In my computer science days, we learned to watch for edge cases: extreme situations that challenge the system. How will the system handle an email address with an ‘ñ‘ in it, or an email 1,000 letters long? Did we write a program that only handles the obvious cases, or one that truly encompasses all situations?
Too Simple = False Security
When we plan lessons for gifted students, we should look for the edge cases of the skills we’re teaching.
Typical cases are usually too simple and students fall into a sense of false security. Rather than truly mastering the skill, students develop pattern recognition that gets them through the common cases.
Concentrating on the edge cases keeps them on their toes, and helps me determine who sorta gets it and who has mastered it.
Simple vs Compound
The textbook might use this as a simple sentence:
John borrowed a lawnmower.
While this is their compound sentence:
John borrowed a lawnmower, but Jill bought a leaf blower.
My students will differentiate between these, no problem, but they’re probably using unreliable clues such as:
- “compound sentences are longer than simple sentences”
- “compound sentences have conjunctions”
So look for some edge cases that break these unreliable patterns, like so:
I borrowed a seventy–year–old lawnmower with a broken blade, rusty paint job, and a missing wheels.
This is a lengthy simple sentence with a giant predicate, a one letter subject, plus the conjunction “and.” This edge case will catch students who have an 80% understanding of the topic, but would have squeaked by had I used my textbook’s typical examples.
One Step Algebra
26 delightful mathematical curiosities - simple enough for elementary students, yet rich with deep possibilities. Learn more...
As we learn algebra, most students have no need for “the steps,” since they can “see” the answer.
2x = 36, Oh! x must be 18
This leads to the endless spiral in which I moan about the importance of “showing work” and they point out that they “got it right!”
Instead, look for cases that push the envelope in some way. Perhaps including decimals will cause enough strain that they’ll actually learn how to solve for a variable.
0.5x = 36
Maybe you’ll need to include fractions and decimals and negative numbers before some students are pushed to their natural limits.
-1/2x = 36.5
Parts Of Speech
Finally, we can find edge cases with parts of speech. Words that have multiple meanings will filter out students who truly understand from students who get it enough to fake the easy ones.
I care about careless kids who don’t give a care about how careful they are when skateboarding.
Phew! If a student can identify the part of speech for each of those words, I know they understand the topic.
The Buck Stops Here
Don’t let high-level learners slip by with a weak understanding of material while pulling off a top grade. These types of questions are indispensable in differentiating between students who have mastery and those who are fooling you with their natural smarts.
Photo by nerovivo
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