**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!

Algebra is the most important and simple topic in mathematics and I am here to share simple and clear definition of algebra that is ,Its a branch of mathematics that substitutes letters in place of numbers means letters represent numbers.

ReplyDeleteAlong with the question papers, the Uttarakhand Board will release the UK Board 10th model paper. The Uttarakhand Board 10th question papers will be available in pdf format on the official website, UK Board Question Paper Class 10 Students will be able to comprehend and analyse the exam structure, marking system, and significant themes of the UK Board 10th exams by using UK Board 10th question papers.

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