Category mistake

A category mistake can be coarsily described as the "error of assigning to something a quality or action which can only properly be assigned to things of another category". For instance, a math student saying that "the limit of a function approaches 1" commits a category mistake. The student assigns "approaches 1" which is an attribute of a function to a limit value which is a number.

The purpose of this page is twofold:

• Describing the corresponding bottleneck and the related literature.
• Collecting category mistakes which hinder student learning in various disciplines.

Description of bottleneck

Students attach properties to the wrong kind of objects.

Collection of category mistakes

Mathematics

1. Alcock and Simpson mention four examples for category mistakes in mathematics:
   • Saying that every point in a compact set is compact.
   • Considering the first two vectors in $\{(1,0),(0,1),(1,1)\}$ as linearly independent and the third as linearly dependent.
   • Thinking that a sequence converges in a certain region.
   • Viewing $\{4,\{-3,2,-1/7\},\{\{17,5\}\}\}$ as a set of six elements rather than four.
2. In an Decoding interview on students' difficulties with limits the interviewee mentions the example described at the beginning of this page. See Limits.