Contextual embedding
Definition
Contextual embedding places a question in a specified setting and requires the solution to use that setting’s definitions or constraints.
Explanation
The context needs to do mathematical work. Adding a story around an unchanged exercise is different from introducing definitions that affect which inferences are valid.
In a predicate logic question, for example, the solution may need to preserve distinctions among several quantified statements. The rubric can require each inference to identify the rule used, making it possible to examine the derivation as well as the conclusion.
A correct conclusion does not rescue an invalid proof step. Conversely, finding an invalid step does not show that the conclusion itself is false.
Scope and evidence
This page uses the term as an assignment-design strategy from the AIED work. It is distinct from an embedding representation in machine learning.
Related concepts
Invalid syntactic shortcut · Iterative perturbation process · Axiomatic replacement