In order to evaluate new educational material the contentment of students with this material is often measured. However, just because a student is contented doesn't mean that he/she has actually learned something. Is there any research investigating the correlation between students contentment and the educational quality of the presented material?
From Clark, Richard, Paul A. Kirschner, and John Sweller. "Putting students on the path to learning: The case for fully guided instruction." (2012):
Even more disturbing is evidence that when learners are asked to select between a more-guided or less-guided version of the same course, less-skilled learners who choose the less-guided approach tend to like it even though they learn less from it... Similarly, more-skilled learners who choose the more-guided version of a course tend to like it even though they too have selected the environment in which they learn less.
Reference cites Clark, Richard E. "Antagonism between achievement and enjoyment in ATI studies." Educational Psychologist 17.2 (1982): 92-101.
I would recommend you to specify the term "educational quality". I think there is a study indicating that in German schools, the two educational goal variables of students' motivation and students' mathematical knowledge are negatively correlated across clases, so you have a trade-off there. I guess, students' contentment would be positively correlated with their motivation. Correlations are not transitive, however, so I cannot say anything about contentment and mathematical learning. You might also benefit from specifying your target group. The correlation you asked for my differ across groups of students (school, university, vocational education, pensioners).
Vast numbers of students are trained from early childhood to engage in a ruthless competition for grades. When such students are required to take math courses, if they're not interested in understanding math, the course degenerates into one in which getting good grades depends only on believing and obeying and working hard, rather than on understanding. Such students learn that mathematics consists of meaningless algorithms. That is a lie. They are content when they excel in the competition for grades. That differs from understanding.
But what is the correlation? Has a study been done? I wonder if there is anyone with expertise either in education or in mathematics who is competent to conduct such a study.