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#*Considering the first two vectors in <math>\{(1,0),(0,1),(1,1)\}</math> as linearly independent and the third as linearly dependent. | #*Considering the first two vectors in <math>\{(1,0),(0,1),(1,1)\}</math> as linearly independent and the third as linearly dependent. | ||
#*Thinking that a sequence converges in a certain region. | #*Thinking that a sequence converges in a certain region. | ||
#*Viewing <math>\{4, \{-3,2,-1/7\},\{\{17,5\}\}\}</math> as a set of six elements rather than | #*Viewing <math>\{4, \{-3,2,-1/7\},\{\{17,5\}\}\}</math> as a set of six elements rather than three. | ||
#In an Decoding interview on students' difficulties with limits the interviewee mentions the example described at the beginning of this page. See [[Limits]]. | #In an Decoding interview on students' difficulties with limits the interviewee mentions the example described at the beginning of this page. See [[Limits]]. | ||
Latest revision as of 16:25, 2 April 2026
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".[1] 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
- Alcock and Simpson[2] mention four examples for category mistakes in mathematics:
- Saying that every point in a compact set is compact.
- Considering the first two vectors in as linearly independent and the third as linearly dependent.
- Thinking that a sequence converges in a certain region.
- Viewing as a set of six elements rather than three.
- In an Decoding interview on students' difficulties with limits the interviewee mentions the example described at the beginning of this page. See Limits.
References
- ↑ Magidor, O. (2025). Category Mistakes. In E. N. Zalta & U. Nodelman (Ed.), The Stanford Encyclopedia of Philosophy (Spring 2025). Metaphysics Research Lab, Stanford University.
- ↑ Alcock, L., & Simpson, A. (2008). Ideas from Mathematics Education—An Introduction for Mathematicians.
