“I don’t get it” tells you a learner is stuck.
It doesn’t tell you where.
Here’s a common algebra question:
Which equation represents this relationship?
“Seven times a number, n, is 12 less than the square of that number.”
The choices are:
A. 7 + n = n² − 12
B. 7n = n − 12
C. 7n = 12 − n²
D. 7n = n² + 12
E. 7n = n² − 12
Before I explain anything, I ask the student to tell me what the language means.
What does “seven times a number” mean?
What does “the square of that number” mean?
If 7n is 12 less than n², which quantity is larger? How would you get from the larger quantity to the smaller one?
Problem solving can’t begin reliably until those relationships mean something.
Once they do, I ask the student to translate small to big.
Start with the smallest complete piece of meaning.
“Seven times n” becomes 7n.
That eliminates A.
“The square of n” becomes n².
That eliminates B.
Now check the complete relationship.
If 7n is 12 less than n², begin with n² and subtract 12.
That eliminates C and D.
E remains:
7n = n² − 12.
The student didn’t have to hold the entire sentence and all five choices in mind before doing something with them.
Each piece of comprehension produced an action. Each action reduced what remained.
Students often call the errors they make on questions like this “silly mistakes.”
Often, they tried to translate too much at once. A small misunderstanding then traveled through the rest of the problem.
One piece at a time, each meaning can be checked as the relationship is built.
The same principle applies before any strategy begins.
If a problem uses the word “integer,” I stop there first.
Can an integer be negative?
Is zero an integer?
If the student can’t answer those questions, the problem isn’t yet what to do. It’s what the words mean.
This is Functional Learning in two layers:
Comprehension as translation.
Problem solving as sequencing what to do next.
Problem solving can’t compensate for missing comprehension. It depends on it.
So when a student says, “I don’t get it,” or “I keep making silly mistakes,” I ask:
What is the smallest piece you can explain?
What can you write from that piece?
How does it fit the whole?
What can you eliminate now?
Then we take the next piece.
The answers show me what to teach next.
Great learners are built, not born.