[not in handout, see intranet]
Anderson 2005

Solving equations such as

3x – 5 = 7

“In the experiment to be modeled in detail 10 students ages 11 to 14 spent 6 days practicing solving such equations. The first day (Day 0) they were given private tutoring on this class of equations, using the unwind principle, and practiced paper and pencil solutions of such problems with a private human tutor. On the remaining 5 days they practiced on a computer the solution of three classes of equations:

0-step: e.g., 1x + 0 = 4

1-step: e.g., 3x + 0 = 12,     1x + 8 = 12

2-step: e.g., 7x + 1 = 29”

Results
Over the 5 days of training, the students got about half a second faster. At the end, the simplest equations took 2 seconds, and the 2-step equations 4.5s.

The computer simulation reproduces this speedup.

gif  pdf of the 2005 article on the author's web pages.