Step

A step is an observable part of the solution to a problem.

Because steps are observable, they are partly determined by the user interface available to the student for solving the problem. For instance, suppose a student is solving 12-2*x=25 for x on paper, and the student writes

• 12-2*x=25
• 2*x=13
• x=7.5

These three lines comprise three steps in solving the problem. Note that the last step is incorrect; steps can be incorrect and/or irrelevant to solving the problem. Note also that the student has done several mental algebraic operations per step. Although our analyses would be much easier if students applied just one knowledge component per step, that is not always the case.

In the algebra illustration above, the last step was the answer to the problem, and the others were intermediate steps that are not strictly necessary for solving the problem; some instructors might accept a solution that lacked the intermediate steps. However, some problems require filling out forms or construction other multi-part solutions. For instance, consider a problem whose answer requires defining axes for a Cartesian graph and plotting 3 points on it. A typical user interface for such a problem would result in these steps:

• label the x-axis
• choose the minimal value for the x-axis
• choose the maximal value for the x-axis
• choose the tick mark spacing for the x-axis
• label the y-axis
• choose the minimal value for the y-axis
• choose the maximal value for the y-axis
• choose the tick mark spacing for the y-axis
• plot the first point
• plot the second point
• plot the third point

This whole collection of steps comprises the solution. Unlike the algebra illustration, no single step is "the answer" nor are some steps "intermediate."