Extrastromgmints has it spot-on regarding the wider ability range in top schools, than is often touted.
The top schools will have a higher percentage of their cohort with the very top CAT scores, but all have a ‘tail’ of differing lengths and couldn’t fill their places otherwise.
Notice that even quite poor schools will have some children who score similar results and gain all top grades at GCSE and A Level. Numbers might be very low, but they exist.
Largely speaking, the results of schools reflect their intake….the school isn’t the biggest determinant in their results. So, lots of bright kids with high CAT scores will do well. They are generally easy to teach and retain information and can pick up skills quickly.
There are advantages (and disadvantages) of being in a cohort where most are of similar high ability. Students can bounce ideas off each other, they are likely to have similar high aspirations, less disruption and the class can move at a fast speed. These features often lead to a more pleasant learning experience, rather than the results themselves being drastically different to what might be achieved elsewhere. Although selective schools can have difficult to teach students, what selection often brings as a key benefit for any parents in reality, is social selection and the ‘benefits’ of that, rather than in reality significant result outcome differences.
A disadvantage is the lack of experience of a range of society. Personally I see that as a disadvantage, although others choose selective precisely for this factor. Especially when children are in selective or private education from 4-18, their narrow little bubble might have protected them, but also excluded them from a key part of education, which is learning about other people and how to mix with a range of people.
134 is a great score and bodes well for your DD. Having a family who are interested in education and will support her in whatever school she goes to is also a key advantage she has that many lack and nothing else can really compensate for.