In this assessment (on the next two pages), you will write the first two interactions of a sample Micro-Lesson outline about “Aspect Ratio” in aeronautics. (You will not need to write an entire outline.) This topic was deliberately chosen to be something you are likely unfamiliar with; want to assess your inherent writing ability. Please spend some time to review the guidelines and links to information about the topic given below. You will be assessed on your ability to construct engaging, Socratic interactions based on the guidelines provided.
What’s a Micro-Lesson?
Micro-Lessons are simulated, text-based conversations between the student and an interactive, virtual tutor. View this Example Micro-Lesson. Micro-Lessons are built on four main pillars:
- Conversational–A micro-lesson is intended to recreate the thrill of learning in a one-on-one setting with a world-class private tutor. That process takes the form of a conversation between the tutor and student. So the tutor should not drone on and on (i.e. lecture), and the questions posed should feel like questions you would expect in a face-to-face conversation. Even though you will write possible answer choices for students, they should feel like natural responses to the question. The student should be able to think of an answer to each question posed without looking at the answer choices.
- Socratic–An excellent tutor is not one that just spits out information and asks you to do some practice questions. Students learn and retain knowledge better if they are part of the process of constructing that knowledge. Our tutor poses questions that lead the student towards knowledge of the concept being learned. Questions shouldn’t just be checking for understanding; we want thought-provoking questions that challenge students to think critically, deliberately, and reflectively.
- Engaging and Interactive–Micro-lessons should not feel at all like a textbook. Be exciting, clever, fun, and humorous. Micro-lessons should feel snappy: each Socratic question leads to the next without large blocks of text where a student might zone out. The tutor also provides insightful and unique feedback for every student response. Since practice questions are presented afterwards to reinforce the material and assess student understanding, the micro-lesson itself should focus only on teaching the concept.
- Amplification Through Simplification–Examples and writing should not be convoluted. Use as few details as are necessary to teach a concept. That focuses the student’s attention on what is important and prevents them from getting confused by extraneous details. Similarly, the writing should be as concise and clear as possible while staying fun and engaging.
List of Content to be Covered in the Lesson “Aspect Ratio of Airplane Wings”
• Introduce the importance of wing geometry from airplane construction and operation
• Give mathematical definition of Aspect Ratio: AR = s^2/Area = s/mean chord
• Discuss what AR practically means: High AR = long and skinny, Low AR = short and wide
• Explain that AR varies inversely with induced drag, so a higher AR leads to less drag at low to medium speeds → Discuss how this would be helpful for airplanes
• Examine some deficiencies of high-aspect ratio: maneuverability, strength, practicality (storage, useable airfields, use of wing for fuel/wheels/etc.)
Assumed knowledge of student for this concept: Knows 4 force components (weight, drag, lift, thrust), span of a wing, chord of a wing, types of drag
(Assume the student is undergraduate level and this lesson is relatively early in an aeronautics course, though not one of the very first lessons.)
List of Content to be Covered in the Lesson “Benefit-Cost Ratio and its use in Project Selection”
• Definition: BCR compares the expected nominal costs of the project to the potential nominal benefits
• Provide basis for why we would want to compare Benefits and Costs in this way
• Formula: BCR = Benefits/Costs → Get student to recognize this as the formula
• Discuss why you should choose the project with the largest benefit-cost ratio (all else being equal)
a. Give example with same profit but extreme differences in cost and benefit:
A = Cost of $1M and Benefit of $5M
B = Cost of $100M and Benefit of $104M
b. Based only on this information, which project do you think would be better to do?
i. √ A
ii. B → Costs and Benefits during project selection are usually just estimates. Imagine your costs run over by just 5% compared to your estimate. → now this loses money.
iii. They are equally attractive.
c. Indeed. But someone might suggest just comparing the profits of the two projects.
a. [no intro needed]
b. Which project has more profit?
iii. √ Their profits are the same → That’s true.
c. You calculate the profit by subtracting the cost from the benefit. So if you just compared simple profits, you can’t decide between these two. But A is able to produce the same profit with a much smaller investment.
a. [no intro needed]
b. Instead of comparing profits (Benefit minus Cost), how could you use Cost and Benefit to explain that A is preferable to B?
i. √ Divide Benefits by Costs
ii. Multiply Benefits and Costs
iii. Add Benefits and Costs
c. This formula, called the Benefit-Cost Ratio or BCR, is used to compare projects to find the one with the best value for the company without taking time into consideration. The higher the ratio, the better the project, all other things being equal.
a. In the given example, the BCR for Project A is 5 and for B is 1.04. Suppose the expected benefit for Project B decreases so that it is expected to lose money.
b. What would happen to the BCR of Project B?
i. ✓Decrease to a positive number below 1
ii. Decrease to 0
iii. Decrease to a negative number
c. That’s right. Benefit will be less than Cost and they will both be positive, so the BCR will be between 0 and 1. For example, if the new expected benefit for Project B was $95M, then its BCR would be 95/100 = 0.95.
a. You find out that Project A will take 10 years to complete while Project B only takes 6 months.
b. How does this affect the attractiveness of Project A compared to Project B?
i. √ Makes Project A less attractive
ii. Makes Project A more attractive
iii. Doesn’t affect the attractiveness
c. Taking a much longer time makes the project less appealing because it is longer before you realize that profit and can use that money for something else. Also, the value of the profit after 10 years will almost surely be smaller than after only 6 months.
So while BCR is a very simple economic model to apply, it does have many limitations, not only dealing with time, multiple income/cost flows, varying interest rates, etc.