Mathematics
Domain 5 tests the concrete-to-abstract sequence of the math materials and the indirect preparation already done in sensorial and practical life. Questions often hinge on which material comes next and what control of error the material carries.
Foundations
- Mathematics rests on order, sequence, and exactness; the red rods, pink tower, and constructive triangles indirectly prepare quantity and geometry.
- Rules: quantity before symbol, concrete before abstract, and no rule taught before the material has shown it.
The 3–6 sequence
- Numbers 1–10: number rods (red and blue, 10 cm to 1 m), sandpaper numbers, number tablets, then matching quantity to symbol.
- Zero and odds and evens: spindle boxes teach 0 as an empty set; cards and counters leave visible remainders for odd and even.
- Decimal system: golden beads - unit, ten, hundred, thousand. Lay out, count, exchange, and play bring-me games. Ten of a category always exchange for one of the next.
- Operations: addition, subtraction, multiplication, division with golden beads and strip boards, then the stamp game, then bead frames.
- Teens and tens boards, hundred board, then memorization work.
Control of error
The material corrects the child. A ten-bar that holds nine beads looks wrong beside the hundreds; a strip board shows a remaining quantity. The adult prepares the material and steps aside so the error becomes visible.
Worked example
A child builds 3,452 with golden beads but starts the four hundreds beside the tens, leaving a gap in the layout. Reasoning: she is laying out quantity, not yet reading place value. The correction is the exchange game and bring-me commands such as 'bring me four hundred', which force comparison - not a lecture on columns or a worksheet of the numeral.
Traps that cost marks
- Worksheets and numeral tracing before quantity work.
- Skipping the exchange game, which shows up later as borrowing errors.
- Counting-on counters for addition before golden beads give the concept.
- Correcting answers aloud instead of letting material reveal the error.
- Introducing the stamp game before bead operations are secure.