So these apps reportedly get a child the equivalent of 18 months of mathematical development in 6 weeks of short, fun sessions? In that case, it does seem the £15.99 price is off by at least an order of magnitude, but I suspect we disagree on the direction.
There's a PDF called "unlocking talent" on the onebillion website, but that crashes iOS Chrome so I haven't been able to read it. It's not peer reviewed. It's not blinded.
I can find plenty of published research for stuff which is pure horseshit - brain gym - or for stuff approachig horseshit in the way it's applied - Omega 3; learning styles; a lot of "cures" for dyslexia.
So far I have a press release from a company saying "trust us, our app works" with nothing to corroborate it.
What do you get for £16?
Sorting and matching
Counting to 3
Lines and patterns
Counting 4 to 6
Where is it?
Counting 7 to 10
Patterns and shapes
Counting 1 to 10
Comparing
Add and take away.
That's an under whelming list. It's the bare knuckle minimum you'd tolerate if you had a 1:90 teacher:pupil ratio.
Tldr: give them the money because educating Malawian children is good, but for your own children buy a book and do it yourself.
For comparison, there are UK private primary schools that will cost you about GBP 12k/year that deliver far less measurable benefit (if any) than that, that are still wildly successful at attracting students.