I also want students to "go deep", as we used to say in our pickup touch football games. That means going for a long pass that could result in glory but more often results in a missed pass. Still, you learn from it for next time.
What does it mean for students to go deeper? Deeper learning means not staying on the surface. Teachers can ask deep questions, but students need to ask deep questions too.
Bloom’s Taxonomy was the reference point I was given in my undergrad education courses. Bloom's verbs categorized how we learn. “Define” is a superficial learning interaction and “critique” is deeper.
I have been spending some time the past few months working with the Common Core State Standards. They seem to like using seem to use Webb’s Depth of Knowledge (DOK) which is another frame of reference and common language to understand "rigor," or cognitive demand.
There are four DOK levels that grow in cognitive complexity: recall, skill/concept, strategic thinking, extended thinking.
Most teachers I encounter, especially at the college level, have little interest in the labels. They may enjoy a discussion or argument about what the levels mean, but their only interest in a taxonomy for learning is how to get to those higher or deeper levels.