Make Math Moments Academy › Forums › Full Workshop Reflections › Module 4: Teaching Through Problem Solving to Build Understanding › Lesson 41: The Stage of Mastery › Lesson 41: The Stages of Mastery Action › Reply To: Lesson 41: The Stages of Mastery Action

The concept I decided to focus on for this assignment is a major one in algebra and prealgebra and has to do with student’s basic understanding of how functions work. The Lesson Goal is “understand that a function assigns to each xvalue (independent variable) exactly one yvalue (dependent variable)…” Traditionally I’ve used mapping diagrams, sets of ordered pairs, the vertical line test, etc. and still a number of kids get the meaning of functions backwards. What I’d like to use is the analogy of a Coke machine. Here’s how students might progress through it.
Unconsciously Incompetent
With a vending machine you put something in and get something out.
Consciously InCompetent
When you press Coke, you should get Coke.
Consciously Competent
I can tell whether or not the machine is working based on whether or not my selection (input) matches what I get out (output).
Unconsciously Competent
When you press Coke, you should get Coke, but if you always get Sprite instead, it doesn’t mean the machine is not functioning, it could just mean someone put in Sprite where Coke belonged.
Consciously Masterful
A function is where I get one output for each input, whether or not it was the output I originally expected.