- confident and happy students are worse in mathematics.
If the kids feel happy and confident in the math classes, their actual results are worse than for the kids who don't feel as happy.
For example, all ten nations with the happiest math students scored below the average. And all ten nations with the least happy math kids excelled.
Also, almost all attempts to connect mathematics with daily life make the results of the learning process worse: the nations that teach math "practically" are at the bottom.
I personally find all these conclusions completely obvious. Suffering and good results in math are, in principle, two different things - two instructors with the same results can still have very different personalities and one of them can be a better source of happiness. But it can't be unexpected that these two quantities (suffering and results) will be heavily correlated for most students.
If too many students are too happy in the math classes, be sure that it is simply because not much is expected from them. It can't be otherwise. If teaching of mathematics is efficient, it is almost guaranteed that a large group or a majority must dislike the math classes. Mathematics is hard and if it is not hard, it is not mathematics.
If a teacher with a fixed personality and teaching habits is asked to make the students happier, it is clear that a decrease of the expectations is what you get in more than 90% of cases.
Also, the attempts to connect mathematics with the daily life are nothing else than a form of lowering of the standards. They are a method to make mathematics more attractive for those who like to talk even if they don't know what they're talking about. They are a method to include mathematics between the social and subjective sciences. They give a wiggle room to transform happiness, confidence, common sense, and a charming personality into good grades. If the curriculum plans at Harvard include the thesis that the teaching of math and sciences should be based on their relevance for the life of the society, it is completely clear that these are nothing else than plans to make Harvard a mediocre school in the way it teaches these subjects.
It is just another method to make these subjects less hard - where the word "hard" refers both to "difficult" as well as to the adjective that appears in "hard sciences". Happiness and confidence are surely very important things but I still tend to think that schools are not places where these goals should be viewed as primary.
The author of the study that urges the officials to rethink whether the happiness factor is too important is aptly called Tom Loveless. ;-)
Also, one shouldn't be surprised that if the students learn the exact sciences and math properly, many of them will inevitably have a feeling that they don't know why all this wisdom is true. Those who are not satisfied with the mathematical arguments and procedures and look for "illuminating" explanations usually look for non-mathematical and unscientific explanations of the insights.
If these "external explanations" become an official method of teaching the subjects, the results simply can't be good because in mathematics, it is the hard mathematical arguments that are essential, not the easy non-mathematical ones. It is clear that the students can't understand all the logical relationships between all the insights immediately. Some of them will understand them later, some of them won't. But even without any understanding of the relationships between all the facts and ideas, there is a lot of stuff that a student may learn or may fail to learn.