I would like to learn a functional programming language to see a different programming paradigm.
My background in programming: Java (I have just passed the SCJP exam), some ruby and very limited Rails. I use bash for basic sysadmin tasks. I use Ubuntu 9.04.
As a second goal I would like to use fp to show kids (14-18 years olds) how math and cs interrelated. The guys are very good at programing (they are learning Python and Java at politechnical high school from the first year). However as tests show, they have difficulties with math esp. basic concepts of discrete math. I think we can develop their math skills by using programming (and I possibly that can be the topic of my teacher training thesis). I think a language with very basic vocabulary would serve this project best.
If your primary goal is to work with teens, it makes sense to use the functional-language pedagogy and technology that is proven to work with teens, and that is PLT Scheme (aka DrScheme) with the How To Design Programs book (also free online). These guys have got great results from middle school through 3rd semester university. They have resources for teachers as well.
Many respondents like SICP. It is a wonderful book—but not to learn from. If you already know Scheme, it is a good book to admire, but SICP is less about functional programming and more about how to implement all known interesting computer-science ideas in Scheme.
If your primary goal is to learn a really new programming paradigm, then Scheme lacks some features that are very important to many functional programmers:
If you want exciting ideas, try Haskell; Haskell makes it a lot harder for you to program your old thoughts in the new language. Instead, Haskell forces you to think new thoughts. In addition to many other resources, Real World Haskell is free online.
Final note: SO has had many similar questions on learning functional programming.
If you are doing this for learning, then definitely Scheme with SICP. It's going to be hard and frustrating and will blow your mind if you don't have experience with this stuff, but you will learn a lot.
If you want to use functional programming in practice then F#, Scala and Clojure are worth looking at.
I vote for Haskell, which has the following advantages:
Scala and Clojure both run the JVM so you might be more familiar with their environments.
Since you're already familiar with Python, why not just use its functional capabilities? For more, see this (draft) HowTo.
My question is what approach is likely to be best for the teens you're working with. If they're willing to learn something new and different, Scheme is an excellent choice as a functional language. It's as basic as they come. If you want to keep to a more familiar syntax, Haskell might be your answer.