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“They really want to understand. I appreciate that as a teacher.”

“Log10 of 1000 equals 3,” one student states. “Log3 of 243 equals … 5,” his classmate says.

“If I have Log to the base of X of Y is equal to Z, what does that mean in terms of revising that as an exponential statement?” High School Math Teacher David asks his class. “Emma, please.” “It would be X to the power of Z equals Y,” she suggests. “Fantastic, well done. This is a much higher level of abstraction, understanding the pattern. We want to look at numerical examples first and then understand the general rule.”

The students continue working on logarithms and exponential functions individually. Does Bassma find the new concept hard? “No, I don’t think it’s that difficult, actually.” Impressed, we ask David how he taught them.

“First, I introduced the idea of inverse functions,” he points to the board. “These are number machines which they haven't seen since Primary School. We introduced the idea that you can reverse the function and go back to your starting number: 3 - 1 is 2 because 2 + 1 is 3. And you can do the same thing with the square root: the square root of 100 is 10 because 10 squared is 100. That’s how we got to this idea that you can justify a log statement with an exponential statement.”

They got that?
“Yes, I was quite impressed.These guys are on the ball as a class. They absorb. It is really nice. They really want to understand. I appreciate that as a teacher.”