Reading guide:
Background
This paper presents a cognitive model for multicolumn subtraction
which is based on the basic assumption that students are taught a
correct procedure for doing the subtraction, but might not have
learned all of the parts (what they call rule deletion). This results
in what they call a bug -- a systematic error.
Things to watch out for
- The key to understanding the mechanism is understanding the GAO
graph mechanism which is described in section 2.2 Figure 1 gives an
example. Really dig into this and try to figure out how it as used
as a "program" in the head of the student solving a subtraction
problem.
- A repair kicks in when an impasse is reached. Make sure you
understand what these concepts mean here.
- Critics and filters are not really central to the theory.
- Section 3.1 is really nice because it lays out a useful set of
criteria for evaluating how good a particular theory/model is. The
rest of this section discusses repair theory with respect to these
criteria.
Last modified: Wed Sep 30 20:20:28 CDT 2009