Confirmation bias is a quality of human mental processes which makes us tend to think in terms of positive examples and tests that would confirm our working hypothesis, rather than negative examples or tests that would falsify the conjecture.
The term was coined by P. C. Wason after his 2-4-6 task experiment, where he asked the participants to find a rule which governed whether a triples of numbers would fit or not. First, they were told that $(2,4,6)$ fits. Then the subjects would ask about their own triples of numbers and the experimenter would answer if that triple fits or not. Only a small percent of people found the true rule, which was "any increasing sequence", instead generating more specific rules like "the middle is the average". The problem was that participants offered triples that would align with their hypothesis, rarely trying falsifying it. In fact some test subjects didn't get any "negative results", that is, the rule could have been "any triple of numbers".
Confirmation bias in math education:
Confirmation bias happens in math education in two flavors: student's and teacher's.
The student's version is when the pupils try to solve some problem, but aren't critic about their own opinions. Perhaps this is most important to science education, but in math pattern recognition plays a huge role and fallacious reasoning hurts progress.
However, I'm more interested in the teacher's flavor, which is of different kind. It regards how the teacher thinks of his/her students, for example,
- if the teacher suspects that the student has some problem, he will try to help before checking if it really is that problem;
- if the teacher thinks that the child does not understand some concept, he/she will try to prove that it indeed is the case;
- the teacher my want to stress why his/her solution is better than some other solution presented by the student (perhaps not even accepting it).
- Is the teacher's confirmation bias a serious problem?
- How could we make the teachers aware of it (not as frequently, but even colleagues from university fall for this)?
- How could I make some particular teacher aware of it (as a parent, or as a student)?