**Not. So. Hot.**

Then, as I helped students in our Math Lab, I realized something--recursive definitions are not that obvious to students.

I think what happened here was a classic case of it's-so-obvious-to-the-teacher-she-automatically-thinks-it's-obvious-to-everyone-else. We've all had teachers like this. My absolute favorite prof from grad school loved the phrase, "Oh, this is kindergarten stuff!" Which usually had one of two effects on me: (1)

*Ahhhh!! This is NOT kindergarten stuff! I just spent the majority of my weekend trying to figure this out!*(2)

*Where in the world did you go to kindergarten? Remind me to send my kids there.*

But I digress.

What hit me was that when I see something like:

I automatically think, "If I want to find a certain term, I need to sum up the two previous terms." Furthermore, I know that

means the same thing as the previous equation.

On the other hand, when my students saw a recursive definition, I'm pretty sure they thought, "WTF. Skip it."

So, this semester I paid much more attention to these types of sequences. The very first thing I did regarding recursive definitions was show a slide with this at the top:

I asked students to fill in the blanks and then asked them three questions:

- What do the dot, dot, dots mean?
- What do we call the term before a_n?
- What about the term after a_n?

We then did some examples with

an=an−1+an−2

I made them write "The fourth term is equal to the third term plus the second term." And so on.

Then came

which everyone was convinced was a totally new problem (darn you, indices!). But, once we did the same examples (finding a_4, etc.), I think/hope all minds were changed.

After working some specific examples, where initial values were given, I gave them an exit ticket of something like:

List the first five terms of the sequence defined by:

a_1 is the number of boys in the room; a_2 is the number of girls;

a_1 is the number of boys in the room; a_2 is the number of girls;

I think about 80% of students got it with zero help from me. Not perfect, but I'll take it this time around!

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