Automatic Knowledge Graphs for Assessment Items and Learning Objects

As I mentioned in this post, we’re having fun layering questions and answers with explanations on top of electronic textbook content.

The basic idea is to couple a graph structure of questions, answers, and explanations into the text using semantics.  The trick is to do that well and automatically enough that we can deliver effective adaptive learning support.  This is analogous to the knowledge graph that users of Knewton‘s API create for their content.  The difference is that we get the graph from the content, including the “assessment items” (that’s what educators call questions, among other things).  Essentially, we parse the content, including the assessment items (i.e., the questions and each of their answers and explanations).   The result of this parsing is, as we’ve described elsewhere, precise lexical, syntactic, semantic, and logic understanding of each sentence in the content.  But we don’t have to go nearly that far to exceed the state of the art here. Continue reading “Automatic Knowledge Graphs for Assessment Items and Learning Objects”

Pedagogical applications of proofs of answers to questions

In Vulcan’s Project Halo, we developed means of extracting the structure of logical proofs that answer advanced placement (AP) questions in biology.  For example, the following shows a proof that separation of chromatids occurs during prophase.

textual explanation of entailment using the Linguist and SILK

This explanation was generated using capabilities of SILK built on those described in A SILK Graphical UI for Defeasible Reasoning, with a Biology Causal Process Example.  That paper gives more details on how the proof structures of questions answered in Project Sherlock are available for enhancing the suggested questions of Inquire (which is described in this post, which includes further references).  SILK justifications are produced using a number of higher-order axioms expressed using Flora‘s higher-order logic syntax, HiLog.  These meta rules determine which logical axioms can or do result in a literal.  (A literal is an positive or negative atomic formula, such as a fact, which can be true, false, or unknown.  Something is unknown if it is not proven as true or false.  For more details, you can read about the well-founded semantics, which is supported by XSB. Flora is implemented in XSB.)

Now how does all this relate to pedagogy in future derivatives of electronic learning software or textbooks, such as Inquire?

Well, here’s a use case: Continue reading “Pedagogical applications of proofs of answers to questions”