It is an old approach that is gaing recent popularity. gaining momentum = building, growing popularity, support, adoption gaining new momentum = growing in support that it did not previously/recently have

What about this sentence? each bringing their style to bear in working for common goals.

Single-sex education means schools with one gender. They study seperately girls schools or boys schools. This approach gains an approval by the community.

it means that more and more people are becoming interested and are talking about single-sex education. I do not know what single-sex education is.