When I teach math classes, one goal I have in mind is to help students develop the cluster of thinking skills usually called analytical skills or critical thinking skills. And I think that math classes can help develop analytical and critical thinking.
These skills include being able to apply mathematical reasoning, but also other skills: to be able to take big problems and break them down in to smaller one, to be able to combine two ideas to create a third idea, to be able to generalize a concept to apply it to similar situations.
Are there currently accepted measures of how good learners are at these skills?
While I really think math and science courses help develop these skills, I would love to not only learn more about them, but to be able to point to research that says these skills are developed by quality math and science instruction. Can I get some leads on that research?
My own Google Scholar searches come up with mostly noise level results.