Hand a five-year-old the symbol "7" and ask what it means, and you'll often get a shrug, or a number recited from memory with no weight behind it. Hand the same child seven beads and ask them to make two equal groups, and something different happens: they push beads around, notice one is left over, and arrive at a fact instead of a guess. That difference is the entire premise of Montessori maths.
The sequence matters more than the material. A Montessori maths lesson moves through three stages in order, and skipping ahead is where most children quietly start to struggle: first the quantity (beads, rods, counters, something you can hold), then the symbol (the numeral that names what you just held), and only then the abstraction (doing it in your head, on paper, without the beads in front of you). Most classroom maths starts at stage two, the symbol, and hopes the quantity catches up later. For a lot of children it does. For plenty of others, especially children who later turn out to have dyscalculia or a general maths learning difficulty, it never quite lands, and by age eight or nine they're memorising procedures without understanding, which is a much more fragile kind of knowing.
This is also why Montessori materials look the way they do. The bead chains for skip-counting are colour-coded by number, not because it's pretty, but because a child can recognise "the orange chain" as two before they can reliably read the digit. The golden bead material for place value uses physically different-sized units, tens, hundreds and thousands, so that a child feels the size difference between 9 and 90 in their hands before anyone tries to explain it with a diagram. None of it is decorative. Every material is a rehearsal for an abstract idea, done at a pace the child controls.
That last part, the pace, is the piece that's hardest to give a child in a classroom of twenty-five, and it's the whole reason live, one-to-one teaching matters for this method. A Montessori lesson isn't a script; it's a conversation that adjusts in real time to whether a child's hands are still needed or can be put away. Online doesn't have to mean watered down. It means the same bead work, the same sequence, the same patient watching for the moment a child stops needing the concrete version, just with a screen between the teacher and the table instead of a classroom.
At Mount Shine, this is the foundation stage for ages three to six, and it's also where we start noticing, gently and early, if a child needs more time with quantity than most, which is often the first real signal of a maths learning difference, long before a formal diagnosis is possible. Getting the sequence right isn't just good pedagogy. For some children, it's the difference between a maths struggle that gets caught at six and one that doesn't get named until they're failing tests at eleven.