Math is certainly not my expertise, but i was fascinated by a video that they showed, actually, at my children's school. And one of the big things that just really sticks with me has to do with a lot of what you're describing. What gets lost is when we just have them doing things that they've memorized, but they don't actually mean anything to them. It's just this, you know, data in, data out. But there's no mind actually being leveraged in that process.
Silvia Heubach discusses mindset, metacognition, and math on episode 246 of the Teaching in Higher Ed podcast
Quotes from the episode
The more you can make stories and connections and reasons, the better it allows the student to learn.
—Silvia Heubach
Learning happens when students do work.
—Silvia Heubach
When you try a new methodology … you have to sell it to the students.
—Silvia Heubach
The teacher is a coach that can help you, but you need to do the practice.
—Silvia Heubach