Keep in mind that Montessoris theory is ~100 years old; it kept up very well but there are shortcomings; IMO especially in the realm of pre-numeric mathematics.
The base of the critique is that Montessori does not provide a conclusive, foundational Layer of (Pre-)Mathematics - a model of more or less depending sub-skills - which would enable A) Educators to better understand their pupils or what they need to further their skills[1] B) enable the invention of new Material. She basically states that children need Material X, Y and Z, but not how and why the work with the material enables them to start using math.
[1] = Which is very important for pupils with different learning paths and/or disabilities.
The base of the critique is that Montessori does not provide a conclusive, foundational Layer of (Pre-)Mathematics - a model of more or less depending sub-skills - which would enable A) Educators to better understand their pupils or what they need to further their skills[1] B) enable the invention of new Material. She basically states that children need Material X, Y and Z, but not how and why the work with the material enables them to start using math.
[1] = Which is very important for pupils with different learning paths and/or disabilities.