A word (or 231) on functions

In math, the 6th grade students are beginning to work on algebraic functions.  These are hard for lots of students (including and especially 6th grade me).

There are two main reasons why:

1. Algebra requires computation, and computation is hard.  It requires lots of memorizing and instant recall, or tedious operations that can lead to mistakes and frustration.  This part is just practice practice practice.  I think as adults, we have computed so many times (bills, tips, budgets, gas mileage, etc.) that we forget how hard it was to learn and master.
2. Algebra is really a language of notation for thinking.  Learning languages is also hard.  Just like English is a language for communicating meaning, algebra is a language for communicating mathematic phenomena.  Equations and expressions are types of sentences and phrases, but with very specific meanings, that we are not fully used to in English.   f(n) = n +1 is just saying for every number input, a number one bigger is output.  f(2) = 3 and f(3) = 4.

At this time, students are probably not thinking of the myriad careers (science, engineering, medicine, business, teaching Special Education, accounting, making sure they have money in their bank account at the end of the month) that use functions every day.  But, children are not always known for their long term planning and experience, so let's all try to remind them of the importance of trying functions out.