A study in 1990 found that female learners, when learning mathematics, performed much better when a rote learning approach was employed. This would go against the argument that females tend to do better in environments where students are engaged in discovery learning. In the same study, males performed better when they took an autonomous approach to learning maths.
Admittedly, the study did find that when it came to problem-solving, rather than learning, females performed better in groups, while males performed better solving problems individually. However, the argument that old rote learning styles of memorization and recall benefitted boys does not stand.
It becomes difficult to say with any degree of certainty that one method of teaching favours one gender. The reality is far more complex with individual learners sometimes favouring more auditory forms of teaching, others more tactile forms and others more visual forms.
The school system is not designed to benefit one specific gender, but one group of learners. In schools where discovery learning is encouraged, more social and auditory learners might excel. In schools where other teaching techniques are adopted, visual learners or tactile learners may flourish. The school system will always benefit one segment of learners, but it is not possible to draw clear distinctions based on gender.