Hope it’s not too late but I would hold back on assuming your daughter has inherited some kind of dyscalculia.
The thing about maths is that it builds up in layers, and if you’re missing a basic layer (like number bonds or times tables) then everything is much more difficult and overwhelming. A simple example is when a child gets muddled up with adding large numbers because they’re still using their fingers to count. It is likely she is missing some basic maths knowledge and over the years this has prevented her understanding more complex lessons. That’s why she only got 4 correct on her maths test.
I partially agree with the ed psych. It is to do with ‘working memory’ but your daughter is not at fault. Everyone has a ‘small’ working memory because we can only think of so much at once. Your daughter actually lacks basic maths knowledge in her long term memory.
The fact that she did well on her reading test proves she can learn. Schools are much better at teaching children to read nowadays (dyslexia is virtually unheard of now). If the maths ‘layers’ are missing from year one, then she likely internalised ‘maths is hard’ and in every lesson she avoided effort, perhaps copied her friends. The adults may have been focusing on the other children with SEN, while this ‘good girl’ who can read so well went under the radar. The adults may have told her ‘you’re so wonderful and creative with your reading and writing - this is what you should do in the future’ and then in pursuit of praise and status she invested more in her English lessons.
I suspect this is a deficiency in teaching and learning. What help at school did she get to catch up from year 1? Did anyone talk with you about simple things that could’ve been done at home? Why are you finding out now that she got only 4 questions correct? I feel for your daughter. How galling to do a year 6 test and feel so confused throughout.
She needs catch up, not a diagnosis.
The non-selective school, provided they are in catchment, cannot refuse your daughter a place. Most secondary school will run a suite of tests and then place pupils in sets. She’d be in a higher set for English, and a lower set for maths. She may finally get the help in maths that she needs. However, the downside is that a lower set may have more high-needs pupils in it and if the school isn’t calm and organised, then behaviour may prevent learning.
The good news is there is plenty of time for catch up and given her intelligence and ability to learn, this could indeed be a success story. You also need to choose a secondary school wisely.