Reply To: Lesson 4-1: The Stages of Mastery Action

[Bryan Henning]

Concept: Finding the midpoint of a line segment given two endpoints (especially ones far away, like (-1,12) and (9, -8)

Unconsciously Incompetent: Draws a picture and attempts to visualize the middle, counting the length down and over on the coordinate grid.

Consciously Incompetent: Same as previous but is aware that there must be a better way.

Consciously Competent: Subtracts coordinates to find x- and y-distance, cuts each distance in half, and adds to/subtracts from one endpoint – may use a diagram like a number line or right triangle

Unconsciously Competent: Finds the average of the x-coordinates and the average of the y-coordinates. Also may use the previous strategy with mental math.

Consciously Masterful: Can explain how both of the above strategies arrive at the same conclusion.