contain the answer to a later question. Or, a question deep in the exam may be the answer to an early question. Objective exams, those exams with multiple choice, true/false, or fill-in-the-blank questions are very good for placing "easter eggs."
"With the exception of Malta and Monaco, which European country has the highest urban density?"
(a) Portugal
(b) Belgium
(c) Spain
(d) Tripoli
"Of the following traits, Belgium represents the country with"
(a) the highest IMR in Europe
(b) 99% population
(c) the highest rate of natural population increase
(d) the highest overall population
These questions dovetail; they are nearly the same question, approached in slightly different ways. The first question represents a small-scale question, asking the taker to consider all of Europe. Then, make a choice concerning which country applies to the prescribed condition.
The second question is a larger-scale question, focused on the quality of a single country with respect to all others. To remain consistent, the taker should select (b) in the first question and select (b) to satisfy the second question. Educators encourage students to go back over exams to verify answers because we know exams contain questions in these forms. Now, a 100-question exam is not going to be 50% redundant, with reflections of questions throughout. Perhaps only 10% of the questions will be reflections of other questions. However, 10% is a letter grade.
In writing assignments, be congruent in your responses. In teaching Weather and Climate, one of the concepts nearly all students struggle with is the notion of Air Pressure. Air molecules are susceptible to gravity like every other aspect of our physical world (though at the quantum level, I'm not so sure). Our Earth's gravity pulls air molecules to the surface, creating air pressure of about 14.7 pounds per square inch (14.7 psi) acting upon our bodies at mean sea level (MSL). As we elevate ourselves, whether by climbing a mountain, hang-gliding, or diving from a high-altitude aircraft, fewer air molecules are around us, pushing and bumping into us, thus the pressure of air on our bodies is less. At 8,000 ft, for example, air pressure is about 10 psi, about 33% less pressure than at mean sea level. Denver, Colorado is the "Mile-High City," being about 5,280 ft above MSL.
Most people understand as we climb a hill or mountain, the air becomes thinner, oxygen becomes less prevalent, and breathing becomes labored. However, in my Weather and Climate course I ask two questions. The first question asks students to explain why air pressure decreases as altitude increases. The first question tells the student air pressure decreases with altitude, and requires them to explain why. More than 50% of the responses consist of explanations similar to the following:
"Air pressure is less at high altitude because the molecules are more spread out."
The response is not entirely wrong. The air molecules are more dispersed. Dispersion does not answer the question; dispersion only describes a characteristic of the upper atmosphere. Dispersion does not explain the fundamental physics behind the dispersion. Dispersion of air molecules does not explain the better answer of gravity pulling molecules down. Air molecules move very fast, faster than you might imagine. Air molecules do not reach escape velocity; otherwise they would all eventually shoot off into space, leaving behind a cold, lifeless world. Gravity compels the molecules back to Earth, thankfully. The primary concern with the above responses is the lack of attention paid to lecture notes, lecture videos, and the textbook content, as the answer is clearly stated in all three resources.
The second question involves climbing.
"You have won a trip to Tanzania to climb Mt. Kilimanjaro, elevation 19,341 ft. Would you expect to experience more ear popping from the surface to 10,000 ft, or from 10,000 ft to the summit at 19,341 ft?"
The second question is the application of the knowledge evidenced in the first question. Over 50% of students respond with some form of the following reply.
"A person will experience more ear-popping from 10,000 ft to the summit because the air gets more dense as one climbs the mountain."
"Because air pressure increases with altitude the person will have painful ear-popping the closer he gets to the summit."
Congruence between the first question and the latter question collapses for most students. Even though they realize the air is thinner at altitude, they mistakenly conflate ear-popping as being an issue with higher pressure, rather than pressure change, and then wrongly invert the atmospheric pressure column. A person climbing will experience greater ear-popping from the ground to 10,000 ft because the greatest change in atmospheric pressure occurs at lower altitudes. Air pressure does not change in direct proportion to changes in altitude; air pressure change is more logarithmic, changing rapidly with small changes in altitude. From 10,000 ft to the summit, less air is pushing on the ear drums so ear-popping should be less painful and less frequent.
Student writing assignments often contain errors in logic and congruence. These errors can be significant and can indicate a lack of true learning, flaws in conceptualizing theories, techniques, and methods used in science.
We call this phenomenon, "missing the point."
Next: "Point Values"
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